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Contents
1 Introduction
1.1 The Connection Between X-ray Astronomy and Radio Pulsars . . . .
1.2 Historical Overview of Imaging X-ray Telescopes and Their Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 The Chandra X-ray Observatory and This Thesis . . . . . . . . . . .
1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Refereed Journals . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 Conference Proceedings . . . . . . . . . . . . . . . . . . . . .
1.5 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Part I: Instrumentation
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2 The Chandra X-ray Observatory and ACIS
2.1 Overview . . . . . . . . . . . . . . . . . . . .
2.2 Scientific Instruments . . . . . . . . . . . . .
2.2.1 HRMA . . . . . . . . . . . . . . . . .
2.2.2 Imagers . . . . . . . . . . . . . . . .
2.2.3 Transmission Gratings . . . . . . . .
2.3 ACIS . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Basic Description . . . . . . . . . . .
2.3.2 Event Detection and Grading . . . .
2.3.3 Electronics . . . . . . . . . . . . . . .
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3 Absolute Calibration of X-ray CCDs Using Synchrotron
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Storage Ring Current . . . . . . . . . . . . . . . . .
3.3.2 Effects of the Chopper Wheel . . . . . . . . . . . .
3.4 Pileup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 A Brief Description . . . . . . . . . . . . . . . . . .
3.4.2 Pileup Correction . . . . . . . . . . . . . . . . . . .
3.5 Model Fitting . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Detector Model . . . . . . . . . . . . . . . . . . . .
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3.5.2 Fitting Results . . . . . . . . . . . . . . . . . . . .
3.5.3 Spatial Uniformity . . . . . . . . . . . . . . . . . .
3.5.4 Preliminary Assessment of Wavelength Shifter Data
3.6 Quantum Efficiency of the Reference Detectors . . . . . . .
3.6.1 Methodology . . . . . . . . . . . . . . . . . . . . .
3.6.2 Relative Efficiencies of Transfer Standard Detectors
3.6.3 Uncertainties . . . . . . . . . . . . . . . . . . . . .
3.6.4 Model Limitations . . . . . . . . . . . . . . . . . .
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4 Measurement of the Sub-pixel Structure of Chandra CCDs
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Experimental Method . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Moiré Phenomena . . . . . . . . . . . . . . . . . . . . .
4.2.3 Data Acquisition . . . . . . . . . . . . . . . . . . . . .
4.3 Data Analysis and Results . . . . . . . . . . . . . . . . . . . .
4.4 Determination of the Channel Stop Dimensions . . . . . . . .
4.5 Determination of the Gate Structure Dimensions . . . . . . . .
4.6 Additional Results . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Clocking Effects . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Evidence of Charge Cloud Diffusion . . . . . . . . . . .
4.7 Prospects for Sub-pixel Resolution . . . . . . . . . . . . . . .
4.8 Charge Loss in the Channel Stops . . . . . . . . . . . . . . . .
4.9 Improvement to the Mesh Technique . . . . . . . . . . . . . .
4.9.1 Refined Experimental Method . . . . . . . . . . . . . .
4.9.2 Data Analysis and Results . . . . . . . . . . . . . . . .
5 Charge Loss in the Channel Stops
5.1 Introduction . . . . . . . . . . . . . . .
5.1.1 Evidence for Charge Loss in the
5.2 Voltage and Temperature Dependence
5.2.1 Measurement method . . . . . .
5.3 Future Prospects . . . . . . . . . . . .
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Mesh Data
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Part II: Astrophysics
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6 X-ray Observations of Young Rotation-powered Pulsars
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Essential Pulsar Physics . . . . . . . . . . . . . . .
6.1.2 High-energy Observations . . . . . . . . . . . . . .
6.2 PSRs B1046−58 and B1610−50 . . . . . . . . . . . . . . .
6.2.1 Background . . . . . . . . . . . . . . . . . . . . . .
6.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 PSR B1046−58 . . . . . . . . . . . . . . . . . . . . . . . .
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6.4.1 Image Analysis . . .
6.4.2 Flux Estimation . . .
6.4.3 Timing . . . . . . . .
6.5 PSR B1610−50 . . . . . . .
6.5.1 Image Analysis . . .
6.5.2 Flux Estimation . . .
6.6 Discussion . . . . . . . . . .
6.6.1 PSR B1046−58 . . .
6.6.2 3EG J1048−5840 . .
6.6.3 PSR B1610−50 . . .
6.6.4 Lx − Ė Relationships
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7 The New Pulsar-Supernova Remnant System
SNR G292.2−0.54
7.1 Introduction . . . . . . . . . . . . . . . . . . .
7.2 Observations . . . . . . . . . . . . . . . . . . .
7.3 Data Reduction . . . . . . . . . . . . . . . . .
7.3.1 Image Analysis . . . . . . . . . . . . .
7.3.2 Timing Analysis . . . . . . . . . . . . .
7.3.3 Spectral Analysis . . . . . . . . . . . .
7.4 Discussion . . . . . . . . . . . . . . . . . . . .
7.4.1 General properties of G292.2−0.54 . .
7.4.2 X-ray properties of G292.2−0.54 . . . .
7.4.3 AX J1119.1−6128.5 . . . . . . . . . . .
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PSR J1119−6127 and
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8 X-ray Observations of the High Magnetic Field Radio Pulsar PSR
J1814−1744
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8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
8.2 Archival Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.2.1 ROSAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
8.2.2 ASCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
8.3.1 The X-ray Luminosity Upper Limit of PSR J1814−1744 . . . 200
8.3.2 Beaming and Source Variability . . . . . . . . . . . . . . . . . 204
8.3.3 Implications for Magnetar Models . . . . . . . . . . . . . . . . 207
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
A Acronyms
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B Derivation of the Moiré Equation
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C A Novel Approach for Measuring the Channel Stop and Gate Parameters
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C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
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C.4
C.5
Charge Loss in the Channel Stop . . . . . . . . . . . .
Simplified CCD Geometry and Origin of Event Grades
Measurement of Channel Stop Parameters . . . . . . .
Measurement of Gate Lengths . . . . . . . . . . . . . .
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D Expression for Signal-to-Noise Ratio
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E The
E.1
E.2
E.3
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Central X-Ray Point Source in Cassiopeia A
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . .
Observations and Analysis . . . . . . . . . . . . . . . .
E.3.1 ACIS Data Reduction . . . . . . . . . . . . . .
E.3.2 X-Ray Spectral Fitting . . . . . . . . . . . . . .
E.3.3 X-Ray Timing . . . . . . . . . . . . . . . . . . .
E.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . .
E.4.1 Classical Young Pulsar . . . . . . . . . . . . . .
E.4.2 Cooling Neutron Star . . . . . . . . . . . . . . .
E.4.3 Accretion onto a Neutron Star or Black Hole . .
E.4.4 Comparison with AXPs, SGRs, and Radio-quiet
E.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . .
E.6 References . . . . . . . . . . . . . . . . . . . . . . . . .
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Point Sources
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List of Figures
1-1 X-ray telescope image quality . . . . . . . . . . . . . . . . . . . . . .
1-2 QE of imaging X-ray telescope focal plane instruments . . . . . . . .
1-3 Energy resolution of imaging X-ray telescope focal plane instruments
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2-1
2-2
2-3
2-4
2-5
2-6
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Chandra X-ray Observatory . . . . . . . . . . . . . . .
Principle of Wolter-I optics and a view of the HRMA .
Chandra High Resolution Camera (HRC) . . . . . . . .
Chandra Advanced CCD Imaging Spectrometer (ACIS)
The High Energy Transmission Grating (HETG) . . . .
MIT Lincoln Laboratories CCID-17 . . . . . . . . . . .
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3-1 PTB White Light beamline at BESSY . . . . . . . . . . . . . . . . .
3-2 Synchrotron spectra as a function of height above the electron orbital
plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-3 Storage ring current of BESSY during the June 1996 user shift . . . .
3-4 CCD light curve from BESSY (DEA electronics) . . . . . . . . . . . .
3-5 CCD light curve from BESSY (LBOX electronics) . . . . . . . . . . .
3-6 Light curves for different chip positions . . . . . . . . . . . . . . . . .
3-7 Histograms of events frame−1 from BESSY data . . . . . . . . . . . .
3-8 Description of pileup . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-9 Observed BESSY spectra for a range of storage ring currents . . . . .
3-10 Raw and pileup-corrected BESSY spectra . . . . . . . . . . . . . . . .
3-11 Cross section of the gate structure compared to the Slab and Stop model
3-12 Best-fit model for w103c4 from BESSY measurements . . . . . . . . .
3-13 Best-fit model for w190c1 from BESSY measurements . . . . . . . . .
3-14 Best-fit model for w190c3 from BESSY measurements . . . . . . . . .
3-15 Uniformity map of w190c1 . . . . . . . . . . . . . . . . . . . . . . . .
3-16 PTB/BESSY absolute efficiencies vs. MIT CSR relative efficiencies for
reference detectors w190c3 and w103c4. . . . . . . . . . . . . . . . .
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4-2
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Two views of the thin metal foil (mesh) . . . . . . . . . . . . . . .
View of the experimental setup use for initial mesh measurements
Raw and deconvolved moiré data . . . . . . . . . . . . . . . . . .
Representitive Pixels measured with the 4µm mesh . . . . . . . .
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4-5 SEM photograph of an ACIS CCD cleaved to show the channel stop
structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4-6 The five parameter model used in determining the dimensions of the
channel stop. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4-7 Variation in detection efficiency due to differing amounts of attenuation
in the dead layers of the channel stop. . . . . . . . . . . . . . . . . . 94
4-8 Contour plots for channel stop model parameters . . . . . . . . . . . 96
4-9 Best-fit HEXS channel stop model compared to experimental data. . 97
4-10 SEM photograph of an ACIS CCD cleaved to expose the gate structure 99
4-11 The fifteen parameter model used to describe the gate structure. . . . 99
4-12 Quantum efficiency across the gate structure, determined from O Kα
data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4-13 QE across the gates with clocking scheme: φ1 low, φ2 and φ3 high . . 102
4-14 QE across the gates with clocking scheme: φ1 and φ3 low, φ2 high . . 104
4-15 Attenuation length and charge distribution width as a function of energy105
4-16 Chandra HRMA encircled energy surfaces projected onto a schematic
of sub-pixel locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4-17 Pixel maps of shoulder and photopeak events . . . . . . . . . . . . . . 109
4-18 SEM photographs of the 1.4 µm mesh . . . . . . . . . . . . . . . . . . 110
4-19 Improvements to the mesh technique . . . . . . . . . . . . . . . . . . 111
4-20 Comparison of results using meshes with 4 and 1.4 µm holes . . . . . 112
4-21 Representitive Pixels measured with the 1.4 µm mesh . . . . . . . . . 113
4-22 Attenuation due to absorption in the channel stop, as determined with
the 1.4 µm mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4-23 Contour plots for channel stop parameters at two energies . . . . . . 116
4-24 Combined contour plots, entire redistribution function . . . . . . . . . 117
4-25 Combined contour plots, photopeak only . . . . . . . . . . . . . . . . 119
5-1
5-2
5-3
5-4
5-5
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Spectra of split events at 1487 eV . . . . . . . . . . . . . . .
Fraction of shoulder across the Si K edge . . . . . . . . . . .
Potential through the channel stops for positive and negative
Shoulder profiles at several different gate voltages . . . . . .
Typical spectrum for the charge loss measurements . . . . .
Growth of the shoulder as a function of temperature . . . . .
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gate bias
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6-1 ASCA images of PSR B1046−58 . . . . . . . . . . . . . . . . . . . . . 146
6-2 ASCA images of PSR B1610−50 . . . . . . . . . . . . . . . . . . . . . 153
7-1
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ASCA images of PSR J1119−6127 . . . . . . . . . . . . . . . . . . .
ROSAT images of PSR J1119−6127 . . . . . . . . . . . . . . . . . . .
Spectral extraction regions for G292.2−0.54 from ASCA and ROSAT
Spectra of G292.2−0.54 overlayed with best-fit MEKAL model . . . .
Spectra of G292.2−0.54 overlayed with best-fit MEKAL model . . . .
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7-6 ASCA and ROSAT images of G292.2−0.54 showing the location of
dark cloud DC 292.3−0.4 . . . . . . . . . . . . . . . . . . . . . . . . . 186
7-7 ASCA image of region around AX J1119.1−6128.5 . . . . . . . . . . 190
8-1 P − Ṗ diagram for radio pulsars and AXPs . . . . . . . . . . . . . . . 197
8-2 Count-rate diagram for PSR J1814−1744 . . . . . . . . . . . . . . . . 203
B-1 Sketch of the moiré phenomena . . . . . . . . . . . . . . . . . . . . . 222
C-1 Redistribution functions at 525 eV with different voltages . . . . . . . 226
C-2 Cross-section of an idealized CCD. . . . . . . . . . . . . . . . . . . . 227
C-3 Overhead view of a 2 × 2 array of pixels . . . . . . . . . . . . . . . . 228
E-1 Chandra image of Cassiopeia A . . . . . . . . . . . . . . . . . . . . . 242
E-2 ACIS spectrum of the Cas A point source . . . . . . . . . . . . . . . 247
13
14
List of Tables
2-1 ASCA grades and their corresponding event type for X-rays . . . . .
3-1 Summary of synchrotron measurements made at PTB beamlines at
BESSY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2 Readout times for LBOX data . . . . . . . . . . . . . . . . . . . . . .
3-3 Readout times for LBOX data . . . . . . . . . . . . . . . . . . . . . .
3-4 Final readout times for the LBOX and DEA . . . . . . . . . . . . . .
3-5 CCD detection efficiency model parameters . . . . . . . . . . . . . . .
3-6 CCD model parameter fit results from synchrotron radiation measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-7 Uniformity of w190c1 determined from BESSY measurements . . . .
4-1
4-2
4-3
4-4
Summary of initial mesh measurements. . . . . . .
Channel stop values derived from HEXS data . . .
Channel stop values derived from the entire SRF . .
Channel stops values derived from photopeak data .
.
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45
52
62
62
63
68
73
77
. 88
. 95
. 116
. 118
6-2 Astrometric and spin parameters for PSRs B1046−58 and B1610−50 143
6-3 ASCA SIS detection of PSR B1046−58 . . . . . . . . . . . . . . . . 149
7-1
7-2
7-3
7-4
Astrometric and spin parameters for PSRs J1119−6127 and B1509−58.
Spectral fit parameters for SNR G292.2−0.5 . . . . . . . . . . . . . .
X-ray temperature dependence on elemental abundances . . . . . . .
X-ray flux and luminosity for SNR G292.2−0.5 . . . . . . . . . . . .
163
175
184
189
8-1 Comparison of PSR J1814−1744 and 1E 2259+586 . . . . . . . . . . 203
8-2 Pulse properties of known AXPs . . . . . . . . . . . . . . . . . . . . 205
E-1 Selected Chandra observations of Cas A . . . . . . . . . . . . . . . . 240
E-2 X-ray spectral fits for Cas A point source . . . . . . . . . . . . . . . 246
15
16
Chapter 1
Introduction
1.1
The Connection Between X-ray Astronomy
and Radio Pulsars
The X-ray study of rotation-powered or radio pulsars has had a close link with Xray astronomy from its very beginning. After the discovery of Sco X−1 as the first
extra-solar X-ray source by rocket-borne Geiger counters (Giacconi et al. 1962), the
next source of celestial X-rays identified was the Crab nebula (Gursky et al. 1963;
Bowyer et al. 1964). With the detection of radio pulsar NP 0532 inside the Crab
nebula (Staelin & Reifenstein 1968) and the subsequent detection of optical (Cocke,
Disney, & Taylor 1969) and X-ray (Fritz et al. 1969; Bradt et al. 1969) pulsations,
it became clear that a rapidly spinning neutron star is not only responsible for the
pulsed emission, but is also powering the nebular emission as well.
In general, X-ray observations of rotation-powered pulsars offer a unique opportunity to simultaneously resolve fundamental questions about neutron stars. Studying
the spectrum and morphology of the pulsar’s synchrotron nebula (or plerion [Weiler
& Panagia 1978]) is crucial for determining basic properties about the relativistic
pulsar wind and probing the density of the surrounding medium. Measuring the temperature of the cooling surface of the pulsar (T ∼ 105 − 106 K for ages less than
17
one million years) provides a way to understand the thermal evolution of NSs and
to constrain the equation of state (Ögelman 1995). Detecting pulsed magnetospheric
emission and comparing it to the pulsations seen at other wavelengths allows study of
the pulsed-emission mechanism (i.e. Polar-cap or Outer gap models; see, e.g., Harding et al. 2000). Lastly, searching for the remnant of a supernova (SN) that created a
pulsar is vital for not only quantifying the fraction of neutron stars borne in SNe, but
for providing an independent distance and age estimate for the pulsar and measuring
its velocity and magnetic field (e.g., Frail, Goss, & Whiteoak 1994).
Although the properties of the Crab generated great interest in studying rotationpowered pulsars in the X-ray band, it was only with the launch of Einstein in 1978
that more than just the most energetic and closest objects (like the Crab) could
systematically be studied. This major advance in observational capabilities resulted
from Einstein’s optics, the first orbiting X-ray telescope for astronomy.1 with true
focusing optics (Giacconi et al. 1979). These mirrors with their FWHM of ∼500
could not only resolve small-scale features but also greatly reduced the contribution
of the diffuse X-ray background (XRB), allowing detection of relatively faint (i.e.,
< 10−12 ergs s−1 cm−2) sources.
Among the significant observations made with this satellite were the discovery of
two young, highly energetic pulsars PSRs B0540−69 and PSR B1509−58 (Seward,
Harnden, & Helfand 1984; Seward & Harnden 1982). PSR B0540−69 is located in the
LMC, and with similar age, energy and spin period, is often referred to as the twin
of the Crab. PSR B1509−58 was discovered inside SNR MSH 15−52, and although
it has a relatively long period of 150 ms, has an age under 2000 years old and a large
magnetic field of ∼1013 G due its huge period derivative (B ∝ [P Ṗ ]1/2). More than ten
pulsars were detected with Einstein, and Seward & Wang (1988) found an empirical
relationship between X-ray luminosity Lx and spin-down luminosity (Ė ∝ Ṗ P −3 )
1
Prior to Einstein, focusing optics were employed in sounding rocket payloads that made five-
minute long astronomical observations. Reflecting mirrors were also used in X-ray telescopes flown
on Skylab for Solar observations.
18
indicating Lx ∝ Ė.
The X-ray study of pulsars continued with launch of the ROSAT in 1990 (Trümper
1983). Its large collecting area and high spatial resolution allowed detection of synchrotron nebulae, all with linear size of a few parsecs, around several Galactic radio
pulsars, including PSRs B1706−44, B1951+32, and B1823−23 (Finley et al. 1998;
Safi-Harb, Ögelman, & Finley 1995; Finley, Srinivasan, & Park 1996). In total, more
than twenty radio pulsars were detected with ROSAT, and Becker & Trümper (1997)
found a relation between Lx and Ė similar to that of Seward & Wang (1988), although
with a slightly different correlation between the two quantities.
The mid 1990’s saw the commissioning of three major X-ray telescopes, ASCA
(Tanaka, Inoue, & Holt 1994), RXTE (Bradt, Rothschild, & Swank 1993), and
BeppoSAX (Boella et al. 1997), each of which has significant sensitivity to hard
(E > 2 keV) X-rays. The discovery of additional young pulsars at high energies
has continued, most notably the 16 ms PSR J0537−6910 with RXTE (Marshall et
al. 1998) and the 69 ms and 65 ms PSRs J1617−5055 and J1811−1926 with ASCA
(Torii et al. 1998; Torii et al. 1997). PSR J0537−6910, located in the LMC, is
remarkable not only for having the fastest spin period of any known non-recycled (i.e.
not a millisecond pulsar) rotation-powered pulsar, but also being the most energetic,
with Ė slightly larger than the Crab. PSR J1617−5055, located near (but probably
unrelated to SNR RCW 103), is very energetic (Ė ∼ 1037 ergs s−1 ) and is a known
radio emitter (Kaspi et al. 1998) Although PSR J1811−1926 has a characteristic age
of 20 kyr, its association with SNR G11.2−0.3, which has been claimed to be the
remnant of a historical supernova observed in 386 AD, would indicate its true age
is less than 2000 yr (Torii et al. 1998). Another important result was the report
by several authors of large, 10 − 200 size pulsar wind nebulae (PWNe) around most
rotation-powered pulsars observed with ASCA (Kawai & Tamura 1996; Shibata et al.
1997; Kawai, Tamura, & Saito 1998). Surprisingly, these putative PWNe were more
than an order or magnitude larger than those seen with either Einstein or ROSAT.
19
1.2
Historical Overview of Imaging X-ray Telescopes and Their Instrumentation
The steady progress in X-ray observations of pulsars, and at the same time, their
limitations (e.g., the Crab still remains the only pulsar whose X-ray emission is wellmodeled [Kennel & Coroniti 1984; Gallant & Arons 1994; Hester et al. 1994]) is best
understood by examining the properties of each of the major observatories. As mentioned above, a new era began with the launch of Einstein, the first X-ray telescope
with focusing optics (500 FWHM angular resolution in the 0.2 − 4.5 keV passband;
Giacconi et al. 1979). Einstein’s imaging focal plane detectors consisted of three High
Resolution Imagers (HRI), microchannel plate devices with intrinsic resolution better
than 100 (Kubierschky et al. 1978) and two Imaging Proportional Camera (IPC), flow
proportional counters with 1.0 5 resolution (Gorenstein et al. 1975). Einstein also had
three non-imaging spectroscopic instruments: the Solid State Spectrometer (SSS), a
Si(Li) detector (Joyce et al. 1978), the Focal Plane Crystal Spectrometer (FPCS), a
Bragg crystal spectrometer (Canizares et al. 1977), and the Objective Grating Spectrometer (OGS), a dispersive grating used with the HRI (Giacconi et al. 1979). However, the focal plane instrumentation on Einstein had serious limitations. Although
the powerful spectrometers had resolution as high as E/∆E ∼ 1000, they had no
spatial resolution. The HRI had limited spectral resolution with E/∆E ∼ 0.5 − 1
and relatively low quantum efficiency (QE) of order 10 − 20%. The IPC had better
efficiency, with QE above 50% over a significant part of their operating range, but
comparable spectral resolution and at best, modest spatial resolution.
The next major advancement for X-ray astronomy came in 1990 with the launch of
the German-led X-ray satellite ROSAT (Trümper 1983). ROSAT used X-ray mirrors
similar to those flown on Einstein, with larger collecting area and a slightly softer
0.1 − 2.4 keV passband (Aschenbach 1988). Focal plane instruments were limited to
three imagers, the Position Sensitive Proportional Counters (PSPC-B and PSPC-C)
and the microchannel plate High Resolution Imager (HRI) (Pfeffermann et al. 1986).
20
These cameras were nearly identical to their Einstein analogs, with improved spatial
resolution (3000 for the PSPCs and 1.00 7 for the HRI) and similar quantum efficiencies.
Unfortunately, like the Einstein microchannel plates, the ROSAT HRI had no spectral
resolution, and although they had a factor of two improvement over the Einstein IPC,
the PSPCs still only had a energy resolution of E/∆E ∼ 2.
Einstein and ROSAT dramatically demonstrated the power of focusing X-ray optics. It became clear that continuing the level of advancement made possible by
these two observatories required focal plane instruments that would not only fully
utilize the spatial resolution of the mirrors, but would have spectral capabilities beyond those of imaging proportional counters or microchannel plate detectors. Even
before the launch of these telescopes, the X-ray community recognized the need for
such instruments and began exploring the use of charge coupled devices (CCDs) to
fill this role. With the promise of near unity quantum efficiency, gain linearity, and
good temporal, spectral, and spatial resolution, they represented what Fraser (1989)
called the “all-singing, all-dancing detector.” During the 1980’s several groups began
developing CCD technology optimized for X-ray detection (see Fraser 1989 and references therein), and with the 1993 launch of ASCA, the fourth Japanese satellite for
astronomy, CCDs were finally employed on an X-ray astronomy telescope.2
A joint Japanese-US collaboration, ASCA consists of four co-aligned mirrors with
moderate angular resolution (half power diameter or HPD ∼30) (Serlemitsos et al.
1995), each with its own focal plane instruments: two Gas Imaging Spectrometers
(GIS-2 and GIS-3), gas scintillation proportional counters (Ohashi et al. 1996), and
two Solid-state Imaging Spectrometers (SIS-0 and SIS-1), X-ray CCD cameras (Burke
et al. 1994). Both types of detectors have excellent detection efficiency, with QE
∼ 10 − 95% over their large passbands. The GIS has modest energy resolution
(E/∆E ∼ 1 − 15), while the SIS energy resolution (E/∆E ∼ 9 − 40) approaches that
of some of the purely spectroscopic instruments flown on Einstein. ASCA ranks as a
2
The first non-solar X-ray observation using CCDs occurred during a five-minute rocket flight in
1990 (Berthiaume et al. 1994).
21
milestone mission not only for employing the first X-ray CCDs, but also for having
the first focusing optics with significant effective area above 2 keV. In fact, with the
SIS providing softer energy response and the GIS providing higher energy response,
ASCA has imaging capabilities spanning a wide 0.4 − 12 keV passband.
Although ASCA observations have contributed to significant advances for X-ray
astrophysics, the limitations of its mirrors did not allow the full potential of the CCDs
to be exploited. For example, the precise localization possible from the small pixel size
(27 µm × 27 µm) was not utilized, as the 1 mm arcmin−1 plate scale requires ∼10,000
pixels to enclose the PSF. The 1.0 5 angular resolution results in a large background,
dominating the low instrumental background inherent to CCDs and preventing detection of sources fainter than ∼10−14 ergs s−1 cm−2. Uncertainties in the mirror
calibration and response, significantly larger than those of the better constrained
CCD models, are the main contributor to systematic uncertainties in astrophysical
parameters obtained from spectral fitting. With the launch of the Chandra X-ray
Observatory (CXO) and its CCD cameras, the full capabilities of these remarkable
detectors are finally being demonstrated.
1.3
The Chandra X-ray Observatory and This Thesis
Chandra, formerly the Advanced X-ray Astrophysics Facility (AXAF; Weisskopf,
O’Dell & Van Speybroeck 1996), is the third of NASA’s Great Observatories.3 Chandra represents the culmination of more than twenty years of planning and preparation and is arguably one of the most ambitious astrophysical observatories every
built. The power of the telescope results from a grazing incident optic (the High
Resolution Mirror Assembly, or HRMA) that allows spatial resolution of better than
half an arcsecond. To fully utilize these remarkable mirrors, an equally impressive
3
The Great Observatories are a suite of four spaced-based telescopes, each designed for studies
in a particular energy band: the Space Infrared Telescope Facility for infrared, the Hubble Space
Telescope for optical and UV, CXO for X-rays, and Compton Gamma Ray Observatory for γ-rays.
22
detector is required. The Advanced CCD Imaging Spectrometer (ACIS) is one of two
primary focal plane instrument employed by Chandra (Burke et al. 1997). The ACIS
detectors have excellent spatial resolution (one pixel corresponds to 0.00 5) and spectral
resolution4 (E/∆E ∼ 20 − 50) with high detection efficiency (∼20 − 90%) across the
0.1−10 keV X-ray band. Chandra’s second focal plane instrument is the microchannel plate High Resolution Camera (HRC), a successor to the HRI cameras flown on
Einstein and ROSAT with similar characteristics (Zombeck et al. 1995; Murray et al.
1997). Both the HRC and ACIS have two separate arrays, an imaging array (HRC-I
and ACIS-I) intended for wide field imaging and a spectroscopic array (HRC-S and
ACIS-S) to be used in conjunction with transmission gratings that can be inserted
into the optical path. Figure 1-1 compares the spatial resolution of the four telescopes
discussed above, while Figures 1-2 and 1-3 compare the QE and energy resolution of
the imaging focal plane instruments of these telescopes. The most striking feature
among the observatories is the superior imaging quality of Chandra and the excellent
performance characteristics of ACIS.
Part I: Instrumentation
This thesis consist of two distinct parts. In Part I, I discuss various aspects of the
calibration of ACIS. In Chapter 2, I first give a brief description of Chandra and
all its instruments before explaining in detail those facets of ACIS germane to this
thesis. Chandra scientific objectives demand extremely accurate knowledge of the
instrumental response; for example, the goal for knowledge of the detection efficiency
is of order 1%, and the corresponding goal for the energy-scale is of order 0.1% (Weisskopf et al. 1996). To meet these requirements, a multi-faceted calibration approach
was conceived and implemented. A crucial first step is the absolute calibration of
flight-quality CCDs that serve as the reference standards for the actual flight devices.
In Chapter 3, I describe the calibration performed at the PTB beamlines at the
4
After Chandra’s launch, some of the ACIS detectors suffered radiation damage, degrading their
resolution compared to pre-flight performance.
23
Figure 1-1 Encircled energy plots for four different X-ray telescopes. ROSAT, Einstein, and ASCA performance measured at 1.49 keV, Chandra performance measured
between 0.5 − 2 keV. References– ROSAT and Einstein: Aschenbach (1988); ASCA:
Serlemitsos et al. (1995); Chandra: Dewey et al. (1999).
BESSY synchrotron facility in Berlin, where the CCDs were exposed to undispersed
synchrotron radiation, whose intensity is known to better than 1% in the 0.3 − 4 keV
band, providing a primary standard for the absolute detection efficiency calibration
of the reference standards (see also Bautz et al. 2000). I present the analysis of the
raw data and discuss the fit of a parameterized model of the CCD to the well-known
synchrotron spectrum.
In the course of reviewing the best-fit values, it became clear that the synchrotron
data could not uniquely constrain all the model parameters. In particular, degeneracies exist in the structural parameters of the channel stop, an implant of SiO2 and
p+ -type Si that defines the horizontal boundary of the CCD pixels. Determination of
the channel stop dimensions is crucial for an accurate measure of the CCD detection
efficiency at low energies, as the characteristic absorption length of soft X-ray (E . 2
24
Figure 1-2 Quantum efficiency (QE) as a function of energy for the imaging focal
plane detectors on different X-ray telescopes. For clarity, we do not include all instruments. However, we note that the QE for the HRI cameras on both Einstein
and ROSAT are similar to that of the Chandra HRC, the QE for the ASCA SIS
is similar to that of the Chandra ACIS, and the Einstein IPC is similar to that of
the ROSAT PSPC. References– Chandra ACIS: this work; Chandra HRC: Patnadue
(1999); ROSAT PSPC: Pfeffermann et al. (1986); ASCA GIS: Ohashi et al. (1996).
N.B. Calibration information does not exist for the PSPC above 2 keV.
keV) in Si and SiO2 is comparable to the thickness of the channel stop components. In
Chapter 4, I describe a technique I refined to non-destructively measure these structures in situ (Pivovaroff et al. 1998; Pivovaroff et al. 1999). The experiment uses a
thin metal film with periodically spaced holes placed in front of the CCD. This mesh
is slightly misaligned with the orientation of the CCD pixels, and when illuminated
with X-rays, a moiré pattern results. I then fit a model of the channel stop to the
deconvolved moiré data and adjusted the parameters using a best fit minimization
technique similar to the one employed for the analysis of the synchrotron data.
Another important aspect of calibration is to characterize the redistribution or response function, the output of the CCD when exposed to X-rays. For example, when
25
Figure 1-3 Energy resolution (E/∆E) as a function of energy for the imaging focal
plane instruments of four X-ray telescopes. In general, there has been a steady
improvement in energy resolution from microchannel plates (HRI & HRC) to gas
counters (IPC, PSPC, & GIS) to CCDs (SIS & ACIS). References– Chandra ACIS:
Bautz et al. (1998); Chandra HRC: Patnadue (1999); ASCA SIS: Gendreau (1995);
ASCA GIS: Ohashi et al. (1996); ROSAT PSPC and HRI: Pfeffermann et al. (1986);
Einstein IPC and HRI: Giacconi (1979).
illuminated with monochromatic X-rays, in addition to a Gaussian peak, additional
features in the CCD spectrum may include low energy tails or shoulders as well as
fluorescence and escape lines. The mesh data discussed in Chapter 4 clearly demonstrate that some of the redistribution features are localized to particular regions of
the pixel, including the channel stops (see also Prigozhin et al. 1999). Guided by the
results of the mesh experiments, I performed additional measurements to study and
constrain the mechanisms responsible for certain response features, including recombination effects in the p+ -type Si and the existence of surface traps at the Si–SiO2
interface. In Chapter 5, I present the results of these experiments.
26
Part II: Astrophysics
The spatial and spectral capabilities of the HRMA-ACIS combination are ideally
suited for the detailed study of X-ray emission from rotation-powered pulsars. The
“first light” observation of the young SNR Cas A beautifully demonstrates the truly
amazing results possible with this telescope. The Chandra observations also revealed
the existence of a previously unknown point source at the center of the SNR. In
Appendix E, I reprint a recently accepted paper (Chakrabarty et al. 2000) I coauthored on analysis of this data. Unfortunately, since Chandra’s successful launch
in July 1999, very few observations of rotation-powered pulsars are publicly available.
Instead, I analyzed data from ROSAT and ASCA, including observations with the SIS,
which employs MIT-developed CCDs that are the predecessor to the ACIS detectors.
Sufficient archival data exist from both the CCD cameras and the GIS detectors to
systematically study many rotation-powered pulsars.
In particular, I discuss observations of four young radio pulsars. PSRs B1046−48
and B1610−50 are energetic (∼1036 ergs s−1 ) pulsars with only limited previous Xray work. In Chapter 6, I present detailed analysis of ASCA data on both objects,
with an emphasis on image analysis. In marked contrast to other authors (Kawai &
Tamura 1996; Shibata et al. 1997; Kawai, Tamura, & Saito 1998), I find no evidence
for large, spatially extended emission from either pulsar. I interpret the emission from
PSR B1046−58 as that from a spatially unresolved synchrotron nebula. This evidence
also supports the results of Kaspi et al. (2000) who suggest that PSR B1046−58 is
the counterpart to the previously unidentified γ-ray source 3EG J1048−5840. No
X-ray emission is seen from PSR B1610−50. The derived luminosity upper limit is
used to constrain the pulsar’s velocity, which provides evidence against a previously
claimed PSR/SNR association (Pivovaroff, Kaspi, & Gotthelf 2000).
In Chapter 7, I continue discussing young pulsars and present analysis of PSR
J1119–6127, an extremely young pulsar recently discovered in an on-going search of
the Galactic plane for radio pulsars. Data include both pointed ASCA and serendipitous archival ROSAT observations. Each telescopes detects emission, ∼150 in extent
27
and centered on the position of the radio pulsar. This high-energy emission is spatially coincident with G292.2−0.54, a similarly sized shell of radio emission (Crawford
2000; Crawford et al. 2000). Taken together, this evidence supports the interpretation of G292.2−0.54 as the SNR associated with PSR J1119−6127. The interesting
high-energy morphology of G292.2−0.54 and its emission are discussed. Pulsed Xrays from PSR J1119−6127 may be present, although the emission may also be an
enhancement in the SNR or a chance superposition of an unrelated object with the
position of the radio pulsar. I discuss models supporting these various scenarios.
In Chapter 8, I discuss another recently discovered radio pulsar PSR J1814−1744.
While this pulsar has a rather modest spin-down luminosity (Ė ∼ 1032 ergs s−1 ) and
an age approaching 100,000 yr, it has the highest known magnetic field of any radio
pulsar. In fact, its spin parameters are very similar to those of anomalous X-ray
pulsars (AXPs; see, e.g., Mereghetti & Stella 1995 and Gotthelf & Vasisht 1998),
suggesting that this may be a transition object between the radio pulsar and AXP
populations, if AXPs are isolated, high magnetic field neutron stars as has recently
been hypothesized. I present archival X-ray observations of PSR J1814−1744 made
with ROSAT and ASCA (Pivovaroff, Kaspi, & Camilo 2000). X-ray emission is not
detected from the position of the radio pulsar. The derived upper flux limit implies
an X-ray luminosity significantly smaller than those of all known AXPs. This conclusion is insensitive to the possibility that X-ray emission from PSR J1814−1744 is
beamed or that it undergoes modest variability. When interpreted in the context of
the magnetar mechanism, these results argue that X-ray emission from AXPs must
depend on more than merely the inferred surface magnetic field strength. This suggests distinct evolutionary paths for radio pulsars and AXPs, despite their proximity
in period–period derivative phase space.
28
1.4
Publications
A large fraction of the work presented in this thesis has previously appeared in refereed journals or in conference proceedings. Below, I give a complete list of these
publications.
1.4.1
Refereed Journals
D. Chakrabarty, M. Pivovaroff, L. Hernquist, J. Heyl, and R. Narayan, “The Central
X-ray Point Source in Cassiopeia A,” Astrophysical Journal, accepted, 2000.
M. Pivovaroff, V. Kaspi, and F. Camilo, “X-ray Observations of the High Magnetic
Field Radio Pulsar PSR J1814−1744,” Astrophysical Journal, v.535, 2000.
M. Pivovaroff, V. Kaspi, and E. Gotthelf, “ASCA Observations of the Young Rotationpowered Pulsars PSRs B1046−58 and B1610−50,” Astrophysical Journal, v.524,
p.436, 2000.
M. Bautz, G. Prigozhin, M. Pivovaroff, S. Jones, S. Kissel, and G. Ricker, “X-ray CCD
Response Functions, Front to Back” Nuclear Instruments and Methods, A, v.436, p.40,
1999.
M. Pivovaroff, S. Jones, M. Bautz, S. Kissel, G. Prigozhin, G. Ricker, H. Tsunemi,
and E. Miyata, “Measurement of the Sub-pixel Structure of AXAF CCDs,” IEEE
Transactions on Nuclear Science, v.45, p.164, 1998.
1.4.2
Conference Proceedings
M. Bautz, M. Pivovaroff, S. Kissel, G. Prigozhin, T. Isobe, S. Jones, G. Ricker, R.
Thornagel, S. Kraft, F. Scholze, and G. Ulm, “Absolute Calibration of ACIS Xray CCDs Using Calculable, Undispersed Synchrotron Radiation,” Proceedings of the
SPIE, v.4012, 2000.
M. Pivovaroff, V. Kaspi, and E. Gotthelf, “ASCA Observations of Galactic Rotationpowered Pulsars,” ASP Conference Series: IAU Colloquium #177, in press, 2000.
M. Pivovaroff, V. Kaspi, and F. Camilo, “X-ray Observations of the High Magnetic
Field Radio Pulsar J1814−1744,” ASP Conference Series: IAU Colloquium #177, in
press, 2000.
29
G. Prigozhin, M. Pivovaroff, S. Kissel, M. Bautz, and G. Ricker, “Charge Loss in the
Channel Stop Regions of the X-ray CCD,” 1999 IEEE Workshop on Charge Coupled
Devices and Advanced Image Sensors, Japan, 1999.
M. Pivovaroff, S. Kissel, G. Prigozhin, M. Bautz, and G. Ricker, “In situ Measurements of the Channel Stop Structure in AXAF CCDs,” Proceedings of the SPIE,
v.3765, p.278, 1999.
G. Prigozhin, M. Pivovaroff, S. Kissel, M. Bautz, and G. Ricker, “Novel Backside
Illuminated Structure with Improved Energy Resolution,” Proceedings of the SPIE,
v.3765, p.285, 1999.
V. Kaspi, J. Lackey, M. Pivovaroff, J. Mattox, E. Gotthelf, R. Manchester, M. Bailes,
and R. Pace, “Gamma-ray Observations of the Young Radio Pulsars PSRs B1046-58
and J1105−6107, Journal of the Italian Astronomical Society, v.69, p.959, 1998.
M. Bautz, M. Pivovaroff, F. Baganoff, T. Isobe, S. Jones, S. Kissel, B. LaMarr, H.
Manning, G. Prigozhin, G. Ricker, J. Nousek, C. Grant, K. Nishikida, F. Scholze,
R. Thornagel and G. Ulm, “X-ray CCD Calibration for the AXAF CCD Imaging
Spectrometer,” Proceedings of the SPIE, v.3444, p.210, 1998.
M. Pivovaroff, M. Bautz, S. Kissel, G. Prigozhin, T. Isobe and J. Woo, “Flight X-ray
CCD Selection for the AXAF CCD Imaging Spectrometer,” Proceedings of the SPIE,
v.2808, p.182, 1996.
S. Jones, M. Bautz, S. Kissel and M. Pivovaroff, “Using Tritium and X-ray Tubes as
X-ray Calibration Sources for AXAF CCD Imaging Spectrometer CCDs,” Proceedings of the SPIE, v.2808, p.158, 1996.
M. Bautz, S. Kissel, G. Prigozhin, S. Jones, T. Isobe, H. Manning, M. Pivovaroff, G.
Ricker, and J. Woo, “X-ray CCD Calibration for the AXAF CCD Imaging Spectrometer,” Proceedings of the SPIE, v.2808, p.170, 1996.
30
1.5
Acronyms
Below, I list all the acronyms used throughout this thesis. For convenience, I repeat
this list in Appendix A.
ACIS
ASCA
AXAF
AXP
BESSY
CCD
Chandra
DEA
Einstein
FHWM
GIS
HETG
HPD
HRC
HRI
HRMA
IPC
LBOX
LETG
MOS
PSPC
PSF
PSR
PTB
ROSAT
RP
SEM
SIS
SN
SNR
SRF
XRT
XSPEC
Advanced CCD Imaging Spectrometer: detector on Chandra
Advanced Satellite for Astronomy and Cosmology: X-ray telescope
Advanced X-ray Astrophysical Facility, renamed Chandra
Anomalous X-ray Pulsar
Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung
Charge Coupled Device
Chandra X-ray Observatory: X-ray telescope
Detector Electronics Assembly
Einstein Observatory: X-ray telescope
Full-width at Half Maximum
Gas Imaging Spectrometer
Low Energy Transmission Grating: spectroscopic instrument on Chandra
Half-power Diameter
High Resolution Camera: detector on Chandra
High Resolution Imager: detector on Einstein and ROSAT
High Resolution Mirror Assembly: Chandra mirrors
Imaging Proportional Camera: detector on Einstein
Lasagna-box Electronics
Low Energy Transmission Grating: spectroscopic instrument on Chandra
Metal Oxide Semiconductors
Position Sensitive Proportional Counter: detector on ROSAT
Point Spread Function
Pulsar
Physikalisch-Technische Bundesanstalt
Röntgensatellit: X-ray telescope
Representative Pixel
Scanning Electron Microscope
Solid-state Imaging Spectrometer
Supernova
Supernova Remnant
Spectral Redistribution Function
X-ray Telescope: ASCA mirrors
X-ray Spectral Fitting Package
31
32
Part I: Instrumentation
33
34
Chapter 2
The Chandra X-ray Observatory and
ACIS
2.1
Overview
The Chandra X-ray Observatory (CXO; formerly the Advanced X-ray Astrophysics
Facility [AXAF]) was launched by the Space Shuttle Columbia on 1999 July 23. After
an Inertial Upper Stage boosted the satellite out of a low-earth orbit and separated
from the telescope, Chandra fired its own Integral Propulsion System several times to
put telescope in a highly elliptical orbit. The final orbit has a perigee of 1.0 × 104 km
and an apogee of 1.4 × 105 km (approximately one-third the distance to the moon)
and an orbital period of 64 hr (Weisskopf et al. 2000).
Chandra is an incredibly complex telescope, with many subsytems for pointing,
stability, data processing, telemetry and spacecraft control. Figure 2-1 is a schematic
of the telescope with just a few of these components identified. Below, I concentrate
on the scientific instruments, which can be classified as optics, detectors, and gratings.
35
Figure 2-1 View of the Chandra X-ray Observatory showing the HRMA, four scientific instruments (two types of gratings, HRC, and ACIS) and major satellite components. From the “Chandra Propers’ Observatory Guide, Rev.2.0”,
http://asc.harvard.edu.
2.2
2.2.1
Scientific Instruments
HRMA
At energies above ∼10 eV, photons scatter at incident angles greater than ∼1◦ . Mirrors constructed for any imaging X-ray application then must utilize grazing incidence
reflection. Figure 2-2 (top) illustrates the principles of one such design, the Wolter-I
optic that consists of a parabolic primary and a hyperbolic secondary. To provide
sufficient collecting and good angular resolution requires very smooth, large, nearlycylindrical pieces of glasses, a difficult and (usually) prohibitively expensive endeavor.
The High Resolution Mirror Assembly (HRMA) gives Chandra unprecedented angular resolution at X-ray energies (HPD < 0.300 ) and is arguably one of the finest
optics ever fabricated. Figure 2-2 (bottom) is an exploded view of the four concentric shells of the HRMA. The 10 m focal length results in the enormous size of the
observatory.
36
Figure 2-2 Top: Principle of Wolter-I optics as it pertains to Chandra. Incident light
reflects of one of the four primary mirrors (parabolas), reflects again of the surface of
the secondary mirrors (hyperbolas) and is focused to a spot 10 m away. Bottom: View
of the High Resolution Mirror Assembly (HRMA), showing a cross section of each of
the four concentric pairs of mirrors and the location of the focus spot. Courtesy of
Martin Weisskopf.
37
2.2.2
Imagers
Chandra has two focal plane instruments, the Advanced CCD Imaging Spectrometer (ACIS) and the High Resolution Camera (HRC). Both detectors consist of two
sub-arrays, one capable of wide field imaging and the other intended to be used in
conjunction with the retractable gratings for spectroscopic studies.
HRC
The HRC utilizes microchannel plates and shares a technological heritage with the
HRI instruments that flew on both Einstein and ROSAT. Figure 2-3 shows the lay-out
of the HRC and gives the relevant dimensions for the detectors. The imaging array
(HRC-I) is a monolithic square microchannel plate (MCP) with a 300 × 300 field of
view (FOV). The spectroscopic array (HRC-S) consists of three smaller rectangular
arrays abutted together to a make a single, long array. While it is possible to image
with this sub-array, its design (e.g., its narrow width and optical blocking filters)
has been optimized for use as a readout detector for the Low Energy Transmission
Grating (LETG).
While the HRC has no spectral resolution and only modest quantum efficiency
when compared to ACIS (see Figures 1-2 and 1-3), it has two important advantages
over ACIS. First, its pixels are twice as small as those of ACIS, giving it a plate
scale of 0.13 arcsec pixel−1, allowing it to better sample the intrinsic resolution of
the HRMA. Thus, the HRC will produce the X-ray images with the highest spatial
resolution ever.1 Second, the HRC has time resolution of 16 µs, compared to 3.3 s
resolution of ACIS.2 Resolution on these time scales can benefit several types of
science, most noticeably the study of pulsed emission from rotation-powered pulsars.
1
2
All of the X-ray missions now being planned only require ∼500 resolution.
ACIS can be operated in a 1-D mode that provides millisecond resolution, although complications
exist with the analysis of this data format.
38
Figure 2-3 Schematic diagram of the HRC, showing both the imaging and spectroscopic arrays. Courtesy of Steven Murray.
ACIS
ACIS consists of ten individual charge coupled devices (CCDs), with a flight heritage
based on the Solid-state Imaging Spectrometer (SIS), the CCD cameras on ASCA.
Four of the chips are abutted into a 2 by 2 array (ACIS-I), which has a 170 × 170 FOV
and is intended for imaging of extended sources. The other six chips are arranged in
a 1 by 6 array (ACIS-S), intended primarily to be used as the read-out for the High
Energy Transmission Grating (HETG). However, as two of the chips in this array
are back-illuminated (BI) detectors and have superior low-energy quantum efficiency
compared to the chips in the ACIS-I, imaging observations with ACIS-S will be common. Figure 2-4 is a photo of the engineering model of ACIS, clearly showing the
arrangement of the ACIS-I and ACIS-S arrays.
39
Figure 2-4 The engineering model of ACIS, clearly showing both the 2 by 2 imaging
and 1 by 6 spectroscopic arrays.
2.2.3
Transmission Gratings
Chandra has two grating assemblies that can be inserted into the optical path between
the HRMA and focal plane instruments to obtain high resolution (E/∆E > 1000)
spectra. The gratings diffract X-rays at an angle β, dispersing the incident radiation
analogous to the way a prism spreads white light into the familiar rainbow of colors.
The energy of the photon is determined from the well-known grating equation sin β =
mλ/p (where m is the order number, λ is the photon wavelength and p is the period
spacing) and the location of the photon-interaction on the imager, not the intrinsic
energy resolution of the detector.
40
HETG
The High Energy Transmission Grating (HETG) consists of two sub-sets of gratings,
the High Energy Grating (HEG) and Medium Energy Grating (MEG). Each grating
assembly consists of hundreds of different facets fixed in a circular support structure.
The HEG facets have spacing period p half that of the MEG and provides better
resolution at high energies. Figure 2-5 shows the HETG and sketches the way it
disperses X-rays focused by the HRMA. The individual facets that comprise the
HEG and LEG are rotated with respect to one another, so that the dispersed spectra
occupy different parts of the detectors and can be analyzed separately. As the HETG
was designed for high-energy spectroscopy, ACIS is the read-out detector of choice.
Figure 2-5 Sketch of the High Energy Transmission Grating (HETG), showing the
grating elements and basic principles behind dispersive spectroscopy. From the
“Chandra Propers’ Observatory Guide, Rev.2.0”, http://asc.harvard.edu.
LETG
The Low Energy Transmission Grating (LETG) operates on the same principles of the
HETG. Unlike the HETG, though, the LEG consists of only type of facet, which has a
41
much larger period p than either the HEG or MEG. The HRMA+LETG combination
provides the highest resolution spectra capable with Chandra. Because the LETG
is optimized for low-energy (E < 0.5 keV) spectroscopy, the HRC is the read-out
detector of choice.
2.3
2.3.1
ACIS
Basic Description
Effectively, CCDs are a series of Metal Oxide Semiconductors (MOS) capacitors
ganged together for operation as a single array. Charge generated through photoabsorptions are collected in a potential well. The charge is then transferred (clocked)
from neighboring capacitors to an amplifier stage, where the resultant output is converted from an analog to a digital signal by read-out electronics. For a general review
of semiconductor devices, the reader is referred to the books by Grove (1967) and
Pierret (1989). The PhD thesis of Gendreau (1995) on the ASCA SIS is an excellent
source for details specific to X-ray CCDs and is particularly useful, given the similarities between the detectors employed for ACIS and the SIS. Below, I only discuss
those aspects of CCDs particularly relevant for this thesis.
The CCDs fabricated by MIT Lincoln Laboratory for ACIS (CCID-17) have
been optimized for high detection efficiency (0.2 − 0.9), excellent energy resolution
(E/∆E ∼ 20 − 50), and precise spatial resolution (0.005, when the 24 µm × 24 µm
pixel is coupled with the HRMA) in the 0.2 − 12 keV band-pass (Burke et al. 1997).
X-ray photons with energies above 4 keV have characteristic absorption lengths in
silicon on order of tens of microns, and to ensure that most photoabsorptions occur
in the depleted region of the detector, the devices are fabricated of high resistivity
(ρ=7000 Ωcm) bulk, p-type silicon3. To image and resolve the energy of individual
3
Measurements of the flight devices reveal that depletion depths of 70 µm are achievable with
the combination of high ρ silicon and appropriate bias voltages.
42
photons requires the use of a shielded framestore architecture. This design allows a
fast transfer of charge from the image section to the framestore section; the latter is
then slowly read out during the next integration cycle to minimize the introduction of
read noise. The actual framestore architecture consists of two separate sections that
feed into two independent serial registers which provides great flexibility in clocking
out the charge from the CCD. See Figure 2-6 for a detailed schematic of the CCD.
Image Section
Charge Transfer
Direction
Framestore Section
A
B
C
D
Amplifier Node
Split readout registers
Figure 2-6 Schematic of a MIT Lincoln Laboratory CCID-17 CCD.
The three phase clocking scheme used to transfer charge in the ACIS CCDs requires three distinct gates. Each gate consists of a polysilicon layer deposited above
a dielectric layer of Si3 N4 and SiO2. Gates are separated by differing amounts of
insulating SiO2, and slight variations in thickness, width and shape exist between the
three types of gates. The gates run the length of the CCD parallel to the interface of
the image and framestore sections. Three neighboring gates define one pixel, with the
43
boundary location dependent on the biasing of the gates. Channel stops, consisting
of implanted p+ regions and their insulating oxide layer, run perpendicular to, and
lie beneath, the gate structure. These structures confine the charge clouds created by
the photoelectric absorption and define the horizontal boundaries of a pixel. These
structures are described in detail in Chapter 4.
Normally, radiation is incident to the surface of the CCD that has the gates. Photons thus must first pass through the gate structure and channel stops before they
can interact in the depleted silicon. At low energy (E < 2 keV), the characteristic
absorption length of photons is comparable to the thickness of these structures, reducing the low-energy detection efficiency. One approach for increasing the QE is to
reverse the orientation of the device, such that the radiation does not have to propagate through the gates to interact in the depleted silicon. A device operated in this
fashion is referred to as back illuminated (BI), compared to the more common front
illuminated (FI) CCDs described above. In order for this method to be effective, additional processing steps must be performed, including thinning the undepleted bulk
silicon. However, this step introduces non-linearity and diminishes the spectral resolution of the detectors. Furthermore, as these thinned devices have smaller depletion
depths, the BI CCDs have lower high-energy (E > 5 keV) QE than the FI CCDs.
Thus, the best type of device depends critically on its intended application and the
scientific objectives. ACIS employs both types of detectors, with two BI chips (S1
and S3) and four FI chips comprising the ACIS-S array, and four FI chips comprising
the ACIS-I array.
2.3.2
Event Detection and Grading
An event is registered when the charge generated by photoelectric absorption is drawn
into the electrostatic potential well created by the gates. If the charge is confined to
one pixel, a single pixel event results. If an interaction takes place close to a pixel
boundary, the charge will be collected by two neighboring pixels (a split event), and
if an interaction takes place near a pixel corner the charge can be divided between
44
three or four pixels (also a split event). Our standard analysis technique considers
a 3 × 3 island of pixels in which the center pixel is the local maximum and is also
above an event threshold value, Te . If surrounding pixels are above a split threshold
value, Ts , where Ts < Te , their signal is added to the central pixel’s and the event is
classified according to the distribution of charge in the 3 × 3 island.
The relative proportion of a particular event type or grade to all events is referred
to as the branching ratio. Using the nomenclature from the ASCA SIS instrument
(Tanaka, Inoue, & Holt 1994), a grade 0 event refers to a single pixel event, grade
2 refers to events split between vertical neighbors, grade 3 and 4 refers to events
split between horizontal neighbors, and grade 6 refers to both three and four pixel
events. Table 2-1 presents the mapping between ASCA grades and event types. The
proportion of events in each event grade is a strong function of photon energy. As the
initial charge cloud size and the mean interaction depth increase with photon energy,
the probability of a split event increases. The larger the interaction depth, the larger
the contribution of diffusion to the charge cloud size, and therefore, the larger the
probability that the event will occupy more than one pixel.
Table 2-1: ASCA grades and their corresponding event type for X-rays
ASCA GRADE
Event Type
0
Single Pixel
2
Vertically Split
3,4
Horizontally Split
6
L-shaped and Square
In addition to providing a convenient method to classify the way charge is distributed among pixels, event grades also contain information about the origin of an
event. As high-energy particles (e.g. electrons and protons) pass through a CCD,
they deposit a significant amount of ionizing radiation, generating in some cases as
many as several hundred events. However, these events usually have charge deposited
45
in at least five or six pixels of the 3 × 3 detection islands discussed above. As the
grade of these types of events (grades 5 or 7) are not part of the standard sub-set
of grades listed in Table 2-1, particle-induced background events can be effectively
discriminated purely on the basis of event grade.
Throughout this thesis, event grade and event type are used interchangeably. For
example, a photon interaction that has all its charge collected in one pixel is referred
to either as a single-pixel event or grade 0, or g0.
2.3.3
Electronics
Two types of read-out electronics were used for all the experiments described in this
thesis. The first generation of electronics is referred to as LBOX, so dubbed because
of the similarity of the stacked PC boards to a lasagna. The second generation is
called the DEA (Detector Electronics Assembly). While the operating principles are
the same, there are several differences in the basic design of each system that translate
to differences in CCD performance. Because the LBOX was designed for low power
consumption and this was less of a concern for the DEA, the DEA can read-out the
same detector in a shorter time (3.3 s compared to 7.0 s for clocking the entire detector). Thus, for a given source flux, DEA-driven CCDs are less susceptible to pile-up,
that is two distinct X-ray events mistaken as one. (See §3.4 for a complete discussion
of pile-up.) The other difference is in the noise characteristics of the electronics. The
LBOX has RMS noise of ∼4–5 electrons, while the DEA has RMS noise of ∼2–3
electrons. At low energies (E < 0.5 keV), the energy resolution becomes dominated
by the contribution to read-out noise. Hence, DEA-driven CCDs have the highest
spectral resolution.
46
Chapter 3
Absolute Calibration of X-ray CCDs
Using Synchrotron Radiation
3.1
Introduction
Each of the ten CCDs that comprise the ACIS focal plane had to be precisely calibrated for Chandra. We have used the calculable undispersed synchrotron radiation
at the Physikalisch-Technische Bundesanstalt (PTB) beamline at BESSY I as the
primary radiometric standard. For logistical reasons it proved impractical to calibrate the flight detectors directly at PTB, so we have instead calibrated flight-like
ACIS CCDs there. These absolutely calibrated detectors were then used as transfer
standards in our laboratory at MIT to determine the efficiency of the flight devices.
In this Chapter, I describe the measurement method and the analysis of the raw
data in detail, and present the results of the absolute calibration of ACIS transfer
standard detectors. I also briefly discuss the measurement and modeling errors which
limit the accuracy of the calibration of the reference standards.
47
3.2
Measurements
The laboratory of the Physikalisch-Technische Bundesanstalt (PTB) at the BESSY
I electron storage ring provided a broad-band (0.1 − 4 keV) source radiation source
of calculable intensity (Arnold & Ulm 1992). The spectral flux was calculable with
relative uncertainty below 1% from knowledge of the geometry of the detector with
respect to the orbital plane, the electron energy, ring current and magnetic field of
the bending magnets.
Figure 3-1 illustrates the experimental set-up at the PTB laboratory. A standard
MIT vacuum chamber, modified to hold two CCDs simultaneously, was mounted to
the PTB beamline via a ceramic electro-isolator to eliminate electrical interference
between the CCD electronics and the BESSY facility. A gate valve and turbo pump
located between the CCDs and the storage ring allowed the chamber to be connected
and pumped down to the requisite vacuum without compromising the integrity of the
storage ring. The CCDs were operated at the nominal flight temperature of −120◦ C.
PTB White Light Beam Line at BESSY
* not to scale
Bending Magnets (B=1.494 T)
Trajectory of Electrons (W=797.6 MeV)
in the Storage Ring (I=10-30 electrons)
Turbo Pump
Translation
Stage
11
00
00
11
Cooled Diodes
Chopper Wheel (2% transmission)
5 mm Aperture
Gate Valve
CCD
SR
(Ψ,Σ y , d, a,b)
MIT Vacuum Chamber
Protective Wall
SR
d =16.14 m
Figure 3-1 Sketch of the PTB laboratory, showing the basic geometry of the beamline
and the interface between it and the CCDs.
Even a single electron in the storage ring would produce a flux high enough to
cause significant pileup that would have degraded the calibration accuracy. (Pileup
occurs when more than one photon interacts in a pixel during a single CCD exposure;
see §3.4 for a detailed discussion). Two measures were taken to reduce the flux to
an acceptable level. First, a chopper wheel with 2.00% transmission was inserted
into the beam line to limit the incident flux. Second, the CCD exposure time was
48
decreased by reading out only 256 of the 1026 rows in the device. This readout mode
reduced the exposure time by a factor of four. Even with these measures in place, it
was necessary to operate the storage ring at very low current. Typical ring currents
ranged from 10 to 30 electrons, although measurements with as few as 2 electrons
and as many as 50 electrons were performed to calibrate pileup effects.
The process of reading out 256 rows of the CCD limited the amount of the detector
that could be calibrated during one measurement. To ensure that all the incident
photons would fall on an active area of the detector (a necessary requirement for the
determination of absolute quantum efficiency) a five mm high aperture was placed in
the beam line and carefully centered on the electron orbital plane. The five mm slit
produced an illumination pattern 216 pixels tall1, with the CCD columns nominally
aligned perpendicular to the orbital plane. The detector chamber was mounted to a
two dimensional translation stage fitted to the end of the PTB beamline. To calibrate
an entire detector, the chamber was moved an appropriate distance in the y direction,
a 256-row swath of the CCD was read out, and the image was visually inspected to
check that all the photons hit the active area. This procedure was repeated four or
five times to calibrate the entire chip. The chamber was then moved in the horizontal
direction to illuminate a second CCD inside the chamber. By placing two chips inside
the chamber, the overhead associated with thermally cycling the CCD, venting the
chamber, switching CCDs, re-evacuating the chamber and finally cooling the CCDs
was reduced. This configuration allowed calibration of as many as four chips in a
single 48-hour period.
At least once during each user shift accurate measurements of the bending magnetic field were made, using methods described by Arnold & Ulm (1992) and references
therein. To continuously monitor the electron beam current, four Si photodiodes were
placed in the direct synchrotron radiation in the PTB beamline as near as possible
1
Although the 5 mm slit corresponds to 208 CCD rows, the inherent divergence and width of
the synchrotron emission pattern, coupled with the ∼1 m separation between the aperture and the
CCD, widens the pattern to 216 pixels.
49
to the storage ring. The photodiodes were cooled to liquid nitrogen temperature to
reduce dark current noise. The photo-current decreased in obvious steps with the
occasional loss of one of the stored electrons, thus allowing the number of the stored
electrons to be determined without uncertainty.
Given these parameters, the synchrotron radiation from the storage ring can be
derived by Schwinger’s equation (Schwinger 1949; Riehle & Wende 1986):
I(λ)SR = I SR,k (λ) + I SR,⊥(λ) =
2eρ2 I
2 2 2
2 2
2 2
[1
+
(γψ)
]
K
(ξ)
+
[1
+
(γψ)
]
(γψ)
K
(ξ)
2
1
3ε0 λ4 γ 4 cosψ
3
3
(3.1)
with
γ=
W
,
m0 c2
ξ=
2π
2 32
[1
+
(γψ)
] ,
3γ 3 λ
ρ=
W
.
ecB
W , e, and m0 are the energy, charge and rest mass of the electrons, I is the current
of the electrons in the storage ring, B is the magnetic induction of the bending
magnet at the tangent point of the electron beam to the observation point, and
ψ is the opening angle between the orbital plane and the observation point. Kx
is the modified Bessel function, order x of the the second kind, and c and ε0 are
fundamental constants. Thus, the spectral photon flux can be expressed in terms of
eight measurable quantities:
ΦE = ΦE (E; W, B, I, ψ, Σy , dSR , a, b)
(3.2)
where Σy characterizes the vertical size and divergence of the electron beam at the
source point of the radiation, dSR is the distance from the beam to the observation
point, and a and b are the height and width of the limiting aperture. The other
quantities are the same as above. Typical values are as follows: W = 797.6 MeV,
B = 1.494 T, I = 10 − 30 electrons, ψ = 10−3 arc seconds, σY = ±2.5 mm, dSR =
16.14 m, a = 40 mm, and b = 5.0 mm.
Horizontal variation of ΦE is less than 10−3 over the width of the CCD (Riehle
50
& Wende 1986). Due to its dependence on the opening angle ψ, ΦE varies strongly
as the observation point moves out of the orbital plane of the electrons. Figure 3.2
shows how the synchrotron spectrum softens as the height above the orbital plane
increases. The calculated ΦE is for one electron in the storage ring with no chopper
wheel. For typical integration times and ring currents, the detected flux above 4 keV
was negligible.
Similar measurements were also performed using the PTB Wavelength Shifter
(WLS) beamline. Additional magnets are introduced into the normal storage ring
configuration, thus boosting the energy of the electrons and shifting the energy of the
synchrotron radiation. Figure 3.2 also shows how the WLS spectrum changes as a
function of height above the orbital plane. Although the spectrum extends beyond
20 keV, the decrease in CCD quantum efficiency at high energies limits the detection
of photons to below 14 keV. The WLS experiments will be discussed in greater detail
in §3.5.4.
Figure 3-2 PTB White Light BESSY spectra as a function of height above the orbital
plane, for both the normal bending magnets (0.3 − 4 keV) and the wavelength shifter
(0.3 − 15 keV).
51
A total of eleven devices were characterized during six separate 48 hour shifts.2
Table 3-1 lists the name of the chip, the date and number of measurements made,
and additional experimental information (e.g., type of readout electronics).
Table 3-1: Summary of synchrotron measurements made at PTB beamlines at
BESSY.
Data
Storage Ring
Chip
Chip Type Date
Sets Current (electrons) Positions Electronics
w34c3
FI
Mar 95
7
10 − 5
4
LBOX 3
...
FI
Apr 95
17
49 − 10
4
LBOX 3
...
FI
May 95
6
20 − 12
5
LBOX 6
...
FI
Aug 95
3
20 − 19
1
LBOX 3
w103c1
FI
Mar 95
7
11 − 5
4
LBOX 3
w102c3
FI
May 95
6
16 − 10
5
LBOX 6
w103c2
FI
May 95
5
17 − 12
5
LBOX 6
w103c4
FI
May 95
6
20 − 10
5
LBOX 6
...
FI
Aug 95
5
19 − 18
5
LBOX 3
w147c3
BI
Aug 95
15
19 − 2
5
LBOX 3
w148c4
BI
Aug 95
6
4
5
LBOX 3
w190c1
FI
Jun 96
5
35 − 32
5
DEA 14
...
FI
Jun 96
5
15
5
LBOX 3
...
FI
Dec 96†
6
10 − 4
5
DEA 17
w190c3
FI
Jun 96
5
35 − 30
5
DEA 14
...
FI
Jun 96
5
15 − 12
5
LBOX 3
w168c2
FI
Dec 96†
5
10 − 7
5
DEA 17
w203c2
FI
Dec 96†
19
13 − 4
5
DEA 17
† Wavelength shifter measurements
Typical measurements consisted of acquiring 2000 frames, with frame integration
(or readout) times in the range 0.83 − 1.53 s, depending on which readout electronics
(i.e. LBOX or DEA) were used. While storage ring currents varied from a minimum
of 2 to a maximum of 49 electrons, the ring current was normally adjusted to either
15 or 30 electrons (again, dependent on the readout electronics) in order to ensure a
2
The last measurement was done on the Wavelength Shifter beamline.
52
flux of ∼350 counts frame−1 quadrant−1 for a total of 3 × 106 counts in the 0.3 − 4.0
keV band over the illuminated part of the CCD.
Our approach to absolute CCD calibration follows that used, for example, by
Scholze and Ulm (1994) to calibrate a windowless Si(Li) detector. One assumes that
the detector’s spectral redistribution function is known, and that one knows the form
of the detection efficiency as a function of energy. The parameters of the model detection efficiency are then determined from the data using a forward folding approach.
That is, the known incident flux density is multiplied by a trial efficiency function
and the result is convolved with the redistribution function and compared with the
observed pulseheight distribution. Model parameters are adjusted until a satisfactory
match between predicted and observed pulseheight distributions is obtained. The
first step of this process is to reduce the raw data.
3.3
3.3.1
Analysis
Storage Ring Current
Absolute calibration requires knowing the incident radiation I(λ)SR , which is directly
proportional to the storage ring current I (see Equation 3.1). As a result, we must
know the number of electrons in the ring for any data. Theoretically, this is trivial,
as the Si(Li) diodes monitoring the storage ring provide this information. In practice,
though, the uncontrolled loss of electrons requires filtering the raw data to produce
smaller sets taken with constant storage ring current.
In general, there is no a priori way to determine when an electron may be lost from
the storage ring. While the probability does increase with the number of electrons
in the ring (in the high current limit, I drops exponentially) and the quality of the
vacuum (typically lower than 10−9 T), for the low-electron operating range of our
measurements, losses are purely stochastic. Roughly one half of our total data sets
required such additional processing.
Figure 3-3 plots the beam current measured by the cooled Si(Li) diodes as a
53
function of time for w190c3 in June, 1996. Drops in current (i.e. loss of one or more
electrons) are clearly visible and the sampling time of the diodes is sufficiently high
that, in theory, the loss of an electron should be able to be localized within one or
two CCD frames (1 − 2 s). However, as the MIT acquisitions computers operate
independently of the PTB network, synchronization between the CCD and Si(Li)
diode is only reliable to within a minute. Although a seemingly small amount of time,
as many as ∼70 frames are taken during this span. An uncertainty in the number
of electrons for this much of the data translates to an overall uncertainty as large
as 3.5%, unacceptably high for precision calibration. Figure 3-3 also shows another
problem with relying solely on the diode data. During the first CCD measurement,
the current appears to drop from 35 to 0 electrons. In reality, the diode simply
warmed up, giving a false reading.
Figure 3-3 The storage ring current, as monitored by Si(Li) diodes, as a function of
time for chip w190c3 in June, 1996. The times we made a CCD measurement are
marked by the heavy lines. The rapid drop at hour 6.7 is not real, but due to a
problem with the Si(Li) diodes. An electron was lost during the second, third, and
fourth measurements, while no electrons were lost during the last measurement.
54
Because of these difficulties, I took an empirical approach for analyzing the white
light data and computing the beam current. First, I reduced each data set in its
entirity, using event thresholds appropriate for the readout electronics. Valid grade
02346 events were then extracted from each frame, and the light curve (events per
frame) of each quadrant were summed together to increase the signal to noise. These
summed light curves were then visually inspected for a decrement in the overall
counting rate. Figures 3-4 and 3-5 show summed lightcurves for data taken in June,
1996 with chip w190c3 using the DEA and LBOX electronics, respectively. If the
storage ring current dropped, as shown in Figure 3-4, the data was divided into two
discrete sets, one with the higher electron current m+1, the other with the lower
electron current m. To make sure the ring current was constant throughout each
set, I estimated the frame at which the loss occurred (Floss) and then discarded 100
frames before and after Floss when making the subsequent data sets with m+1 or m
electrons.
3.3.2
Effects of the Chopper Wheel
An important step in the BESSY calibration is the determination of the absolute
normalization. This calculation requires quantifying several parameters, including
the total exposure time. Given that we have a discrete number of frames (usually
2000), if we know the integration time per frame, the total exposure time is simply the
product of these quantities. For uninterrupted X-ray sources, the readout time should
simply be that value loaded into the sequencer commands of the readout electronics.
For the white light data, however, the situation is complicated by the presence of the
attenuating chopper wheel.
As stated earlier, a chopper wheel with rotation frequency 6.75 Hz and 2% transmission was placed in the beam-path to prevent significant pileup. The chopper wheel
is asynchronous with respect to the clocking of the CCDs, and as the readout times
for both LBOX (1.526 s) and DEA (0.837 − 0.882 s) electronics are not fundamentals of the chopper wheel frequency, the number of times the CCD sees the beam
55
Figure 3-4 Light curve of grade 02346 events from w190c3, June 1996. Data points
are shown with error bars. The shift in the counting rate at frame ∼1350 was caused
by the loss of a single electron (33 to 32 electrons) in the storage ring. The bimodal
distribution is due to the chopper wheel. The data is divided into two sets (frames
1 − 1200 and frames 1400 − 2000) and the mean of both distributions from each set
is plotted as a solid line. See §3.3.2 for a discussion of the chopper wheel.
(hereafter flashes) oscillates between two consecutive integer values during the measurements. Figure 3-6 are the lightcurves for the LBOX (top) and DEA (bottom)
electronics/sequencer configurations used for the PTB/BESSY experiments in June,
1996. The lightcurve data represents events summed from all four quadrants of a
particular chip. The five panels of each plot correspond to a different y position (e.g.,
y001) on each chip.
While the LBOX data hints at some periodic trend in the data, the DEA lightcurves
clearly shows the bimodal nature of the data. In principle, if the chopper frequency
and the CCD readout times are stable, one should be able to model the beating between the chopper and the readout rate to determine how many flashes were seen in
each frame, and from this information, calculate the readout time. In practice, how56
Figure 3-5 Light curve of grade 02346 events from w190c3, June 1996. Data points
are shown with error bars. The bimodal distribution is due to the chopper wheel.
The mean of each distribution is plotted as a solid line. The storage ring current was
constant at 20 electrons during this measurement.
ever, this task is very complicated. In fact, of the seven different electronics/sequencer
combinations3, only the y001 data taken with the DEA in June 96 is close enough to
resonance (refer to Figure 3-6 [bottom]) to easily understand the beat phenomena.
Attempts to fit a time-dependent model proved impossible, given the random drift in
CCD data acquisition and data loss (e.g., if the load on the computer is sufficiently
large, the DSP may not have time to transfer a data frame). Instead, I developed
an empirical method using only the lightcurve data and the known chopper wheel
frequency. The technique relies on the fact the any given frame will see either N or
3
All the LBOX data taken used readout times of 1.526 s. The December 1996 DEA data had a
readout time of .8370 s. The June 1996 DEA data had a different readout time for each y position.
57
Figure 3-6 Summed light curves as a function of chip y position for w190c1, taken in
June, 1996 for LBOX electronics (top) and DEA electronics (bottom). The panels of
each plot move from position y001 to y769, top to bottom. The LBOX data is consistently random, while the DEA data is clearly quasi-periodic, with the periodicity
strongly varying on y position.
58
N+1 integer number of flashes, as described by:
N<
readout time
< N + 1.
1/chopper frequency
(3.3)
For the LBOX data (readout time 1.526 s), a frame will see either 10 or 11 flashes,
while for the DEA data (readout times 0.837 − .892 s), a frame will see either 5 or
6 flashes. A priori, we would expect a histogram of the total events per frame to be
some combination of two Poisson distributions. A typical data set has 2000 frames,
so these Poisson distributions should be well-modeled by Gaussians. The integral of
each Gaussian function represents the number of frames that saw N or N+1 flashes.
If AN and AN +1 are integrals of each Gaussian and f is the chopper frequency, the
frame time is:
1
FT =
f
!
(N AN ) + [(N + 1) AN +1 ]
.
AN + AN +1
(3.4)
Figure 3-7 shows the histograms of the number of frames as a function of event
rate/frame for the LBOX and DEA electronics/sequencer configurations. The solid
line is the two Gaussian model fit to the data. The qualitative difference between
the LBOX and DEA data is due to the percentage difference between seeing N or
N+1 flashes. For the DEA data, seeing 6 rather than 5 flashes results in an relative
flux increase of 20%. For the LBOX data, seeing 11 rather than 10 flashes only
results in a relative increase of 10%. Thus in the case of the LBOX data, the two
Gaussians overlap. The residuals show that models agree quite well with the data,
with a systematic under estimation of the data between the two distributions. This
discrepancy can be understood by referring back the y001 lightcurve for the June 96
DEA data (Figure 3-6 [bottom, top panel). The transition between 6 and 5 flashes
and 5 back to 6 (frames 100 − 110 and 125 − 135) are smooth, not sudden. During
these transitions, the CCD sees five flashes during the normal readout time and sees
a sixth during the frame-store transfer.
As the two Gaussian models fit the data well, the last step is to fit models to a
number of data sets and calculate readout times for the various electronics/sequencer
59
Figure 3-7 Histograms of the number of frames that have a given (event frame−1 ) value
for data from chip w190c1 taken in June, 1996. Best-fit Gaussians to the bimodal
distributions are overplotted. The bottom panels are the data–model residuals. Since
the LBOX (top) readtimes are much longer than those of the DEA (bottom), the
fractional difference in the total number of flashes for LBOX data is smaller, resulting
in significant overlap in the LBOX distributions.
60
combinations. As (AN + AN +1) must equal the number of data frames collected M,
Equation 3.4 reduces to
1
AN
N +1−
.
FT =
f
M
(3.5)
Tables 3-2 and 3-3 contain data for the LBOX and DEA configurations from several different user shifts. Each table contains the chip name, date of experiment, y
position, calculated and programmed (i.e. sequencer-based) readout time, and the
tabulated and actual number of frames. The error on the readout time only depends
on the error on AN , the area under the best-fit Gaussian. As the area is proportional
to the product of the centroid and width of the Gaussian, and the errors associated
with each are highly correlated in a complicated fashion, I estimate the error on AN
√
assuming Poisson statistics in the limit of large numbers, i.e σAN = AN . Hence, the
error on FT is
σF T =
1
f
AN
.
M
(3.6)
There are a number of consistency checks that can be done on these data. Does
the sum of AN and AN +1 equal the number of frames in a run? Do data from different
chips or different days agree with each other? Is the empirical readout time less than
or equal to the nominal readout times? Except for one or two runs, the total number of
frames is equal to the number of actual frames in a run. For a given configuration, the
empirical times seem to agree, independent of chip or date of measurement. Table 3-4
has the weighted average readout times for both the model and the data from the
sequencer code. The readout time derived for the LBOX is slightly higher in value
than the sequencer time, but well within statistical agreement.
After properly separating the raw frames into individual sets with constant currents I, we extract X-ray events from the raw data, saving the location, pulse-height
value, and frame number of each event in an event list. Finally, the event list is
filtered by event shape (“grade”) as it would be by the ACIS on-board processors.
ASCA event grades 02346 (essentially 1-, 2-, 3- and 4-pixel events) are accepted for
this analysis. A pulse height spectrum of the filtered events is then generated.
61
Table 3-2: LBOX data from user shifts in April 1995 & June 1996.
Chip
w34c3
w34c3
w34c3
w34c3
w34c3
w34c3
w34c3
w34c3
w34c3
w34c3
w190c1
w190c1
w190c1
w190c1
w190c1
w190c3
w190c3
w190c3
w190c3
w190c3
Run Information
Date
Y Pos
Apr 95
y001
Apr 95
y001
Apr 95
y256
Apr 95
y512
Apr 95
y768
Apr 95
y768
Apr 95
y512
Apr 95
y256
Apr 95
y001
Apr 95
y001
Jun 96
y001
Jun 96
y209
Jun 96
y417
Jun 96
y625
Jun 96
y768
Jun 96
y768
Jun 96
y625
Jun 96
y417
Jun 96
y209
Jun 96
y001
Readout Time
Empirical
Programmed
1.521 ± 0.005
1.525
1.530 ± 0.005
1.526
1.504 ± 0.003
1.526
1.518 ± 0.003
1.527
1.523 ± 0.003
1.525
1.508 ± 0.003
1.526
1.575 ± 0.002
1.526
1.494 ± 0.003
1.526
1.613 ± 0.001
1.526
1.563 ± 0.004
1.526
1.522 ± 0.003
1.525
1.525 ± 0.003
1.526
1.520 ± 0.003
1.526
1.530 ± 0.003
1.526
1.525 ± 0.003
1.525
1.527 ± 0.003
1.526
1.525 ± 0.003
1.526
1.528 ± 0.003
1.524
1.525 ± 0.003
1.526
1.517 ± 0.004
1.525
Number of Frames
Empirical Actual
706 ± 26.7
699
710 ± 26.6
711
1777 ± 42.2
1776
1975 ± 44.6
1964
1974 ± 44.4
1978
1981 ± 44.5
1982
1951 ± 43.9
1974
1945 ± 44.0
1958
1981 ± 44.5
1983
511 ± 22.9
498
1982 ± 44.5
1980
1972 ± 44.5
1965
1958 ± 44.2
1959
1996 ± 44.8
1985
1951 ± 44.1
1954
1969 ± 44.4
1964
1958 ± 44.2
1962
1956 ± 44.2
1956
1985 ± 44.6
1979
1299 ± 36.1
1294
Table 3-3: DEA data from the user shifts in June 1996.
Chip
w190c1
w190c3
w190c1
w190c3
w190c3
w190c1
w190c3
w190c3
w190c1
w190c3
w190c3
w190c1
w190c3
w190c3
Run Information
Date
Y Pos
Jun 96
y001
Jun 96
y001
Jun 96
y209
Jun 96
y209
Jun 96
y209
Jun 96
y417
Jun 96
y417
Jun 96
y417
Jun 96
y625
Jun 96
y625
Jun 96
y625
Jun 96
y769
Jun 96
y769
Jun 96
y769
Readout Time
Empirical
Programmed
0.861 ± 0.001
0.882
0.863 ± 0.002
0.883
0.848 ± 0.002
0.874
0.848 ± 0.003
0.871
0.846 ± 0.002
0.870
0.834 ± 0.002
0.859
0.837 ± 0.004
0.858
0.835 ± 0.003
0.857
0.821 ± 0.002
0.845
0.821 ± 0.004
0.848
0.822 ± 0.003
0.846
0.813 ± 0.002
0.839
0.813 ± 0.003
0.839
0.812 ± 0.002
0.838
62
Number of Frames
Empirical Actual
1927 ± 43.3
1982
1672 ± 40.2
1731
1959 ± 44.0
1982
699 ± 25.9
730
1222 ± 34.7
1240
1978 ± 44.2
2000
644 ± 25.2
651
1287 ± 35.7
1300
1976 ± 44.2
2000
529 ± 22.7
541
1369 ± 36.6
1400
1959 ± 43.8
2000
1955 ± 43.7
2000
2006 ± 44.9
2000
Table 3-4: Derived readout times for various electronic configurations compared to
those from the sequencer electronics.
Electronics Y Pos
LBOX
all
DEA
y001
DEA
y209
DEA
y417
DEA
y625
DEA
y769
3.4
3.4.1
Empirical
1.528 ± 0.002
0.8618 ± 0.003
0.8473 ± 0.003
0.8342 ± 0.003
0.8215 ± 0.003
0.8126 ± 0.003
Times
Programmed/Sequencer
1.526 ± 0.001
0.8823 ± 0.003
0.8721 ± 0.003
0.8579 ± 0.003
0.8455 ± 0.003
0.8385 ± 0.003
Pileup
A Brief Description
Pile-up modifies the apparent energy and grade of detected X-ray events. The mechanism modifying the apparent energy is the obvious one: if two photons interact within
the same pixel during a single exposure, the resulting charge cloud may be ascribed
erroneously to a single event of incorrect energy. The event shape modification can
occur if two photons land in adjacent pixels, and in this case the incident photons
might not be detected at all. This can happen if such piled-up events are mistaken
for particle background events and are thus rejected by the event selection algorithm.
Figure 3-8 illustrates both pileup scenarios.
3.4.2
Pileup Correction
If the storage ring current is sufficiently high, pileup may affect both the shape and
normalization of the pulse-height spectrum. As the number of electrons in the ring
increases, the overall number of detected photons decreases and the number of events
with incorrect energy assignment increases. Figure 3-9 shows spectra, normalized to
total integration time and beam current, spanning a wide range of currents (14 −
63
■
E1 =
★
E2 =
■
E1 > E2
★ ■
★
■
■
★
■
■
■
E1 ; E 2
E1+ E 2
0
Figure 3-8 Possible outcomes from pileup. Two photons, with energies E1 and E2
and E1 > E2 , interact within the pixel. In the first case, their interaction sites are
far enough apart for each event to be recognized separately. In the second case, they
neighbor one another and are classied as a single event with energy E1 + E2 by the
detection algorithm. Here, pileup results in the loss of one X-ray and assigns an
incorrect energy to the second X-ray. In the third case, the events also neighbor one
another, but due to the location of the charge within the 3 × 3 identification region
(the shaded region), the detection algorithm rejects this an invalid event. Here, pileup
results in the loss of both X-rays.
49 electrons). The change in spectrum as a function of current must obviously be
accounted for to ensure an accurate absolute calibration. We have used a model
that relies on extensive laboratory data and first principles to correct the effects of
pile-up. The details of this method are explained in detail elsewhere (Jones 2000).
Here we summarize this technique and its application to the analysis of our absolute
calibration.
The probability of such redistributions was determined as a function of energy
(Jones 2000) from pseudo-monochromatic measurements at twelve energies spanning
1.4 − 10 keV, each containing a series of measurements over a wide range of incident
fluxes, from a low flux limit with no pileup to a high flux limit with significant
pileup. This information was then interpolated and folded into a model that allows
the correction of polychromatic or continuous spectra.
Figure 3-10 shows a pulse-height spectrum with a beam current of 19 electrons.
64
Figure 3-9 White Light spectra taken with ring currents of 14, 30, and 49 electrons
with device w34c3 in April, 1995. Data for all three spectra come from the same
quadrant and y position. The spectra have been normalized for total integration
time and current, and then arbitrarily scaled so that the highest channel is equal to
unity. The loss of X-rays at lower energies and the migration of some of these event
to higher energies clearly increases with the number of electron.
The spectrally integrated flux (from 0.3 − 4 keV) for a typical exposure was approximately 60 events s−1 cm−2 per electron of beam current. At a typical fluence (for
19 electron beam current and a 1.526 s exposure time) of 5×10−3 events pixel−1
frametime−1, approximately 3% of all events were lost to pileup.
Spectrally, the effects of pile-up appear as a deficiency of low-energy events and
an excess high-energy flux. As a check on the pileup model, we have compared
the pileup-corrected spectrum with a channel-by-channel linear extrapolation of the
observed pulseheight spectrum to zero storage ring current; as is shown in Figure 3-10,
the agreement is excellent.
65
Figure 3-10 PTB White Light BESSY spectra. The graph compares the raw, “uncorrected” piled-up spectrum, to two methods of pileup correction: “corrected”, using a
first principles approach with laboratory data, and “extrapolated”, using a channelby-channel interpolation to the zero storage ring current limit, and hence no pileup
limit. The agreement between the two correction methods is very good.
3.5
Model Fitting
3.5.1
Detector Model
Here, I describe the detector model used to analyze the synchrotron radiation data.
The model contains a number of simplifying assumptions. The influence of these
assumptions on the accuracy of our results is briefly discussed in §3.6.4.
It is convenient to describe the detector model in two parts. The detection efficiency model predicts the probability that an incident photon will interact in the
device in such a way as to produce a valid, detectable event. The redistribution
model predicts the pulse-height distribution of valid events obtained in response to
a monochromatic incident beam. Here “valid” events are those which meet certain
66
criteria designed to reduce detector background by discriminating between particleinduced and photon-induced events. For these measurements we use event selection
criteria similar to those used in the ACIS flight instrument.
The detection efficiency model is the so-called “slab and stop model” (Gendreau
1995) in which the complex CCD deadlayer structure (Burke et al. 1997) is greatly
simplified. A sketch of one cross-section through the gate structure of these 3-phase
CCDs is shown in Figure 3-11. Our model greatly simplifies this structure. In particular, the deadlayer over each pixel is assumed to consist of two regions: an electrode
region and a channel-stop region. Within each region the deadlayer is taken to be
a sandwich of layers, each homogeneous in planes parallel to the detector. Thus the
electrode region of the deadlayer is modeled as a sandwich of Si, SiO2, and Si3N4,
while the channel stop region consists of deadlayers of Si and SiO2 of finite width.
Two additional model parameters are the width of the pixel and the depletion depth.
Even in this simplified model, the parameters cannot be uniquely determined by
the undispersed synchrotron radiation data alone. Instead, we rely on independently
determined values from other experiments. In particular, Prigozhin et al. (1998) have
measured the depletion depth at higher energies; we fix the depletion depth at the
measured value in these fits. We note that the depletion depth is large enough that
it does not strongly affect the response in the 0.3 − 4 keV spectral band. The channel
stop parameters have also been measured, using the mesh technique, as described in
Chapter 4. Table 3-5 summarizes the model parameters.
3.5.2
Fitting Results
The predicted synchrotron spectrum (with free normalization) and the CCD efficiency
model are fit to the pileup-corrected pulseheight spectrum using the XSPEC (Arnaud
1996) spectral fitting package. The CCD model parameters and normalization are
varied to minimize the chi-squared associated with the fit. Parameters are allowed to
vary or are fixed in the fits according to Table 3-5. Only data in the spectral range
67
Table 3-5: CCD detection efficiency model parameters
Parameter Description Status in Model Fits
Si gate thickness
varied
SiO2 gate thickness
varied
Si3 N4 gate thickness
varied
Depletion depth
fixed; determined by branching ratio method †
Channel stop width
fixed; determined by SEM measurements ‡
SiO2 stop thickness
fixed; determined by SEM measurements ‡
Si p+ thickness
fixed; determined by mesh experiments ‡
Pixel width
fixed at 24 µm design value
†: see Prigozhin et al. (1998)
‡: see Chapter 4
0.3 − 4 keV are considered in these fits.
Figures 3-12, 3-13, and 3-14 show the best fit models with the data for individual
quadrants of detectors w103c4, w190c1, and w190c3. Table 3-6 shows the best-fit parameters, the RMS error, and the normalization accuracy for each reference detector
as well as listing the values of parameters held constant in the fitting process.
The model fits for all three CCDs are reasonably good, although devices w190c1
and w190c3 have lower RMS and χ2ν values than w103c4. The most prominent systematic trend in the residuals (the ratio of data to model) is a feature around 1.8 keV.
An underestimation of the Si Kα fluorescence could help contribute to the narrow
feature, as analysis of the response function model suggests that it underestimates
the fluorescence line strength. Another potential source of error is the use of the
Henke optical constants (Henke, Gullikson, & Davis 1993) in the current detector
model. EXAFS measurements (Prigozhin et al. 1998a) show large deviations from
the tabulated Henke values around both the O Kα and Si Kα absorption edges.
In the analysis reported here, we integrate events within a 5 mm × 6 mm region
of the detector. The predicted synchrotron flux is integrated over the corresponding
angle. Thus, we integrate the spectrum within ±2.5 mm of the orbital plane of the
68
One Pixel
One Pixel
SiO2 Gate Insulation
Poly Silicon
Gates
Si3N4 Layer
SiO2 Layer
Depleted
Silicon
Figure 3-11 Cross section of the gate structure of the ACIS CCD along the transfer
channel. Left: Representation of the actual structure that includes overlaps and
different thicknesses for each gate. Right: Simplified structure used in the Slab and
Stop model of Gendreau (1995).
storage ring. In our fits for detection efficiency model parameters we allow a single,
energy-independent scale factor (or normalization) to modify the calculated incident
flux density. The normalization scales as the product of the total integration time
t, area illuminated A, and beam current I. In practice, the normalization norm is
calculated by
norm = IAt = IA(Nframe F T fchop),
(3.7)
where Nframe is the number of frames, F T is the frame time and fchop the frequency of
the chopper wheel previously discussed in §3.3.2. For most measurements (i.e. 2000
frames and 15−30 electrons) and a 208 pixel×254 pixel region, typical values for norm
range between 100 and 300. This normalization parameter allows for events which
penetrate the gate structure but are rejected as background events. The fraction of
such events (which we may call the background branching ratio) is known to be 1%
or lower in the zero-pileup limit, and essentially independent of energy in the 0.3 − 4
keV band. Therefore the ratio of the best fit value of the flux normalization to that
calculated from Equation 3.7 is expected to greater than 0.99 but less than one. These
are the numbers reported in Table 3-6.
For devices w190c1 and w190c3, the best-fit flux normalizations are within 1% of
unity, while for w103c4 the normalization is 0.95. The reason for this discrepancy is
69
Figure 3-12 Observed pulse-height distribution and best-fit model from undispersed
synchrotron radiation measurements for device w103c4, quadrant B. The data are
an accumulation of 975 exposures, each with integration time 1.526 s, taken with a
storage ring current of 10 electrons.
70
Figure 3-13 Observed pulse-height distribution and best-fit model from undispersed
synchrotron radiation measurements for device w190c1, quadrant A. The data are
an accumulation of 1483 exposures, each with integration time 0.847 s, taken with a
storage ring current of 33 electrons.
71
Figure 3-14 Observed pulse-height distribution and best-fit model from undispersed
synchrotron radiation measurements for device w190c3, quadrant B. The data are
an accumulation of 2000 exposures, each with integration time 0.813 s, taken with a
storage ring current of 30 electrons.
72
Table 3-6: CCD model parameter fit results from synchrotron radiation measurements
Chip
w190c3
w190c1
w103c4
Si†
0.259
0.261
0.291
SiO2 ‡
0.354
0.358
0.202
Free
Si3 N4
0.031
0.029
0.030
Norm♦
0.999
0.993
0.947
Si
0.35
0.35
0.35
Fixed
SiO2 W
0.45 4.1
0.45 4.1
0.45 4.1
DD4
71.3
70.6
57.9
RMS
Resid.
2.54%
2.26%
3.74%
χ2ν /dof
1.227/875
1.094/916
1.380/1807
Note: All dimensions are in µm. χ2ν is the reduced χ2 value, where ν is the degrees of freedom.
The first three fixed parameters are the dimensions assumed for the channel stop, where
Si and SiO2 are the thicknesses the p+ implant and oxide, and W is the width.
† Typical 90% confidence limit is ±0.008 µm
‡ Typical 90% confidence limit is ±0.011 µm
♦ Normalization values represent the ratio of the best-fit value to the expected value.
The 90% confidence limits from fitting are 0.005.
4 Depletion depths are determined from a technique developed by Prigozhin et al. (1998)
not understood. The w103c4 data were obtained with the early generation LBOX
detector electronics which provided slower readout, lower gate bias (and hence, lower
depletion depth) and slightly higher noise than the flight-like DEA electronics used
with the other two detectors. The pileup corrections for the two data sets are comparable, since the storage ring current was adjusted to compensate for the difference
in frame exposure times. However, the effective exposure time determination (see
§3.2) is less certain for the shorter exposure time. In principle, the normalization
differences could be variations in the valid-event branching ratios of the two devices,
although the relative quantum efficiency measurements discussed below are not consistent with this hypothesis. It should be noted that the w103c4 data were obtained
a year earlier than the the w190c3 and w190c1 data.
It is interesting to compare the best-fit parameters for chips w190c1 and w190c3.
These two CCDs were produced on the same silicon wafer, so they should have similar
gate thicknesses. The differences between the derived thickness for the Si, SiO2 , and
Si3N4 layers are well within the statistical errors.
73
3.5.3
Spatial Uniformity
Extensive measurements at MIT CSR (Bautz et al. 1998) have shown that the spatial
variation of quantum efficiency, for front-illuminated devices, is quite small (< 2%,
RMS) on scales as small as 0.77 mm2. Because the intensity and shape of the synchrotron spectrum changes over the illuminated detector area, we have not attempted
to constrain the small-scale uniformity of the reference detectors directly from the
synchrotron measurements. On larger scales, however, we confirm that the detector
response is extremely uniform.
Figure 3-15 (top) shows the cumulative intensity map obtained for w190c1 during
the June 1996 user session. The storage ring current was constant at 15 electrons as
each of five subsections of the detector was illuminated during this experiment. The
variation in the vertical direction is real and reflects the variation in the synchrotron
radiation as a function of the opening angle ψ (see Equations 3.1 and 3.2 and Figure 310). The dark vertical gaps are either quadrant boundaries or defective columns. The
mean counting rate is ∼12 events pixel−1. Figure 3-15 (bottom) plots the same data,
but summed in the direction parallel to the quadrant boundaries. The uniformity of
the detector is evident, with the only deviations from linearity being due to boundaries
or bad columns. We note that ACIS flight detectors generally have much higher
cosmetic quality than this reference detector.
Table 3-7 shows the average current-normalized counting rate (cts sec−1 electron−1
ring current), for each quadrant of w190c1 at four different CCD positions. Each position is labeled by the location of the first row exposed in the measurement (e.g., the
y209 data illuminated rows 209 − 417); the data are normalized by the value measured at y001. The defective columns have been removed for this analysis. Excepting
the y768/quad D value (a suspect data point given the numerous defective columns
there), the mean of the values in the table is 1.000 and the sample deviation is 0.003.
The expected photon counting errors are of order 0.001 in relative efficiency. These
results demonstrate that the broad-band responsivity of the CCDs in the 0.3 − 4 keV
spectral band varies by less than 1% on spatial scales of 5 mm.
74
Figure 3-15 PTB/BESSY data for w190c1 (June, 1996). Top: Intensity map of total
counts from a series of five observations illuminating different portions of the detector.
The pattern in the vertical direction reflects the variation in synchrotron radiation
intensity as a function of distance out of the orbital plane. Dark vertical features are
either quadrant boundaries or defective columns. Bottom: Same data shown as above,
summed in the direction parallel to the quadrant boundaries. The only significant
deviations from uniformity are due to the quadrant boundaries or defective columns.
75
3.5.4
Preliminary Assessment of Wavelength Shifter Data
The December 19996 user shift at the PTB BESSY laboratory was dedicated to measurements made with the Wavelength Shifter (WLS). With incident radiation well
above 15 keV, it was hoped the measurements would extend the absolute calibration
of the reference standards up to the high energy limit of Chandra. Another goal of this
measurement was to provide an independent determination of the depletion depths.
Unlike the White Light measurements which can only constrain the low energy quantum efficiency which is dominated by the gate thicknesses, the harder spectrum of
the WLS provides photons that easily penetrate the entirity of the depleted silicon,
allowing accurate determination of the depletion depth, and hence, the high energy
quantum efficiency.
Initial analysis of the WLS data reveals two potential problems with the quality of
the data. Reduced data products indicate that the electronics were performing suboptimally during half of the measurements. The problems can be simply characterized
as a spatial and temporal variation in the bias levels of the detectors. Although I
explored several techniques to correct for these effects, it is unclear how well they will
work. It was known that the WLS would produce many more photons than the White
Light beam for a given ring current. Anticipating problems with pileup, the storage
ring currents were reduced from typical White Light operating conditions by at least a
factor of two. Unfortunately, the extent that pileup influences high energy spectra has
only recently been fully appreciated. Given the experimental set-up and the manner
in which BESSY data acquired, it may be extremely difficult to accurately correct
for pileup. For example, even if the storage ring current is constant, the beating of
the chopper wheel with the CCD readout time discussed in §3.3.2 leads to different
pileup conditions within any single data set. In fact, initial fitting indicates that the
WLS data has significantly more pileup than the White Light data.
76
Table 3-7.
Uniformity of w190c1 determined from BESSY
measurements
CCD Position
Quad A
Quad B
Quad C
Quad D
y209
y417
y625
y768
0.999
1.003
1.000
0.998
0.997
1.002
1.001
0.996
0.998
1.004
1.002
1.002
1.003
1.008
1.000
0.978
Note. — Average counting rate per quadrant per exposure time
(for ASCA grades 02346) at four positions on device w190c1, relative
to that at CCD position y001. As the storage ring current was 15
electrons for each measurement, no pile-up correction was required for
this uniformity measurement. Defective columns (see Figure3-15) have
been accounted for. Statistical errors for all measurements are 0.001.
These data were acquired with the LBOX electronics in June, 1996.
77
3.6
Quantum Efficiency of the Reference Detectors
3.6.1
Methodology
At high energies (E > 4 keV) the quantum efficiency (QE) is governed by the thickness
of the depletion region. The depletion region thickness varies, at most, slowly with
position. At low energies (E < 4 keV), the QE is determined by the opacity of
various dead layers comprising the CCD gates and channel stops. Thus, the QE can
be represented by
QE(E) = A(E, ddepl )T dead (E, ~p).
(3.8)
The term A(E, ddepl ) accounts for the finite thickness of the depletion region and is
of the form
A(E, ddepl ) = 1 − e−(ddepl /λSi(E))
(3.9)
where λSi (E) is the energy dependent absorption length in silicon and ddepl is the
depletion depth. The term T dead (E, ~p) represents the spatially averaged transmission
through the dead layers of the CCD, including the gate structure and channel stops
(see Figures 4-5 and 4-10). The vector ~p represents the parameters required to describe
the channel stop and the parameters required to describe the gate structure. In
general, T dead (E, p~) is of the form
T dead (E, ~p) =
X

αi
i
Y

e(−di,j /λi,j (E))
(3.10)
j
where αi is the fractional area of the ith pixel sub-section and di,j and λi,j (E) are the
the thickness and characteristic absorption length of the j th component of the dead
layer that comprises the ith pixel sub-section.
The most accurate detector models (see Chapter 4) require fifteen parameters for
the gate structure and five for the channel stops. In practice, though, the complicated
78
architecture of an X-ray-sensitive CCD can be accurately represented by significant
simplification. One such model is the Slab and Stop model (Gendreau 1995). In this
model, the gate structure reduces to three slabs of Si, Si3 N4, and SiO2, as shown
in Figure 3-11. The channel stop reduces to a block of Si and SiO2 with fractional
pixel coverage w (the width of the block divided by pixel dimension). Under these
assumptions, Equation 3.10 becomes

T dead (E, p~) = 
3
Y

e
−(d/λ(E))
gate
"
[1 − w] + w
2
Y
#!
e
−(d/λ(E))
,
(3.11)
CS
where the superscript on the product term indicates the number of constituent materials used for the gates or channel stops. Thus, the QE of an ACIS device can be
characterized from the eight parameters listed in Table 3-5.
The characteristic absorption length λ(E) at energy E is calculated from the
optical constants of Henke (Henke, Gullikson, & Davis 1993). We supplement the data
near the absorption edges of nitrogen, silicon, and oxygen with measurements made by
Prigozhin et al. (1998a) using thin wafers of exactly the same material as the CCDs.
Due to X-ray Absorption Fine Structure (EXAFS), the actual optical constants vary
rapidly and deviate significantly from those tabulated by Henke near the absorption
edges. Figure 3-16 (top) shows the absolute quantum efficiencies determined from
the synchrotron data. The higher efficiency of w103c4 is attributable to its relatively
thin gate oxide layer.
3.6.2
Relative Efficiencies of Transfer Standard Detectors
Reference standard detectors w190c3 and w103c4 were calibrated with respect to one
another at MIT CSR using the procedures described above for calibration of the flight
detectors relative to the reference standards. The relative efficiencies so obtained
were compared to the predictions of models derived from the (separate) synchrotron
79
Figure 3-16 PTB/BESSY absolute efficiencies vs. MIT CSR relative efficiencies for
reference detectors w190c3 and w103c4.
measurements of these two devices. Results are shown in Figure 3-16 (bottom). The
solid line plots the ratio of the QE of w103c4 to that of w190c3. The points show
the discrete relative measurements made at MIT CSR vs. the expectations from the
synchrotron calibration. Error bars are 0.6% and represent the accuracy with which
relative calibration at MIT can be repeated.
The ratio of the two models agrees quite well with the relative quantum efficiency
data: for the five energies measured at MIT within the BESSY passband, the residuals
(measured ratio minus modeled ratio) have a mean of -0.008 and a standard deviation
of 0.01. Thus the mean is consistent with 0 at the 2-sigma level, provided the standard
deviation is taken to be measure of the random errors in the residuals. The latter
assumption is a good one, given that the errors in the relative quantum efficiency
measurements are thought to have a standard deviation of 0.6%. This result suggests
80
that the normalization differences required by the best fits to the synchrotron data
do not result from differences in the response of the detectors. Instead, they suggest
the presence of some as-yet unmodeled effect in the synchrotron measurements.
3.6.3
Uncertainties
We have identified quantitative bounds on systematic measurement errors and on
some kinds of modeling errors. Taken together, these checks furnish confidence that,
for front-illuminated devices, the absolute quantum efficiency errors are smaller than
5% in the 0.3 − 4 keV band. Narrow band efficiency measurements are probably
accurate to better than 1.5%, except at energies in the immediate vicinity of the
characteristic silicon absorption edges.
As discussed earlier, the best-fit flux normalizations for w190c3, w190c1, and
w103c4 are 0.999,0.994, and 0.947, respectively, with uncertainties equal ±0.005 (90%
confidence limits). The large discrepancy from unity for w103c4 is somewhat surprising, as the largest known deviation (from misidentification of events and background
based on grade discrimination; see §2.3.2) expected is ∼1%. The simpliest view
of these results is that any residual systematic errors in the broad-band quantum
efficiency are under 5%. This interpretation is supported by the gate structure parameters derived from the best-fit results, which are within 50% of those expected,
given the fabrication process used (see Burke et al. 1994 and Burke et al. 1997 for
details). This agreement confirms the validity and reliability of the Slab and Stop
model. Another important check for the accuracy of the absolute calibration comes
from the relative efficiency measurements made at MIT with an accuracy of better
than 2%.
3.6.4
Model Limitations
The systematics present in the fit residuals, the non-unity RMS values, and the rather
large χ2ν values indicate limitations in the absolute calibration. At least four distinct
81
factors may be contributing to the overall uncertainty. The most obvious of these is
the use of the Slab and Stop model, which ignores gate overlaps and variations in both
the length and width as shown in Figure 3-11. When the penetration length of incident
radiation is sufficiently large, the gates become optically thin (see Equation 3.8) and
the errors becomes negligible. However, immediately above the oxygen and silicon
absorption edges, the penetration length of the X-rays is comparable to the thickness
of the gate structure. It is at these energies that the QE model is most sensitive to
the measured parameters. We note that this is precisely where the largest systematic
deviations from unity occur for the best-fit models.
Related to these uncertainties is the use of the standard Henke absorption coefficients (Henke, Gullikson, & Davis 1993) in our analysis. Measurements by Prigozhin
et al. (1998a) indicate significant deviations extending for ∼50 eV beyond the absorption edges of silicon and oxygen. While the spectral resolution of the detector
tends to smooth the fine structure, we have not yet established the magnitude of error
introduced by neglect of fine structure.
Another source of error is our use of a phenomenological representation of the
spectral redistribution function in the analysis of synchrotron radiation data. The
response to a monochromatic input is modeled as the sum of several Gaussians plus
a phenomenological low-energy tail. A better, physically-grounded model of the redistribution function is now available (Prigozhin et al. 2000), but has not yet been
used to analyze the synchrotron data.
Finally, the channel stop parameter values used in the fits have not been measured
directly for any of the reference detectors. Although great effort has been undertaken
to develop an accurate method to measure these parameters (and is, in fact, the
entire topic of the following Chapter of this thesis), these techniques have not yet
been applied to the reference detectors. It is hoped that mesh measurements can be
made on at least one of the reference detectors.
82
Chapter 4
Measurement of the Sub-pixel
Structure of Chandra CCDs
4.1
Introduction
As already discussed, the ambitious scientific objectives of Chandra require precise
knowledge of the instrumental response, i.e. energy scale, spectral resolution and
detection efficiency. For example, the calibration goal for the quantum efficiency
(QE) of the ACIS detectors is 1% accuracy (Weisskopf et al. 1995). In §3.6.1, we
found that the most accurate model of the low energy detection efficiency requires
determination of the dimensions of the sub-pixel structures (i.e. the channel stops
and each of three gates). At sufficiently low energies (E . 4.0 keV), the characteristic
absorption length of X-rays is sufficiently smaller than the depletion depth (between
60 and 70 µm for ACIS devices) that the expression for QE reduces to:

QE(E) = 
3
Y

e
−(d/λ(E))
[1 − w] + w
gate
" 2
Y
#!
e
−(d/λ(E))
,
(4.1)
CS
where the three terms in the gate product represent absorption by layers of Si, SiO2,
and Si3N4 and the two terms in the second product represents absorption by the
p+ -type Si and SiO2 that comprise the channel stop, which covers a fractional area
83
w of each pixel.
In Chapter 3, I showed that broad-band synchrotron data give excellent constraints on the three gate parameters for the QE model, provided that all other
relevant parameters are frozen. In general, these data cannot uniquely constrain all
six parameters in Equation 4.1. Among the most significant of the degeneracies is that
between the overall width of the channel stops, on the one hand, and the thickness
of the gate structure, on the other hand. This ambiguity in gate structure parameter
values can lead to large errors in the estimated detection efficiency, particularly near
the characteristic absorption edges where the gate opacity can be large.
The measurements reported in this Chapter were made to improve the ACIS
calibration accuracy by resolving some of these ambiguities. In particular, I discuss
one approach for the measuring the channel stop structure, represented by a model
with five parameters. This technique also provides constraints on the dimensions of
the three different polysilicon and SiO2 layers that comprise the actual gate structure.
Our method also shows a correlation between event grade and location of the event
interaction within a pixel, information that has the promise of yielding sub-pixel
spatial resolution.
Closer examination of our preliminary results revealed inconsistencies between
some of the measurements. Specifically, the thickness of the channel stop oxide and
p+ -type silicon determined from measurements at low and high energies did not agree.
We began investigating the nature of charge collection in the channel stop region and
discovered that the amount of charge collected from an event interacting in the p+ type silicon depends on the voltage applied to the gate directly above the channel
stop. These results are discussed in §4.8.
While the sub-pixel structure is clearly visible in the preliminary data, higher
resolution would allow more accurate measurements and significantly reduce the the
rather complicated analysis. Armed with our better understanding of the physics
of charge collection in the channel stop region, we modified our experimental technique to significantly improve the quality of our sub-pixel measurements. In §4.9, I
84
discuss these improved data and present a self-consistent model that allows accurate
determination of the thicknesses of the channel stop materials.
4.2
4.2.1
Experimental Method
Concept
We used a metal foil with regularly spaced holes (hereafter, mesh) to illuminate the
CCD with very narrow beams of monochromatic X-rays and observe the dependence
of the detector response on the location of photon interaction inside the pixel. When
the mesh is placed close to the CCD surface and rotated with respect to the axes
defined by the gate structure and channel stops, a moiré pattern is formed when the
device-mesh combination is illuminated with X-rays. This technique was first used
with CCD detectors by Tsunemi et al. (1997). Changes in relative count rates reflect
attenuation of the incident flux by the dead layers of the sub-pixel structure. By
repeating the measurements at a number of X-ray energies, specifically energies above
and below both the Si Kα and O Kα absorption edges, the widths and thicknesses of
the gates, channel stops, and insulators can be uniquely determined.
The mesh used in our first experiments consists of a 10 µm thick copper foil with
a square array of 4 µm diameter holes spaced every 24 µm. Refer to Figure 4-1
(left) to see a section of the mesh and its orientation to the CCD. For the range
of X-ray energies used, the mesh has a maximum transmission of 6.0 × 10−3 , but
typical transmissions are generally below 7.0 × 10−5 . The mesh was stretched taught
to remove wrinkles and was held parallel to the surface of the CCD to keep the
illumination pattern circular and uniform. It also needs to be as close to the CCD as
possible to minimize the broadening of the point spread function (PSF) due to finite
beam divergence and diffraction effects. To meet all three requirements, we fabricated
a special fixture to hold the mesh. Figure 4-1 shows a cross section of this holder.
85
10 µ m Cu Foil
4 µ m dia. hole
X-rays
24 µ m
24 µ m
Mesh
θ∼1ο
Gap = 200 microns
Mesh Holder
CCD Holder
CCD
24 µ m
Pixel
Figure 4-1 Two views of the thin metal foil or mesh. Right: Schematic of the mesh
showing its orientation with respect to the CCD. Left: Fixture used to hold the mesh
close to the CCD surface.
4.2.2
Moiré Phenomena
The mesh holes have a nominal periodicity of 24 µm, corresponding to the pitch of the
ACIS CCD pixels. Smaller spacings would result in two different holes illuminating
the same pixel and would mix the spatially dependent response of the pixel. At the
same time, the mesh must be rotated with respect to the axes defined by gates and
channel stops to ensure an equal and complete mapping of the pixel’s response to the
incident photons. The resulting data can be understood in the context of a moiré
pattern.
The details of the moiré phenomena are presented in Appendix B. For a mesh
with periodicity D0 , not equal to the CCD pixel pitch D ≡ 24 µm, rotated an angle
θ with respect to the CCD, the angle ϕ the moiré pattern makes with respect to the
CCD is given by:
π
1 − cos(θ)
ϕ = − θ + tan−1
2
sin(θ)
!
D0
; ≡
D
(4.2)
Typically, the mesh was rotated about one degree with respect to the CCD. The
values of ϕ observed were on order of five degrees, indicating that the mesh spacing
D0 is not equal to 24 µm. Given the tolerances used in the mesh fabrication and the
possibility of deformation due to thermal and mechanical stresses, the deviation of
the periodicity from 24 µm is not unexpected. The dimension of the spacing does not
86
affect the results, as long as it stays constant during the course of the experiment.
4.2.3
Data Acquisition
After the mesh holder was fixed to the CCD housing, the CCD-mesh assembly was
placed in a vacuum chamber and cooled down to the standard operating temperature
of –120◦ C. Two different systems were used to produce the monochromatic X-ray
beam. A grating monochromator and electron impact source (IFM) produced photons
corresponding to the O Kα line (525 eV) and a photon fluorescence source (HEXS;
Jones et al. 1996) was used to excite the Kα lines of Al, Si, P, Cl and K. The use
of the specialized holder illustrated in Figure 4-1 (right) kept the mesh taught and
parallel and placed it within 200 µm of the surface of the CCD, the closest distance
achievable while preventing the risk of damage to the flight quality CCD from accidental contact with the mesh. The gap, however, effectively increased the diameter
of the mesh holes by geometric shadowing. To reduce this effect, the divergence of
the incident beam was minimized by using an aperture and placing the CCD as far
away from the source as possible, while maintaining an acceptable incident flux rate.
Baffles were also used to prevent specular reflection from widening the beam pattern.
Figure 4-2 shows the experimental set-up. Given the location of the X-ray source,
the CCD and the nominal 4 µm diameter of the holes, the X-rays cast an image of
diameter 4.2 µm on the CCD. The large distance between the CCD and X-ray source
and the small open area of the mesh (2.8%), required significant time to accumulate
statistically significant data. Table 4-1 summarizes all the data acquired, including
which X-ray source was used, the photon energy and the corresponding Kα emission
line, the number of distinct measurements, the total integration time, and total number of events in the monochromatic line.
87
19.1 cm
121.9 cm
121.9 cm
52.8 cm
1: IFM
2: HEXS
X-ray Source
2.54 cm dia. spot size 0.80 cm aperture
2.46 cm baffle
mesh-CCD
mesh
CCD
200 µ m
expanded view
Figure 4-2 View of the experimental setup use for initial mesh measurements. The
IFM and HEXS X-ray sources have their own beam lines and use different vacuum
vessels to house the CCDs, but the same apertures were used and placed at the same
distances in both cases. Dimensions are in inches, unless otherwise noted.
Table 4-1: Summary of initial mesh measurements.
X-ray Kα Energy
Source
(eV)
IFM
O
525
HEXS Al
1487
HEXS Si
1740
HEXS P
2015
HEXS Cl
2622
HEXS K
3312
4.3
Data Time
Sets (hour)
3
8
4
98
4
129
5
91
2
81
2
81
Total Events
in Line
6.1 × 105
1.8 × 105
2.4 × 105
4.4 × 105
1.3 × 105
4.7 × 105
Data Analysis and Results
Analysis begins by performing a bias correction on each of the raw CCD images and
extracting the events that lie in the photo-peak of the monochromatic line. We then
88
filter the data by selecting suitable event grades, single pixel (grade 0), horizontally
split events (grades 3 and 4), vertically split events (grade 2), and corner events (grade
6), and create the fundamental moiré pattern for each types. Each fundamental
pattern consists of a collection of smaller moiré cells which reveals the pixel’s spatial
response to the photons. These individual moiré cells must be rotated before the data
can be summed together to form one representative pixel (hereafter RP) for the entire
CCD. Due to uncertainties in the mesh rotation angle θ and the mesh periodicity D0 ,
we do not rely on Equation 4.2 to calculate the rotation angle ϕ, but rather determine
it from the data using essentially a Fourier technique. The left panel of Figure 4-3
shows a sample of the raw, unrotated moiré pattern (O Kα, grade 0) that is a direct
output of the illumination of the mesh-CCD system. The right panel of Figure 4-3
repeats the RP in a 3 × 3 array to make it easy to see the boundary regions of the
pixel.
Figure 4-3 Raw and deconvolved moiré data. Left: The fundamental moiré pattern
for single pixel (grade 0) events at O Kα (525 eV). The individual moiré cells are
clearly discernible. Right: The representative pixel (RP) repeated in a 3 × 3 array.
The vertical stripe in the fundamental image is a quadrant boundary in the CCD.
detection algorithm.
Figure 4-4 displays a grid of 3 × 3 RP arrays for grade 0, grade 2, grades 3 and
4, and grade 6 events for three of the six Kα line energies (O Kα, Cl Kα, and Si
Kα). Each column has the same energy, and each row has the same grade. The
89
characteristic absorption length increases from left to right. The confinement of
event grades to particular regions of the pixel (i.e. grade 2 events only occur along
the vertical boundaries of the pixel) offers conclusive, experimental proof that event
grades have physical significance that corresponds to photons that interact in the
center, the edges or the corners of the pixel. This information is explored further in
Section 4.7 when the possibilities of obtaining sub-pixel resolution are explored. The
figures also contain graphs of the count rates for the RP summed in the direction
parallel to the channel stops (the horizontal graphs) and the direction parallel to
the gates (the vertical graphs). These one dimensional rate plots clearly show the
attenuating effects of the sub-pixel structures, and it is analysis of these data that
provides information about the channel stops and gates.
4.4
Determination of the Channel Stop Dimensions
Conceptually, the approach for determining the channel stop dimensions is very direct. The deficiency of detected photons predicted by a model of the channel stop is
convolved with the PSF of the mesh holes. The resultant convolution is compared to
the experimental data, and the channel stop model parameters are allowed to vary,
using a χ2 fit statistic to determine the best fit parameters.
Channel stops are fabricated using a standard LOCOS technology (Burke et al.
1994), where a portion of the Si3 N4 insulating layer is etched away and boron is
implanted in the opening, forming a strip of p+ -type silicon. Then the silicon is
oxidized, thickening the insulating layer of SiO2 directly above the implanted stop.
Figure 4-5 is an SEM measurement of a CCD cleaved to expose the channel stop. The
black and white bands at the top of the image are the polysilicon gates and insulating
oxide, respectively. The elongated, hexagonal structure is the SiO2 insulator between
the p+ region (not visible in this image) and the gates. The thin white structure
between the gates and hexagonal insulator is the Si3 N4. The p-p+ transition cannot
90
Figure 4-4 3× 3 arrays of grade 0, grade 2, grades 3 and 4, and grade 6 Representative
Pixels (RP). Each column has the same energy, and each row has the same grade.
The data are presented in order of increasing silicon attenuation length: O Kα (left),
Cl Kα (middle), and Si Kα (right).
91
be seen in this photograph. We adopt a five parameter model to represent the channel
stop. Figure 4-6 shows the five parameter channel stop model we adopt in our fitting.
Figure 4-5 SEM photograph of an ACIS CCD cleaved to show the channel stop
structure. The broad black and white bands near the top of the image are the
polysilicon gate and insulating layer of SiO2, respectively. The elongated, hexagonal
structure is the SiO2 insulator between the p+ region (not visible in this image)
and the gate structures. The thin white structure between the gates and hexagonal
insulator is the Si3N4. The bar is 1.0 µm.
SiO2 Gate Insulation
Poly Silicon
Gates
1
Si3N4 Layer
SiO2 Layer
2
4
3
Implanted p+ Silicon
5
1 CS SiO2 Thickness
3 Si3N4 Thickness
2 Si3N4 Thickness
4 CS Transition Width
5 CS Box Width
Figure 4-6 The five parameter model used in determining the dimensions of the channel stop.
In addition to constructing a realistic channel stop model, the success of this technique depends on use of an accurate PSF for the mesh and accounting for additional
processes that effectively broaden the PSF (i.e. diffraction, diffusion of the charge
92
cloud, distortions to the PSF caused by using a non-parallel X-ray beam). Computing
such an aperture function (hereafter AF) analytically is a daunting task. Fortunately,
the AF can be ascertained from the mesh data itself. Horizontal and vertical split
events come from photons that interact within an electron cloud size diameter of the
pixel boundary. The spatial distribution of vertical split events (∆v split) is given by
the convolution (⊗) of three terms:
∆v split = P SF ⊗ Ci ⊗ D,
(4.3)
where PSF is the point spread function of the mesh hole, Ci is the initial charge cloud
size1, and D is a term that describes how the initial charge cloud diffuses as the cloud
moves under the influence of the electric field created by the potential applied to the
gates. The amount the initial charge cloud diffuses varies dramatically with energy,
so we use an unique AF for data taken at each energy. The number of detected events
(Ndetected ) is given by:
Ndetected = P SF ⊗ Ci ⊗ D ⊗ MCS ,
(4.4)
where PSF, Ci , and D are the same as above and MCS is the model of the channel
stop. If we define the AF as the (∆v split )
AF ≡ ∆v split = P SF ⊗ Ci ⊗ D,
(4.5)
Equation 4.4 simply becomes
Ndetected = AF ⊗ MCS .
(4.6)
The data presented in Figure 4-7 shows the relative amount of attenuation caused
1
Analysis of double crystal monochromator data performed by Prigozhin et al. (2000) indicate
that the initial cloud sizes range between 10 and 100 nm.
93
by the channel stops. The amount of attenuation is governed entirely by the characteristic attenuation lengths of the Kα photons in Si, SiO2, and Si3 N4 and therefore
does not simply monotonically increase with increasing photon energy.
Figure 4-7 Variation in detection efficiency due to differing amounts of attenuation in
the dead layers of the channel stop.
Fitting the channel stop model to data from only one energy results in degeneracies
in the best fit parameters. To constrain these parameters, we perform a simultaneous
fit of several data sets taken at different energies. The upper two panels of Figure 48 show the χ2 confidence plots for the O Kα data set and the P Kα data sets.
The contours are for the 68%, 90% and 99% confidence levels. The box and wing
parameters have large uncertainty, but the constant slope of the contours does indicate
a bound to the total width. The situation is similar for the thicknesses of the Si p+
layer and the insulating SiO2. By simultaneously fitting multiple data sets, a tighter
constraint can be placed on the model. The bottom panels of figure 4-8 show the χ2
contours for the five HEXS data sets (Al,Si,P,Cl, and K). Taken together, these data
provide a good measure of the width parameters and the p+ and SiO2 thicknesses.
Table 4-2 lists the parameter, the range of parameter space and grid size used, and
94
the derived best fit-value (90% confidence level) from the simultaneous fitting.
Table 4-2: Channel stop values derived from HEXS data
Name
box width
wing width
Si thickness
SiO2 thickness
Si3 N4 thickness
Search range Step size Best-fit value
3.1 − 4.5 µm .16 µm
4.2+.3
−.4 µm
+.19
0.12 − 1.2 µm .12 µm
.35−.12 µm
0.12 − 1.2 µm .12 µm
.35+.06
−.03 µm
0.12 − 1.2 µm .12 µm
.71+.17
−.11 µm
0.0 − 0.05 µm .01 µm
insensitive
Comparing the O Kα χ2 contours with the combined HEXS data χ2 contours in
Figure 4-8 reveals that the data taken with the two different X-ray sources do not
completely agree. This difference is shown in Figure 4-9, which plots the predicted
attenuation, based on the HEXS best fit parameters, and the data for all six energies.
The models work well for all but the O Kα data.
At the time of these experiments, the best explanation for the degeneracy was the
use of an overly simplistic model that did not properly account for all the relevant
physics. Key to our model was the assumption that the gate structures and channel stops are dead layers. However, it was known that this is not entirely correct.
Prigozhin et al. (2000) have explained the origin the low energy tail of the spectral
redistribution function as being associated with low-penetrating X-ray events. They
show that when a photon interacts near the gate oxide or nitride, only a fraction of
the charge is collected. We speculated that similar processes may occur for photons
that land close to the SiO2 region of the channel stop.
A larger uncertainty was the exact physical process that occurs in the doped p+
stop. The dopant concentration decreases non-linearly as a function of distance from
the insulating oxide layer. It seemed plausible that the charge from photons interacting in the lower p+ concentration regions is fully collected. Another possibility
was that the charge from X-rays interacting in a region of moderate p+ concentration
95
Figure 4-8 χ2 contour plots for box width vs. wing width and Si p+ depth vs. SiO2
depth. Contours are the 68 %, 90 %, and 99 % confidence levels. The top row is
for the O Kα data, the middle row for the P Kα data, and the bottom row for the
simultaneous fit of all five HEXS measurements.
96
might only be partially collected. If these effects were real, we speculated that incorporating them into our model would improve the detection efficiency beneath the
channel stop, particularly at low energies. This increase in detection efficiency at O
Kα energies would lead to better agreement between data and theory.
In fact, we have shown that incomplete charge collection is the relevant process
for events interacting in the channel stops. In Chapter 5, I explain the experiments
undertaken to study and explain this phenomena. As I show in §4.9, this effect must
be accounted to properly interpret the mesh data.
Figure 4-9 Best-fit HEXS channel stop model compared to experimental data.
97
4.5
Determination of the Gate Structure Dimensions
The determination of the gate structure dimensions follows a method analogous to
that used in the channel stop analysis. The single event and vertically split RPs
are added together and summed in the direction parallel to the gates, excluding the
corner and horizontal regions of the RP where grade 6 and grade 3 and 4 events occur.
A model of the gates is convolved with the same AF used for the channel stops (refer
to Section 4.4), the convolution is compared to the data, and the model is adjusted
until χ2 is minimized.
After the channel stops are implanted in the bulk silicon, the gates are formed using a triple-polysilicon process (Burke et al. 1994). A layer of polysilicon is deposited
on the Si3 N4-SiO2 dielectric layer that covers the bulk silicon. Roughly two-thirds
of the polysilicon is etched away in a piece-wise, periodic fashion (i.e. 16 µm of every 24 µm is removed), and the remaining strips are oxidized, creating a protective
layer of SiO2 over the first gate (gate φ1). The entire deposition-etching-oxidation
process is repeated twice more to form the second and third gates (φ2 and φ3 , respectively). Figure 4-10 is a SEM measurement made on a CCD cleaved to expose the
gate structure. The black and white structures towards the top of the image are the
polysilicon gates and insulating SiO2 layers, respectively. The upper, parallel band
running across the middle of the image is a dielectric layer of Si3N4 , and the lower,
parallel band is a dielectric layer of SiO2. The bulk silicon on which these structures
are grown is not visible in this image. This particular photograph shows the overlap
between a φ2 and φ1 gate. Figure 4-11 shows the fifteen parameter model used to
represent the gate structure. In our fitting we fix the thickness of the uniform nitride
and oxide layers that run between the polysilicon gates and bulk silicon. We further
simplify the model by not including the small width (less than 0.2 µm in the SEM
98
photographs) of insulating SiO2 that occurs between gates.
Figure 4-10 SEM photograph of a CCD cleaved to expose the gate structure. The
white structure closest to the top of the image is the insulating SiO2 layers grown on
top of the polysilicon gates, the two black structures (the flat one on the left side and
the reverse sigmoidal one on the right side of the photos). The upper, parallel band
running across the middle of the image is the Si3 N4 layer and the lower, parallel band
is another SiO2 layer. The bulk silicon on which these structures are grown is not
visible in this image. The bar in the photo is 1.0 µm. This particular photograph
shows the overlap of a φ2 gate (the reverse-sigmoidal black structure) on a φ1 gate.
One Pixel
10
SiO2 Gate Insulation
Poly Silicon
Gates
Si3N4 Layer
11
13
4
7
12
14
5
φ1
8
15
6
9
φ2
φ3
2
3
SiO2 Layer
Depleted
Silicon
1
1,2,3 Gate Width
7,8,9
Gate Thickness 13,14,15 Gate Overlap Thickness
4,5,6 Gate SiO2 Thickness 10,11,12 Gate Overlap
Figure 4-11 The fifteen parameter model used to describe the gate structure.
99
Figure 4-12 compares the best fit model with the raw the O Kα data. The best fit
parameters are printed in the upper right. The dashed line shows the efficiency predicted by the model and normalized to previously determined quantum efficiencies.
Qualitatively, the model fits the data quite well and produces reasonable parameter
values, i.e. they are consistent with the dimensions determined by SEM measurements similar to Figure 4-10. Unfortunately, the number of free parameters in the
model produces results in large uncertainties in the best fit parameters. When determining the structure of the channel stops, we relied on multiple data sets to break
the degeneracy in the model. In the case of the gate structure, however, only the O
Kα data shows statistically significant variation in detection efficiency. For the five
data sets taken at other energies, the characteristic absorption lengths in Si and SiO2
are much larger than the thickness of the polysilicon and oxide layers. The relative
thinness of the gates (compared the attenuation lengths) results in nearly uniform attenuation across the pixel and prevents a further refinement in the parameter values
determined from the O Kα data.
While the current data do not provide the exact dimensions of all the layers that
comprise the gate structure, it does provide some useful constraints. The different
quantum efficiencies under each of the gates clearly indicates that the polysilicon and
SiO2 layers that comprise φ3 are thinner than the layers that comprise φ2 , which in
turn are thinner than the layers that comprise φ1 . The shape of the three, broad curves
in the data give some measure of the width of each of the gates. Additional information, either from design specifications (the total width of all three gates cannot exceed
24 µm) or independent measurements (e.g., SEM studies or the CCD’s response to
undispersed synchrotron radiation [Chapter 3]), provides further constraints on the
dimensions of the gate structure.
100
Figure 4-12 Quantum efficiency across the gate structure, best fit model with the data
at O Kα. The best fit parameters appear in the upper left of the plot. The dotted
line shows the predicted attenuation due to the absorption of photons in the dead
layers of the gate. Refer to Figure 4-11 for the physical structure of gates φ1, φ2 , and
φ3 .
101
4.6
4.6.1
Additional Results
Clocking Effects
In addition to acting as a probe for the sub-pixel architecture, the mesh-moiré experiments nicely illustrate the effects of different gate bias schemes. Typically, gates φ2
and φ3 are held high and gate φ1 is held low (refer to Figure 4-11 for gate definitions.)
This configuration places the vertical potential energy maximum, and hence the vertical pixel boundary, in the middle of φ1 . Thus, the peak location for grade 2 events
should correspond to the middle of φ1 . Figure 4-13 plots the quantum efficiency across
the pixel. Again, the dashed line shows the model gate structure. The dotted line
shows the grade 2 contribution to the total quantum efficiency. The location of the
peak beneath φ1 is additional proof that grade 2 events result from photoabsorptions
that occur close to the vertical boundary of a pixel.
Figure 4-13 Quantum efficiency across the gate structure for O Kα. The hashed
line shows the data, the solid line shows the model (the sum of grade 0 and grade 2
events), and the dotted line shows the location and contribution of the grade 2 events.
Clocking scheme: φ1 low, φ2 and φ3 high.
102
When the bias on either φ2 or φ3 is switched to the low state2, the location of the
grade 2 distribution peak should shift to the new location of the vertical potential
energy maximum. To first order, when only φ2 is held high, the grade 2 peak should
shift to the region between φ1 and φ3 (refer to Figure 4-14 [top]). To first order, when
only φ3 is held high, the grade 2 peak should shift to the region between φ1 and φ2
(refer to Figure 4-14 [bottom]). In both of these cases, the exact location of the grade
2 peak is influenced by the differing thicknesses and widths of the polysilicon gates
and insulators, and deviations from the first order predictions are expected.
Physically, the device does not change so the low energy quantum efficiency of the
CCD remains constant, independent of the particular bias configuration. At the same
time, the branching ratios of grade 2 (g2) events, and correspondingly, grade 0 (g0)
events3 are clearly influenced by the bias scheme. Ideally, all events would be single
pixel events to maximize the energy resolution performance of the CCD.4 A judicious
choice of bias schemes (φ2 and φ3 high, φ1 low) guarantees that the location of the
vertical pixel boundary will occur under the least efficient portion of the detector,
and hence, guarantees the highest grade 0 branching ratio.
4.6.2
Evidence of Charge Cloud Diffusion
The mesh-moiré experiments also give insight into the role diffusion plays in the
increase in the size of the charge cloud. After the initial photoelectric absorption
and creation of the charge cloud by secondary electrons, the cloud drifts upward
towards the gates under the influence of the electric field in the depletion region.
Although the fields are strong and diffusion times are small, the cloud does expand
radially. This process can again be seen by examination of the vertical split events.
2
At least one gate must be high to create the potential minimum needed to define a vertical
boundary between pixels.
3
The sum of the g0 and g2 branching ratios must be constant for the overall detection efficiency
to be constant.
4
Every pixel has a σnoise term associated with it. When summing charge from multiple pixels,
the σnoise terms get added in quadrature.
103
Figure 4-14 Quantum efficiency across the gate structure for O Kα. The hashed
line shows the data, the solid line shows the model (the sum of grade 0 and grade 2
events), and the dotted line shows the location and contribution of the grade 2 events.
top: Clocking scheme: φ1 and φ3 low, φ2 high. bottom: Clocking scheme: φ1 and φ2
low, φ3 high.
104
Figure 4-15 contains the widths (FWHM) from a Gaussian+constant fit to the grade
2 distributions.
Figure 4-15 Attenuation length and charge distribution width as a function of energy
Top: the Gaussian FWHM of the grade 2 events as a function of attenuation length
of the incident photons. Bottom: the Gaussian FHWM of the grade 2 events (right
axis) and the attenuation length (left axis) as a function of photon energy. The solid
line is the attenuation length, the discrete points are the measured widths. Errors on
the FWHM values are much smaller than the symbols used.
The distributions are the convolution of the mesh PSF with the charge cloud after
it has diffused to the potential energy minimum. In fact, this convolution of mesh
PSF, initial charge cloud size, and diffusion effects is the AF defined in Equation 4.5.
As the PSF and initial charge cloud size are largely independent of energy, the widths
provide a way to study the effects of diffusion. The upper panel plots the FWHM
vs. attenuation depth in Si and shows the expected trend that the widths increase
with increasing attenuation length. The lower panel plots both the FHWM (left
105
axis) and the Si attenuation length (right axis) vs. energy. The data indicate that
the width of the distribution is not a monotonically increasing function of energy.
To quantitatively model the diffusion process requires both a 2-D simulation of the
electric potentials as well a model of the charge distribution within the initial cloud
and is beyond the scope of this paper. However, data of this nature will certainly
help such efforts.
4.7
Prospects for Sub-pixel Resolution
In addition to revealing the dimensions of the sub-pixel structure, this technique
provides information that may be useful in improving the spatial resolution of the
CCD beyond that of a 24 µm × 24 µm pixel device. The origin of different event
grades has long been considered to depend on the location of the photon interaction
within a pixel (e.g., Janesick, Elliott, & Garmire 1985 and Bautz et al. 1987), and
these mesh experiments conclusively prove that supposition. These mesh experiments
conclusively prove that the event grade is dependent on the location of the photon
interaction within a pixel. Referring to the plots of the RP arrays in Figure 4-4, it
is clear that grade 0 events come from photons landing in the pixel center, grade 2
events come from photons landing close to the vertical pixel boundaries, while grade
3 and 4 events come from photons landing near the horizontal pixel boundaries, and
grade 6 events come from photons landing in the pixel corners.
The confinement of certain event grades to a specific area of the CCD is effectively
like having smaller pixels inside a 24 µm pixel and is the key to obtaining subpixel resolution. The ratio of single pixel events to multiple pixel events is a strong
function of energy and penetration depth of the photon into Si. As the percentage
of multiple pixel events increase, these mini-pixels will increase in size. Figure 416 shows two 3 × 3 pixel grids. Both grids show a geometric area (computed from
the branching ratios) for the different event grades discussed above, one for Si Kα
photons (1.740 keV) and one for Cu Kα photons (8.040 keV). Superimposed on each
106
Si Kα 1740 keV
One Pixel
33% Enclosed
Energy
Cu Kα 8040 keV
6
2
3
0
6
2
6
66% Enclosed
Energy
4
6
Figure 4-16 Chandra HRMA encircled energy surfaces projected onto a schematic of
sub-pixel locations.
107
of these grids are the 33 % and 66 % enclosed energy curves for the Chandra HRMA.
A full, mathematical investigation has not been performed, but the hope is that
by comparing the branching ratios from an astronomical observation with ground
calibration data, the source location can be determined to better than one pixel.
4.8
Charge Loss in the Channel Stops
Channel stops occupy a noticeable fraction of a CCD pixel. At low energies, a significant fraction of photon interactions will occur in the vicinity of the oxide and p+
implant and have a noticeable effect on the redistribution function. We have performed a series of experiments to study and understand these important processes.
I explain these measurements in great detail in Chapter 5. Here, I summarize the
results germane to the mesh experiments.
The region inside the doped p+ silicon is effectively field free. Any photon interacting there creates an electron cloud which spreads out in all directions due to diffusion.
Some fraction of the cloud will reach the surface and recombine, if there is a potential
well for the electrons at the Si-SiO2 interface due to a positive gate voltage. In this
case, not all the charge will be collected. If the gate voltage is negative, electrons are
reflected back into silicon and eventually get collected into the CCD potential well in
the buried channel. In this case electron cloud does not suffer any charge loss. Those
events landing in the channel stop beneath a negatively biased gate will contribute
to the main, Gaussian-shaped photopeak, while those landing beneath a positively
biased gate will contribute to the “shoulder,” a tail extending to the low-energy side
of the main peak.
The dramatic influence the gate voltage has is vividly seen in the mesh data.
Figure 4-17 (top) shows a spectral redistribution function for for monochromatic data
at 525 eV, with the photopeak and shoulder features delineated. RPs have been
generated from events that interact in the horizontal boundary region between two
neighboring pixels (grades 346) for both the shoulder (bottom left) and photopeak
108
(bottom right). Events beneath the two gates held high (+5 V) contribute to the
shoulder, while events beneath the gate held low (−5 V) contribute to the peak.
Clearly, the p+ implant is not dead, as we had previously assumed.
Figure 4-17 Top: Monochromatic 525 eV spectrum of standard grade (i.e. 02346)
events, showing the selection criteria for main peak (“Photopeak”) and shoulder
(“Shoulder”) events. Bottom: Combined RP maps for all horizontally split events,
including the 3- and 4- pixel events (grade 6) that are near the corner of a pixel. The
shoulder events (left) are localized to regions beneath the two gates with positive bias,
while the the photopeak events (right) only occur beneath the gate with negative bias.
109
Figure 4-18 SEM photographs of the front (left) and back (right) of one hole from
the 1.4 µm × 1.4 µm mesh. The concentric features on the back of the surface result
from the fabrication process. The bar at the bottom of each photograph is 1 µm.
4.9
4.9.1
Improvement to the Mesh Technique
Refined Experimental Method
Armed with our improved understanding of the charge loss mechanism, we refined our
expermental method. The first change involved the mesh itself. While our previous
results clearly imaged the different regions of the pixel, increased spatial resolution
would afford higher precision measurements. We obtained a new mesh consisting of
a 10 µm thin nickel film which has large (tens of microns), rectangular holes. These
holes are then filled in, via electro-forming. The final result is a mesh with square
holes 1.4 µm on a side. Figure 4-18 shows the front (left) and back (right) surfaces
around one of these holes. The spacing between holes was also increased to 48 µm, a
factor of two larger than the previous mesh.5 This mesh has transmission properties
similar to the earlier one due to the their nearly identical atomic numbers. In the
0.277 − 0.704 keV energy range of the new measurements, the transmission is less
than 1 × 10−11 .
5
Due to certain measurements not discussed in thesis, a spacing twice that of the pixel dimension
is desirable. See, e.g., Tsunemi et al. (1999).
110
The next improvement involved changing the way the mesh was held fixed with
respect to the CCD. We discovered that we could place the mesh virtually on top of
the detector. Due to the finite distance between the X-ray and CCD, the gap between
the mesh and detector should be as small as possible to reduce the broadening the
spot size due to beam divergence and diffraction. Figure 4-19 shows the arrangement
of the new mesh and CCD, while the right panel shows raw data with the moiré effect
and count-rate variation clearly visible. Compare to Figures 4-1 and 4-3 (left).
Monochromatic X-rays
12 µ m Ni Foil
48 µ m
48 µ m
1.4 µ m square hole
θ∼1ο
24 µ m
Pixel
Figure 4-19 Improvements to the mesh technique. Left: Schematic showing the orientation of the new mesh with respect to the CCD. Compare with Figure 4-1 Right:
Raw data obtained from the experimental set-up shown to the left. The intensity
variation seen in the moiré pattern is due to attenuation by the sub-pixel structure.
There is marked improvement in resolution compared to the previous results using
the mesh with large holes shown in Figure 4-3 (left).
The last change was in the source of X-rays. Before, we primarily used a photon
fluorescence source whose spectrum contained a relatively large amount of continuum.
Now, we exclusively use the IFM as the source of X-ray. This electron impact source
and grating monochromator provide a spectrally purer source of X-rays than the
HEXS. Elimination of contaminating spectral background removes any uncertainty
in the origin of events outside the main photopeak and allows us to make an RP from
events taken from the entire span of the spectral redistribution function. Figure 4-20
illustrates the resolution gained when these three refinements are applied to mesh
experiment.
111
Figure 4-20 Mesh data taken at 525 eV. Top: Data acquired using the mesh with 4
µm holes. Bottom: Data obtained after refining the technique and using a mesh with
1.4 µm holes. In each case, the representative pixel (RP) has been repeated in a 3 × 3
array to show the change in detection efficiency across the pixel boundaries.
112
Figure 4-21 3 × 3 arrays of grade 0, grade 2, grades 34, and grade 6 Representative
Pixels (RP). Each column has the same energy, and each row has the same grade.
The data are presented in increasing order of total attenuation length (Si × SiO2):
C Kα (left), Fe Lα (middle), and O Kα (right) . Low counting statistics account for
the poor resolution of the grade 34 & grade 6 C Kα data.
113
Using the new mesh, a series of measurements were made at energies of 277 eV,
525 eV and 704 eV, corresponding to the emission lines of C Kα, O Kα, and Fe Lα,
respectively. Figure 4-21 displays RPs generated from various grades (02346) drawn
from the entire SRF. (For additional comparison between the two implementations of
the mesh technique, see Figure 4-4). Due to the low characteristic absorption lengths
at 277 eV, the detection efficiency at C Kα is quite low, particularly over the channel
stops. The relatively sparse data results in the course resolution of the horizontally
split 2-pixel events (g34) and 3- and 4-pixel events (g6).
4.9.2
Data Analysis and Results
For the analysis below we only consider the measurements made at 525 eV and 704 eV,
as a second CCD gate structure different from the first, was used for the measurement
at 277 eV.6 The first step is to calculate the decrease in detection efficiency due to
attenuation by channel stop. Unlike the previous experiment, RPs were generated
using events drawn from the entire SRF. We use the same five-parameter channel
stop model as before (Figure 4-6) and approach, i.e. generating an AF, folding the
convolution of the model and AF through the data, and minimizing χ2. Figure 4-22
shows the attenuation due to the channel stops.
A convenient way to understand the best-fit data is to take slices through the
multi-dimensional parameter space parallel to the plane of two related parameters,
e.g. Si and SiO2 thickness. Figure 4-23 shows contour plots for each energy. The
68% and 99% confidence limits are drawn and the best-fit value is denoted by the
star. The degeneracy between the two parameters is easily understood as the model
cannot differentiate between attenuation by purely Si or SiO2 or some combination
of both.
However, by simultaneously fitting the data at these two energies, one below
and one above the O Kα absorption edge (534 eV) where the ratio of characteristic
6
The first device suffered a failure after the first two experiments.
114
Figure 4-22 The RPs generated from 1.4 µm mesh measurements at 525 eV and
704 eV have been summed in the direction parallel to the channel stops. The drop
in detection efficiency results from attenuation by the constituent materials of the
channel stop.
absorption lengths are markedly different, the degeneracy can be broken. Figure 424 shows the combined contour plot. Table 4-3 shows the range of parameter space
searched and the best-fit values.
The 90% confidence limits encompass a tightly constrained region around the
best-fit values of 0.0 µm (Si p+ depth) and 0.39 µm (SiO2 depth). We note that,
as expected we analyzing events taken from the entire SRF, the thickness of the p+
layer is zero. A similar analysis for the two width parameters yields best fit values
of 4.3 µm for the box width and 0.3 µm for the wing width. We estimate systematic
uncertainties to be ∼10%.
While the measured value of 0.0 µm for the implant parameter is correct for data
115
Figure 4-23 χ2 contour plots for the Si p+ depth versus SiO2 depth for data at 525 eV
(left) and 704 eV (right). The contours correspond to the 68% and 99% confidence
levels, and the star shows the best-fit value.
Table 4-3: Channel stops values derived from considering the entire SRF from under
all the gates
Name
Search range
box width
3.1 − 4.8 µm
wing width
0.11 − 1.1 µm
Si thickness
0.0 − 1.3 µm
SiO2 thickness
0.0 − 1.3 µm
Si3 N4 thickness 0.0 − 0.05 µm
Step size
Best-fit value
0.16 µm
4.3 ± 0.3 µm
0.12 µm
0.3 ± 0.1 µm
0.08 µm
0.0+.04
−.02 µm
0.08 µm 0.39 ± 0.03 µm
0.01 µm
insensitive
drawn from the entire SRF, we still have yet to determine the thickness of the Si p+
layer. This information can be obtained by carefully selecting only a portion of the
RP data. As shown in Figure 4-17 (bottom), photo-absorptions in the channel stop
implant under gates with high voltages contribute to the shoulder, not the photopeak.
If we exclude that portion of the RP that contains the low gates (roughly one-third
of the pixel) and only draw events from the photopeak of the SRF, the p+ layer is
effectively dead. When we perform our fitting, then, we expect a non-zero value for the
Si thickness. Again, we fit the two data sets simultaneously to break the degeneracy.
Figure 4-25 shows the combined contour plot for Si and SiO2 thickness. Table 4-4
116
Figure 4-24 χ2 contour plots showing Si p+ depth versus SiO2 depth for the simultaneous fit of data taken at 525 eV and 704 eV. Data is drawn from the entire spectral
redistribution function. The contours correspond to the 68% and 99% confidence
levels, and the star shows the best-fit value.
lists the area of parameter space searched and the best-fit parameters derived from
the photopeak data beneath the high gates.
The model now has best-fit values of 0.32 µm (Si p+ depth) and 0.47 µm (SiO2
depth). Systematic uncertainties are now estimated to be ∼20%, a factor of two larger
than before since only a subset of the data is being considered. The difference derived
for the oxide thickness in the two analyses are entirely consistent with one another,
given the measurement errors. Finally, we note that box width derived in this case is
slightly narrower (∼0.3 µm smaller) than the values determined when using the RP
generated from the entire span of the SRF. This result is not entirely unexpected, as
two-dimensional modeling of the potential fields beneath the channel stops indicates
117
Table 4-4: Channel stops values derived from considering only the photopeak events
under the high gates.
Name
Search range
box width
3.1 − 4.8 µm
wing width
0.11 − 1.1 µm
Si thickness
0.0 − 1.3 µm
SiO2 thickness
0.0 − 1.3 µm
Si3 N4 thickness 0.0 − 0.05 µm
Step size Best-fit value
0.16 µm
3.8+.2
−.1 µm
0.12 µm 0.1 ± 0.1 µm
0.08 µm
0.32+.07
−.03 µm
0.08 µm
0.47+.01
−.08 µm
0.01 µm
insensitive
that the strong lateral fields present at the edge of the implant region may sweep
out charge before it has a chance to experience charge-loss at the p+ implant–SiO2
interface. This would effectively reduce the width of the implant, as measured with
our current analysis. In our future implementation of the mesh technique, our channel
stop model will have independent variables for the width of the oxide layer and Si p+
region.
118
Figure 4-25 χ2 contour plots showing Si p+ depth versus SiO2 depth for the simultaneous fit of data taken at 525 eV and 704 eV. Only data from the photopeak has
been used in the region of the pixel where the gate voltages were +5.0 V. This particular subset of data ensures that the doped p+ region will effectively be dead for
this analysis. The contours correspond to the 68% and 99% confidence levels, and
the star shows the best-fit value.
119
120
Chapter 5
Charge Loss in the Channel Stops
5.1
Introduction
Channel stops occupy a noticeable fraction of a CCD pixel and can seriously distort
the shape of the response function of the device. The mesh experiments clearly
demonstrate that X-ray photons interacting within silicon near the pixel boundary
separating two columns of the array produce signal charge in two adjacent pixels
and produce horizontally split events (see Figure 4-4). Such events are formed either
in the heavily doped p+ channel stop region or directly beneath it. The effects of
the channel stop are easily seen by comparing the spectrum of vertically split events
to those horizontally split. Figure 5-1 shows the response of an ACIS device to
monochromatic photons at 1487 eV (the energy of the Al Kα emission line). Only
the horizontal events have the noticeable shoulder extending to the low energy side
of the Gaussian.
Examining changes in this feature’s behavior with energy, we found that the total
number of counts in the shoulder agrees well with the calculated number of photons
interacting within a thin layer of silicon near the Si-SiO2 interface. The calculation
predicts a sharp increase of the relative intensity of the low energy shoulder at the Si
absorption edge which is indeed observed, as shown in Figure 5-2.
This means that the low energy shoulder in the response function of the horizon121
tally split events originates from electron clouds formed inside the p+ channel stop
region that suffer some charge loss. Their pulse heights, consequently, are shifted
down in energy. Electron clouds formed below p+ layer in the depleted bulk of silicon
are collected into potential wells without any loss and they form the main peak in
the histogram.
Figure 5-1 CCD response to monochromatic photons of energy 1487 eV. The dashed
line is from vertically split events (grade 2), while the solid line is from horizontally
split events (grade 3 & 4). The vertically split events are described well by a single
Gaussian, while the horizontally split events have a noticeable shoulder extended to
low energies. This shoulder is formed by charge clouds undergoing some charge loss.
5.1.1
Evidence for Charge Loss in the Mesh Data
With the knowledge that horizontally split events are undergoing charge loss, we reanalyzed the mesh data by generating RPs from events drawn from different parts
122
Figure 5-2 Fraction of shoulder events as a function of energy of incoming X-ray
photons. A jump at 1839 eV suggests that these events are formed in a thin layer of
silicon near Si–SiO2 interface.
123
of the redistribution function. First, we separate the spectrum of monochromatic
data at 525 eV (the energy of the O Kα emission line) into a photopeak region and a
shoulder region. We then generated RPs separately for each part of the redistribution
function, using only those 2-, 3-, and 4- events from near the channel stops (i.e. g346).
Figure 4-17 (top) shows how the spectrum was divided and the resultant pixel maps
for the shoulder (bottom left) and photopeak (right).
The most surprising result is that there are no shoulder events under the one
gate that is held at low voltage of -5 Volts during the signal integration. Of equal
importance, the intensity of the main peak drops down significantly under the two
gates held at +5 Volts. The channel stop region under these two gates accounts
for all the “lossy” events that migrate from the main peak into the shoulder. This
means that charge loss in the region is entirely determined by the surface potential,
as the penetration of the gate-generated field into the substrate is extremely small,
given the oxide thickness and relatively heavily doped p+ silicon of this LOCOS
structure. Another extremely important conclusion is that the charge loss can be
entirely suppressed by applying to the gate a negative voltage that repels electrons
away from surface. As I showed in §4.9, the amount of the channel stop p+ implant can
be determined by comparing the relative intensities of peak and shoulder events under
the high and low gates at two well-chosen X-ray energies. The measured thickness of
∼0.4 µm is in good agreement with the thickness of the p+ field-free region calculated
from simulations using a software suite from Silvaco (Prigozhin 1999). This suggests
the following model of the charge cloud dynamics.
Any photon interacting with silicon inside the field free region creates a cloud
of electrons which spreads out in all directions due to diffusion. Some fraction of
the cloud will reach the surface and recombine, if there is a potential well for the
electrons at the Si-SiO2 interface due to the positive gate voltage. If the gate voltage
is negative, electrons are reflected back into silicon and eventually get collected into
the CCD potential well in the buried channel. In this case the electron cloud does not
suffer any charge loss. When the cloud is formed in the depleted region underneath
124
the p+ layer, electrons are immediately pulled by an electric field which prevent them
from reaching the surface. All such clouds are also collected without losses and are
detected as part of the main photopeak. Figure 5-3 illustrates the potential wells (as
seen by electrons) for the scenarios with a positive and negative gate bias. (N.B. The
extent of the upward (–5V) and downward (+5V) swings of the potential at the the
SiO2–p+ interface is greatly exaggerated for clarity.)
5.2
Voltage and Temperature Dependence
The complete collection of charge under gates biased at −5 V and the loss of charge
under gates biased at +5 V clearly indicates the existence of a transition point between
partial and total collection. We acquired data spanning a wide range of voltages
applied to the gates of the CCD to find this “no-loss” condition. The mesh technique,
although very powerful, requires complicated analysis and requires an enormous effort
of time for data acquisition. For example, the 1.4 µm mesh only has an open area of
8.5 × 10−4 , reducing the available detector area from 604 mm2 to 0.5 mm2. Instead,
we developed a different approach to quantify the degree of charge loss.
We again used the in-line focusing monochromator (IFM) used for the second series
of mesh experiments. The device was uniformly illuminated with nearly monochromatic (see below) 525 eV X-rays, corresponding to the O Kα emission line. This
photon energy is ideal for studies of the channel stop, as the characteristic absorption
length of silicon is only ∼0.5 µm. Combined with the shallow depth (0.4 µm) of the
implant, this guarantees that more than 70% of the incident photons interact inside
the doped p+ region, thus making the shape of response for horizontally split events
sharply dependent on the degree of surface charge loss. Figure 5-4 shows the rapid
change of the histogram shape as a function of the high level voltage φhigh at the two
integrating gates. For all measurements discussed below, the difference between the
high gate and low gate is always five volts, i.e. φ high − φ low = +5 V.
When the high gate is operated at 0 V, there is no shoulder and the main photo125
p- type Si
p+ type Si
gate
SiO2
poly Si
-5 V
stop oxide
stop
implant
depletion
region
channel stop
silicon substrate
+5 V
Figure 5-3 Electric potential through the channel stops for two possible gate voltages.
In the case of the negative bias, the potential slopes upward at the Si-SiO2 interface,
repelling electrons and preventing recombination. In the case of the positive bias,
the potential slopes downward at the interface. Electrons that fall into the potential
recombine, resulting in incomplete charge collection. The extent of the upward and
downward slopes at the SiO2–p+ interfaces have been exaggerated to illustrate the
effects of the gate voltage.
126
Figure 5-4 SRFs of horizontally spit events at different gate voltages. Two gates were
held high (voltage level φ high) during the data acquisition. The low gate voltage was
maintained 5 Volts lower than the high gates. Incident photon energy is 525 eV.
peak is extremely Gaussian, indicating unity charge collection efficiency in the channel
stop region. At 1.1 V, the peak has begun to broaden asymmetrically. At even higher
voltages of 1.8 and 2.5 V, the redistribution has clearly become bimodal, with a large
shoulder superimposed on the main photopeak.
Horizontally split events are not the only grade affected by charge loss. The
channel stops extend more than 4 µm in width, and charge clouds that have their
origin in the wings of the p+ region (see Figure 4-5) will contribute only to the nearby
potential well of the CCD and therefore will be detected as single pixel (g0) events.
If they suffer some charge loss they form a similar low energy shoulder in single pixel
event histograms. At energies where X-ray penetration depth is comparable with the
p+ layer thickness (e.g. O Kα) this results in a dramatic increase of amplitude of the
127
low energy tail in a histogram.
5.2.1
Measurement method
In order to account for all the events that originate in the channel stop region under
the high gates, we need to sum together grade 034 events. By only including these
three events types, we ensure that all vertically split events from under the low gate
(i.e. grades 2 and 6) do not affect this analysis. After properly accounting for the
individual gain of each amplifier chain, all four quadrants of the device were added
together.
In order to acquire statistically significant data, we used an oxided carbon anode in
the electron X-ray source that produces the radiation incident to the IFM. Although
the monochromator is tuned to filter out all wavelengths except that corresponding
to O Kα, there is some spectral contamination present, including low-level continuum
and the C Kα emission line at 277 eV. Figure 5-5 shows a typical spectra.
As shown in Figure 5-4, the shoulder is easy to discern when the gate voltage is
sufficiently high. However, during the transition from the no-loss to loss condition,
the shape of the SRF changes gradually. In order to detect subtle differences between
each measurement, we use the measurement with φ high = 0 V to generate a template function. Two Gaussian function describes the main O Kα photopeak, a third
Gaussian describes the C Kα photopeak, while a constant and linear terms accounts
for the continuum. The high-gate voltage was stepped between 0 and 2.5 volts, in
increments of 0.23 V. The same experimental conditions were maintained for all measurements, although slight variations in the current of the X-ray source and different
integration times resulted in differences in the total amount of incident X-rays. To
account for these small differences, the redistribution function of grade 2 events was
used to normalize the individual data sets to another. All grade 2 events originate
from the under the low gate, and as that voltage is always negative, the shape of the
O Kα photopeak is invariant for all measurements. Comparing the total counts in
the main photopeak thus provides an excellent method for relative normalization.
128
Figure 5-5 IFM spectrum of 1- and 2- pixel events (g034) beneath gates with a voltage
of 0V. The predominant feature is the O Kα emission line at 525 eV, although there
is also a low level of continuum present. The C Kα emission line, generated from the
anode, is also present.
At each voltage, the template was subtracted to calculate the fraction of lossy
events. Measurements were made at four temperatures, evenly spaced between -120◦
and -80◦ C. Additional measurements with higher gate voltages were also made at
-120◦ C. Figure 5-6 shows all the results.
The measurements indicate that above 2.5 V the fraction of lossy events remains
constant, although the shape of the histogram continues to change. This is consistent
with the assumption that any electron cloud originating inside the heavily doped p+
region, where no internal electric field is present, loses some charge due to diffusion
towards the surface and subsequent recombination. The amount of lost charge in the
individual cloud depends on the field distribution near the surface and continues to
129
Figure 5-6 Fraction of events undergoing charge loss in the channel stop region as
a function of gate voltage. At warmer temperatures, the transition to the no-loss
condition occurs at more positive voltage. For T = −120◦ , notice that the fraction of
lossy events plateaus above ∼2.5 V.
grow at more positive φ high, shifting the shoulder to lower energies in the SRF.
The transition voltage shifts with temperature, as shown in Figure 5-6. Measurements of the flat band voltage as a function of temperature were performed on a
test structure1 equivalent to the channel stop configuration. It showed an identical
temperature behavior as the shift shown in Figure 5-6. Thus, the dependence on
both gate voltage and temperature on the extent of the charge loss mechanism can
be understood as arising from a temperature shift in the flat-band voltage. Similar
measurements that involved changing the integration time over a wide range, did not
1
This test structure consists of a MOS transistor with a gate on the top the LOCOS layer.
130
produce any changes in the shape of the response. Thus, no de-trapping of electrons
were detected.
5.3
Future Prospects
The improvements to the mesh technique (§4.9) and our better understanding of
the physical processes that occur both in the channel stops (this Chapter; see also
Prigozhin et al. 1999) and near the gates (Prigozhin et al. 2000) suggest a number
of additional investigations. The most obvious of these is to determine the dimensions of the gate structure. Previous attempts to constrain these parameters using
the mesh experiments (§4.5) were inconclusive for a number of reasons. The marked
improvement in spatial resolution now available (see Figure 4-21), coupled with measurements at low energies where the characteristic absorption length is small, will
clearly allow study of each gate.
However, measurements with the mesh are incredibly time-intensive, both in terms
of data collection and analysis. There is also risk to the detector associated each time
the mesh is placed on the CCD. (In fact, one device was “killed” during the course of
the experiments described in Chapter 4.) In Appendix C, I describe a novel approach
for determining the dimensions of the polysilicon gates and oxides.
131
132
Part II: Astrophysics
For the first scientific observation with Chandra2 (the “first light” seen with telescope),
the well-studied supernova remnant (SNR) Cassiopeia A (Cas A) was imaged on
1999 August 20 for an effective exposure time of 2.7 ks. These data illustrate the
high spatial and spectral resolution possible when exquisite optics are coupled with
CCDs and clearly reveal the full capabilities of Chandra.
In addition to resolving the incredible structure present in the SNR, including
bright knots, tenuous wisps, and apparent voids, these data revealed a previously
unknown point source near the geometric center of Cas A (Tananbaum 1999). As
part of a collaborative effort, I analyzed and interpreted the Chandra data on this new
source in Cas A. My specific contribution involved the spectral and image analysis
of the ACIS data. The resultant paper, authored by Deepto Chakrabarty, myself,
Lars Hernquist, Jeremy Heyl, and Ramesh Narayan and entitled “The Central X-Ray
Point Source in Cassiopeia A”, has been accepted for publication in the Astrophysical
Journal. I present the paper in its entirety in Appendix E.
The discovery of the (likely) compact object associated with Cas A demonstrates
the way Chandra observations will contribute to all disciplines of X-ray astronomy.
In particular, the unprecedented spatial resolution will be crucial for addressing a
number of questions, including those relating to rotation-powered pulsars discussed in
Chapter 1. Unfortunately, as Chandra experienced several lengthy delays, I relied on
2
Prior to this, other astrophysical sources had been observed with the Chandra. However, the
purpose of these pointings was calibration. For example, several extra-Galactic sources were imaged
to check Observatory focus.
133
data from previous X-ray observatories, specifically ROSAT and ASCA to investigate
several unresolved issues in pulsar astrophysics. In Part II of this thesis, I present
observations of four young rotation-powered pulsars.
134
Chapter 6
X-ray Observations of Young
Rotation-powered Pulsars
6.1
6.1.1
Introduction
Essential Pulsar Physics
Several formulae and concepts are referred to throughout this thesis in the discussion
of pulsars. Below, I give the derivation of three essential quantities, all of which can
be expressed in terms of period P and period derivative Ṗ , two of the most basic
pulsar observables.
Spin-down Luminosity
One of the most fundamental descriptions of a system is it’s total energy. For radio
pulsars, rotational kinetic energy is thought to be the source of the observed pulsed
radiation (hence, the name rotation-powered pulsar) as well as the the pulsar wind
that drives a possible synchrotron nebula. Taking the derivative of the kinetic energy
of a rotating body with respect to time
d
d 1 2
(E) =
IΩ
dt
dt 2
135
(6.1)
and recasting in terms of period P and period derivative Ṗ ,
1
P = 2π
Ω
!
Ω̇
and Ṗ = −2π
,
Ω2
Equation 6.1 becomes
Ė = −4π 2I
Ṗ
,
P3
(6.2)
the spin-down luminosity. For typical neutron star parameters (i.e. radius of 10 km
and mass equal to 1.4 M ) and assuming the neutron star is a rigid sphere with
q
radius of gyration ( (2/5)r), the moment of inertia I equals 1045 g cm2.
Magnetic Field Strength
The observed spin-down of pulsars, characterized by an increase in spin period P and
positive period derivative Ṗ , is thought to be a result of magnetic dipole braking. This
phenomena is the same radiation that results from a rotating magnetic dipole. From
classical electrodynamics, we know that the power radiated for a magnetic dipole m
~
is given by:
P =
2
|m̈2|.
3c3
(6.3)
A neutron star with surface dipole field strength B and radius R has an associated
magnetic moment |m
~ | = BR3 . If the magnetic and rotation axis are separated by
angle α, Equation 6.3 becomes
P =
2B 2 R6 Ω4 sin2 α
3c3
(6.4)
Equating the power radiated with spin-down luminosity (Equation 6.2) and assuming
(sin α) = 1, the surface magnetic dipolar field is:
B=
3I c3 P Ṗ
8π 2 R6 sin2 α
!1/2
= 3.2 × 1019 P Ṗ
136
1/2
G.
(6.5)
Characteristic Time
The age of a pulsar τ can be estimated by starting with the assumption it slows at a
rate proportional to the rotation frequency, raised to the power n, the braking index:
Ω̇ ≡ −kΩn .
(6.6)
After taking an additional derivative with respect to time, it is trivial to show
ΩΩ̈
.
Ω̇2
n=
(6.7)
Integrating Equation 6.6,
dΩ
= −kΩn
dt
Ω
Ω(−n+1) t0 =τ
= −k t0|t0 =0
(−n + 1) Ω0

(−n+1)
Ωn  Ω(−n+1) − Ω0
τ =
−n + 1
Ω̇
"
1 P
P0
τ =
1−
(n − 1) Ṗ
P


n−1 #
.
(6.8)
If the pulsar does in fact slow via magnetic dipole braking, Equations 6.2 and 6.5 can
be used to show Ω̇ ∝ Ω3 or that the braking index is three. Under most circumstances,
it is safe to assume P P0 and Equation 6.8 reduces to the characteristic age:
τc =
6.1.2
P
.
2Ṗ
(6.9)
High-energy Observations
X-ray observations of radio pulsars provide a powerful diagnostic of the energetics
and emission mechanisms of rotation-powered neutron stars. As magnetic dipole
braking slows the pulsar, it loses rotational kinetic energy at a rate Ė = 4π 2 I Ṗ P −3
137
(see §6.1.1). Though pulsars have traditionally been most easily studied at radio
wavelengths, only a small fraction (10−7 to 10−5 ) of the “spin-down luminosity” Ė
manifests itself as radio pulsations. Instead, it is believed that a significant fraction
of the luminosity emerges as a relativistic wind of positrons and electrons. When
this wind is confined by the surrounding medium, an observable synchrotron nebula
or pulsar wind nebula results. Measurements of the morphology and spectrum are
essential for determining the content and energy spectrum of the wind, probing the
ambient density, and understanding the shock acceleration mechanism.
In addition to this (possibly extended) non-thermal emission, there are two other
distinct physical processes that can produce observable X-ray emission. The first is
thermal emission, resulting from either the initial cooling of a young neutron star
(Page 1998 and references therein) or from polar-cap reheating in older pulsars (e.g.,
Wang & Halpern 1997 or Greiveldinger et al. 1996). If the polar region is misaligned
with the rotation axis, pulsed radiation results as the heated cap sweeps across our
line of sight. Cooling emission may also be slightly modulated, due to the thermal
gradient across the entire surface of the neutron star, as in the case of the Vela pulsar
PSR B0833−45 (Ögelman, Finley & Zimmermann 1993). Whatever the source of the
thermal energy, blackbody emission is independent of the spin-down luminosity Ė.
The last type of emission is non-thermal magnetospheric emission, produced by
either polar cap or outer gap emission mechanisms, is responsible for the classic
“pulsar phenomenon,” which is characterized by sharp pulsations with high pulsed
fraction (see, e.g. Seward & Harnden 1982). The most famous example is the Crab
pulsar, whose pulsed X-ray spectrum is characterized by a power law with photon
index 2 (Toor & Seward 1974). The energy for pulsed magnetospheric emission originates from the spin-down and is seen from pulsars having high Ė at the extremes
of the age distribution, from young pulsars with ages less than 104 yr like the Crab,
PSR B1509−58 and the two LMC pulsars PSR B0540−69 and PSR J0537−6910 to
the million-year old millisecond pulsars like PSR J0437−4715 and PSR B1821−24
(Seward & Harnden 1982; Seward, Harnden, & Helfand 1984; Marshall et al. 1998;
138
Becker & Trümper 1993; Saito et al. 1997).
X-ray observations of pulsars are also important for searching for the remnant of
the supernova that created the pulsar. Direct studies of the remnant are useful for
numerous reasons, including measurement of the elemental abundances and determination of the shock conditions in the SNR through spectral analysis. More important
for pulsar studies, identifying the remnant of a supernova that created a pulsar is
crucial for quantifying the fraction of neutron stars borne in SNe. Moreover, associations can provide independent distance and age estimate for the pulsar (e.g., Frail,
Goss, & Whiteoak 1994). With a statistically significant sample of associations, it
is possible to constrain the birth properties of neutron stars, including initial period,
magnetic field, and velocity distribution.
Since the launch of Einstein and the onset of true imaging X-ray astronomy, a
growing number of radio pulsars have been detected in X-rays. Table 6-1 is a partial
list of pulsars, ranked by spin-down flux (Ė/(4πd2 )), down to a limiting flux of of
6 × 10−11 ergs s−1 cm−2. In addition to the observable spin parameters and related
quantities for each pulsar, Table 6-1 lists its X-ray properties, including the luminosity
and size of any pulsar wind nebula. It is important to note that only approximately
half of the pulsars listed have had pulsed X-ray emission detected, and even fewer
have had an extended synchrotron nebula detected.
While studying pulsars that span the entire age distribution allows a complete
population synthesis, it is the youngest members (i.e. those with characteristic ages
less than 100,000 years) that are best-suited for advancing our understanding of neutron star physics for three important reasons. First, emission from a synchrotron
nebula appears to scale with Ė (Seward & Wang 1998; Becker & Trümper 1997). As
the youngest pulsars tend to have the highest Ė, these source have the brightest X-ray
luminosities and are most easily detectable. Second, most neutron star cooling models, independent of their particular assumptions, universally predict that the surface
of the neutron star cools dramatically when it reaches an age of ∼100,000 years (see,
139
140
Pa
33
89
69
151
102
40
124
16
101
134
125
139
50
267
63
408
232
197
607
(ms)
a
15
421
124
135
1537
93.0
5.8
95.9
51.3
75.0
134
128
85.0
479
208
15.8
4023
495
5.8
465
P_
1.3
11.4
8.1
1.6
17.4
107
20.4
5.0
21.3
15.8
15.4
25.9
1.7
20.3
63.4
1.6
7.4
538
20.7
4:5 1038
6:9 1036
1:6 1037
1:8 1037
3:5 1036
3:7 1036
2:0 1036
4:9 1038
2:9 1036
2:2 1036
2:6 1036
1:3 1036
1:5 1038
4:3 1035
2:5 1036
2:3 1036
1:6 1036
3:0 1034
8:2 1034
c
(kyr)
(erg s 1 )
E_
2.5
0.5
3.3x
4.2x
2.4x
2.5
3.0
47x
4.0x
3.9
4.6
4.2
49
3.0x
7.0
8.0x
7.3
1.5
3.3
(kpc)
da;b
6:0 10
2:3 10
1:2 10
8:3 10
5:0 10
5:0 10
1:8 10
1:8 10
1:5 10
1:2 10
1:0 10
5:9 10
5:1 10
4:6 10
4:2 10
3:1 10
2:5 10
1:1 10
6:3 10
11
10
10
10
10
10
10
10
9
9
9
9
9
9
9
9
8
7
7
_ 4d2
E=
(erg s 1 cm 2 )
3:0 1036
2:1 1033
1:7 1035
2:7 1033
7:4 1035
5:0 1031
6:4 1033
9:0 1034
(erg s 1 )
Lcx pulsed
1:2 1037
9:0 1031
3:4 1033
2:1 1035
6:6 1032
1:6 1033
2:0 1032
1:2 1036
4:7 1033
5:8 1032
< 8:0 1032
< 2:7 1032
8:5 1036
1:3 1033
3:8 1033
2:0 1032
< 7:0 1032
2 1031
< 1:2 1032
(erg s 1 )
Ld
x syn neb
300
<
1000
30
< 30
< 30
<
< 0:02
< 6:1
< 7:0
2
< 2:4
0.3
< 1:4
10
0.6
0.8
< 2:6
< 1:6
0.7
< 3:4
1.0
1.70
20
< 1:50
80
5400
7000
< 30
< 700
3800
< 3:00
lin (pc)
ang ( )
nebular sizee
231
234
289
256
146
97
271
707
583
30
153
57
68
467
253
76
45
129
DMa
(pc cm 3 )
3.0
3.0
6.8
13
1.3
3.0
5
15
40
14
9
8
4.0
10
7
15
20
0.3
7
(1021 )
(cm2 )
NH
Properties and X-ray Characteristics of Selected Rotation-powered Pulsars
1
2,3
4,5
6,7
8
9
Ch.6
10,11
12
13,14
14
14
15,16
17
18,19
20,Ch.7
Ch.6
21,22
14
ref


References. | (1) Harnden & Seward 1984; (2) Ogelman
1995; (3) Ogelman,
Finley, & Zimmermann 1993; (4) Torii et al. 1998; (5) Kaspi et al. 1998; (6) Seward

et al. 1984; (7) Marsden et al. 1997; (8) Finley et al. 1998; (9) Sa-Harb, Ogelman,
& Finley 1995; (Ch.6) Chapter 6; (10) Wang & Gotthelf 1998; (11) Marshall et

al. 1998; (12) Finley, Srinivasan, & Park 1996; (13) Becker & Trumper 1997; (14) Finley & Ogelman
1994; (15) Finley et al. 1993; (16) Seward & Harnden 1994; (17)

Harrus, Hughes, & Helfand 1996; (18) Kaspi et al. 1997; (19) Gotthelf & Kaspi 1998; (20) Camilo et al. 2000; (Ch.7) Chapter 7; (21) Ogelman
& Finley 1993; (22)
Greiveldinger et al. 1996.
a Period (P ), period derivative (P_ ), distance (d), and dispersion measure (DM) come from the Princeton pulsar catalog, except for PSRs J1617 5055, J0537 6910,
and J1105 6107 when we referred directly to the discovery papers.
b A subscript x indicates that the X-ray analysis assumed a distance dierent from that given by the Princeton pulsar catalog.
c Luminosities are for the 2 10 keV band and assume a powerlaw spectrum, except for PSRs B0833 45 and B1055 52 when the values are bolometric blackbody
luminosities. See references for spectral model details.
d Luminosities are for the 2 10 keV band and assume a powerlaw spectrum. See references for spectral model details.
e Nebular dimensions are in either angular ( ) or linear (pc) diameter. Except for PSRs B0531+21 and B1509 58 which have denite elongation, most PWNs are
roughly symmetric.
B0531+21
B0833 45
J1617 5055
B1509 58
B1706 44
B1951+32
B1046 58
J0537 6910
B1823 13
B1800 21
B1757 24
B1727 33
B0540 69
B1853+01
J1105 6107
J1119 6127
B1610 50
B1055 52
B1737 30
Name
Table 6-1.
e.g., Page 1998 and references therein). Thus, only neutron stars in their youth emit
the soft thermal X-rays that can be used as a cooling diagnostic. Finally, pulsars have
lifetimes of millions of years, while SNRs are usually observable for a mere fraction of
this time, usually less than 50,000 years (see, e.g., Gaensler & Johnson 1995). Only
those pulsars with ages below this upper limit can hoped to be associated with their
SNRs.
The focus of the second half of this thesis is the analysis and interpretation of
X-ray observations of four young radio pulsars, two of which have never been studied
before. In this chapter, after a brief introduction of concepts important to pulsar
physics, I discuss pulsars PSRs B1046−58 and PSR B1610−58. Of particular interest
for these two objects is whether their X-ray emission agrees with the empirical Lx − Ė
relationships found in the literature. Also intriguing is whether they have large pulsar
wind nebula (i.e. greater than 100 in extent), as claimed by some authors (Kawai &
Tamura 1996; Shibata et al. 1997; Kawai, Tamura, & Saito 1998) and in marked
contrast to all other nebula found around young pulsars, as seen in Table 6-1.
In Chapter 7, I present studies of PSR J1119−6127, a very young pulsar recently
discovered in an on-going survey of the Galactic plane for radio pulsars being performed at the 64 m radio telescope at Parkes, Australia (Lyne et al. 2000). Recent
radio interferometric measurements have confirmed the existence of a supernova remnant there. I analyze X-ray observations of this new PSR-SNR system from both
ASCA and ROSAT. Chapter 8 focuses on PSR J1814−1744, another young pulsar
discovered in the Parkes survey. This pulsar’s properties are very similar to anomalous
X-ray pulsars (AXPs), a new class of object only detectable through their high-energy
emission. Based on its X-ray properties, I discuss various models for AXPs and their
relation to radio pulsars.
141
6.2
6.2.1
PSRs B1046−58 and B1610−50
Background
PSR B1046−58 was discovered by Johnston et al. (1992) during a 1400 MHz survey
of the Galactic plane for radio pulsars. PSR B1046−58 has Ė = 2.0 × 1036 ergs
s−1 , characteristic age τC = 20 kyr, and properties reminiscent of the Vela pulsar.
The dispersion measure (DM) toward the pulsar is 129 pc cm −3. Using the Taylor &
Cordes (1993) DM–distance relationship, the distance to PSR B1046−58 is estimated
to be d ≈ 3.0 kpc. The large Ė/4πd2 value (a useful indicator of the detectability
of its putative pulsar wind nebula) make it a strong candidate for X-ray emission.
Kaspi et al. (2000) have found evidence for γ-ray pulsations from an EGRET point
source spatially coincident with PSR B1046−58.
PSR B1610−50 was also discovered in the Johnston et al. survey. PSR B1610−50
is the fourth youngest Galactic pulsar (τc = 7.4 kyr) and has Ė = 1.6 × 1036 ergs s−1
and DM = 586 pc cm−3. PSR B1610−50 occupies an interesting position in the age
phase-space of known pulsars: its age is between those of the youngest pulsars (τc .
2 kyr), like the Crab and PSR B0540−69, and those in their “adolescence” (τc ∼ 1020 kyr), like Vela and PSR B1046−58. Caraveo (1993) proposed that PSR B1610−50
is associated with the nearby supernova remnant Kes 32. However, using the DMderived distance of 7.3 kpc and assuming the system’s age is τc , we find that the
pulsar’s implied transverse velocity is vt > 2300(d/7.3) km s−1 , significantly higher
than the mean pulsar velocity (e.g. Lyne & Lorimer 1994). If it is traveling with so
high a speed, one might expect strong ram-pressure confinement of its wind and a
correspondingly high X-ray luminosity from the resultant synchrotron emission (see
e.g. Cheng 1983; Wang, Li, & Begelman 1993; Finley, Srinivasan, & Park 1996;
Romani, Cordes, & Yadigaroglu 1997; Wang & Gotthelf 1998).
Previous X-ray work on PSRs B1046−58 and B1610−50 has been limited in scope.
Becker & Trümper (1997) published a ROSAT-band (0.1−2.4 keV) luminosity for
142
Table 6-2. Astrometric and spin parameters for PSRs B1046−58 and B1610−50
Parameter
PSR B1046−58
Right ascension (J2000)a
10h48m 12.s6
a
Declination (J2000)
−58◦ 320 03.008
Period, P (s)b,c
0.124
Period derivative, Ṗ (s s−1 )b
95.9 × 10−15
Epoch of period (MJD)
49403.0
Dispersion measure, DM (pc cm−3 )b
129.09(1)
Characteristic age, τc (kyr)
20.4
−1
Spin-down luminosity, Ė (ergs s )
2.0 × 1036
d
Distance, d (kpc)
3.0
−2 e
Column density, NH (cm )
(0.40 − 1.4) × 1022
PSR B1610−50
16h14m 11.s6
−50◦ 480 01.009
0.232
493 × 10−15
48658.0
586(5)
7.4
1.6 × 1036
7.3
(1.8 − 2.2) × 1022
a
Radio positions, from Stappers, Gaensler, & Johnston (1999) are uncertain
by < 0.100.
b
Data obtained from the Taylor et al. (1995) pulsar catalog. This information
is not used for the timing analysis of PSR B1046−58.
c Ephemeris
for PSR B1046−58 was obtained from radio timing observations
at the 64-m Parkes radio telescope in New South Wales, Australia.
d
Derived from the Taylor & Cordes (1993) DM-distance model.
e
Lower limits were derived from the Seward & Wang (1988) estimate of 10
neutral hydrogen atoms per free electron; upper limits were derived from Dickey
& Lockman (1990).
143
PSR B1046−58 of 4 × 1032 ergs s−1 , but gave no further analysis. Kawai, Tamura,
& Saito (1998) presented ASCA data on both pulsars, but restrict their attention to
a single Gas Imaging Spectrometer (GIS) image of each pulsar. For both PSRs
B1046−58 and B1610−50 they reported the detection of a large nebula (tens of
arcminutes) associated with each pulsar. This paper undertakes a detailed analysis
of the archival ASCA data, with an emphasis on image analysis.
6.3
Observations
ASCA (Tanaka, Inoue, & Holt 1994) observed PSR B1046−58 on 1994 January 27
and PSR B1610−50 on 1994 March 25. We present an analysis of the data obtained
from the public archive. For both observations, data were taken with all four imaging
spectrometers, each in the focal plane of its own foil mirror: two Solid State Imaging
Spectrometers (SIS-0, SIS-1) employing charge coupled devices (CCDs), and two Gas
Imaging Spectrometers (GIS-2, GIS-3) employing gas scintillation proportional counters. These spectrometers offer moderate energy (∼5%) and imaging (∼20 ) resolution
in their ∼1 − 10 keV energy band-pass. The SIS has superior imaging and spectral
capabilities, while the GIS has a higher effective area above ∼2 keV and a greater
net observation time than the SIS. To facilitate pulsation searches, GIS data were
collected in the highest time resolution configuration (0.488 or 3.906 ms depending
on data acquisition rate). SIS data were acquired in 4 CCD mode with 16 s integrations (PSR B1046−58) and 2 CCD mode with 8 s integrations (PSR B1610−50)
using a combination of FAINT and BRIGHT modes (see The ASCA Data Reduction
Guide.1 The data were filtered to exclude times of high background contamination
using the standard REV2 screening criteria. This rejects time intervals of South Atlantic Anomaly passages, Earth block, bright Earth limb in the field-of-view, and
periods of high particle activity. The resulting effective observation times per single
detector are 18 ks (GIS) and 15 ks (SIS) for PSR B1046−58, and 11 ks (GIS) and
1
http:legacy.gsfc.nasa.gov/docs/asca/abc/abc.html.
144
8.4 ks (SIS) for PSR B1610−50.
6.4
PSR B1046−58
6.4.1
Image Analysis
ASCA Data
Flat-fielded images were generated by aligning and co-adding exposure-corrected images from the pairs of instruments. Exposure maps were generated with the FTOOL
ascaexpo, ASCA software which uses the satellite aspect solution, instrument map
(GIS), chip alignment, and hot pixel map (SIS) to determine the exposure time for
each sky image pixel. The exposure correction was highly effective in removing the
GIS instrumental structure due to the window support grid. Figure 6-1 (top left)
displays the resultant smoothed broad-band (0.8 − 10 keV) image for the GIS. The
image reveals emission confined to a slightly oval ∼40 × 70 region, elongated along
the direction parallel to declination. Though the statistics are limited, the emission
appears to be concentrated in regions near the top and bottom of the oval.
The pulsar location, determined by radio interferometric measurements made by
Stappers et. al (1999), is marked by a cross and lies near the bottom of the emission
region. The dashed square indicates the region shown in SIS images (Figures 6-1
[top right] - [bottom right]). The two ellipses represent the 95% and 99% positional
error boxes of the γ-ray source 3EG J1048−5840 (Hartman et al. 1999; see below for
additional discussion). Figure 6-1 (top right) displays the central region of the broadband (0.4 − 10 keV) image for the SIS, while Figures 6-1 (bottom left) and (bottom
right) show the soft-band (0.4 − 2 keV) and hard-band (2 − 10 keV) images for the
same region. A cross marks the location of PSR B1046−58 and the arcs represent the
errors ellipses for 3EG J1048−5840. Due to its superior spatial performance, the SIS
resolves the smooth emission seen by the GIS into four point sources (hereafter called
Src 1, Src 2, Src 3, and Src 4) possibly situated in a region of faint diffuse emission.
145
Figure 6-1 ASCA images of the PSR B1046−58 field: flat-fielded images of the region
around the pulsar, whose location is marked by the cross. Top left: broad band
(0.8 − 12 keV) GIS image shows an oval shaped region of X-ray emission with the
pulsar located at its southern tip. The two ellipses represent the 95% and 99% error
boxes for the γ-ray source 3EG J1048-5840. The dashed square delineates the SIS
region displayed in b)−d). Top right: The broad band (0.4−10 keV) SIS image clearly
showing the three labeled sources embedded in a diffuse emission region. Bottom left:
The soft band SIS image (0.4 − 2 keV) revealing the soft, probably thermal nature of
Src 2. Note that Srcs 1, 3, and 4 are very weak in this band. Bottom right: The hard
band (2 − 10 keV) SIS image showing the hard nature of Srcs 1, 3 and 4. We identify
Src 1, offset 2000 from the radio position of PSR B1046−58 and the only source inside
the 95% error circle of the pulsed γ-ray source 3EG J1048−5840, as the synchrotron
nebula of PSR B1046−58. Contours approximately correspond to the 4σ, 5σ, 6σ, 7σ,
8σ, and 9σ levels. Count rates are in units of 10−5 cps pixel−1 for the GIS and 10−6
cps pixel−1 for the SIS.
146
The number of detected counts at the pulsar position is too small to fully resolve
the familiar cross pattern of the X-ray telescope (XRT) PSF, as the morphology is
dominated by Poisson fluctuations (see Hwang & Gotthelf 1997 §2.2 for a discussion of
the significance of peaks in similarly processed images). To estimate the significance
of the detections, we ignore the complexities of the ASCA point-spread function and
compare the number of photons collected from a small aperture centered on the
source with that from a 120 − 180 diameter concentric annulus. The relatively small
number of counts available in the source region makes the approximation reasonable.
Unfortunately, the close proximity of the four sources complicates this analysis. An
optimally sized2 40 diameter aperture captures the majority of flux from the pulsar
position as well as an undetermined amount of flux from neighboring sources, resulting
in an overestimation of the pulsar’s putative X-ray emission. Use of a smaller 20
diameter aperture eliminates the contamination from the neighbors but neglects the
flux in the broad wings (∼30) of the XRT PSF. Rather than artificially inflating the
significance of a detection, we employ the 20 diameter aperture with the understanding
that our calculations may underestimate the strength of a source. Using the formalism
outlined in Appendix D, we estimate the detection significance (the signal-to-noise
ratio, S/N) with an expression that accounts for both the source and background
variance.
Table 6-3 presents relevant information for the four sources detected by both SIS
detectors, including source positions, count rates, detection significance σ, and hardness ratio H, where H ≡ counts(2 − 10 keV)/counts(0.4 − 2 keV). Src 1 is relatively
hard (H = 0.70 ± 0.30) and is strongly detected with a significance of 4.5σ (44 background subtracted counts). Src 2 is primarily soft (H = 0.55 ± 0.18) and is strongly
detected with a significance of 6.1σ (69 background subtracted counts). Src 3 is hard
(H = 1.55 ± 0.82) and has a significance of 3.9σ (38 background subtracted counts),
while Src 4 is the hardest source (H = 2.15 ± 1.70) and has a significance of 3.4σ.
2
Here, optimal refers to an aperture that maximizes the number of source counts captured within
the extraction region, relative to the background contribution. See e.g. Gotthelf & Kaspi (1998).
147
In an attempt to reduce the influence of the diffuse emission and contamination from
neighboring sources, centroid positions for Src 1, Src 3, and Src 4 were determined
from analysis of the hard-band image in Figure 6-1 (bottom right) and the position
for Src 2 was determined from the soft-band image in Figure 6-1 (bottom left). Combining the ∼1500 centroid uncertainty for each source with the ∼2000 revised pointing
uncertainty (Gotthelf 1996) for ASCA results in an overall source position uncertainty
of order ∼2500 .
Src 1 lies 2000 from the radio position of the pulsar, within the positional errors.
Assuming approximately 4 sources per square degree with comparable flux to Src 1
(Gendreau, Barcons, & Fabian 1998) and a SIS spatial resolution of 30 , we estimate
the probability of a chance superposition of Src 1 with the pulsar’s position to be of
order 0.008. Src 2 lies 9200 away from the radio position, making it extremely unlikely
that it is the X-ray counterpart of the pulsar.
Our images differ significantly from those produced by Kawai et al. (1998) from
the same ASCA data. In particular, we do not find any evidence for a large (∼10−200 )
nebula around the pulsar. Our reanalysis of the GIS data and analysis of the SIS data
provide support for emission from the pulsar (Src 1) that is unresolved by the ASCA
PSF. Our disparate conclusions result primarily from the consideration of the SIS
data with its superior spatial resolution, which shows that the oval shaped region in
the GIS image actually represents emission from the four sources resolved by the SIS.
We have also employed different procedures in the GIS analysis. Specifically, we have
used an exposure correction that removes the significant structure produced by the
GIS support grid and we have smoothed the data with a 3 × 3 boxcar function (∼4500
on a side) that approximates the core of the PSF3 . When a much larger smoothing
function is used, Poisson fluctuations, individual sources, and structure arising from
the support grid (if not accounted for) can be blended into an apparent large, diffuse
3
A similar procedure is also performed on the SIS data. The data are first rebinned ×4, then
smoothed with a 5 × 5 boxcar function (∼3000 on a side).
148
Table 6-3.
RA
(J2000)
Src
Src
Src
Src
1
2
3
4
10
10
10
10
48
48
48
48
11.6
15.1
04.4
15.1
ASCA SIS detection of PSR B1046−58
Declination
(J2000)
-58
-58
-58
-58
31
30
28
28
46
34
26
57
Count Rate
(×10−3 cps)
Background Rate
(×10−3 cps)
Hardness
Ratio, H
3.99±0.42
4.87±0.43
3.62±0.38
3.27±0.38
2.10 ± 0.04
2.18 ± 0.04
2.15 ± 0.05
2.21 ± 0.04
0.70 ± 0.30
0.55 ± 0.18
1.48 ± 0.82
2.15 ± 1.70
S/N
(σ)
4.5
6.1
3.9
3.4a
Note. — The positions for Src 1, Src 3, and Src 4 were derived from the hard band
(2 − 10 keV) image; the position for Src 2 was derived from the soft band (0.4 − 2 keV)
image. Total uncertainties in the source positions are ∼2500 . Count rate is the total source
plus background count rate in an aperture centered on the source position. Background
rate is the count rate in a 120 − 180 diameter annulus concentric with the source position,
normalized to the source aperture. Refer to the Appendix D for the definition of significance
and further discussion on all the measured quantities. The hardness ratio H is defined as
counts in the hard band (2 − 10 keV) divided by counts in the soft band (0.4 − 2 keV).
a This
significance is for the 2 − 10 keV band. The broad-band significance is 3.2σ.
149
region of emission.
ROSAT Data
PSR B1046−58 was also observed on 1996 March 8 by the HRI (High Resolution
Imager) on-board ROSAT for 23 ks. Several point sources are clearly detected in the
HRI FOV, but none is coincident with the position of the radio pulsar. The upper
limit for a source at the radio position is <1× 10−3 cps. This result is in disagreement
with the detection of PSR B1046−58 with the HRI reported by Becker & Trümper
(1997) . A source is present, however, α(J2000) = at 10h 48m 13.s 0, δ(J2000) =
−58◦ 300 4400 , 8000 away from the pulsar’s radio position. This ROSAT source is only
1900 away from SIS Src 2; given the apparently soft spectrum of Src 2 and the 2500
positional uncertainty of the ASCA sources, suggests that they are the same source.
To try to identify this source (SIS Src 2), we searched several optical catalogues.
The only coincident source, located ∼800 from the ROSAT position, was found in the
Digital Sky Survey. Using the photometric calibration provided for the UK Schmidt
Camera, we estimate a V magnitude of ∼13.4. Positive identification of this optical
source with the X-ray source detected by both ROSAT and ASCA requires spectroscopic data not presently available.
There are no other ROSAT sources spatially coincident with the remaining three
SIS sources, which is not surprising given their harder spectra. Furthermore, no extended or diffuse emission is seen in the HRI data. This suggests that the faint diffuse
emission seen in the SIS data may not be physically significant. One possible origin of
this diffuse structure could be a blending of Poisson fluctuations with emission from
the closely grouped point sources scattered by the broad PSF of the ASCA mirrors.
6.4.2
Flux Estimation
While the observations allow detection of the four sources, the low statistics prevent
useful spectral analysis. However, the hardness ratio H of the SIS sources and the
lack of ROSAT counterparts for all but Src 2 give some information about the sources.
150
Srcs 1, 3, and 4 must either be absorbed non-thermal sources or thermal sources with
temperature of at least several keV. Src 2 appears to be either an intrinsically soft
thermal source with temperature on order of 50 eV or is a non-thermal source with
a very steep power law that is undetectable above 2 keV in the SIS.
To extract a flux estimate for the X-ray counterpart of the pulsar, we assume a
spectral shape and adjust the overall normalization to match the count rate4 of Src 1.
The canonical synchrotron nebula spectrum is characterized by a power law with
photon index α = 2, where N(E) ∝ E −α (see, e.g., Seward & Wang 1988 and Becker
& Trümper 1997). The neutral hydrogen column density NH can be constrained by
combining the Seward & Wang (1988) approximation of 10 neutral hydrogen atoms
per free electron with the DM or by using the HI maps of Dickey & Lockman (1990).
The former yields NH = 4.0 × 1021 cm−2 , the latter yields NH < 1.4 × 1022 cm−2.
We adopt a value between these two rough estimates of NH = 5 × 1021 cm−2. After
folding the spectral model through the instrument (SIS+XRT) response, we obtain
an unabsorbed 2 − 10 keV flux of (2.5 ± 0.3) × 10−13 ergs cm−2 s−1 . Folding these
parameters through the ROSAT instrument response yields an expected HRI count
rate of (2.3 ± 0.3) × 10−3 cps, in rough agreement with the upper limit (1 × 10−3 cps)
calculated above. The assumed spectral model and NH also agree well with the
observed hardness ratio.
6.4.3
Timing
We carried out a timing analysis for PSR B1046−58 using the combined data from
the two GIS detectors. We selected events in the 2 − 10 keV band from a 40 diameter
aperture centered on Src 1, using data acquired at the high and medium data rates
only. A total of 472 events, a large fraction (∼60%) of which are due to the background, were folded using an ephemeris obtained from radio timing observations of
4
Here, the count rate is that determined in § 6.4.1, adjusted to account for the flux in the broad
XRT wings that falls outside the extraction aperture.
151
PSR B1046−58 at the 64-m Parkes radio telescope in New South Wales, Australia.
Table 6-2 contains the ephemeris. As the putative pulse shape is unknown, we employed the H-test (de Jager 1994) to search for pulsations. For a duty cycle δ = 0.5,
the 3σ upper limit to the pulsed fraction is 0.31. For increasingly sharper pulse shapes
of δ = 0.3 and 0.1, the 3σ upper limits are 0.22 and 0.12, respectively. The absence
of pulsations from the GIS data is consistent with the work of Saito (1998).
6.5
PSR B1610−50
6.5.1
Image Analysis
Flat-fielded images were generated using the same prescription given in §3.1. Figure 62 (top left) displays the resultant smoothed broad-band (0.8 − 12 keV) image for the
GIS. A cross marks the location of the pulsar determined from radio interferometric
measurements (Stappers, Gaensler, & Johnston 1999)5 . The dashed rectangle shows
the SIS FOV. The black contours are an overlay of 843 MHz MOST observations of
the supernova remnant Kes 32 (Whiteoak & Green 1996). The flux in the lower left
quadrant results from scattered emission from the X-ray bright supernova remnant
RCW 103, located 330 from the GIS optical axis. The scattered intensity has the
gradient and shape expected when the 120 extent of the SNR is folded through the
broad wings of the ASCA XRT (Gotthelf, Petre, & Hwang 1997). Examination of the
soft-band (0.8 − 2 keV) and hard-band (2 − 12 keV) images in Figures 6-2 (top right)
and (bottom left) reveals that the contamination is largely confined to E < 2 keV, due
to the intrinsic spectral nature of RCW 103 and the decrease in the XRT scattering as
a function of increasing energy. The SIS images have the same properties as the GIS
images; for brevity, we only present the hard-band (2 − 10 keV) image in Figure 6-2
(bottom right).
5
The interferometric pulsar position differs from the published catalog value by 5700 (Taylor et
al. 1995). No signal is present at either position.
152
Figure 6-2 ASCA images of the PSR B1610−50 field: flat-fielded images of the region
around the pulsar, whose location is marked by the cross. The dashed rectangle
represents the SIS FOV, and the contours, corresponding to 0.04, 0.18, 0.31, 0.44, 0.57,
and 0.70 Jy beam−1 , are from 843 MHz MOST observations of the supernova remnant
Kes 32. Top left: The broad band (0.8 − 12 keV) GIS image of the PSR B1046−58
field. Scattered emission from the nearby supernova remnant RCW 103 is responsible
for the large flux gradient that begins in the southeast FOV and extends to th edge
of the SIS FOV. Top right: The hard band (2 − 12 keV) GIS image shows enhanced
emission that traces the radio emission from Kes 32. No significant flux is seen from
the pulsar location. The previously known Einstein source 2E 1611.1−5018 is visible
at the top of the FOV, while an unidentified source is located approximately due
south of the pulsar position. Bottom left: The soft band (0.8 − 2 keV) GIS image
explicitly shows the extent of the scattered emission from RCW 103. Note the distinct
lack of emission from Kes 32. Bottom right: The hard band (2 − 10 keV) SIS image
similarly shows the correspondence between the radio contours and X-ray emission
and no emission from PSR B1610−50. Count rates are in units of 10−5 cps pixel−1
for the GIS and 10−6 cps pixel−1 for the SIS.
153
We again ignore the complexities of the PSF and search for emission from the
pulsar by comparing the number of photons collected from an (optimal) 40 diameter
aperture centered on the radio location and with those collected from a 60 − 110 diameter concentric annulus. By restricting our search to E > 2 keV, we greatly decrease
the amount of scattered emission from RCW 103. Our choice of background annulus
avoids emission from Kes 32 and roughly contains the same amount of scattered flux
as the source aperture region, allowing a reliable significance calculation. No emission was detected by either the GIS or SIS, and the combined detection significance
is below 2σ.
As first noted by Kawai et al. (1998), the ASCA observation provides the first Xray detection of the supernova remnant Kes 32. The low statistics prevent a detailed
comparison of the X-ray emission with the elongated, shell-like radio morphology. To
first order, the X-ray flux traces the radio intensity particularly along the western rim,
as is evident in both the SIS and GIS images. The absence of X-ray emission from the
direction of PSR B1610−50 contradicts a previous report of a large nebula powered
by the pulsar (Kawai, Tamura, & Saito 1998). Contamination from the scattered
RCW 103 emission and effects of smoothing with a function larger than the size of
the ASCA PSF (see the discussion in §6.4.1) can account for the discrepancy.
Two additional sources are also present in the GIS data. At the top of the GIS
FOV, the Einstein source 2E 1611.1−5018, a low-mass X-ray binary with J2000 coordinates α(2000) = 16h 14m 54s , δ(2000) = −50◦ 260 2100 , is clearly visible. This source
is detected in both the hard and soft bands and was also detected by ROSAT. The
second source, located south of the pulsar position and just outside the SIS FOV, is
only seen above 2 keV. Data from both GIS detectors provide a 4.1σ detection (47
background-subtracted counts). Its J2000 coordinates are α(2000) = 16h 14m 18s ,
δ(2000) = −50◦ 560 4300 , with a position uncertainty of ∼10 . The source-like enhancements along the south-eastern edge of the GIS FOV result from scattered flux from
RCW 103 and image processing artifacts.
154
6.5.2
Flux Estimation
The non-detection of PSR B1610−50 can be used to place an upper limit on the flux
from the pulsar. Starting with the observed background rates6 of 8.2 × 10−3 cps,
we derive a 3σ upper limit on the pulsar’s count rate. We restrict our analysis to
the GIS data, as these have a larger field of view for background estimation. We
again use the canonical synchrotron nebula spectral model to estimate the flux and
constrain the column density following the approach taken in §6.4.2. We adopt a
value of NH = 2 × 1022 cm−2, consistent with the Seward & Wang estimate and the
Dickey & Lockman upper limit. After folding the spectrum through the appropriate
instrument response (GIS+XRT), we calculate a 3σ upper limit to the unabsorbed
2 − 10 keV flux of 1.5 × 10−13 ergs cm−2 s−1 .
6.6
Discussion
The importance of the detection of weak emission from PSR B1046−58 and the
non-detection of PSR B1610−50 is most readily understandable in the context of
the growing body of work on the X-ray properties of young (τc < 105 yr) rotationpowered neutron stars. More than twenty of these objects have been detected, with
three distinct physical processes responsible for the observed X-ray flux. As discussed
earlier, these are thermal emission (either pulsed or unpulsed), pulsed magnetospheric
emission, or emission from a synchrotron nebula (or plerion).
6.6.1
PSR B1046−58
For an age of 20 kyr, cooling models (see, e.g., Ögelman 1995) predict thermal
emission from PSR B1046−58 to have an effective surface temperature of at most
kT ≈ 120 eV and a maximum bolometric luminosity of 2.3 × 1033 ergs s−1 . Assuming
a 10 km neutron star radius, a 3 kpc distance and NH ≈ 5 × 1021 cm−2, we find that
6
The background count rate is for an extraction region of radius 20 .
155
the ASCA count rates should be no higher than 8 × 10−3 cps (SIS) and 2 × 10−3
cps (GIS). While these rates are comparable to the observed rates from the pulsar
direction (refer to Table 6-3), the predicted count rate should fall to undetectable
levels above 1.5 keV, in contradiction with the observations. Thus, cooling thermal
emission cannot produce the observed flux from PSR B1046−58.
The apparently hard spectrum of the radiation suggests a non-thermal origin,
either from the magnetosphere or from a synchrotron nebula. Magnetospheric emission is strongly pulsed, and given the upper limits on pulsations from the GIS data, it
is extremely unlikely that magnetospheric emission contributes any significant fraction of the flux. Deeper observations could reveal pulsations arising from either the
magnetosphere or the modulation of thermal, surface emission.
The most probable source of emission is synchrotron radiation powered by a relativistic pulsar wind. The most famous pulsar wind nebula surrounds the Crab pulsar
(Rees & Gunn 1974; Kennel & Coroniti 1984; Emmering & Chevalier 1987; Gallant &
Arons 1994). In pulsar wind nebulae, the wind of relativistic electrons and positrons
(and possibly heavy ions, Hoshino et al. 1992) are confined, accelerated at the reverse
shock, and radiate synchrotron emission. Using the flux range calculated in § 6.4.2
the 2 − 10 keV luminosity is Lx = (2.7 ± 0.3) × 1032 d23.0 ergs s−1 , where d3.0 is the
distance in units of 3.0 kpc. The conversion efficiency of the spin-down luminosity
Ė into ASCA-band emission is = (1.3 ± 0.1) × 10−4 .
The ∼30 broad wings of the ASCA PSF severely limit detailed morphological
studies of the synchrotron nebula. As the emission appears consistent with a point
source, we can place a conservative 30 diameter upper limit on its angular extent.
The limited spectral resolution also prevents us from considering whether the faint
extended emission surrounding the four SIS sources could be the supernova remnant
associated with PSR B1046−58, a reasonable speculation given the pulsar’s apparent
youth. Ultimately, the nature of the extended emission and its possible relation
to PSR B1046−58 will only be resolved through observations with sufficiently high
spatial and spectral resolution that would, for example, allow the detection of emission
156
line features commonly found in other young supernova remnants.
6.6.2
3EG J1048−5840
On a list ranked by Ė/d2 , a parameter that has proven to be an excellent indicator
of γ-ray detectability, PSR B1046−58 is the ninth, with six of the eight sources
higher being γ-ray pulsars. PSR B1046−58 thus represents an excellent candidate
for observable high-energy γ-ray emission. Indeed, in a companion paper, Kaspi et
al. (2000) suggest an association between PSR B1046−58 and the unidentified high
energy γ-ray source 3EG J1048−5840 based on the detection of significant pulsations
from the γ-ray source at the radio pulsar period.
Identifying X-ray counterparts to unidentified EGRET sources is a useful way of
significantly reducing the uncertainty in the position of the γ-ray source, on the assumption that the source spectrum extends into the X-ray band, true for both blazars
and pulsars (e.g., Kubo et al. 1998; Becker & Trümper 1997). In Figure 6-1 (top left),
we show the 95% and 99% confidence spatial contours of 3EG J1048−5840 overlayed
on the broad-band GIS image (R. Hartman, personal communication). Fortunately,
the archival ASCA observation covers the entire γ-ray error box. The three detected
ASCA sources discussed above (§3.1) are the only significant X-ray sources in the
field; one or more of them is therefore probably the source of the γ-ray emission.
The ASCA source nearest (within the 95% contour) the best-fit 3EG J1048−5840
position is Src 1, which we have identified with PSR B1046−58. It therefore represents the most likely counterpart to 3EG J1048−5840, and supports the evidence
presented by Kaspi et al. (2000). Src 2, outside the 95% contour but within the 99%
region, was shown (§3.2) to have a soft spectrum, hence is unlikely to be the γ-ray
source counterpart. The unidentified hard-spectrum Src 3 lies well outside the 95%
contour but just within the 99% contour, so we cannot formally preclude its being
the counterpart. However, were it the counterpart, it would most likely have to be
a second young, energetic pulsar in the field, as it has no obvious radio counterpart,
hence cannot be a blazar, since all known γ-ray emitting blazars are bright radio
157
sources ((Mattox et al. 1997)).
6.6.3
PSR B1610−50
The non-detection of PSR B1610−50 obviously prevents a study of the emission
characteristics of the pulsar. However, derived upper limits are important for studying and understanding the X-ray properties of young rotation powered pulsars as a
population, particularly given this pulsar’s place in age-space between the youngest
Crab-like pulsars and the older Vela-like pulsars.
At an age τ = 7.4 kyr, the Ögelman (1995) cooling model predicts thermal emission from the surface of the neutron star with a characteristic temperature kT ≈ 130
eV. With the large column density towards the pulsar and its distance, though, the
absorbed flux in the 2 − 10 keV band would be Fx = 2.1 × 10−17 ergs s−1 cm−2,
orders of magnitude below the ASCA detectability threshold. Pulsed magnetospheric
emission is also expected to be present, given that pulsars with similar Ė exhibit
pulsed non-thermal emission. However, as the total flux in the pulsed radiation is
usually less than that from a synchrotron nebula, we only used the non-thermal X-ray
emission expected from the nebula in our calculation of an upper flux limit in §3.3.
For a flux limit Fx < 1.5 × 10−13 ergs s−1 cm−2 and a distance of 7.3 kpc, the 2 − 10
keV luminosity is Lx < 9.6 × 1032 d27.3 ergs s−1 . The conversion efficiency of the
spin-down luminosity Ė into ASCA-band emission is < 6.1 × 10−4 .
If we assume that PSR B1610−50 has an X-ray emitting synchrotron nebula,
it is likely to be confined by ram pressure, as there is no evidence from X-ray or
radio observations of a confining shell (i.e. SNR) around the pulsar (Green 1998).
Relying on the work of Arons & Tavani (1993) and others, Gotthelf & Kaspi (1998 and
references therein) show that the cooling efficiency for relativistic pairs of positrons
and electrons is:
≡
σ
ρ
v
γ
tf
= 3.6 × 10−4 (
)(
)1/2(
)( 8 ),
−1
ts
0.005 1 H atom
100 km s
10
158
(6.10)
where tf and ts are the time scales for the pulsar wind flow and synchrotron cooling, σ
is the ratio of magnetic energy flux to the kinetic energy flux of the wind (σ ≈ 0.005 for
the Crab pulsar, Kennel & Coroniti 1984) , ρ is the ambient density, v is the pulsar’s
velocity, and γ is the post-shock pair Lorentz factor. (Thompson et al. 1995). The
bolometric luminosity in synchrotron emission for the highest energy pairs is Ls ≈ Ė.
If PSR B1610−50 has wind properties similar to the Crab pulsar, the velocity must
be . 170 km s−1 given the absence of X-ray emission. This velocity is inconsistent
with an association between the pulsar and Kes 32. Unless the pulsar resides in an
extremely underdense region, i.e. ρ . 5.4 × 10−3 cm−3 , or has very different wind
properties compared to the Crab pulsar, PSR B1610−50 does not have the transverse
velocity suggested by Caraveo (1993).
6.6.4
Lx − Ė Relationships
The luminosity measured for PSR B1046−58 and the upper limit derived for PSR
B1046−58 can be considered within the context of two previously determined empirical correlations between spin down luminosity Ė and X-ray luminosity Lx : the Seward
& Wang (1988) relationship (hereafter SW88) derived from Einstein data (0.2 − 4.0
keV band), log Lx = 1.39 log Ė − 16.6, and the Becker & Trümper (1997) relationship
(hereafter BT97) derived from ROSAT data (0.1 − 2.4 keV band), Lx = 10−3 Ė. To
estimate the scatter associated with these models, we have computed the root mean
square (RMS), defined here to be the square root of the variance, using the data
presented by the authors in their papers. For the Einstein model, the RMS scatter
is a factor of ∼7, while for the ROSAT model, the RMS scatter is a factor of ∼4.
33
For PSR B1046−58, SW88 predicts 7.2 51
ergs s−1 , compared to the observed
1.0 × 10
33
(5.0±0.5)×1032 ergs s−1 , while BT97 predicts 2.0 8.0
0.5 ×10 , compared to the observed
(5.3 ± 0.5) × 1032 ergs s−1 . In both cases, the relationships overestimate Lx by factors
33
−1
of at least several. For PSR B1610−50, SW88 predicts 5.3 37
0.8 ×10 ergs s , compared
33
with the derived upper-limit 1.3 × 1033 ergs s−1 , while BT97 predicts 1.6 6.4
0.4 × 10 ,
compared with the derived upper-limit 1.4×1033 ergs s−1 . For this pulsar, the derived
159
upper-limits lie within the range of predicted values.
One possible source of error is the distance derived from the Taylor & Cordes
(1993) DM-d model. Distances are uncertain to ∼25−50%, translating to a potential
error as a large as a factor of ∼3 when converting flux to luminosity. Increasing
the distance by ∼25−50% leads to a corresponding increase in Lx and helps improve
the agreement between model and observation. The discrepancies between model
and observation also suggests that the current Lx − Ė relationships, while certainly
illustrating a correlation between spin-down and X-ray luminosity, may overlook important factors like the pulsar’s velocity or the ISM conditions in its vicinity.
160
Chapter 7
The New Pulsar-Supernova Remnant
System PSR J1119−6127 and SNR
G292.2−0.54
7.1
Introduction
PSR J1119−6127 was discovered by Camilo et al. (2000) in an on-going survey of the
Galactic plane at the Parkes 64−m radio telescope in Parkes, Australia (Lyne et al.
2000). While its period of 0.4 s is relatively long compared to that of the young Crablike pulsars, its period derivative of 4 × 10−12 is the largest of any known radio pulsar.
The characteristic age, calculated from these spin parameters, is τc ≡ P/2Ṗ = 1600 yr
(see Equation 6.9), third youngest among any pulsars. In addition to its extreme
youth, PSR J1119−6127 also has an extremely large inferred surface magnetic field
of B ≡ 3.2 × 1019 (P Ṗ )1/2 G = 4 × 1013 G (see Equation 6.5), ranking second among
all known rotation-powered pulsars.
PSR J1119−6127 is also noteworthy as it is one of only a few pulsars that has an
accurately measured second period derivative P̈ , which allows determination of the
braking index n ≡ ν ν̈/ν̇ 2 = 2 − (P P̈ /Ṗ 2 ) (see Equation 6.7). Even more important is
that the value of n = 2.91(5) makes PSR J1119−6127 the neutron star with a braking
161
index closest to three, the value expected if a pulsar spins down via magnetic dipole
braking. In many ways, PSR J1119−6127 is similar to PSR B1509−58, another longperiod young pulsar for which n is measured. Table 7-1 presents the spin parameters
and derived quantities for both of these pulsars. In the same way that the discovery
of PSR B0540−69, taken with the Crab pulsar, established the existence of a class of
fast, young pulsars with large spin-down luminosities, PSR J1119−6127 suggests that
PSR B1509−58 is also the archetypical member of a class of young, high-magnetic
field pulsars with periods of hundreds of milliseconds.
After the pulsar’s discovery, relevant publicly accessible data archives were searched
for observations with PSR J1119−6127 in their field of view. A Galactic survey performed with the Molonglo Observatory Synthesis Telescope (MOST) at 843 MHz
revealed a faint ring-like shell, ∼140 in extent and approximately centered on the
position of the pulsar. A brief ROSAT PSPC observation shows X-ray emission coincident with a portion of the radio shell. Recently, radio interferometric observations of
PSR J1119−6127 and its vicinity have been made with the Australia Telescope Compact Array (ATCA) at several frequencies (Crawford 2000; Crawford et al. 2000).
These data not only confirm the existence of the shell-like emission, but have a spectral index consistent with that of all other known SNRs. These multi-wavelength data
clearly prove the existence of a SNR, and taken together with the prospect of detecting emission from the pulsar, warrant a deep X-ray observation. Below, we present
detailed analysis of both the pointed ASCA and serendipitous ROSAT observations.
7.2
Observations
ASCA (Tanaka, Inoue, & Holt 1994) observed PSR J1119−6127 during a 36 hour
period spanning 1999 August 14 − 15 as part of the AO−7 Guest Observer program
(sequence number 57040000). The mean MJD of this observation (51404.4) is just six
days after a glitch reported by Camilo et al. (2000). See § 7.3.2 for more details. To
achieve the time resolution necessary for pulsation searches, the GIS (Gas Imaging
162
Table 7-1. Astrometric and spin parameters for PSRs J1119−6127 and B1509−58.
Parameter
PSR J1119−6127
Right ascension (J2000)
Declination (J2000)
Period, P (ms)
Period derivative, Ṗ
Second period derivative, P̈
Epoch of period (MJD)
Braking index, n
Dispersion measure, DM (pc cm−3)
Characteristic age, τc (yr)
Spin-down luminosity, Ė (ergs s−1 )
Magnetic field, B (G)
11 19 14.30
−61 27 48.5
407.64
4.023 × 10−12
3.59 × 10−23
51398
2.91 ± 0.01
707
1606
2.34 × 1036
4.1 × 1013
PSR B1509−58
16 15 55.62
−59 08 09.0
150.66
1.537 × 10−12
1.31 × 10−23
48355.00
2.837 ± 0.001
253
1554
1.77 × 1037
1.5 × 1013
Note. — Information for PSR B1509−58 is taken from Kaspi et al.
(1994), that for PSR J1119−6127 is taken from Camilo et al. (2000).
163
Spectrometer) was operated in a slightly non-standard mode. Time resolution of
0.488 ms or 3.91 ms (depending on the telemetry rate) was achieved by sacrificing
information about the time characteristics (or “Risetime”) of detected events, one
way to differentiate between background and celestial X-ray photons. (See §7.3.1 for
a discussion on the ramifications of this operation mode.)
The SIS (Solid-state Imaging Spectrometer) can be operated in one-, two-, or fourchip mode, with a corresponding field of view (FOV) of 110 × 110 , 110 × 220 , or 220 × 220
and time resolution of 4 s, 8 s or 16 s. Given the extent of the radio shell, fourchip mode with its large FOV would have been the ideal operation mode. However,
after more than six years in the harsh radiation environment of a low-Earth orbit,
the SIS detectors have degraded significantly. Longer integration times result in the
accumulation of large amounts of dark current, greatly reducing spectral resolution.
As a compromise between achieving a FOV wide enough to encompass a large
fraction of the shell and obtaining potentially useful spectroscopic information from
the CCDs, the SIS was operated in two-chip mode. As for PSRs B1046−58 and
B1610−50 (see Chapter 6), the data were analyzed using the standard (i.e. REV 2)
screening criteria suggested in the The ASCA Data Reduction Guide.1 The resulting
effective exposure times for each type of detector are 37 ks (GIS) and 34 ks (SIS).
ROSAT (Trümper 1983) serendipitously observed the field around PSR J1119−6127
with the Position Sensitive Proportional Counter (PSPC) on 1996 August 14 during
an 11 ks pointed observation of NGC 3603 (sequence number RP900526N00). After retrieving the data from the NASA-maintained HEASARC archive, we used the
already-processed and filtered data for our subsequent analysis. PSR J1119−6127 is
located 310 away from the optical axis, and due to vignetting and obscuration from
the mirror support structure, the effective exposure time for a 150 diameter circle
centered on the pulsar is between 6.4 − 8.9 ks.
1
http://legacy.gsfc.nasa.gov/docs/asca/abc/abc.html.
164
7.3
7.3.1
Data Reduction
Image Analysis
ASCA
Flat-fielded images are generated by aligning and co-adding exposure-corrected images from pairs of instruments. First, exposure maps were generated with the FTOOL
ascaexpo, software that incorporates the satellite aspect solution and instrument information (i.e. GIS grid structure and SIS chip alignment and hot-pixel lists) to calculate the exposure time for each sky image pixel. The possibility of detecting extended
emission coincident with the radio shell makes folding detector effects accurately into
this procedure crucial. This is particularly relevant for the GIS, as removing artifacts
from the window support grid and the X-ray background are the only way to detect
low surface brightness features. The recently released FTOOL mkgisbgd2 can be used
for generating a reliable GIS map.
Unfortunately, this software relies upon input data that were screened using Risetime information, making it inappropriate for our observation. To remedy this datatype mismatch, we have undertaken re-analysis of the 2.1 Msec of archival data that
mkgisbgd uses. The data sets consists of all high latitude GIS observations taken between 1993 June and 1995 December. Using the masks generated by Ishisaki (1997) ,
all sources brighter than 2 × 10−13 ergs s−1 cm−2 are subtracted from the field of view.
Then, the data were analyzed using the standard REV 2 criteria, omitting the step dependent on the Risetime parameter. Finally, these appropriately-screened data were
used with mkgisbgd to generate detector maps valid for our observations. Refer to
the HEASARC web site2 for additional details.
Next, the SIS data are rebinned by a factor of 4 (6.0 73 pixel−1) and data from
both instruments are smoothed with a kernel representing the point spread function
(PSF) of the X-ray telescope (XRT) and detector combination. We approximate this
2
http://heasarc.gsfc.nasa.gov/docs/asca/mkgisbgd/mkgisbgd.html
165
function with a Gaussian of σ = 3000 for the SIS and σ = 4500 for the GIS. Finally,
we correct the astrometric position of the smoothed images for known errors in the
pointing solution using the FTOOL offsetcoord3.
Figure 7-1 shows the resultant images for both the GIS (left) and SIS (right).
X-ray events were filtered by energy to make images in three different bands: broad
(0.8− 10.0 keV [top]), soft (0.8− 3.0 keV [middle]), and hard (3.0− 10.0 keV [bottom]).
The color scale for each plot indicates the count rate in units of counts s−1 arcmin−2.
In each plot, the radio position of PSR J1119−6127 is marked by a cross. Each plot
also displays the contours from the recent 20 cm ATCA radio observations (Crawford
2000; Crawford et al. 2000) of the field around the pulsar. Contour levels span from
10% to 90% of maximum (7.1 mJy beam−1 ) in increments of 10%. Both instruments
show significant emission from a nearly-circular region that roughly matches the radio
SNR morphology. On the basis of this and other evidence presented below, we classify
this extended emission as the previously unidentified X-ray bright supernova remnant
G292.2−0.54. The right (western) side of the SNR exhibits marked enhancements in
X-ray flux at energies below 3 keV, while at higher energies the emission is relatively
uniform throughout the entire SNR.
In addition to the X-ray bright SNR, the GIS shows evidence for a hard point-like
source in the middle of G292.2−0.54. To estimate the significance of this detection,
we compare the number of photons detected in a small aperture centered on the
source with those from a concentric annulus, used to estimate the local background.
Since the broad wings of the GIS+XRT PSF has extent of ∼40, ideally the source
aperture would be of similar size, and the background annulus would have large inner
and outer radii (e.g, 50 and 90 ). However, in our case the source is embedded in
non-uniform diffuse emission, greatly complicating the analysis. As a compromise,
we use a source aperture of radius 2.0 5 and a background annulus with radii 3.025
and 5.0 0, realizing that the derived detection significance σ will only provide a lower
3
For a full description of this procedure and the specific parameters used, refer to
http://heasarc.gsfc.nasa.gov/docs/asca/coord/updatecoord.html.
166
Figure 7-1 ASCA images of the field around PSR J1119−6127. Images are from the GIS
(left) and from the SIS (right). Images for three separate energy bands are shown in each
row: broad-band (0.8 − 10 keV [top]), soft-band (0.8 − 3.0 keV [middle]), and hard-band
(3.0 − 10 keV [bottom]). In each image, the location of PSR J1119−6127 is marked by
a cross. The contours are from 20 cm ATCA observations and range from 10% to 90%
of the maximum value (0.7 mJy beam−1 ) in increments of 10%. The color bars in each
plot indicate counts sec−1 arcmin−2. The X-ray emission, classified here as the previously
unknown SNR G292.2−0.54, roughly traces the radio morphology in the broad- and hardbands, although significant enhancement is seen on the western (right) side of the SNR
below 3 keV. A hard point-like source is clearly
167 evident in the GIS image.
limit to the source strength. Using the signal-to-noise ratio defined in Appendix D,
we calculate a significance of σ & 4.0 for the 158 background-subtracted photons
detected with energies between 3 − 10 keV. To explore the possibility that the source
is an instrumental artifact, we examined individual images from GIS–2 and GIS–3.
Emission is present in both detectors at the above position, verifying the celestial
nature of the source.
No point-like source is seen in the hard-band SIS image, although there is enhanced
emission at the source position derived from the GIS data. Using aperture and annulus
radii (2.00, 3.025, and 4.05, respectively) appropriate for the smaller SIS+XRT PSF, we
calculate a significance of σ & 3.5 for the 59 background-subtracted photons detected
between 3 − 10 keV. The lack of a strong point-like feature in the SIS when one is
present in the GIS is not uncommon and results from instrumental effects, including
the larger effective area of the GIS (Gotthelf, private communication).
Fitting a two-dimensional Gaussian to the GIS source distribution, we measure a
position of α (J2000) = 11h 19m 4.s 5, δ (J2000) = −61◦ 280 3200 with a formal positional
uncertainty of ∼1000 . We classify this source as AX J1119.1−6128.5. The absolute
pointing uncertainty of ASCA, after making the known corrections mentioned above,
has an error radius of 3000 at the 90% confidence level (Gotthelf et al. 2000). The
source is located 8200 away from PSR J1119−6127, more than twice as large as the
combined positional errors. However, we note that in at least one documented case,
the ASCA-measured position of a source was 8000 from the well-established position
(Gotthelf et al. 2000). Thus, while the offset of the GIS source from the pulsar is
larger than expected, it does not preclude the possibility that the source is the X-ray
counterpart of PSR J1119−6127, especially if other evidence supports the association.
ROSAT
Analysis of the ROSAT data is easier, as there is only data from a single camera
(PSPC-B). We use the FTOOL pcexmap to generate an exposure map that accounts
for instrumental effects and telescope vignetting. The exposure map was rebinned
168
by a factor of 2 (150 pixel−1) and used to produce flat-fielded images in the standard
ROSAT soft (0.1 − 0.4 keV) and hard (0.5 − 2.0 keV) bands. X-ray events extracted
within a 70 radius from PSR J1119−6127 were used as input to the FTOOL pcrpsf to
estimate the PSF of mirror+PSPC combination, which is well-described by a Gaussian
with width σ = 1.04. The flat-fielded images were then smoothed with a slightly
smaller Gaussian (σ = 1.025) to ensure that any small-scale features in the images
would be real.
Figure 7-2 shows the resultant images for the soft (left) and hard (right) bands.
Just as the case with the ASCA data, a cross marks the position of PSR J1119−6127
and the contours are from the ATCA observations (Crawford 2000; Crawford et al.
2000). No emission from the SNR is detected in the soft band. However, in the hard
band, emission coincident with western side of the radio shell is strongly detected.
No X-rays are detected from the pulsar in either band. The morphology of the hard
ROSAT band (0.5 − 2.0 keV; Figure 7-2 [right]) agrees very well with that of the soft
GIS band (0.7 − 3.0 keV; Figure 7-1 [middle left]).
The agreement between the two telescopes offers the chance to check the absolute pointing of ASCA. Due to its large FOV (2◦ in diameter) and its soft-energy
sensitivity, the PSPC usually detects emission from several nearby stars in any given
pointing. The positions of well-resolved point-sources were checked for optical counter
parts using the SIMBAD catalog.4 Four bright stars were found, and the mean offset
between the optical and X-ray positions is 1800 . Thus, we take the absolute position
uncertainty of these PSPC data to be 1800 . Next, we cross-correlated the morphology
between the PSPC and GIS data. Unfortunately, the ∼arc-minute spatial resolution
of both images, combined with the different responses of both instruments, makes
a detailed alignment check impossible. While an offset of more than ∼10 between
the ASCA and ROSAT observations can be ruled out, this does not represent an
improvement to the ASCA uncertainty of 0.05 already discussed.
4
http://cdsweb.u-strasbg.fr/Simbad.html.
169
Figure 7-2 ROSAT PSPC images of the field around PSR J1119−6127. In each image, the location of PSR J1119−6127 is marked by a cross. The contours are from
20 cm ATCA radio observations and range from 10% to 90% of the maximum value
(0.7 mJy beam−1 ) in increments of 10% (Crawford 2000; Crawford et al. 2000).
The color bars in each plot indicate counts sec−1 arcmin−2 . Left: The soft-band
(0.1 − 0.4 keV) image shows no emission coincident with either the radio contours or
the pulsar. Right: The hard-band (0.5 − 2.0 keV) image clearly shows emission from
the western side of the SNR and has the same morphology and intensity distribution as the soft-band GIS image (Figure 7-1 [middle left]). No X-ray counterpart to
PSR J1119−6127is visible.
7.3.2
Timing Analysis
Pulsations from PSR J1119−6127 were searched for by extracting events from a
circular region centered on the position of AX J1119.1−6128.5. After the arrival
times were bary centered using the FTOOL timeconv, the data were folded into ten
phase bins using the post-glitch radio ephemeris corresponding to the mean MJD of
the ASCA observation. Here, the rotational phase of the pulsar is described by
1
1
φ(T ) = νT + ν̇T 2 + ν̈T 3 + . . . ,
2
6
(7.1)
where T denotes the pulsar proper time.
The ASCA observation of PSR J1119−6127 occured very close to the time the pulsar glitched (Camilo et al. 2000). Although the X-ray data was apparantly taken after
170
the glitch, the timing data discussed by Camilo et al. (2000) cannont exactly contrain
the date of the glitch. Hence, the possibility exists that the pre-glitch ephemeris is
the appropriate one to use for the folding. However, given the small differences in the
pre- and post-glitch values of ν and ν̇ and the total length T of the observation, the
difference in phase is ∆φ = 1 × 10−3 . The results are thus insensitive to the actual
date of the glitch.
The emission from G292.2−0.54 significantly contaminates the signal from AX
J1119.5–6128.5 and could prevent the detection of X-ray pulsations from PSR J1119–
6127. To minimize this possibility, we extracted data using combinations of four
different aperture radii (ranging between 20 and 50 in increments of one arcmin) and
twelve different energy bands (e.g., 0.8− 10 keV and 1− 5 keV). Because the SNR and
putative pulsar emission have different spectral and spatial properties, one combination of selection criteria should have the highest sensitivity for detecting pulsations.
Given the limited statistics of the observation, there is no way to a priori determine
the appropriate combination of aperture size and energy band. Instead, all resultant
pulse profiles were searched for pulsations using both the H-test (de Jager 1994) and
χ2 (Leahy et al. 1983) to search for significance. No pulsation was found in any of
the data sets. We derive an upper limit on pulsations by injecting a pulsed signal
with duty cycle of 50% into the list of arrival times. Accounting for the background
contribution to the total number of counts (see §7.3.1), we adjust the strength of the
signal until it is detectable at a significance of 3σ. The upper limits from folding
3 − 10 keV photons within a 30 radius of AX J1119.1−6128.5 are typical of all the
values. For the ∼170 background-subtracted counts (∼650 counts in total), the 3σ
upper limit on pulsations for a 50% duty cycle is greater than 50%.
7.3.3
Spectral Analysis
We restrict our spectral work to only the ASCA GIS and ROSAT PSPC data. We
define regions where it is appropriate to sum counts together and construct a single
spectrum for a given area. One such region is the western side of the SNR, bright in
171
soft X-rays. We extract a spectrum for both the GIS and PSPC from an ellipse 170 ×70
in extent, with major axis parallel to lines of constant right ascension and centered in
the middle of the bright SNR emission. A natural complement to this spectrum is one
drawn from the eastern side of the G292.2−0.54. Here, only the GIS, with its highenergy (i.e. E > 2 keV) sensitivity, can provide spectroscopic information. In this
case, the spectrum is drawn from a crescent-shaped region, slightly larger than the
radio shell and excluding the point-source and the western side. Figure 7-3 displays
the broad-band GIS (left) and hard-band PSPC (right) images, with the spectrum
areas indicated. We also extract a GIS spectrum for the point source from a circular
region with radius of 2.05, also shown in Figure 7-3 (left).
Figure 7-3 Broad-band GIS image (left) and hard-band PSPC image (right) around
PSR J1119−6127. The position of PSR J1119−6127 is marked by a cross. The black
ellipse indicates the region used to extract the “Western side” spectrum, while the
crescent-shaped region defined by the largest circle and the partial ellipse indicates
that used to extract the “Eastern side” spectrum. The smaller concentric circles
indicate the regions used to extract the spectrum of the point source. The inner-most
circle defines the source region, while the outer two circles define the background
annulus.
172
G292.2−0.54
The large PSFs of both ASCA and ROSAT results in a contamination of the source
flux with diffuse X-ray background (XRB) as well as emission from the SNR. This
requires a background spectrum, describing the non-source contribution, to be subtracted from the data to ensure a reliable fit. Ideally, the background should be taken
from a nearby region that is source free and located at the same off-axis angle, which
not only accounts for the XRB but for any local diffuse emission, always a possibility
when looking in the Galactic plane. While this task is trivial for the PSPC and its
2◦ FOV, the situation is more complicated for the GIS.
While more than 50% of the GIS FOV is unoccupied by G292.2−0.54, this region
is not appropriate for extracting a background, as the broad wings and scattering
properties of the XRT result in reflection properties that are strongly dependent on
both incident energy and off-axis angle (see, e.g., Gendreau 1995). Instead, we use the
FTOOL mkgisbgd and the 2.1 Msec of high-latitude data rescreened without using the
Risetime parameter (see §7.3.1 for details). In addition to producing a background
spectrum with high fidelity (e.g. between 200 − 3000 counts in each GIS channel
for the Eastern region), this method inherently accounts for instrument background,
as the background events are selected from exactly the same portion of GIS used in
extracting the source spectrum. The only potential difficulty with this technique is
if local emission is present, specifically in the form of Galactic ridge emission (e.g.
Kaneda et al. 1997). However, studies with Exosat show that such emission rapidly
decreases for Galactic longitudes |l| < 40◦ (Warwick et al. 1985). For the region
around PSR J1119−6127 (l = 292◦ ), no such component should be present.
Once we generated source and background spectra, response functions (detector
energy redistribution matrices) were retrieved from HEASARC and ancillary response
functions (ARFs; matrices that contain information about the effective area of the
mirror and quantum efficiency of the detector) were generated using the FTOOLS
ascaarf and pcarf. Initially, we treated the two sides of the G292.2−0.54 separately,
jointly fitting the three data sets from the Western Side (GIS-2, GIS-3, and PSPC) and
173
then independently fitting the two data sets from the Eastern Side (GIS-2 and GIS3). However, it became clear that regardless of the model used, the only difference
between the fit parameters from the two sides (after scaling for differences in sky
areas) is in column density NH .
In light of this information, we simultaneously fit all five data sets to a single
spectral model. Free parameters are two values of NH (one for each side), the spectral
characterization (e.g. temperature for a plasma model), and three normalization
values, two for the Western Side (GIS-2+GIS-3 and PSPC) and one for the Eastern
Side (GIS-2+GIS-3). The energy range fit is restricted to those bands where the signal
is statistically significant: 0.4 − 2.0 keV (PSPC), 0.7 − 7.0 keV (GIS-Western Side),
0.7 − 8.0 (GIS-Eastern Side). Data were then rebinned such that each backgroundsubtracted energy bin had a minimum of 20 counts, allowing us to use the χ2 statistic
as our goodness-of-fit estimator. All fitting is performed with XSPEC v.10.0 (Arnaud
1996) using standard models.
A search of the literature finds a bevy of different models to characterize emission
from SNRs. Here, we use a thermal bremsstrahlung model and the MEKAL5 plasma
model as representative thermal spectra and a simple power-law to explore nonthermal models. Elemental abundances have been frozen at the values determined
by Anders & Grevesse (1989). Table 7-2 lists the results of our fits, including derived
parameters and their 90% confidence limits. The measured absorbed fluxes for the
Western region are F 0.7−7
keV
= 2 × 10−12 ergs s−1 cm−2 (ASCA) and F 0.4−2
7 × 10−13 ergs s−1 cm−2 (ROSAT) and for the Eastern region is F 0.7−8
keV
keV
=
= 3×
10−12 ergs s−1 cm−2 (ASCA). Although the power-law model has the lowest χ2, the
F -test (see, e.g., Bevington & Robinson 1992) indicates that all three models describe
the data equally well. However, the rather large reduced χ2 values (χ2ν = 1.6 − 1.7)
indicate an inconsistency between the data and each model.
Figures 7-4 and 7-5 display spectra from different regions of G292.2−0.54, plot-
5
http://heasarc.gsfc.nasa.gov/docs/journal/meka6.html.
174
Table 7-2. Spectral fit parameters for SNR G292.2−0.5
Western Side
Norma
(10−3)
Normb
(10−3)
Eastern Side
NH
Norma
(1022 cm−2 )
(10−3)
kT
(keV)
Photon
Index
NH
(1022 cm−2 )
P.L.
···
2.3 ± 0.1
0.28+0.07
−0.06
0.97+0.13
−0.11
0.62+0.12
−0.11
1.6 ± 0.2
2.0+0.4
−0.3
332/211
T.B.
4.1+0.6
−0.5
···
0.11+0.05
−0.04
0.81+0.07
−0.06
0.51+0.09
−0.08
1.3 ± 0.2
1.6 ± 0.2
366/211
MEKAL
3.5+0.4
−0.3
···
0.16+0.06
−0.05
2.0 ± 0.1
1.3 ± 0.2
1.5 ± 0.2
4.2 ± 0.4
351/211
Model
a Parameter
for the ASCA (GIS2+GIS3) data.
b Parameter
for the ROSAT PSPC data.
χ2 /dof
Note. — P.L. refers to power law, T.B. to thermal bremsstrahlung. Norm refers to the normalization used
R for a particular model: power law–(photons keV−1 cm−2 s−1 ), thermal bremsstrahlung–((3.02 × 10−15 /(4πD2)) ne nI dV ),
R
or MEKAL–((10−15 /(4πD2 )) ne nH dV ).
All uncertainties represent the 90% confidence limits.
175
Figure 7-4 ASCA GIS and ROSAT PSPC spectra of G292.2−0.54. The solid lines
represent the best-fit MEKAL models for the data. The PSPC (top) and GIS (middle) spectra from the western side of the SNR are very soft compared to the highly
absorbed GIS spectrum (bottom) of the eastern side. Both the MEKAL and powerlaw spectral models describe the data equally well. The data in black are from GIS–2,
while the data in red are from GIS–3.
176
Figure 7-5 ASCA GIS and ROSAT PSPC spectra of G292.2−0.54. The solid lines
represent the best-fit power-law models for the data. The PSPC (top) and GIS
(middle) spectra from the western side of the SNR are very soft compared to the
highly absorbed GIS spectrum (bottom) of the eastern side. Both the MEKAL and
power-law spectral models describe the data equally well. The data in black are from
GIS–2, while the data in red are from GIS–3.
177
ted with the best-fit MEKAL and power-law models, respectively. For clarity, we
present the data for a given region and instrument separately: PSPC western side
(top), GIS western side (middle), GIS eastern side (bottom). The large χ2 is mainly
attributable to systematic errors in the fit, easily seen in the residuals below 2 keV
in the spectra from the western side and above 5 keV in the spectra from the eastern
side. Attempts to improve the fit by addition of a second spectral component do not
work for two reasons. First, while some of the excesses (i.e Model/Data > 1) appear
to be emission-like features, there are no known lines at these energies. (For the same
reason, adjusting the elemental abundances in the MEKAL model does not improve
the fit.) Second, although the approximately 1000 counts in each GIS spectrum and
the 500 counts in the PSPC spectrum allow a fairly tight constraint on a single model,
there is not sufficient data to fit a combination of two models. Inevitably, the best-fit
parameters for the additional component tend towards the limits of the parameter
space and resulted in unphysical values (i.e. normalizations of order 10−10 − 10−12 or
temperatures of only a few eV).
AX J1119.1−6128.5
A serious challenge in fitting the spectrum of the point source is the relatively low
number of source photons (173 background-subtracted counts between 0.7 − 5 keV).
Given that it is not detected with ROSAT nor in the soft-band of the GIS, this source
must either be intrinsicly hard (e.g., temperature of several to tens of keV) or highly
absorbed. With three times more events in the 2− 5 keV band than in the 0.7− 2 keV
band and very few events above 5 keV, either scenario is plausible.
Due to the limited statistics, it is impossible to fit the spectrum if all three parameters (NH , kT or Γ, and normalization) are allowed to vary. (The strong co-variance
between the parameters results in a degeneracy effectively the size of the entire phase
space.) Instead, we only require 10 background-subtracted counts per energy bin and
fix the column at NH = 1.5 × 1022 cm−2 , the value determined using the MEKAL
model for the eastern side of G292.2−0.54. While these modifications to the fitting
178
scheme, compared to those used for G292.2−0.54, introduce additional uncertainty,
it does allow at least a coarse characterization of the spectral nature of the point
source.
For a power-law model, the photon index is Γ = 1.4+1.0
−1.2 and the normalization
is (8 ± 8) × 10−5 . For a thermal bremsstrahlung model, the temperature is kT =
+0.9
−5
13+∞
−11 keV and the normalization is (1−0.3 )×10 . (Here, the upper limit on kT reflects
the lack of ASCA’s response above 10 keV. Refer to Table 7-2 for the normalization
units). The measured absorbed flux is F 0.7−5
keV
= 2 × 10−13 ergs s−1 cm−2 .
Our decision not to undertake analysis of the ASCA SIS data is motivated by
several factors. First, radiation damage has greatly reduced the performance of the
SIS. While the SIS initially had the best energy resolution of the three instruments,
at the time these data were acquired, this was no longer true. Second, reduction
of spectroscopic SIS data requires the use of several phenomenological models to
account for radiation-induced effects. Though these have proved useful, the lack of
an underlying physical model and unaccounted-for effects make any analysis suspect.
For example, Ueda et al. (1999) have found that the absolute detection efficiency of
the SIS, normalized to the GIS, decreased monotonically from 12% to 18% over an
18 month span they studied. Finally, the smaller FOV of the SIS only encompasses
∼60% of the SNR area, with a sizable fraction of the bright western region falling
off the CCDs. Hence, for this observation, the SIS cannot provide any additional
information not already present from analysis of the more reliable GIS and PSPC
data.
7.4
7.4.1
Discussion
General properties of G292.2−0.54
One of the main arguments supporting the interpretation of the extended emission
as an SNR is its correlation with the morphology of the radio shell, recently shown
to have radio spectral properties consistent with other known SNRs (Crawford 2000;
179
Crawford et al. 2000). The presence of PSR J1119−6127 in the middle of the radio
and X-ray emission not only strengthens this reasoning, it provides a way to test the
consistency of the claimed association. For if PSR J1119−6127 and G292.2−0.54 are
the remnants of the same supernova, the age of the SNR must be that of the pulsar
and its properties should be those of a young remnant.
It is common to estimate the pulsar’s age with the charateristic age τc . In most
circumstances, when τc is used there is a risk of greatly underestimating the pulsar’s
age, since τc → ∞ as n → 1 (see Equation 6.9). Fortunately, this is not a concern
for PSR J1119−6127 as the braking index is in fact measured to be 2.9 and τc =
1600 years. Of course, if the current spin period is still close to that of the initial
period, then τc will over-estimate the age of pulsar. Thus, ∼1600 yr represents a hard
upper limit.
Our next step is to determine the distance of the system. One such estimate
comes from the Taylor & Cordes (1993) DM-distance relationship. However, the
dispersion measure of PSR J1119−6127 (DM = 707 pc cm−3 ) implies a distance
of more than 30 kpc, well outside of the Galaxy! This spuriously large value is
easily understood, as the Galactic longitude of PSR J1119−6127 (l = 292◦ ) is nearly
tangential to the Carina spiral arm, intersecting it at distance of 2.4 and 8.0 kpc.
The best explanation for the large DM measured is that there must be clumping
of dense, dispersive material in the direction of the pulsar. The Taylor & Cordes
model, which lacks fine structure (i.e. small-scale clumps), simply underestimates
the electron density, and hence overestimate the distance, for this particular lineof-sight. Fortunately, a reasonable upper limit on the distance can be obtained by
assuming that PSR J1119−6127 lies no further than the second intersection point or
8 kpc. We also note that in this particular direction, the edge of the Galaxy only
extends ∼10 kpc from the Sun (Georgelin & Georgelin 1976; Taylor & Cordes 1993),
limiting the maximum error in the distance to 25%.
The diameter of G292.2−0.54 extends ∼140 in radio and ∼170 in X-rays. The
slightly larger extent in the X-rays may either be real or an artifact of the larger
180
PSFs of ASCA and ROSAT, compared to the ATCA beamsize. We adopt an angular
size of (15 ± 2)0 to encompass both measurements. Taken with the age and distance
estimates, we calculate a mean expansion velocity of v = (10 ± 1.4)D8 × 103 km s−1 ,
where D8 is the distance to the pulsar parameterized in units of 8 kpc. This velocity
is consistent for that of a 1600 yr old SNR still evolving in the free expansion phase.
It implies a kinetic energy for the initial explosion of E51 = (1 ± 0.3)Mej D82 , where
E51 is the explosion energy in units of 1051 ergs and Mej is the ejected mass in units
of solar masses M .
Of course, G292.2−0.54 may also be in the Sedov-Taylor (ST) phase. For adiabatic expansion, rSNR = 1.15(Et2 /ρ)1/5 (Taylor 1950; Sedov 1959), where rSNR is
the linear radius of the SNR, E is the explosion energy, t is the SNR’s age, and ρ is
the mass density. Using the measured size of the SNR and recasting in terms of the
ambient particle density n into which the SNR is expanding, (E51/n) = (130± 80)D85 .
Remnants only enter ST evolution after sweeping up 20 times their ejected mass Mej
(Fabian, Brinkmann, & Stewart 1983; Dohm-Palmer & Jones 1996). We approximate
the material swept up by the SNR by assuming a constant density ρ = nmH inside
the volume occupied by G292.2−0.54; this requires n > (0.04 ± 0.02)Mej D8−3 cm−3 .
Substituting into the expression determined for the ratio of explosion energy to particle density (E51/n) requires E51 > (5 ± 4)D82 Mej , where Mej is again expressed in
terms of solar masses M.
The implied ratio (E51/Mej ) is as much as one hundred times higher than those
found for most young Galactic SNRs (see, e.g., Smith 1988). We note that the
only other well-documented large value for (E51 /Mej ) is for G320.4−01.2, the SNR
associated with PSR B1509−58 (Gaensler et al. 1999 and references therein). This
correlation further strengthens the argument that PSR J1119−6127 belongs to a class
of pulsars typified by PSR B1509−58. It also raises the possibility that their unusual
properties (i.e. large magnetic field and rapid spin-down rate) may be partially explained by an common evolutionary scenario. For example, Gaensler et al. (1999)
suggest that the progenitor of PSR B1509−58 was a massive star that later evolved
181
into a helium star before it underwent a supernova.
7.4.2
X-ray properties of G292.2−0.54
Spectrum
At first, one of the most surprising aspects of the spectrum is the lack of obvious
line features commonly seen in young SNRs like Cas A (e.g., Hughes et al. 2000),
Tycho (Hwang & Gotthelf 1997), MSH 15−52 (e.g., Tamura et. al 1996), and Puppis A (Winkler et al. 1981; Berthiaume et al. 1994). However, from the MEKAL fits
(Figure 7-4), it is clear that after this line-rich spectrum is folded through the GIS
response, the only lines that should be visible are possibly the Fe K species around
6.7 keV. In fact, the residuals above 6 keV are smaller for the MEKAL model (Figure 7-4 [bottom]) than for the power-law model (Figure 7-5 [bottom]), indicating that
these lines may be present.
One difficulty with either of the thermal models is the large derived temperatures
of kT ≈ 4 keV. Typically, even young remnants with ages less than 1000 yr have
temperatures closer to 2 keV (Koyama et al. 1996 and Sakano et al. 1999). One
plausible explanation for this apparent discrepancy is the use of a simple plasma
model assuming solar elemental abundances. In most cases, SNR spectra with sufficiently high counting statistics (a minimum of several thousand source counts) or
high energy resolution (E/∆E of several hundred, as in the case of the Focal Plane
Crystal Spectrometer on Einstein) require non-solar abundances and at least one nonequilibrium ionization (NEI) model to properly describe the data (e.g., Hughes et al.
2000, Winkler et al. 1981, and Hayashi et al. 1994).
While the lack of any obvious line features prevents us from attempting to fit more
realistic models, we explored this possibility by adjusting the abundances of the three
metals with the largest number densities relative to H, namely Si, S, and Fe. Table 73 lists the best-fit MEKAL temperatures obtained when the abundances have been
multiplied by factors of 1.5, 2.0 and 3.0. As the amount of metals is increased, the
182
temperature monotonically drops from 3.5+0.4
−0.3 keV to 2.8 ± 0.2 keV. The goodness of
fit (χ2) also grows, as do the systematic residuals, indicating that abundances factors
of five to ten greater than solar are ruled out. However, it is quite realistic to expect
that the use of a NEI model in conjunction with modestly-enriched abundances would
result in a goodness of fit comparable to that of the power-law or MEKAL model.
The spectral fitting we performed also allows the intriguing possibility that the
emission from G292.2−0.54 is non-thermal in origin. It is well-established that most
young SNRs have a strong non-thermal component (see Allen, Gotthelf, & Petre
[1999] for a recent review). In the most commonly accepted scenario, electrons are
accelerated by the remnant’s shock wave to energies of ∼1 TeV and emit high-energy
radiation via the synchrotron mechanism (e.g., Reynolds 1998). Usually, though, thermal X-rays are also present in the SNR. The notable exception is SNR G347.3−0.5,
which shows no measurable thermal emission down to very low limits (Slane et al.
1999). The photon index Γ measured for G292.2−0.54 (2.3 ± 0.2) agrees very well
with those reported from different regions of G347.3−0.5 (2.2, 2.4, and 2.4). This
spectrum is distinctly harder than those of SNRs that exhibit both thermal and nonthermal emission, like Cas A (3.0 ± 0.2), SN 1006 (3.0 ± 0.2), Kepler (3.0 ± 0.2),
Tycho (3.2 ± 0.1), and RCW 86 (3.3 ± 0.2) (Allen et al. 1997; Allen et al. 1999; Allen,
Gotthelf, & Petre 1999).
While the spectral similarities support the idea that G292.2−0.54 may belong to
a class of non-thermal remnants typified by G347.3−0.5, they are equally compelling
reasons that weaken this line of reasoning. Slane et al. (1999) show that the properties
of G347.3−0.5 can reasonably be explained if the remnant is in a well-advanced Sedov
evolutionary phase and has an age between 19 − 41 kyr. This is in striking contrast
to G292.2−0.54, which is extremely young and is (possibly) just entering the Sedov
phase. Ultimately, the nature of G292.2−0.54, be it a typical young thermal SNR
or a more exotic manifestation of the SNR phenomena, will only be decided with
additional observations.
183
Table 7-3. X-ray temperature dependence on
elemental abundances
kT
(keV)
Abundance
factor
χ2 /dof
3.5+0.4
−0.3
3.4 ± 0.3
3.1 ± 0.3
2.8 ± 0.2
1.0
1.5
2.0
3.0
351/211
376/211
410/211
479/211
Note. — Here, only the most common heavy elements
(Si, S, and Fe) have had their abundances, as determined
by Anders & Grevesse (1989), multiplied by this factor.
184
Help from nearby objects
Another important aspect of the spectrum that requires explanation is the lack of soft
X-rays from the eastern side of G292.2−0.54 (Figure 7-1 [middle row] and Figure 7-2)
and the rather uniformly filled morphology at high energies (Figure 7-1 [bottom row]).
This absence manifests itself via absorption of emission below ∼1.5 keV (Figure 7-4
and 7-5 [bottom]). Again using SIMBAD, we looked for objects in the vicinity of
PSR J1119−6127 that might account for the absorption. A likely candidate is Dark
Cloud DC 292.3−0.4, catalogued by Hartley et al. (1986) during a systematic search
of ESO/SERC Southern J survey plates for optically identified dark clouds. Their
work is an extension of the seminal work by Lynds (1962) to declinations south of
–35◦ . Hartley et al. (19866) approximate the shape and size of each cloud with
an ellipse and use three classes to characterize the density of each cloud. (N.B. the
reported dimensions do not necessarily reflect the shape of the cloud [e.g., if the cloud
is elongated or curved], but do give an accurate estimate of the total area the cloud
occupies.)
DC 292.3−0.4 is described by an ellipse with major and minor axes of 160 . In
Figure 7-6, we overlay the dark cloud, represented by a hatched-circle with diameter 160 , on the hard-band PSPC image (left) and soft-band GIS image (right).
DC 292.3−0.4 appears to be located at a position capable of obscuring the eastern side of G292.2−0.54, and given that the cloud is certainly not spherical, it seems
quite plausible that substructure (e.g., a finger or wisp) extending across the SNR
absorbs the soft X-ray emission.
A more quantitative check is to see if the cloud can account for the difference in
column densities (NH = 1.3 × 1022 cm−2) between the two sides of the SNR. The
cloud’s density (class B) roughly equals the Lynds designation of opacity class (OC)
4 or 5, which, using the calibrated relationship of Feitzinger and Stüwe (1986), AV =
0.70 OC+0.5 mag, gives an extinction AV = 3.3−4.0 from DC 292.3−0.4. The corresponding column density NH can be estimated using NH = 1.7×1021 AV cm−2 mag−1 ,
derived from hN(Hi)/E(B − V )i = 5.2 × 1021 cm−2 mag−1 (Shull & van Steenberg
185
Figure 7-6 Soft-band GIS image (left) and hard-band PSPC image (right) of
G292.2−0.54. The large hatched circle represents the approximate shape of dark
cloud DC 292.3−0.4, which we suggest accounts for a large part of the absorption
of soft X-rays from the eastern side of the SNR. The pulsar location is marked by a
cross. The star marks the location of HD 306313, a B9 star that is positional coincident with enhancements in emission from the western side of the remnant in both
detectors. In each image, contours span between 35% – 95% of the maximum flux in
increments of 10%.
1985) and [A(V )/E(B − V )] = 3.1 (Cardelli, Clayton, & Mathis 1989). Thus, we expect DC 292.3−0.4 to contribute (6−7)×1021 cm−2 to the eastern side of G292.2−0.54,
or roughly half of the additional amount of NH present on this side of the SNR.
The presence of DC 292.3−0.4 also offers the chance to probe the distance to
PSR J1119−6127. Recently, Otrupcek, Hartley & Wang (2000) observed the 115
GHz (J=1-0) transition of CO towards the center of each cloud in the Hartley et al.
catalog. Two features with line of sight velocities of –12.6 km s−1 and 1.6 km s−1 were
detected for the cloud. Adopting the method of Gaensler et al. (1999), these velocities
correspond to minimum distances of –0.2 and 1.7 kpc and maximum distances of 4.7
and 6.6 kpc. The low FHWM measured for these features, combined with the fact that
any cloud optically identified is inherently close, indicates that DC 292.3−0.4 must
be no further than a few kpc. Unfortunately, with no way to discern which feature
corresponds to the cloud, these CO measurements cannot provide an interesting lower
186
limit for the pulsar’s distance. The presence of two features is encouraging, as it
suggests an additional cloud is present along the line of sight and contributes to the
absorption of soft X-rays from the eastern side of G292.2−0.54.
Figure 7-6 also shows the location of HD 306313, a B9 star with apparent magnitude 11.6. Until recently, late B stars were not thought to have high energy emission.
However, analysis of the ROSAT all-sky survey revealed that these stellar types can
in fact be X-ray bright (Berghöfer & Schmitt 1994; Berghöfer, Schmitt, & Cassinelli
1996). While only 10% of B9 stars emit X-rays (Berghöfer et al. 1997), this offers
a possible explanation for the flux enhancements in both the PSPC and GIS images
near the star. The USNO-A2.0 catalog of stars gives a blue magnitude of 12.7 and a
red magnitude of 11.6 for HD 306313. The USNO calibration algorithms6 allow us to
convert to standard B and V colors, and assuming a magnitude uncertainty σ = 0.25
(Grazian et al. 2000) and correcting for the intrinsic color of a B9 star, we calculate
color excesses hE(B − V )i for several stellar classes (i.e. i, iii, v). Finally, adopting
the absolute magnitudes measured by Jaschek & Gómez (1998) for B9 stars and the
reddening law used above, we derive distances of 250 ± 80 pc (B9 v), 550 ± 165 pc
(B9 iii), and 6.3 ± 3.5 kpc (B9 i).
As the PSPC flux (see below) from the entire western region totals 7 × 10−13
ergs s−1 cm−2, we estimate the star would only need to have 1 − 10% of this flux to be
observable. The X-ray luminosity in the 0.1−2.4 keV band for B9 stars ranges between
log (Lx ) = 28.5 − 31.0 (Berghöfer 1997). While the low flux precludes emission from
a distant (i.e. more than a few kpc) supergiant is ruled out, a main sequence or giant
star, with maximum unabsorbed fluxes of 1.3 × 10−12 and 2.8 × 10−13 ergs s−1 cm−2,
could easily result in the bright feature visible in the hard-band PSPC and soft-band
GIS data. Moreover, stellar emission contamination of the SNR spectrum would also
explain the systematic residuals seen below 2 keV. In a detailed spectral study of
A0−F6 stars, Panzera et al. (1999) show that these stars are best described by a
6
http://www.nofs.navy.mil/
187
combination of two Raymond-Smith plasma models with average temperatures of
hkT i ∼ 0.7 keV and hkT i ∼ 0.2 keV. We tried adding a Raymond-Smith component
to our best-fit models, but for the reasons stated in §7.3.3, these attempts were
unsuccessful.
We conclude with an intriguing possibility to be pursued in future observations.
If HD 306313 is confirmed as an X-ray source, with sufficient data its spectral properties can be determined. By comparing its column density with that measured for
the western side of G292.2−0.54, a very constraining upper or lower limit to the
pulsar/remnant system can be obtained.
X-ray luminosity
Table 7-4 presents the flux measured from each side of G292.2−0.54 for each spectral
model and each instrument. Luminosities have been calculated assuming a distance
of 8 kpc and correcting for the effects of interstellar absorption. Formal errors on
Lx are of order 5%, and regardless of the spectral model, the luminosities for a
given region and instrument are within 20% of one another, guaranteeing an excellent
measurement of the total luminosity from G292.2−0.54. While the ROSAT-measured
luminosities are consistently lower than those of ASCA, this is easily understood given
the uncertainties in calibration and differences in telescope sensitivities. The ratio
between eastern and western side luminosities from ASCA is 2.0 ± 0.2, in excellent
agreement with the 2.1 ratio of geometric areas of each region (see Figure 7-3 [left]).
The total 0.5 − 10 keV luminosity from G292.2−0.54 is (7 − 9) × 1035 ergs s−1 .
7.4.3
AX J1119.1−6128.5
Figure 7-7 shows a close-up of the GIS hard-band field surrounding PSR J1119−6127.
The radio position of PSR J1119−6127 is marked by a cross, while an ellipse (semimajor axis 5300 , semi-minor axis 300 ) shows the 95% confidence uncertainty position of the unidentified IRAS point-source IRAS J11169−6111.
188
The position of
Table 7-4. X-ray flux and luminosity for SNR G292.2−0.5
Western Side
ASCA
Spectral
model
ROSAT
Eastern Side
ASCA
F0.7−8 keV
Lx
(10−12 )
(1035 )
F0.7−7 keV
(10−12 )
Lx
(1035 )
F0.4−2 keV
(10−12 )
Lx
(1035 )
Power law
2.4
2.9 ± 0.2
0.67
1.8+0.3
−0.2
3.3
6.0+0.3
−0.2
Thermal brems.
2.4
2.4+0.2
−0.1
0.68
1.5+0.3
−0.2
3.1
4.6 ± 0.2
MEKAL
2.4
2.4 ± 0.1
0.66
1.6 ± 0.2
3.3
5.1 ± 0.1
Note. — All fluxes, in units of (ergs s−1 cm−2 ), refer to the measured absorbed flux for the given
energy band. All luminosities, in units of (ergs s−1 ), are for the 0.5 − 10 keV passband. They have
been corrected for absorption and assume a distance of 8 kpc. All uncertainties represent the 90%
confidence limits.
189
the IRAS source (α (J2000) = 11h 19m 7.s 05, δ (J2000) = −61◦ 270 26.00 3) is offset 6800 from AX J1119.1−6128.5. (Recall that PSR J1119−6127 is offset 8200 from
AX J1119.1−6128.5.) While the position of IRAS J11169−6111 has a large uncertainty and is slightly closer to the ASCA source than PSR J1119−6127, the offsets are
too large to claim that AX J1119.1−6128.5 is the X-ray counterpart of the pulsar or
IRAS source based solely on positionally coincidence. Below, we consider additional
evidence that supports either scenario.
Figure 7-7 Hard-band (3 − 10 keV) ASCA image of the immediate region around
AX J1119.1−6128.5. A dark cross marks the location of PSR J1119−6127, while
a dark ellipse (semi-major axis 5300 , semi-minor axis 300 ) marks the 95% confidence
position of IRAS J11169−6111. Contours correspond to 35 − 95% of the maximum
flux in increments of 10%.
190
X-ray Luminosity
The small number of counts from the point source precludes determining the nature
of the underlying emission mechanism (e.g. thermal or non-thermal). However, by
deriving the luminosity implied for various spectral models, it is possible to check the
consistency of the assumption. All the luminosities reported below assume a distance
of 8 kpc and have been corrected for the effects of interstellar absorption. In the
case when both the photon index and normalization were allowed to vary, the implied
33
ergs s−1 , while in the 0.5− 10 keV
luminosity in the 0.1− 2.4 keV band is 2+7
−2 × 10
band it is 5+64
× 1033 ergs s−1 . The huge spread is due to the large uncertainty
−5
in the photon index (recall Γ = 0.2 − 2.4). When the photon index is fixed at the
canonical value for young pulsars (Γ = 2), the luminosity range narrows dramatically
to (5 ± 2) × 1033 ergs s−1 for both the 0.1 − 2.4 and 0.5 − 10 keV bands. For the
thermal bremsstrahlung model, the formal confidence limit on the temperature is
kT = 13+∞
−11 keV. If we estimate the upper-limit at kT = 20 keV, the luminosity in
the 0.1 − 2.4 keV band is (2 ± 1) × 1033 ergs s−1 , while in the 0.5 − 10 keV band
33
it is 4+4
ergs s−1 . Thus, for either the thermal or non-thermal model, the
−3 × 10
luminosity for AX J1119.1−6128.5 in either commonly-reported band (0.1 − 2.4 or
0.5 − 10 keV) is ∼(1 − 5) × 1033 ergs s−1 .
An Unresolved Synchrotron Nebula?
If AX J1119.1−6128.5 truly has a non-thermal spectrum described by a relatively
flat power law (i.e. Γ . 2), the implied X-ray luminosity is consistent with the
interpretation that it is the X-ray counterpart to PSR J1119−6127. First, we consider
the luminosity with a fixed photon index Γ = 2. The conversion efficiency Ė into
Lx is ≡ (Lx /Ė) = (3 ± 1) × 10−3 for both the ROSAT (0.1 − 2.4) and Einstein
(0.2 − 4.0) keV bands. These values are very close to those predicted by both the
Becker & Trümper (1997 [ = 1 × 10−3 ]) and Seward & Wang (1988 [ = 4 × 10−3 ])
Lx − Ė relationships. However, this apparantly excellent agreement must be viewed
cautiously for three reasons. First, from the discussion in §6.6.4, we have shown
191
that both of these empirical relationships have inherent scatter of at least a factor
of 4. Second, we have assumed assumed a distance of 8 kpc for PSR J1119−6127.
Although it is unlikely that the pulsar is further away or any nearer than 2.4 kpc, a
closer distance could lower Lx by as much as a factor of 10, decreasing by a similar
amount. Finally, we also note that the uncertainty in greatly increases when we
consider the luminosities derived from the spectral fits where both the normalization
and spectral index were free parameters. More than the specific value of or whether
it agrees well with a particular Lx − Ė prediction is the order of magnitude value:
converting one part in a thousand of Ė into X-rays is entirely consistent with the
majority of X-ray detected rotation-powered pulsars. If the pulsar is powering the
observed high-energy emission, the lack of pulsations coupled with the point-like
nature of the source argues that AX J1119.1−6128.5 is an unresolved synchrotron
nebula powered by PSR J1119−6127. This is exactly analogous to the X-ray emission
observed by ASCA from PSR B1046−58 (see Chapter 6).
A Precursor LMXB?
If the ASCA source has a hard (kT > 2 keV) thermal spectrum, no theoretical model
nor previous observational evidence supports interpretating AX J1119.1−6128.5 as
the counterpart to PSR J1119−6127. More likely, especially given the point-like
nature of the ASCA source, the emission from AX J1119.1−6128.5 results from accretion onto a compact object. This scenario is strengthened by the presence of
IRAS J11169−6111, an infra-red point-source. Recently, two different collaborations
have studied this object because of its spatial coincidence with a known S star, red
giants similar to M-class giants with prominent ZrO bands.
Chen, Gao & Jorissen (1995) claim that IRAS J11169−6111 is actually a blend of
three sources. Lloyd Evans & Little-Marenin (1999) discovered two “very red” objects
at the IRAS position, although their observations resolved only a single object at
the telescope. They re-classify the (possibly) composite spectrum as M3. Although
isolated late-type stars can emit X-rays, their spectra are very soft (kT < 0.5 keV)
192
(Hünsch et al. 1998 and references therein) and cannot explain the emission from
AX J1119.1−6128.5. Late-type giants, including M and S stars, in binary systems
with white-dwarfs can have slightly harder spectra, with kT approaching ∼1 keV
(Jorissen et al. 1996; Hünsch et al. 1998), although such a system would still not be
hard enough to explain the ASCA source. Even if this star had unprecedented hard
emission similar to AX J1119.1−6128.5, it would also require that the ratio of X-ray
flux to bolometric flux be several orders of magnitude higher than all other known
X-ray-bright M stars (Hünsch et al. 1998). A much more plausible explanation is
provided by the hard X-ray emitter 2A 1704+241 (4U 1700+24).
This X-ray source was first identified in the Ariel V 2A catatlog (Cooke et al.
1978) and reconfirmed in the fourth Uhuru catalog (Forman et al. 1978). Using data
from Einstein and HEAO–1, Garcia et al. (1983) found the spectrum well-described
by a highly absorbed (NH ∼ 1022 cm−2), hard (kT = 15 keV) thermal bremsstrahlung
model and a 2 − 11 keV luminosity between 1033 − 1034 ergs s−1 . They also identified
the M3 giant HD 154791 as its optical counterpart.
More recently, Gaudenzi & Polcaro (1999) performed detailed optical spectroscopy
of this system and use their results to hypothesize that the observed X-ray emission
is powered by accretion onto a neutron star. Moreover, they claim that this system
is in the process of evolving into a normal LMXB. Dal Fiume et al. (2000) present
recent ASCA and Beppo-SAX observations of 4U1700+24. In agreement with the
results of Garcia et al. (1983), they find that the emission is best described with a
thermal bremsstrahlung model, although with lower temperatures of kT = 6.3 keV
and kT = 3.6 keV for ASCA and BeppoSAX, respectively. They also show that during
both the ASCA and Beppo-SAX, each of which spans 40 ks, the source experienced
variability by a factor of two. Equally intriguing, the time-averaged luminosities
derived for the ASCA and BeppoSAX observations varied by nearly a factor of three.
In contrast to Gaudenzi & Polcaro (1999), Dal Fiume et al. (2000) claim that the Xray emission is powered by accretion from the M3 giant onto a white dwarf. Whatever
the nature of compact object, a similar scenario of accretion from IRAS J11169−6111
193
onto a neutron star or white dwarf could explain both the luminosity and spectrum
of AX J1119.1−6128.5. In this case, the X-ray binary is completely unrelated to
PSR J1119−6127. If the compact object is a white dwarf, the binary is also unrelated
to G292.2−0.54. However, if it the compact object is a neutron star, G292.2−0.54
may be related to either AX J1119.1−6128.5 or PSR J1119−6127.
194
Chapter 8
X-ray Observations of the High
Magnetic Field Radio Pulsar PSR
J1814−1744
8.1
Introduction
Recently, PSR J1814−1744, an isolated radio pulsar with period P = 4 s and large
period derivative (Ṗ = 7.4 × 10−13 ) was discovered (Camilo et al. 2000) in an ongoing
survey of the Galactic Plane for radio pulsars using the 64-m Parkes telescope (Lyne
et al. 2000). The pulsar’s surface magnetic field strength B, inferred under the
assumption of a dipole rotating in vacuo (Equation 6.5), is 5.5 × 1013 G.
This pulsar’s properties are particularly interesting because they are similar to
those of anomalous X-ray pulsars (AXPs). AXPs have spin periods P = 6 − 12 s, and
spin down regularly (see, e.g., Mereghetti & Stella 1995, Gotthelf & Vasisht 1998, and
Kaspi, Chakrabarty, & Steinberger 1999) with period derivatives 10 −12 < Ṗ < 10−11 .
The X-ray luminosities of AXPs are typically several orders of magnitude larger than
their spin-down luminosities (see, e.g., Oosterbroek et al. 1998 and references therein).
Strong observational evidence (see, e.g., Mereghetti, Israel, & Stella 1998) precludes
accretion from a binary companion as the origin of the observed X-rays. Instead, the
195
leading hypothesis to explain AXP properties is that they are isolated neutron stars
with ultra-high magnetic fields, so-called “magnetars” (Duncan & Thompson 1992).
In this model, the X-ray emission is powered either by decay of the large magnetic
field (Thompson & Duncan 1996) or neutron star cooling enhanced by the presence of
the strong field (Heyl & Hernquist 1997a). Assuming magnetic dipole braking, AXPs
have inferred surface dipole magnetic field strengths B = (0.6 − 8) × 1014 G.
While PSR J1814−1744 is a radio pulsar and hence an isolated neutron star, its
spin parameters and hence inferred magnetic field are extreme in the pulsar population: its magnetic field is nearly three times larger than that of PSR B0154+61 (Arzoumanian et al. 1994), the pulsar with the previously known highest field strength1 .
Given that the spin parameters of PSR J1814−1744 are more typical of AXPs than
radio pulsars, the possibility that this is a transition object between these two neutron
star populations must be entertained. In particular, under the magnetar hypothesis,
the mechanism responsible for the production of X-rays in AXPs should be present
in PSR J1814−1744 if the inferred magnetic field is indeed the primary characteristic
relevant to the observed magnetar properties.
The similarity in spin parameters between PSR J1814−1744 and the AXPs is
readily seen in a “P −Ṗ ” plot. Figure 8-1 shows Ṗ versus P for the radio pulsar
population (small dots), with PSR J1814−1744 indicated. The figure also shows
the candidate magnetar population, consisting of five AXPs and two soft gamma
repeaters (SGRs). Immediately noticeable is the proximity of PSR J1814−1744 to
the cluster of AXPs and SGRs at the upper right corner. It is especially close to
1E 2259+586, also indicated (Kaspi, Chakrabarty, & Steinberger 1999 and references
therein). Table 8-1 compares the properties of these two neutron stars.
Here, we present an analysis of archival ROSAT and ASCA X-ray observations
that serendipitously include the location of PSR J1814−1744 within their respective
1
The survey that discovered PSR J1814−1744 also discovered PSR J1119−6127, a radio pulsar
with field B = 4.1 × 1013 G (Camilo et al. 2000).
196
Figure 8-1 P − Ṗ diagram. The small dots are the known radio pulsars. The
crosses are the AXPs and the diamonds are the SGRs. Lines of constant magnetic
field, derived from Equation 1, are shown by the dashed lines. Note the proximity of PSR J1814−1744 (the boxed dot) to 1E 2259+586 (the boxed cross). Pulsar
references–Taylor et al. 1995; Camilo et al. 2000; Young, Manchester & Johnston
1999. SGR references–Kouveliotou et al. 1998; Kouveliotou et al. 1999. AXP
references–see citations in the main text.
197
fields of view (FOV). Emission from the pulsar position was not detected with either
telescope. We note that X-rays from other mechanisms (e.g., magnetospheric emission) are not expected to be observable from PSR J1814−1744. Give its spin-down
luminosity of 5×1032 ergs s−1 and its probably distance of 10 kpc (estimated from the
distance/dispersion measure relation of Taylor & Cordes [1993]), its spin-down flux
(Ė/4πd2 ) implies that any rotation-powered high-energy emission should be too faint
to detect Seward & Wang 1988; Becker & Trümper 1997). Count rate limits from
both observations are used to derive an upper limit on the X-ray luminosity from
PSR J1814−1744 that is significantly smaller than those measured for the known
AXPs. We then discuss the implications of the non-detection for current magnetar
models.
8.2
8.2.1
Archival Data Analysis
ROSAT
A field containing PSR J1814−1744 was observed with the Position Sensitive Proportional Counter (PSPC) instrument aboard ROSAT (Trümper 1983) during 1992 April 2–
8, as part of a study of the Galactic X-ray background (sequence RP900196N00).
The radio timing position of PSR J1814−1744 (Camilo et al. 2000), α (J2000)
= 18h 14m 43.s 0(2), δ (J2000) = −17◦ 440 4700 (23), is located 340 from the optical
axis. The total live time was 7.7 ks. A 0.1 − 2.4 keV broad-band flat-fielded image
was produced using an exposure map that accounts for vignetting and instrumental
structure. The exposure map is a standard data product generated by the NASAmaintained HEASARC during its analysis of all ROSAT observations. No X-ray
emission is present. To calculate an upper limit on the count rate, we compare the
counts collected in an aperture of radius 0.08 centered on the radio position to those
in a concentric annulus with radii 40 and 120 . The aperture radius represents the theoretical half energy width for a point source located 340 off-axis, calculated using the
FTOOL pcrpsf v.2.0.7. Using the expression for the signal-to-noise ration (S/N)
198
derived in Appendix D and requiring S/N > 3σ, the count rate upper limit in the
0.1 − 2.4 keV band is less than 3.2 × 10−3 cps.
8.2.2
ASCA
A field containing PSR J1814−1744 was observed with ASCA (Tanaka, Inoue, &
Holt 1994) on 1996 April 9, as part of a Galactic plane survey (sequence 54005040).
ASCA consists of four co-aligned telescopes, each of which has its own focal plane
detector: two Gas Imaging Spectrometers (GIS-2 and GIS-3) and two Solid-state
Imaging Spectrometers (SIS-0 and SIS-1). The pulsar position falls 130 from the
ASCA optical axis. This puts the source at the edge of the SIS detectors, limiting the
utility of these data. We do not consider them further, focusing instead on the GIS
instruments which have a much larger (250 ) FOV. The effective exposure time for the
GIS is 2 × 11.5 ks. The image obtained from combining data from both GIS cameras
has been corrected for pointing offset2 and exposure and rebinned with a 4500 ×4500 boxcar function. To avoid the large instrument background at the edge of the detectors,
we restricted the image to a circular FOV with 200 radius. The image is dominated by
scattered flux from the nearby (340 ) bright low mass X-ray binary (LMXB) GX 13+1
(Vrtilek et al. 1991). Due to its better mirror performance, ROSAT does not suffer
from this contamination problem. A fan-like pattern, consistent with that from a
bright point source located 340 from the optical axis (see, e.g., Gendreau 1995), and
a shadow from a mirror quadrant boundary fall where expected, given the satellite
roll angle and the alignment of GX 13+1 with the optical axis3 . No X-ray emission
is present from the location of the radio pulsar.
An upper limit on flux from the pulsar is derived following the same prescription
2
This offset arises due to a systematic error with the ASCA star tracker.
The
correction was applied using the FTOOL offsetcoord and the look-up table available at
http://legacy.gsfc.nasa.gov/docs/asca/coord/updatecoord.html.
3
The interested reader is referred to Serlemitsos et al. (1995) for a detailed discussion of the stray
light properties of ASCA.
199
outlined in §8.2.1, with an increase in the radius of the source aperture to 4.0 5 to
accommodate the wider PSF of ASCA. Fortuitously, PSR J1814−1744 is situated in
the middle of the boundary shadow, largely shielding the location of the pulsar from
the scattered flux of GX 13+1. However, the contamination of nearly the entire GIS
FOV from the LMXB complicates the choice of a background region. We considered
using blank-sky data from the same region of the detectors that encompass the source
aperture, which would account for the instrumental and cosmic X-ray backgrounds.
However, the blank-sky background would not include contributions from the diffuse
Galactic plane emission, and most importantly, would not include the scattered flux
from GX 13+1. Hence, we relied upon a relatively contamination-free region from
this observation to calculate the background, selecting a circular region with 40 radius,
located the same distance off-axis as PSR J1814−1744 and containing roughly the
same amount of scattered light as the source aperture. Requiring S/N > 3σ yields
a count rate upper limit in the 2 − 10 keV band of less than 5.6 × 10−3 cps. These
calculations were performed on the unbinned data, and while our approach should
mitigate most of the effects of the contamination from GX 13+1, we recognize it is
impossible to fully account for it. The above upper limit represents a conservative
estimate of the maximum count rate from PSR J1814−1744.
8.3
8.3.1
Discussion
The X-ray Luminosity Upper Limit of PSR J1814−1744
The dependence of the magnetar hypothesis for AXP emission on inferred magnetic
field, coupled with the similarities in the spin parameters of PSR J1814−1744 and
1E 2259+586, suggests that PSR J1814−1744 may also share similar X-ray properties.
Here, we use the spectral properties of 1E 2259+586 as a template to convert the count
rate upper limits from PSR J1814−1744 into an X-ray luminosity upper limit.
The spectrum of 1E 2259+586 is well-studied (Iwasawa, Koyama & Halpern 1992;
Corbet et al. 1995; Rho & Petre 1997; Parmar et al. 1998) and best described by
200
a two-component model, consisting of a black body and power law. Rho & Petre
(1997) combine data from ROSAT, ASCA, and BBXRT (Serlemitsos et al. 1992)
to determine best-fit parameters of Γ = 4.0 for the power law index and kT =
0.43 keV for the black body temperature. The unabsorbed flux is F2−10
keV
= 1.3 ×
10−11 ergs s−1 cm−2 and F0.1−2.4 keV = 4.1 × 10−9 ergs s−1 cm−2 . The distance to
1E 2259+586 has been estimated to be d = 3.6 − 5.6 kpc from the supernova surface
brightness-distance (Σ-D) relationship (Gregory & Fahlman 1980; Sofue, Takahara,
& Hirabayashi 1983; Hughes et al. 1984). While there is great uncertainty in the ΣD relation (see, e.g., Green 1984 and Berkhuijsen 1986), distances to stars in nearby
Hii regions are of similar value (Rho & Petre 1997), resulting in a commonly quoted
distance of 4 kpc.
In order to scale the spectral model of 1E 2259+586 for PSR J1814−1744, we
must first estimate the Galactic absorption (column density NH ) and distance to the
radio pulsar. There are two coarse, yet independent, methods for estimating NH . The
Seward & Wang (1988) approximation of 10 neutral hydrogen atoms per free electron,
combined with the pulsar dispersion measure DM = 834 pc cm−3 (Camilo et al. 2000)
gives NH = 2.6 × 1022 cm−2 . The FTOOL nh, which uses the Hi maps of Dickey &
Lockman (1990), predicts NH = 1.8 × 1022 cm−2 . The DM−d relationship of Taylor
& Cordes (1993) predicts a distance of ∼10 kpc. At this distance, the unabsorbed
X-ray flux of 1E 2259+586 would be reduced to F2−10
keV
= 2.1 × 10−12 ergs s−1 cm−2
and F0.1−2.4 keV = 6.6 × 10−10 ergs s−1 cm−2 .
Figure 8-2 shows the expected count rates in both the ROSAT PSPC and the
ASCA GIS as a function of NH . The rates were calculated by using XSPEC (v.10)
to fold the spectrum of 1E 2259+586, normalized to a distance of 10 kpc, through
the appropriate instrument response matrices. Calculations at several values of NH ,
shown by the symbols, were used to interpolate the count rate as a continuous function
of NH . The dashed lines in each plot represent the measured upper limits. Even when
NH is allowed to exceed the maximum estimate, the predicted count rates are well
above the measured upper limits. Assuming a reasonable compromise value for the
201
column density of NH = 2.2 × 1022 cm−2, the expected ROSAT count rate is a factor
of 13 higher than measured, and the expected ASCA count rate is a factor of 6
higher than measured. Scaling the flux by these ratios, we find for PSR J1814−1744,
ROSAT gives L0.1−2.4
keV
< 6.3×1035 (d/10 kpc)2 ergs s−1 and ASCA gives L2−10
keV
<
4.3 × 1033 (d/10 kpc)2 ergs s−1 . Extrapolating the ROSAT-derived upper limit to the
ASCA band gives L2−10
keV
< 2.0 × 1033 (d/10 kpc)2 ergs s−1 , in good agreement with
the ASCA-derived limit.
Next, we comment on the use of the spectral properties of 1E 2259+586 for calculating our luminosity upper limit for PSR J1814−1744. The spectral properties determined for AXPs are very similar, with power law photon indices in the range Γ =
2.5− 4 and black body temperatures in the span kT = 0.39− 0.71 keV (1E 2259+586:
Rho & Petre 1997; 1E 1048.1−5937: Oosterbroek et al 1998; 1E 1841−045: Vasisht
& Gotthelf 1997; RX J170849.0−400910: Sugizaki et al 1997; 4U 0142+61: White et
al 1996). Their X-ray luminosities (0.5 − 10 keV) differ significantly, however, varying by more than two orders of magnitude. Calculations identical to those described
above show that if PSR J1814−1744 had properties like the other known AXPs, the
expected count rates would all be greater than those predicted from assuming the
spectrum and luminosity of 1E 2259+586. We note that only AXP 1E 1048.1−5937
(inferred surface magnetic field strength 3.6 × 1014 G (Oosterbroek et al. 1998), nominally yields a lower expected count rate than the 1E 2259+586 model (though still
higher than our upper limit), although the particularly large uncertainty in the distance of the former makes its true intrinsic luminosity difficult to know (Corbet &
Mihara 1997).
Thus, if the measured spectral parameters for any of the other AXPs (with the
possible exception of 1E 1048.1−5937) were used in interpreting the count rate upper
limit for PSR J1814−1744, the difference between its X-ray luminosity upper limit
and the luminosity expected from AXP-like emission would only increase.
202
Table 8-1.
Comparison of PSR J1814−1744 and 1E 2259+586
Parameter
Spin period, P (s)
Period derivative, Ṗ
Surface Magnetic Field, B (G)
Characteristic age, P/2Ṗ (kyr)
Spin-down Luminosity, Ė (ergs s−1 )
Reference
PSR J1814−1744
1E 2259+586
4.0
7.0
−13
−13
7.4 × 10
5.5 × 1013
85
4.7 × 1032
Camilo et al. (2000)
4.9 × 10
5.9 × 1013
230
5.7 × 1031
Kaspi, Chakrabarty,
& Steinberger (1999)
Figure 8-2 The diagram shows the count rates expected if PSR J1814−1744 had the
same spectrum and luminosity as 1E 2259+586, as a function of NH . Calculations
at several discrete values of NH , shown by the symbols, were used to interpolate
the count rate as a continuous function of NH . Distances of 10 kpc and 4 kpc were
assumed for PSR J1814−1744 and 1E 2259+586, respectively. The dashed lines
represent the derived upper limit on count rate for the ROSAT PSPC (0.1 − 2.4 keV)
and the ASCA GIS (2 − 10 keV). Assuming a reasonable estimate for the column
density of NH = 2.2 × 1022 cm−2, the expected count rate exceeds the upper limit by
a factor of 13 (PSPC) and 6 (GIS).
203
8.3.2
Beaming and Source Variability
One scenario that must be considered for the lack of emission from PSR J1814−1744
is that the magnetar mechanism is present and emitting X-rays that are beamed
away from our line of sight. The small number of confirmed AXPs prevents any
detailed statistical discussion of beaming. However, the pulsed fraction and pulse
shape of the known AXPs can be used to motivate at least a rough characterization.
For each AXP, Table 8-2 lists the pulsed fraction f, the passband and the pulse
shape. Here, we follow Page (1995) and estimate the pulsed fraction using f =
1/2 × (Nmax − Nmin )/Nmean, where the subscript refers to the maximum, minimum,
and mean counts in the pulse profile. All AXPs have large unpulsed components and
have pulse profiles with smooth or sinusoidal shapes, independent of the number of
X-ray pulses present. Another general trend is that, excepting 4U 0142+61, there is
no evidence for appreciable pulse shape evolution with energy.
These properties are consistent with the predictions of both magnetar models:
that pulsed emission from AXPs is best interpreted as smoothly modulated thermal
emission from the surface of the neutron star (Thompson & Duncan 1996; Heyl
& Hernquist 1997a). See §8.3.3 for additional discussion. The pulsed high energy
component (E > 2 keV), well fit by a power-law model, raises the possibility that
non-thermal magnetospheric processes may also contribute. The lack of AXP pulse
evolution with energy, however, suggests that only a single X-ray emission mechanism
is present in AXPs. This is in contrast to rotation-powered pulsars like the Vela pulsar,
which has a soft, sinusoidal thermal component with low pulsed fraction (Ögelman,
Finley, & Zimmermann 1993) and a sharply peaked non-thermal component that
extends above 100 MeV (Strickman, Harding, & de Jager 1999). Of course, AXPs
and rotation-powered pulsars could have very different pulsed properties, given the
uncertainty in the origin of high-energy magnetospheric emission or the effect that a
high magnetic field would have on this mechanism. For example, distinct thermal and
non-thermal components could be present yet, for reasons unexplained, are locked in
204
Table 8-2.
Pulsar
4U 0142+61
1E 1048.1−5937
1E 1841−045
1E 2259+586
1RXS J170849.0−400910
Pulse properties of known AXPs
f
1
7%
13%
70%
70%
70%
70%
15%
30%
35%
38%
50%
50%
Passband2
Shape
Ref3
0.5 − 1.5
4 − 10
0.5 − 1.5
1.5 − 4.0
4.0 − 8.0
0.5 − 10
1 − 10
0.1 − 2.4
1 − 10
0.1 − 2.4
2−4
4 − 10
two broad symmetric peaks
single peak
single sinusoidal peak
single sinusoidal peak
single sinusoidal peak
single sinusoidal peak
two broad overlapping peaks
two broad asymmetric peaks
two broad asymmetric peaks
single sinusoidal peak
single sinusoidal peak
single broad peak
1,2
1,2
3
3
3
4
5,6
7
8
9
10
10
§3.2 for the definition of f, the pulsed fraction. When not stated by the authors,
we estimate f from the published pulse profiles. (Note: The previously reported value
of 30% for 1E 1841−045 arises from a different definition of f.)
1 See
2
Units are keV.
3 References–(1)
White et al. 1996, (2) Israel et al. 1999b, (3) Corbet & Mihara
1997, (4) (Oosterbroek et al. 1998), (5) Vasisht & Gotthelf 1997, (6) Gotthelf, Vasisht
& Dotani 1999, (7) Rho & Petre 1997, (8) Corbet et al. 1995, (9) Israel et al. 1999a,
(10) Sugizaki et al. 1997.
205
phase, thus appearing to have a common origin.
In either magnetar model, the X-ray emission comes from the hot neutron star
surface. Thus, it seems improbable that PSR J1814−1744 would be oriented with
respect to our line of sight as to make X-ray pulsations undetectable, especially considering that gravitational lensing can make much more than half of the neutron star
surface visible (see, e.g., Page 1995 and Heyl & Hernquist 1998). Note, however,
any magnetospheric emission would be too distant from the neutron star surface to
undergo gravitational lensing, hence could be beamed.
But even if PSR J1814−1744 were aligned in such a way, considerable unpulsed
X-ray emission would be present, as is the case of all the known members of the AXP
population (see Table 8-2). For example, the unpulsed luminosity of 1E 1841−045 is
∼85% of the total observed luminosity (Vasisht & Gotthelf 1997). Even if half of the
flux is present in pulsations directed away from our line of sight, the expected count
rates from PSR J1814−1744 are still well above the upper limits derived from the
archival data. We conclude that, even in the unlikely event that the X-ray emission
is significantly beamed, PSR J1814−1744 should have been detectable as an X-ray
point source under the magnetar hypothesis.
Finally, we discuss the ramifications of source variability in AXPs. Torii et al.
(1998) report variations in flux greater than a factor of ten in the AXP candidate AX J1844.8−0258. Recent observations by Vasisht, Gotthelf, Torii, & Gaensler
(2000) confirm the extreme variability of this object. If this source is firmly established as an AXP by an accurate Ṗ measurement and PSR J1814−1744 has similar
characteristics, there exists the possibility that both serendipitous observations of
PSR J1814−1744 occurred during a low-state and that it is, in fact, an X-ray source.
If instead PSR J1814−1744 undergoes variability by a factor of 2 − 3, as witnessed
in 1E 2259+586 (Corbet et al. 1995 and references therein) and 1E 1048.1−5937
(Corbet & Mihara 1997), X-ray emission still would have been detected.
206
8.3.3
Implications for Magnetar Models
X-ray emission from AXPs has been explained in the context of the magnetar model
by either magnetic field decay (Thompson & Duncan 1996) or neutron star cooling
(Heyl & Hernquist 1997a). Duncan & Thompson (1992) first posited the existence of
magnetars to explain a subset of gamma-ray bursts, including those from the SGRs.
Later (see, e.g., Duncan & Thompson 1994 and Thompson & Duncan 1995), they
discuss how the 1979 March 5 event from SGR 0526−66, which released ∼1044 ergs
in ∼0.2 s (Cline et al. 1980; Evans et al. 1980), could have been driven by a largescale instability and subsequent readjustment of the neutron star’s magnetic field.
For the time scale relevant to the system (∼104 yr), they argue that the instability
is best explained by ambipolar diffusion of the magnetic field out of the stellar core
(Thompson & Duncan 1996). This process conducts energy from the core to the
surface to produce X-ray luminosities in the range Lx ∼ 1035 − 1036 ergs s−1 . The
strong dependence of the surface heat flux on field strength concentrates flux in
the polar regions. The modulation of this intensity gradient gives rise to the X-ray
pulsations.
For 1E 2259+586, this mechanism can explain the observed X-rays if the neutron
star’s characteristic age, P/2Ṗ = 230 kyr, is an overestimate, the true age being
∼ 10 kyr, that inferred for the proposed associated supernova remnant CTB 109
(Wang et al. 1992). If this model is correct, the difference of only 10% in the
magnetic fields of 1E 2259+586 and PSR J1814−1744 seems unlikely to account
for the large difference in their X-ray luminosities, given the similarity of the X-ray
emission from the known AXPs, whose magnetic fields span a much larger range.
Therefore, if the decay of magnetic fields leads to the observed emission from AXPs,
that no X-rays are seen from PSR J1814−1744 argues that 1E 2259+586 is much
younger, even though the characteristic ages indicate otherwise, consistent with the
latter’s association with SNR CTB 109. This suggests that 1E 2259+586 has had a
spin-down history inconsistent with simple dipole braking or that it was born with a
long spin period.
207
Heyl & Hernquist (1997a) have suggested a second model, based on photon cooling, for the production of X-rays in AXPs. They extend into the magnetar regime
(B = 1014 − 1016 G) the work of Shibanov & Yakovlev (1996), who have shown
that when the magnetic field of a neutron star exceeds 1012 G, enhancements in the
conductivity along the field lines due to electron energy quantization result in a net increase in heat flux (Heyl & Hernquist 1997b; Heyl & Hernquist 1998a). In sufficiently
young stars (ages of ∼1 kyr) this leads to a gradual increase in photon luminosity
with increasing magnetic field. The composition of the neutron star envelope has an
even more dramatic effect; the luminosity transmitted through a helium envelope is
six times that transmitted through an iron envelope, while that transmitted through
a hydrogen envelope is ten times that for iron. They then argue that the total mass
of an insulating low-Z layer required for the observed AXP luminosity is modest and
easily attained from either fall-back following the supernova explosion or accretion
from the ISM, if the pulsar has a large birth velocity or the density is high enough.
Heyl & Hernquist (1997b; 1998) consider how the flux varies across the surface of a
magnetar and find a strong angular dependence caused by the anisotropic heat conduction in the outer layers of the neutron star. The temperature gradient, coupled
with the limb darkening expected from magnetized atmospheres (see Heyl & Hernquist 1997b and references therein), results in a modulation of the thermal flux. The
observed pulsed fraction may be reduced by gravitational lensing, which makes more
than half of the neutron star surface visible at a given instance (see, e.g. Page 1995
and Heyl & Hernquist 1998) and effectively smooths the flux gradient discussed above
in §3.1.
This model accounts for both the intensity of the X-ray emission and the pulsed
fractions from 1E 1841−045 and 1E 2259+586 (Heyl & Hernquist 1997a), assuming
the pulsar ages are those of their associated supernova remnant, Kes 73 and CTB 109,
respectively. The absence of X-rays from PSR J1814−1744 again argues that this
neutron star must be much older than 1E 2259+586. Alternatively, PSR J1814−1744
could be equally as young as 1E 2259+586 and may not possess a light-element
208
insulating layer, in spite of the ease with which Heyl & Hernquist (1997a) suggest
them to be formed.
8.4
Conclusions
In summary, we have set an upper limit on X-ray emission from the newly observed
high magnetic field radio pulsar PSR J1814−1744. The upper limit on the flux
implies a luminosity in X-rays well below those of any known AXP. This conclusion is
independent of any beaming given the low pulsed fraction of the known AXPs, and is
robust to modest flux variability. This argues that any magnetar mechanism invoked
to explain X-ray emission from AXPs must depend on more than observed P and
Ṗ , hence on more than merely inferred B field. In the context of the two particular
magnetar hypotheses discussed above, PSR J1814−1744 must be considerably older
than any of the known AXPs, including 1E 2259+586, in spite of characteristic ages
that indicate otherwise. This is consistent with 1E 2259+586 being a much younger
object than its characteristic age suggests, in agreement with its association with
CTB 109. Additionally, it implies that its spin-down history has deviated significantly
from dipole braking, or that it had a large (few seconds) initial spin period. SGRs
and AXPs may thus have markedly different evolutionary paths from radio pulsars,
including even the extreme members of the latter population. Thus, the proximity
of SGRs and AXPs to any radio pulsar in P − Ṗ phase space must be considered
merely coincidental and caution must be used when comparing the different classes
of neutron stars.
209
210
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Appendix A
Acronyms
ACIS
ASCA
AXAF
AXP
BESSY
CCD
Chandra
DEA
Einstein
FHWM
GIS
HETG
HPD
HRC
HRI
HRMA
IPC
LBOX
LETG
MOS
PSPC
PSF
PSR
PTB
ROSAT
RP
SEM
SIS
SN
SNR
SRF
XRT
XSPEC
Advanced CCD Imaging Spectrometer: detector on Chandra
Advanced Satellite for Astronomy and Cosmology: X-ray telescope
Advanced X-ray Astrophysical Facility, renamed Chandra
Anomalous X-ray Pulsar
Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung
Charge Coupled Device
Chandra X-ray Observatory: X-ray telescope
Detector Electronics Assembly
Einstein Observatory: X-ray telescope
Full-width at Half Maximum
Gas Imaging Spectrometer
Low Energy Transmission Grating: spectroscopic instrument on Chandra
Half-power Diameter
High Resolution Camera: detector on Chandra
High Resolution Imager: detector on Einstein and ROSAT
High Resolution Mirror Assembly: Chandra mirrors
Imaging Proportional Camera: detector on Einstein
Lasagna-box Electronics
Low Energy Transmission Grating: spectroscopic instrument on Chandra
Metal Oxide Semiconductors
Position Sensitive Proportional Counter: detector on ROSAT
Point Spread Function
Pulsar
Physikalisch-Technische Bundesanstalt
Röntgensatellit: X-ray telescope
Representative Pixel
Scanning Electron Microscope
Solid-state Imaging Spectrometer
Supernova
Supernova Remnant
Spectral Redistribution Function
X-ray Telescope: ASCA mirrors
X-ray Spectral Fitting Package
219
220
Appendix B
Derivation of the Moiré Equation
One approach to understanding the moiré phenomenon is to consider a periodic function F (x), with period D, defined over a plane, which has lines of constant phase
perpendicular to the x axis. That is,
F (x, y) = F (x + D, y).
(B.1)
Consider a second periodic function F 0, with period D0 and lines of constant phase
which form an angle θ with respect to the x axis, as shown in Figure B-1.
Now, in a coordinate system (x0, y 0) rotated with respect to (x, y), i.e.



0

x 
 x 
 = R2 (−θ) 
,
y
y0
(B.2)
F 0(x0 + D0 , y 0) = F (x0, y 0).
(B.3)


we can write
Then, if a phase is assigned to each point in the plane according to
Φ=
x
x0
; Φ0 = 0 ,
D
D
(B.4)
the locus of points which have a particular phase difference ∆Φ with respect to the
221
two functions, satisfies (if D0 = D)
∆Φ =
x
x0
− ,
D D
(B.5)
1
0
0
1
0
1
0
01
1
D’
D’
y’
D
D
x’
y
θ
x
Figure B-1 Vertical lines of constant phase (light bars) and lines of constant phase
(dark bars), rotated at angle θ with respect to the vertical. The point has phase x/D
in the vertical plane and phase x0/D0 in the rotated plane.
or using Equation B.2
∆Φ =
(1 − cos(θ))x0 + sin(θ)y 0
.
D
(B.6)
The condition for the point to have the same phase in both functions is
∆Φ = n; {n : 0, +1, +2, · · ·}.
222
(B.7)
Combining Equations B.6 and B.7 yields
θ
nD
.
y 0 = −tan( )x0 +
2
sin(θ)
(B.8)
Setting n = 0, the angle α the moiré pattern makes with respect to the rotated plane
is
y0
θ
α ≡ tan−1 ( 0 ) = − ,
x
2
(B.9)
and the angle ϕ the moiré pattern makes with respect to the original lines of constant
phase is simply
ϕ=
π
π θ
− (θ − α) = − .
2
2 2
(B.10)
If the periodicity D0 of the function F 0 is not equal to the periodicity D of the function
F , it is easy to show that Equation B.8 becomes
!
1 − cos(θ) 0
n
D0
y =−
x +
; =
sin(θ)
sin(θ)
D
0
π
1 − cos(θ)
ϕ = − θ + tan−1
2
sin(θ)
223
(B.11)
!
(B.12)
224
Appendix C
A Novel Approach for Measuring the
Channel Stop and Gate Parameters
C.1
Introduction
At energies below ∼2 keV, where the penetration depths of incident photons are
comparable to the thicknesses of sub-pixel structures, quantum efficiency varies dramatically within a pixel due to small differences between the three types of gates and
the presence of the channel stops. The most accurate detector models require precise
knowledge of these structures not only to reliably predict quantum efficiency, but also
to describe the shape of the spectral redistribution function.
While the mesh experiments (Chapter 4) can provide this structural information,
a less risky and time-intensive procedure is desirable. This Appendix discusses a
technique to extract the length of the gates (nominally ∼8 µm), the width of the
channel stops, and the thicknesses of the channel stop oxide and p+ implant. The
methodology follows that used to determine the relative differences in polysilicon
and oxide thicknesses of the gates and first outlined by Prigozhin (1999b). There
is, however, a significant difference between the two methods. Here, we utilize the
fact that the charge-loss mechanism in the p+ implant can be suppressed if the gate
voltage is sufficiently low (Vg . 0 V).
225
C.2
Charge Loss in the Channel Stop
The process of charge loss in the channel stops is discussed in detail in Chapter 5.
Here, we briefly describe the essence of this phenomenon. Figure C-1 shows spectral
redistribution functions obtained with the IFM at 525 eV1. The left panel shows the
pulse-height distribution for single-pixel events (g0), while the right panel shows the
pulse-height distribution for horizontally-split events (g34). The dramatic difference
in the redistribution results from applying slightly different voltages to the gates. The
blue curves are data taken with gate voltages of 0.0 and -5.0 V, the red curves are data
taken with voltage of ±2.5 V. In both case we used the default ACIS clocking scheme,
that is two gates set high, one gate set low, ensuring that vertical pixel boundary falls
beneath the center of the low gate.
Figure C-1 Spectral redistribution function at 525 eV with different voltages (red
curve is 2.5 V, blue curve is 0.0 V) applied to the two, high integrating gates. The
left panel is the pulse-height distribution for single-pixel events (g0); the right panel
is the pulse-height distribution for horizontally-split events (g34).
Front-illuminated device modeling and mesh experiments conclusively prove that
growth of the shoulder results from incomplete charge collection in the p+ implant.
If we assume that the charge loss mechanism is constant throughout the channel
stop implant, the number of events in the shoulder can be used to determine the
1
The feature at 277 eV is the C Kα line due to contamination on the IFM anode.
226
dimensions of sub-pixel structures. Here, our definition of the shoulder only includes
those events generated within the channel stop and does not include events generated
near the Si–SiO2 interface. As the later charge-loss mechanism is independent of gate
voltage, it will be easy to separate the two types of events, even though they occupy
the same energy range in the spectral redistribution function.
C.3
Simplified CCD Geometry and Origin of Event
Grades
Before we derive any equations, we discuss the CCD model assumed for all calculations. Figure C-2 shows a simplified model of an ACIS CCD. Overlaps between
adjacent gates, typically ∼1 µm in length, have been ignored. The elongated, hexagonal shape of the p+ channel stop implant has been approximated as a rectangle.
Pixels are still taken to be 24 µm × 24 µm, that is h1 + h2 + h3 = 24 µm and the
portion of the pixel that does not contain the channel stop is (24 − W ) µm.
h1
o1
h2
g1
h3
o2
g2
o3
g3
da
db
p
gate oxide 1
polysilicon gate 1
gate oxide 2
polysilicon gate 2
gate oxide 3
polysilicon gate 3
channel stop oxide
channel stop p+ implant
W
Figure C-2 Cross-section of a simplified CCD. The model ignores all gate overlaps
and assumes a rectangular geometry for the channel stop implant and oxide.
As stated above, we employed the standard ACIS clocking scheme of two gates
held high, one held low, placing the vertical pixel boundary in the center of the low
227
gate. Figure C-3 contains a top-down schematic of a 2 × 2 array of pixels. The
area occupied by the different gates and the channel stop are marked by hatched
regions. The colors indicate the portion of the pixel where multiple pixel events arise.
Vertically split events (g2) occur under the middle of the low gate, horizontally split
events (g34) occur under the middle of the channel stop, and L-shaped and four-pixel
events (g6) occur in the middle of the intersection region of the low gate and the
channel stops.
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Figure C-3 A 2 × 2 array of pixels showing the origin of different event grades with
respect to the gates and channel stops.
228
C.4
Measurement of Channel Stop Parameters
We begin by deriving the width (W ) of the channel stop, the thickness of the p+ implant (p), and the relative thickness of the oxide ∆d, where ∆d ≡ db − da ). Analysis
of the Si-SiO2 shoulder yields da , so the actual thickness of the oxide can easily be
determined. For these measurements, data is taken with the three clock voltages either all above or all below the voltage required to suppress the charge loss mechanism.
As all measurements will be performed at energies with sufficiently small penetration
depths, slight differences in the depletion depths can be neglected. Suggested voltages are +12/+3 V (hereafter Loss) and 0/-7 V (hereafter NoLoss). The channel
stops contribute events to each of standard event grades (g02346). Using the NoLoss
pulse-height as a template, the fraction F of shoulder events in the Loss pulse-height
distribution is easily obtained. The channel stop spans the length of the pixel, reducing the problem to one dimension. Using our fundamental assumption, that the loss
mechanism occurs throughout the implant, the fraction of shoulder events to total
events becomes:
F =
W exp(−∆d /λSiO2 ) 1 − exp(−p/λSi)
(C.1)
(24 − W ) + W exp(−∆d /λSiO2 )
While this is a rather complicated transcendental equation, but there are only three
unknowns. Measurements made at three energies will provide a unique solution. We
can rearrange Equation 1 and collect like terms to get:
h
W = 24F F 1 − exp(−∆d /λSiO2 ) + exp(−∆d /λSiO2 ) 1 − exp(−p/λSi)
∆d = λSiO2 ln 1 − exp
(−p/λSi)
− F − ln F
p = −λSi 1 − F + F exp
(−∆d /λSiO2 )
229
(C.2)
24
−1
W
24
1−
W
i−1
(C.3)
(C.4)
C.5
Measurement of Gate Lengths
An analogous set of data must be acquired to determine the length of each gate. In
addition to changing the actual voltages on the gates, though, we must also change
which gate is the low gate. The two high gates will always be fixed well above the
threshold voltage, while the low gate will be above the threshold for one set (hereafter
AllHigh) and below for the other set (hereafter mixed). Suggested clock voltages are
+12/+3 V (AllHigh) and +5/-5 V (Mixed).
Since the gates span the length of the entire pixel, the geometry reduces to one
dimension, parallel to the direction of charge transfer. Referring to Figures C-2 & C-3,
event grades g346 evenly sample a cross-section of the polysilicon gates and insulating
oxide layers. If we used the Mixed g346 pulse-height distribution as a template, we
can extract the fraction of events F1 that arise from the p+ implant under the low
gate from the AllHigh pulse-height distribution. By changing which phase is low, we
can derive F2 and F3 . In general, Fx will be of the form:
Fx =
i
hx h (−∆d /λSiO ) 2
exp
1 − exp(−p/λSi) exp(−gx /λSi) exp(−ox /λSiO2 )
24
(C.5)
The last two terms account for the attenuation of incident photons by the polysilicon gate and oxide, with thicknesses gx and ox . Because we can only determine the
thicknesses of the gates with respect to one another, the only measurable quantities
are ∆Dsimn ≡ gm − gn and ∆Doxmn ≡ om − on . Assuming gate 1 is the thinnest and
gate 3 the thickest, it it easy to show that:
F1
=
F2
h1
h2
F2
=
F3
h2
h3
and
!
!
1
(−∆Dsi12 /λSi )
exp
exp(−∆Dox12 /λSiO2 )
1
(−∆Dsi23 /λSi )
exp
exp(−∆Dox23 /λSiO2 )
230
!
(C.6)
!
(C.7)
Using the fact that h1 + h2 + h3 = 24 µm, we obtain:
h2 =
1+
F1
F2
24
(+∆Dsi12 /λSi)
exp
(+∆Dox12 /λSiO2 )
exp
+
F2
F3
exp(−∆Dsi23 /λSi )exp(−∆Dox23 /λSiO2 )
(C.8)
While this expression looks daunting, if the relative gate and oxide thickness
∆Dsimn and ∆Doxmn have been previously determined from either mesh experiments
or similar clocking experiments (Prigozhin 1999b), solving for all the gate lengths
becomes trivial. In fact, data at only one energy is required.
231
232
Appendix D
Expression for Signal-to-Noise Ratio
We define the signal-to-noise ratio S/N as
S/N ≡
S
,
σs
(D.1)
where the S is the signal and σs is its variance. The signal is defined as
S ≡ Ns − b,
(D.2)
where Ns is the number of counts in the source region and b is the background.
The background number b is related to the number of background counts observed
in the background region by
b ≡ βNb ,
(D.3)
where β is the ratio of effective exposure areas of the source region to the background
region. This ratio accounts for the geometric size of the regions and the exposure
time of each sky element comprising the two regions and is of the form
β=
source
X

!, background
X

ti ai
ti ai  ,
i
(D.4)
i
where ti and ai are the exposure time and size of each element of a particular region.
233
In the limit of large numbers, the error associated with a Poisson process is the
square root of the observable. The errors for Ns and Nb are thus
q
σNs =
q
Ns and σNb =
Nb .
As the two regions are physically distinct, the errors are uncorrelated and from the
definition of S given in Equation D.1, σs is
2
2
σs2 = σN
+ β 2 σN
s
b
(D.5)
Using the above expressions, Equation D.1 simplifies to
S
S/N = q
S + b(1 + β)
234
.
(D.6)
Appendix E
The Central X-Ray Point Source in
Cassiopeia A
This Appendix is a self-contained paper authored by Deepto Chakrabarty, myself,
Lars Hernquist, Jeremy Heyl, and Ramesh Narayan. It has been accepted for publication in the Astrophysical Journal.
E.1
Abstract
The spectacular “first light” observation by the Chandra X-Ray Observatory revealed
an X-ray point source near the center of the 300 yr old Cas A supernova remnant.
We present an analysis of the public X-ray spectral and timing data. No coherent
pulsations were detected in the Chandra/HRC data. The 3σ upper limit on the pulsed
fraction is <25% for P > 100 ms, <35% for P > 5 ms, and <50% for P > 1 ms.
The Chandra/ACIS spectrum of the point source may be fit with an ideal blackbody
(kT =0.5 keV), or with blackbody models modified by the presence of a neutron
star atmosphere (kT =0.25–0.35 keV), but the temperature is higher and the inferred
emitting area lower than expected for a 300 yr old neutron star according to standard
cooling models. The spectrum may also be fit with a power law model (photon
index Γ = 2.8–3.6). Both the spectral properties and the timing limits of the point
235
source are inconsistent with a young Crab-like pulsar, but are quite similar to the
properties of the anomalous X-ray pulsars. The spectral parameters are also very
similar to those of the other radio-quiet X-ray point sources in the supernova remnants
Pup A, RCW 103, and PKS 1209–52. Current limits on an optical counterpart
for the Cas A point source rule out models that invoke fallback accretion onto a
compact object if fallback disk properties are similar to those in quiescent low-mass
X-ray binaries. However, the optical limits are marginally consistent with plausible
alternative assumptions for a fallback disk. In this case, accreting neutron star models
can explain the X-ray data, but an accreting black hole model is not promising.
E.2
Introduction
For over three decades, it has been well established that (some) supernova explosions
give rise to strongly magnetized (B ∼ 1012 G), rapidly rotating (P ∼ 10–30 ms) neutron stars (NSs), as in the young radio pulsars found in the Crab Nebula and nearly
a dozen other supernova remnants (SNRs). In some cases, a synchrotron nebula (or
“plerion”) has been detected around the pulsar, powered by non-thermal emission
from the NS. Emission (in some cases pulsed) has been detected at other wavelengths
(optical, X-ray, gamma-ray) arising from thermal and non-thermal processes. However, several clues have recently emerged suggesting that this paradigm is incomplete
(see Kaspi 2000 and Gotthelf & Vasisht 2000 for recent reviews). First, there are the
six slowly-rotating (P ∼ 6 s) “anomalous X-ray pulsars” (AXPs), which seem to be
young isolated NSs and may have extremely strong (B ∼ 1014 –1015 G) surface magnetic fields (Mereghetti 2000). Half of the AXPs are associated with SNRs. Possibly
related are the four known soft gamma-ray repeaters (SGRs), which in quiescence
share many properties with AXPs and may also be associated with SNRs (Hurley
2000).
Also intriguing has been the identification of at least three radio-quiet non-plerionic
X-ray point sources near the centers of SNRs (Brazier & Johnston 1999 and references
236
therein). These objects have X-ray spectra roughly consistent with young, cooling
NSs, but show no evidence for either X-ray pulsations or emission at other wavelengths (in contrast to “normal” young NSs). Finally, the ongoing failure to detect
clear evidence for a young NS in the remnant of SN 1987A in the Large Magellanic
Cloud (LMC) has renewed theoretical interest in alternative models for the aftermath
of a SN explosion, especially with respect to fallback of ejected material onto a newborn NS. Several groups have concluded that, under some circumstances, a newborn
NS might collapse into a black hole (BH) shortly after birth (Brown & Bethe 1994;
Woosley & Timmes 1996; Zampieri et al. 1998; Fryer, Colgate, & Pinto 1999).
Nearby SNRs without known stellar remnants are thus obvious targets for further
study. After SN 1987A, the youngest known SNR in our Galaxy or the satellite Magellanic Clouds is Cassiopeia A. Its parent supernova was evidently noticed (though
misunderstood) by Flamsteed in 1680 (Ashworth 1980). This τhist = 320 yr historical age for Cas A is consistent with its optical expansion time scale (van den Bergh
& Kamper 1983), though somewhat shorter than its X-ray (τx ≈ 500 yr; Vink et
al. 1998) and radio (τradio ∼750–870 yr; Anderson & Rudnick 1995) expansion time
scales. The progenitor of this oxygen-rich SNR was probably a very massive (zero-age
main sequence mass MZAMS > 20M ) late WN-type Wolf-Rayet star which underwent prodigious mass loss via a stellar wind and eventually exploded as a type II
supernova (Fesen, Becker, & Blair 1987). The inferred distance to Cas A is 3.4+0.3
−0.1
kpc (Reed et al. 1995). The remnant subtends 4 arcmin in the sky, is the brightest
non-thermal radio source after the Sun, and has been extensively studied in the radio,
optical, and X-ray bands.
The spectacular “first light” observation of Cas A by the Chandra X-Ray Observatory on 1999 August 20 revealed the presence of a compact X-ray source near the
geometric center of the SNR (Tananbaum 1999). The source morphology is point-like,
with no obvious evidence for extension or a surrounding nebula (e.g., a plerion). The
discovery announcement notes that no obvious counterparts were detected within a
5 arcsec radius of the point source position on 20 cm radio maps or optical images.
237
Aschenbach (1999) detected the Chandra point source in archival 0.1–2.4 keV X-ray
images taken with the ROSAT/HRI in 1995-1996. Pavlov & Zavlin (1999) recovered
the point source in archival 0.5–4 keV X-ray images taken with the Einstein/HRI
in 1979 and 1981, and found that the Einstein, ROSAT, and Chandra count rates
were consistent with a constant X-ray source flux over all the observations. They also
noted that the observed spectrum appeared to be inconsistent with pure blackbody
radiation from the entire surface of a cooling NS. Umeda et al. (2000) speculated
on some possible scenarios for the nature of the point source, based on these early
results.
In this paper, we present a detailed analysis of the X-ray spectral and timing
features of the central point source in Cas A, based on the available public Chandra
data. In §E.3, we give a detailed description of the observation and our data analysis,
including our efforts to verify the instrumental calibration. In §E.4, we discuss our
results in the context of various models for the nature of the point source. We
summarize our finding in §E.5. While completing our manuscript, we learned of
another paper presenting an independent analysis of the spectral data by Pavlov et
al. (1999b). They used a subset of the data that we discuss in our paper, and their
spectral results are consistent with ours within the uncertainties. We include a brief
discussion of their preferred interpretation in §E.4.
E.3
Observations and Analysis
Numerous imaging observations of Cas A have been made by Chandra (formerly
AXAF; Weisskopf, O’Dell & van Speybroeck 1996) since its launch on 1999 July 23,
as part of the mission’s Orbital Activation and Checkout (OAC) calibration program.
All OAC data are immediately in the public domain. Most of the Cas A observations
were made using the AXAF CCD Imaging Spectrometer (ACIS; Burke et al. 1997),
which records both the sky position (0.49 arcsec/pixel) and the energy (∆E ≈ 50–200
eV) of each detected photon in the 0.1–10 keV range, with a time resolution of 3.2
238
s. A few of the observations were made with the High Resolution Camera (HRC;
Zombeck et al. 1995; Murray et al. 1997), which precisely records the sky position
(0.13 arcsec/pix) and arrival time (∆t=16 µs) of each detected photon, but with
modest (E/∆E ∼ 1) energy resolution. No diffraction gratings were in place for any
of the ACIS or HRC observations.
E.3.1
ACIS Data Reduction
As the analysis tools and calibration for Chandra are still under development at
this early stage of the mission, we will describe our data reduction, analysis, and
verification steps in detail. In using the ACIS data to derive a spectrum for the point
source in Cas A, we have restricted our analysis to the four exposures obtained during
1999 August 20–23 with Cas A placed on the back-illuminated (BI) ACIS S3 chip, for
three reasons. First, preliminary analysis showed that the point source spectrum was
relatively soft, and the two BI chips (S1 and S3) have superior low energy response
compared to the front-illuminated (FI) chips. Second, we wished to optimize the
Chandra point spread function by minimizing the off-axis angle of the point source,
and the Chandra aim points for ACIS lie on either the S3 or I3 chips. Inspection
of the Cas A images obtained on the other ACIS chips shows that the point source
is spread out over many more pixels, making it more difficult to separate from the
background; the effective area of the mirror and detector combination at these angles
is also reduced. Finally, the BI chips have not suffered the radiation damage that
degraded the energy resolution of the FI chips soon after launch, and so are better
calibrated at this early stage in the mission. A summary of the observations we used
is given in Table E-1.
We obtained the fully processed (level 2) ACIS event data for these observations
from the Chandra Data Archive. The data were acquired in Timed-Exposure/Faint
mode, with a frame read out every 3.2 s. A substantial number of frames was lost
to telemetry saturation due to the high total count rate from Cas A, resulting in
239
Table E-1. Selected Chandra observations of Cas A
ObsID
Start time (UT)
214
220
221
222
1999
1999
1999
1999
172
1409
1999 Sep 05, 18:45
1999 Oct 23, 18:31
a
20,
22,
23,
23,
00:07
23:27
00:52
01:38
Raper
(00 )
Telapsed
(s)
Tgood
(s)
Naper b
(ct)
Ratec
(ct ks−1 )
ACIS/S3
ACIS/S3
ACIS/S3
ACIS/S3
2.3
2.8
3.9
2.8
3.3
2.0
4.5
3.8
6107
4279
2103
2080
2803
1212
1060
1044
420
150
199
179
115 ± 7
113 ± 10
128 ± 13
125 ± 13
HRC-S
HRC-I
1.3
1.4
3.0
3.0
9485
12770
9485
12770
411
479
43 ± 2
38 ± 2
θ refers to the off-axis angle of the source.
b
c
Aug
Aug
Aug
Aug
Instrument
θa
(0 )
Counts in extracted aperture (including background).
Point source count rate (background subtracted).
240
an overall observation duty cycle of 42%. We filtered the events from the surviving
frames, accepting only those which fell within the “standard” event grade set (grades
0+2+3+4+6) in order to maximize the ratio of X-ray to non–X-ray events, and
additionally discarding events with very large pulse heights as due to cosmic rays.
For all the observations, the ACIS focal plane temperature was −100◦ C.
We did not attempt to improve upon the spacecraft aspect solutions from the
standard processing, but instead proceeded from the assumption that the central
source in Cas A is indeed point-like in morphology, as determined by Tananbaum
(1999). For each observation, we extracted all events located within a given radius of
the centroid position of the point source. Ideally, we would use the calibrated angular
response of the Chandra High-Resolution Mirror Assembly (HRMA) to choose an
extraction radius which encircled some fixed fraction (e.g., 95%) of the flux from a
point source for a given off-axis angle. However, both the focus position of the detector
and the quality of the spacecraft aspect solution were not necessarily optimal in these
early observations. Instead, we measured the radial distribution of source photons
for each observation from the data and estimated a 95% extraction radius. Table E-1
lists the aperture sizes.
The background in the point source region is dominated by the diffuse emission of
the supernova remnant and has strong contributions from both continuum and line
emission (e.g., Holt et al. 1994). The point source is located within a relatively low
surface brightness region of the remnant. Still, the background must be estimated
with care, as there are significant compositional gradients in this part of the remnant,
resulting in varying line strengths with position. After investigating the line strengths
in a number of nearby regions, we selected an off-centered 48 × 15 arcsec2 rectangular
region around the point source (with the point source itself and a small surrounding
buffer region excluded) to estimate the background surface brightness near the point
source. The point source and the background region are shown in FigureE-1.
The ACIS instrumental response may be parameterized by a photon energy redistribution matrix (hereafter RMF), which maps incident photon energy to detected
241
Figure E-1 A broad-band 0.3–10 keV intensity map of Cassiopeia A, as imaged by a
2.8 ks exposure with ACIS S3 (ObsID 214). The upper panel shows the incredible
structure present, including the central point source. The lower panel is an expanded
view of the boxed region in the upper panel. Both the point source and the rectangular
region used for the background region (see §E.3.2) are indicated.
242
pulse height amplitudes (PHAs). Every ACIS chip (1024 × 1026) is divided into four
parallel (256×1026) quadrants, each read out separately by four individual amplifiers.
Each quadrant requires a unique RMF, as each readout amplifier has a different gain.
Additionally, the parallel and serial charge transfer inefficiency in the BI chips leads
to differences in energy resolution and detection efficiency versus position within a
quadrant as well. Consequently, the ACIS instrument team has supplied multiple
position-dependent RMFs for each quadrant. We used the 1999 October 28 version
of RMFs developed for observations taken at a focal plane temperature of −100◦ C.
Fortuitously, the Cas A point source (and nearly all of the selected background
region) lies entirely in quadrant 2 for all four of the S3 observations. Furthermore,
the four observations were located within 250 pixels of each other within the chip
quadrant, minimizing the differences in CCD response. Thus, the four RMFs appropriate for each observation may be combined using an exposure-weighted average,
without any serious loss of accuracy. This allows us to sum the four individual S3
count spectra into a single “grand total” S3 count spectrum with improved statistics.
In addition to the RMFs, an ancillary response function (hereafter ARF) is needed to
characterize the effective area of the HRMA and the quantum efficiency of the ACIS
detector as a function of incident photon energy and off-axis angle. We computed the
appropriate ARF for each observation using software created by members of the ACIS
and High Energy Transmission Grating instrument teams at MIT, and then combined
them by an exposure-weighted average for use with our summed count spectrum.
E.3.2
X-Ray Spectral Fitting
The summed, background-subtracted ACIS count spectrum was analyzed using the
XSPEC v10.00 software package (Arnaud 1996). We rebinned the data at 0.15 keV
resolution (32 ADU/channel) and restricted our analysis to 21 bins in the 0.7–4.0 keV
range, resulting in at least 10 count bin−1 in all but 3 bins at high energy (with a
minimum of 5 count bin−1 and a maximum of 71 count bin−1 ). The rebinned count
spectrum is shown in FigureE-2. In light of the relatively low count rate, our model
243
fitting weighted each bin by 1 + (Ni + 0.75)1/2 rather than Ni1/2 (where Ni is the
number of counts in bin i). This is a superior weighting scheme when Ni is small and
asymptotes to the usual weighting when Ni is large (Gehrels 1986).
We fit several different spectral models to these data: a simple power law, thermal
bremsstrahlung, an ideal blackbody (BB), and two modified BB models. The modified
BB models assume that the emitting object is a NS and account for the effect of a lightelement stellar atmosphere on the emergent spectrum. The strong NS surface gravity
essentially guarantees that the photosphere will be dominated by the lightest element
present (Alcock & Illarionov 1980; Romani 1987). For such atmospheres with T ∼ 106
K, the E −3 dependence of free-free absorption will shift the peak of the emission
blueward from that of an ideal BB (Romani 1987; Zampieri et al. 1995). Previous
authors have shown that neglecting this effect and fitting the Wien tails of such
spectra with an ideal BB model significantly overestimates the effective temperature
and underestimates the emitting area (Rajagopal & Romani 1996; Zavlin, Pavlov, &
Shibanov 1996; Rutledge et al. 1999). To consider this possibility, we employed two
models: the simple analytic spectrum emerging from the power-law atmosphere of
Heyl & Hernquist (1998a; hereafter HH98a), with γ = 3 as appropriate for a lightelement atmosphere; and the more detailed H atmosphere model of Zavlin, Pavlov,
& Shibanov (1996; hereafter ZPS96), developed for a weakly magnetized NS.
For all these models, we included the effect of photoelectric absorption by neutral
gas along the line of sight (Morrison & McCammon 1983), which is a significant
effect at low (. 1 keV) energies. The absorption is typically quantified in terms
of the column density of neutral hydrogen NH toward the source, with a particular
elemental abundance model assumed (e.g., Anders & Ebihara 1982 in our case). With
the relatively small number of low-energy X-ray photons detected from the Cas A
point source, it is difficult to constrain NH precisely. Moreover, its value in this
situation is highly spectral-model–dependent and strongly covariant with the overall
flux normalization. However, NH may also be determined from radio measurements
of the atomic and molecular hydrogen column densities using the 21 cm Hi and 18 cm
244
OH absorption lines, respectively. Keohane, Rudnick, & Anderson (1996) have used
such data to derive a spatially-resolved column density map of the Cas A SNR at 30
arcsec resolution. Using this map, we estimate that the column density towards the
Cas A point source is NH = (1.1 ± 0.1) × 1022 cm−2. However, this estimate must
be used with caution, as the radio maps give no information on small–angular-scale
variations in the column. For each spectral model we employed, we fit the data both
with NH held fixed at this value and with NH as a free parameter.
Our spectral fitting results are summarized in TableE-2, and a typical model fit
is shown in FigureE-2. All of the models gave formally acceptable fits. However, the
BB and NS atmosphere models fit slightly better to the data than the other models,
although with inferred radii considerably smaller than a typical 10 km NS radius.
Note that the quoted parameters for the BB and NS atmosphere models are for an
observer at infinity, assuming the gravitational redshift correction for a 10 km, 1.4M
NS.
Interpretation of our results depends critically upon the reliability of the energy
and effective area calibrations of Chandra, which are still being evaluated by the
instrument teams. To verify the robustness of our conclusions, we made a rough
check of these calibrations by fitting the X-ray spectral data from the 1999 Aug
23 ACIS/S3 observation of SNR E0102−72 (ObsId 1231), the brightest supernova
remnant in the Small Magellanic Cloud (SMC; Hayashi et al. 1994). For comparison,
we also analyzed archival spectral data for the same source as observed by ASCA
on 1993 May 12–13. For both data sets, we restricted our analysis to 0.6–2.6 keV
(an energy band that both contains the majority of the SNR flux and spans a range
similar to that of the Cas A point source) and fit the same plasma model, with fixed
column density and non-solar abundances. The derived plasma temperatures agree to
better than 2%, and the overall normalizations to within 13%, using the preliminary
calibrations.
245
Table E-2. X-ray spectral fits for Cas A point source
NH
(1022 cm2 )
Photon
indexa
C1 b
kT ∞ c
(keV)
d
R∞
bb
(km)
Lx,33 e
χ2red /dof
Power law
1.68+0.39
−0.22
1.1 (fixed)
3.13+0.50
−0.30
2.35 ± 0.12
1.62+1.22
−0.47
0.65+0.07
−0.05
···
···
···
···
43+122
−22
7.4+1.5
−1.0
1.12/18
1.44/19
Thermal brems.
1.39+0.23
−0.13
1.1 (fixed)
···
···
1.37+0.61
−0.40
0.84 ± 0.09
1.47+0.34
−0.26
1.97+0.26
−0.21
···
···
5.2+3.3
−1.9
3.8+0.7
−0.6
0.92/18
1.00/19
Ideal blackbody
0.84 ± 0.15
1.1 (fixed)
···
···
···
···
0.53 ± 0.04
0.49 ± 0.02
0.41+0.08
−0.07
0.52+0.05
−0.04
1.7+1.6
−0.9
2.0+0.8
−0.6
0.69/18
0.77/19
NS atm. (HH98af )
0.85+0.18
−0.15
1.1 (fixed)
···
···
···
···
0.42 ± 0.03
0.38 ± 0.02
0.67 ± 0.12
0.88 ± 0.07
1.8+1.0
−0.6
2.1+0.5
−0.4
0.70/18
0.76/19
NS atm. (ZPS96g)
0.92+0.20
−0.16
1.1 (fixed)
···
···
···
···
0.28 ± 0.03
0.26 ± 0.02
1.80+0.55
−0.35
2.23+0.24
−0.19
2.5+1.6
−0.9
2.8+0.6
−0.5
0.74/18
0.73/19
Model
a Photon
index, defined such that the unabsorbed photon number flux dN/dE ∝ E −Γ .
b Unabsorbed
c For
flux density at 1 keV, in units of 10−3 photon cm−2 s−1 keV−1 .
BB and NS atmosphere models, as measured by an observer at infinity.
d Implied
blackbody radius assuming a source distance of 3.4 kpc, as measured by an observer at infinity.
keV luminosity in units of 1033 erg s−1 assuming a source distance of 3.4 kpc or bolometric luminosity at
infinity for blackbody models.
e 0.1–10
f Analytic
gH
NS power-law atmosphere of Heyl & Hernquist (1998a), with γ = 3.
atmosphere for a non-magnetic NS (Zavlin et al. 1996).
246
Figure E-2 The background-subtracted Chandra/ACIS-S count spectrum of the Cas A
point source, summed from the four individual S3 exposure on 1999 Aug 20–23 for
a total exposure of 6119 s. The dark line shows the spectrum predicted by an absorbed blackbody model with kT ∞ = 0.53 keV and NH = 0.84 × 1022 cm−2 . Other
models (power law, NS atmosphere) predict similar spectra. The present data do not
discriminate strongly between these models.
247
E.3.3
X-Ray Timing
We examined two on-axis observations of Cas A made with the HRC as part of the
OAC program, using the HRC-S and HRC-I detectors respectively. These observations are summarized in Table E-1. We obtained the processed level 2 event data
from the Chandra Data Archive. In both cases, the overall count rate (∼ 140 count
s−1 ) from Cas A was below the telemetry threshold (≈ 184 count s−1 ) where deadtime effects become significant. For each observation, we extracted all events within
3 arcsec of point source centroid. The photon arrival times, provided in terrestrial
time (TT) at the spacecraft, were corrected to barycentric dynamical time (TDB) at
the solar system barycenter using the JPL DE200 solar system ephemeris (Standish
et al. 1992) and a geocentric spacecraft ephemeris.
We binned the events into 0.5 ms time bins and computed a Fourier power spectrum of the resulting time series. No significant pulsations were detected; the highest
peak in the power spectrum had a significance of only 2σ when the number of trials
is accounted for. To improve our statistics, we also computed an incoherent power
spectral sum of 9 ks segments of each observation. Again, no significant pulsations
were found, with the highest peak having a significance of only 0.8σ including the
number of trials. A large pulse frequency derivative might spread a coherent pulsation
over multiple power spectral bins, reducing our sensitivity. However, for the ≈ 10
ks observations used here, a pulse frequency derivative of ν̇ = 1/T 2 & 10−8 Hz s−1
would be required. This is 25 times larger than ν̇ for the Crab pulsar, and & 105
larger than the typical value for an AXP or SGR. To enhance our sensitivity to nonsinusoidal pulse shapes, we also performed a harmonic fold of the power spectrum.
No significant pulsations were detected.
We used our incoherent power spectral sum to estimate an upper limit for the
sinusoidal pulsed fraction of the Cas A point source, accounting for the suppression
of power spectral sensitivity at high frequencies due to binning of the data (e.g., van
der Klis 1989). We find that the 3σ upper limit on the sinusoidal pulsed fraction is
<25% at low frequencies, . 35% for ν < 200 Hz, and . 50% for ν < 1 kHz.
248
Our sensitivity to rapid pulsations depends upon an accurate correction for the
motion of the spacecraft with respect to the barycenter. As a check of our barycenter corrections and of the spacecraft ephemeris, we analyzed a 1999 August 31
HRC-I observation (ObsID 132) of PSR B0540–69, a young 50 ms pulsar associated
with the supernova remnant N158A in the Large Magellanic Cloud, using the same
data analysis procedure as for Cas A. We compared this measurement with a 1999
September 1 observation of an overlapping field with the Rossi X-Ray Timing Explorer
(these data were generously made available by F. E. Marshall of NASA Goddard Space
Flight Center). The frequencies measured in the two data sets were consistent within
the uncertainties, and also agreed with the value extrapolated from a timing model
based on a 1996 BeppoSAX observation (Mineo et al. 1999).
E.4
Discussion
We have shown that the X-ray point source in Cas A has a spectrum well-described
by either an absorbed power law with photon index 2.8–3.6 and unabsorbed 0.1–
10 keV luminosity (7–160)×1033 erg s−1 , or an absorbed BB or modified BB with
kT ∞ ≈ 0.25–0.5 keV and bolometric luminosity L∞ ≈ (1–5)×1033 erg s−1 . Our
Chandra spectral and timing measurements, combined with pre-existing limits at
other wavelengths, severely constrain plausible models for the nature of the X-ray
point source in Cas A.
We begin by pointing out, for completeness, that our steep power law spectral fit
essentially rules out the possibility that the point source is a background galaxy, as
active galactic nuclei (AGN) typically lie within a range of photon indices Γ = 1.2–2.2
(Turner & Pounds 1986). The AGN scenario is also extremely implausible given that
the point source is located within a few arcsec of the expansion center of the SNR
(Tananbaum 1999). Moreover, given the surface density of AGNs on the sky at this
flux level (Boyle et al. 1993), the probability of a chance coincidence is negligible.
There is thus little doubt that the point source is associated with the supernova
249
remnant.
We now summarize the implications of our results for several other interpretations.
E.4.1
Classical Young Pulsar
If the Cas A point source is a classical young pulsar (the conventional product expected for a type II SN explosion), then the X-ray radiation should be predominantly
non-thermal power-law emission from relativistic acceleration of e+e− pairs in the corotating NS magnetosphere (see Romani 1996). The properties of the point source are
compared with the four youngest (< 104 yr) known pulsars1 in Table E-3, all of which
have power law X-ray spectra with Γ = 1.5–1.7. There are several clear distinctions.
The spectral shape of the Cas A point source is considerably steeper than that of the
young pulsars, although its X-ray luminosity is marginally consistent with the lower
end of the young pulsar range. The upper limit on the point source’s X-ray pulse
fraction is lower than those measured in the young pulsars with the possible exception of PSR B0540–69. Radio pulsations have not been detected from Cas A, with an
upper limit of L600 < 530 d23.4 mJy kpc2 for the 600 MHz radio luminosity (Lorimer,
Lyne & Camilo 1998). This non-detection could be explained by beaming, judging
from the observed radio luminosities for the known young pulsars (≈ 900 mJy kpc2
for the Crab and PSR B0540–69, but only ≈ 30 mJy kpc2 for PSR B1509–58 and
PSR J1119–6127; Taylor, Manchester, & Lyne 1993; Kaspi et al. 2000). However,
the Chandra images also show no evidence for a plerion surrounding the point source.
Plerions, powered by synchrotron emission, have been detected around all four of the
classical young pulsars in Table E-3 (and even around some X-ray point sources in
SNRs which are not known pulsars). We conclude that the point source in Cas A is
not a classical young pulsar.
1
A fifth young (τc = 1.6 kyr) pulsar, PSR J1119–6127, has recently been discovered (Camilo et
al. 2000; Kaspi et al. 2000). However, its X-ray spectral properties are not yet determined.
250
251
Cas A
SNR
0.0
Pup A
RCW 103
PKS 1209 52
Crab
MSH 15 52
N158A
N157B
N49
G337.0 0.1?
G42.8+0.6?
1.2
0.0
0.6
2
0.3
0.2
0.2
0.0
0.2
0.2
0.5
0.1
0.0
0.2
5.16
7.47
8
6.41?
11.8
6.45
6.97
11.0
8.69
6.98
0.033
0.150
0.050
0.016
0.075?
/2.5
2.8?/4.0
3.1?/ ?/3.7
?/3.7
3.6/3.3
3.7?/ ?/<3.9
4.0/ 4.8?/ 5.3/4.0
3.1/3.0
3.2/3.2
3.2/3.1
3.7/3.7
3.9/3.6
/3.1
/3.8
log c /log SNR
(yr)
5.0
14.5
47
11.0
7.0
3.0
8.5
10.0
1
4.0
2.0
5.2
47
47
2.0
3.1
1.5
3.4
d
(kpc)
34.5
36.0
35.8
2.5
36.9
34.4
38.6
36.9
35.9
36.9
36.2
35.3
36.6
35.5
33.8{34.6
1.1
2.2
3.4
2.5
4.6
2.9
3.7
4.0
1.74
1.36
1.3
1.6
2.2{3.6
Power law spectrum
Photon
log Lpl
index
(erg s 1 )
0.51
0.64
0.72
0.41
0.39
0.43
0.28
0.56
0.25
0.5
1.4
0.6
1.6
8.9
2.4
2.2
2
0.81
1.1
0.5
34.2
33.9
34.9
35.5
33.5
34.3
33.6
33.9
33.1
33.3
Blackbody spectrum
kT 1
R1
log L1
bb
bb
(keV) (km) (erg s 1 )
Cas A and comparison objects
11
23
<66
10
15c
70
50
50
10
30
10
& 75
65
& 15
20?
< 35
Pulsed
frac. (%)
28,29
30-32
33,34
35-37
16,17
18,19
20,21
22-24
25,26
24,27
8
9,10
11,12
13-15
1-3
4,5
6,7
Ref
Note. | is dened as the ratio between the source distance from the center of the SNR to the radius of the SNR; the characteristic age is dened as
c = P=2P_ ; luminosities are either bolometric (BB) or for the 0:1 10 keV band (PL).
References. | (1) Petre et al. 1982; (2) Petre, Becker & Winkler 1996; (3) Pavlov, Zavlin & Trumper 1999a; (4) Helfand & Becker 1984; (5) Mereghetti,
Bignami & Caraveo 1996; (6) Tuohy & Garmire 1980; (7) Gotthelf, Petre & Hwang 1997; (8) Harnden & Seward 1984; (9) Marsden et al. 1997; (10) Gaensler
et al. 1999a; (11) Finley et al. 1993; (12) Seward & Harnden 1994; (13) Wang & Gotthelf 1998a; (14) Wang & Gotthelf 1998b; (15) Marshall et al. 1998;
(16) Gotthelf & Vasisht 1997; (17) Gotthelf, Vasisht & Dotani 1999b; (18) Corbet & Mihara 1997; (19) Oosterbroek et al. 1998; (20) Torii et al. 1998; (21)
Gaensler et al. 1999b; (22) Sugizaki et al. 1997; (23) Israel et al. 1999a; (24) Kaspi, Chakrabarty & Steinberger 1999; (25) White et al. 1996; (26) Israel et
al. 1999b; (27) Rho & Petre 1997; (28) Vasisht et al. 1994; (29) Woods et al. 1999a (30) Sonobe et al. 1994; (31) Corbel et al. 1997; (32) Kouveliotou et
al. 1998 ; (33) Vancura et al. 1992; (34) Marsden et al. 1996 ; (35) Woods et al. 1999b ; (36) Corbel et al. 1999 ; (37) Hurley et al. 2000
e The
spectral properties and pulse fractions listed for the SGRs are for quiescent emission.
extended radio nebula G10.0 0.3, once identied as a SNR, is now thought to be powered by a massive companion or the SGR itself (Gaensler
2000; Eikenberry & Matthews 2000; Frail, Vasisht & Kulkarni 1997).
d The
a For the Cas A point source and AX J1845 0258, the powerlaw (PL) and (blackbody) BB models are alternative ts to the same data. For all the other
sources, the PL and BB models are each components of a combined model.
b Here, we only include those sources that are well-established and have constrained spectral properties.
c We note that this value is half that reported in the literature, due to a dierent denition of pulsed fraction by these authors.
SGR 1900+14
SGR 1806 20
SGR 0526 66
SGR 1627 41
e
CTB 109
G29.6+0.1
Kes 73
Soft gamma repeatersd
1E 1841 045
1E 1048.1 5937
AX J1845 0258a
RXS J1708 40
4U 0142+61
1E 2259+586
Anomalous X-ray pulsars
PSR B0535+21
PSR B1509 58
PSR B0540 69
PSR J0537 6910
Young classical pulsars
1E 0820 4247
1E 1614 5055
1E 1207 5209
Other non-plerionic X-ray point sources in SNRsb
Point sourcea
Cassiopeia A
Source
Pspin
(s)
Table C-3.
If the Cas A point source is a NS, the absence of both detectable radio pulsations
and a synchrotron nebula may indicate that it lies beyond the so-called pulsar “death
line”, an empirical boundary on the spin-period–magnetic-field plane beyond which
radio pulsars have generally not been detected, presumably because the NS does
not generate enough e+e− pairs to power significant non-thermal emission2 (Chen &
Ruderman 1993). In this case, we would expect a strongly magnetized (B & 1011
G) NS to have a spin period of order at least a few seconds. Conversely, a rapidly
spinning NS (P ∼ 30 ms) would have a very weak magnetic field (B . 108 G), perhaps
consistent with delayed field growth (Blandford, Applegate & Hernquist 1983).
E.4.2
Cooling Neutron Star
An alternative interpretation is that the X-rays from the Cas A point source arise
from thermal emission from a cooling NS. A 300 yr old NS cools primarily via neutrino
emission; standard cooling models predict thermal photon emission from the surface
with kT ∞ = 0.15–0.25 keV (Page & Sarmiento 1996; Page 1998). All of our BB
and modified BB fits for the Cas A point source yield somewhat higher temperatures
(kT ∞ ≈ 0.25–0.5 keV), as well as much smaller BB radii (R∞
bb ≈ 0.6–2.6 km) than
expected for a 10 km NS, even when accounting for a light-element atmosphere.
The NS atmosphere models (HH98a, ZPS96) that we fit to the data were computed
assuming a weak (B . 1010 G) magnetic field, which may be a poor assumption for a
young NS. Qualitatively, however, the presence of a magnetic field of order ∼ 1012 G
will shift the peak of the emission in a light-element atmosphere redward towards the
ideal BB case (Pavlov et al. 1995), thus exacerbating the discrepancy between the
data and standard NS cooling curves. We note, however, that the behavior of spectral
shifts in ultrastrong magnetic fields (B ∼ 1014 –1015 G) has not yet been calculated.
While our inferred temperature is marginally consistent with standard NS cooling
2
The recent identification of a radio pulsar well beyond the death line, PSR J2144–3933 (P = 8.51
s, B ≈ 6 × 1011 G) indicates that this argument must be used cautiously (Young, Manchester, &
Johnston 1999).
252
curves, the small emitting area remains problematic, especially given our limits on
the X-ray pulsed fraction. Strong (B ∼ 1012 –1013 G) magnetic fields will produce a
non-uniform temperature distribution on the surface of a NS, owing to anisotropic
electron conduction through the star’s outer envelope (e.g. Greenstein & Hartke 1983;
Heyl & Hernquist 1998b, 1999). However, the resulting temperature variation across
the surface does not produce small hot spots, but is instead smoothly varying with a
local flux roughly ∝ cos2 ψ, where ψ is the polar angle from the magnetic axis. This
would reduce the effective area of the emitting surface by a factor ∼ 3, far less than
the factor of 30–100 required by our spectral fits.
Similar conclusions motivated Pavlov et al. (1999b) to consider a model in which
the magnetic polar caps are intrinsically hotter than the bulk of the stellar surface, as
a result of horizontal chemical abundance gradients through the conductive envelope.
Light element envelopes transmit heat more readily than ones made of heavy elements
(Chabrier, Potekhin & Yakovlev 1997; Heyl & Hernquist 1997a), so hot polar caps
consisting of hydrogen embedded in a cooler iron crust can, in principle, yield an
emitting area consistent with the spectral fits (Pavlov et al. 1999b). However, such
a model predicts that the emission should be pulsed at the rotation period of the
star, unless either the magnetic and rotation axes are nearly aligned, or the line
of sight nearly coincides with the rotation axis. Pulsed fractions at the level of
10–70% required to account for the putative thermal emission from middle aged
radio pulsars (e.g. Becker & Trumper 1997) and AXPs (e.g., Mereghetti 2000) can
be produced from smoothly varying properties of NS envelopes, such as anisotropic
heat conduction (Heyl & Hernquist 1998b) or directionally dependent opacities (e.g.
Pavlov et al. 1994, Zavlin et al. 1995, Shibanov et al. 1995), even when gravitational
bending of light is included (e.g. Page 1995, Heyl & Hernquist 1998b). An even larger
pulsed fraction will result, in general, from the hot spot model. For example, in the
case of the orthogonal rotator model of Pavlov et al. (1999b), we estimate typical
maximum to minimum flux variations > 2 for 1.4M NSs with radii R > 7 km. This
253
is in severe disagreement with the upper limits we obtain for the pulsed fraction.3
Observationally, we cannot yet exclude the case of a nearly aligned rotator, but it is
not clear that the horizontal abundance gradients required by the Pavlov et al. model
will be stable for long times in the liquid crust.
E.4.3
Accretion onto a Neutron Star or Black Hole
We now consider the possibility that the point source in Cas A is powered by accretion
onto a NS or a BH. This possibility was also raised by Umeda et al. (2000) and Pavlov
et al. (1999b). We assume that the accretion is fed by fallback material left over after
the original supernova explosion (e.g. Chevalier 1989). We prefer such a model to
a binary accretion model since there is no optical/IR evidence for a such binary
companion star (van den Bergh & Pritchet 1986). A very low-mass dwarf companion
might have evaded detection, but such a companion would be unlikely to remain
bound in the binary following the supernova explosion, given the high mass of the
Cas A progenitor.
We begin with the possibility of accretion onto a NS. If the accretion occurs via
a thin disk extending down to the marginally stable orbit at 6GM/c2 , or the NS
surface (whichever is larger), then we expect significant emission from an equatorial
boundary layer where the accreting material meets the star. The emitting zone is
expected to have a radial extent roughly equal to the local scale height of the disk
(Narayan & Popham 1993; see also Inogamov & Sunyaev 1999 for a recent discussion
of boundary layer models). If the boundary layer is optically thick, then it will emit
BB radiation. For an accretion luminosity ∼ 1033.5 erg s−1 . 10−4 LEdd , the scale
height is ∼ 0.1 km, and the effective area of the radiating zone is ∼few km2 . This
is in reasonable agreement with the effective area ∼km2 determined from fitting the
Chandra data (TableE-2). We consider this a viable model, although we note that
3
For special choices of the NS radius, however, gravitational bending of light will make the entire
stellar surface singly visible, eliminating any pulsed component; see, e.g. figure 7 of Heyl & Hernquist
(1998b).
254
the optical thickness of such boundary layers is not well understood.
This boundary layer model requires that the NS have a very weak magnetic field.
Specifically, the magnetospheric radius rm has to be smaller than the stellar radius,
which implies that B < 107 G for the estimated X-ray luminosity. If the magnetic
field is somewhat stronger, then the disk would be terminated at rm . Even in this
case, we might expect a boundary layer to develop at rm , and the model would be
consistent with the observations for fields B . 109 G. We note that for sufficiently
large B, accreting material is centrifugally expelled from the system at rm (Illarionov
& Sunyaev 1975). In this case, very little material would reach the neutron star
and there would be negligible X-ray emission (e.g., Chatterjee, Hernquist, & Narayan
1999; Alpar 1999).
If the NS instead has a magnetic field & 1012 G typical of young radio pulsars,
then boundary layer emission is unlikely to explain the observed X-rays. In this case,
we would have to assume that the accreting material is able to reach the surface of the
neutron star, which would require that the neutron star be spinning quite slowly (in
order to avoid centrifugal expulsion of matter). The effective area of the radiating zone
would again be small, and could thus be consistent with the observations. However,
we would predict strong coherent pulsations in the X-ray signal . Our upper limit of
25% on the pulsed fraction from the Cas A point source does not rule out pulsations
at the level observed in many known B ∼ 1012 G accreting pulsars. More sensitive
searches for pulsation would be very worthwhile.
A third kind of accreting NS model is one in which the accretion disk is truncated
at a large transition radius, and the flow farther in occurs via an ADAF (as in the
Narayan et al. 1997 model for low-luminosity BH binaries). Boundary layer emission
in such a model is not well understood, so we are not in a position to predict the
emission spectrum. However, if the ADAF is terminated at rm and the material then
flows onto the magnetic poles, the spectrum would be similar to the case with a thin
disk which was discussed above.
Accreting BH models face considerably greater difficulty in fitting the observa255
tions. This is because neither a boundary layer nor channeled accretion onto magnetic poles is expected. Therefore, any blackbody emission should be primarily from
the inner accretion disk, with an effective area of several times πR2S, where RS is the
Schwarzschild radius of the black hole. For a 10M BH, the area is ∼ 103 km2, which
is clearly inconsistent with the X-ray data. This means that the X-ray emission from
a BH point source in Cas A would have to originate either via Compton scattering in
an optically thin corona over a thin disk, or via optically thin bremsstrahlung emission from a hot ADAF. We have explored models of this kind, using the modeling
techniques described in Narayan et al. (1997) and Quataert & Narayan (1999), but
we find that we need to fine-tune the models to an uncomfortable degree to fit the
observations.
It is important to note that accretion models are severely constrained by the
observed flux ratio between X-ray and optical bands. The optical limits on a stellar
remnant in Cas A are I & 23.5 and R & 24.8 (van den Bergh & Pritchet 1986).
Applying the extinction corrections estimated by these authors, the X-ray–to–optical
flux ratio is FX/Fopt > 100. Although this is typical for bright X-ray binaries, it
is considerably larger than the ratios observed in quiescent accreting BHs and NSs
with luminosities comparable to the Cas A point source, e.g. FX/Fopt ∼ 1/30 for the
BH system A0620–00 and FX/Fopt ∼ 1/3 for the NS system Cen X-4 (McClintock &
Remillard 2000). Both sources have an X-ray luminosity lower than the point source
in Cas A, and both have optical luminosities significantly higher than the upper limit
for the Cas A source. If the spectra of these sources are characteristic of accreting
BHs and NSs at low luminosities, then accretion models for Cas A are ruled out with
high confidence.
It is possible, however, to evade this conclusion by arguing that these low-mass
X-ray binaries (LMXBs) are a poor comparison to the Cas A point source. First of all,
the quiescent optical emission in some BH binaries has been modeled as synchrotron
emission from a hot advection-dominated accretion flow (ADAF) close to the BH
(Narayan, McClintock & Yi 1996; Narayan, Barret & McClintock 1997). However,
256
if the emission instead comes from a “hot spot” (e.g., where the accretion stream
from the mass donor hits the thin accretion disk), then it is specific to binary systems
and should be absent in systems with a fallback disk. This possibility has not been
modeled in any detail. Also, X-ray reprocessing in the accretion disk is a significant
source of optical emission in LMXBs (van Paradijs & McClintock 1995), especially
since the outer disks evidently subtend a large semi-angle (∼ 12◦ ) at the central object
(de Jong, van Paradijs, & Augusteijn 1996). The reason for such large angles may
be warping of the outer disk (see Dubus et al. 1999; Esin et al. 2000). But if such
warps are induced primarily by binary effects, then a fallback disk in Cas A might
not be similarly warped (although it has been argued that irradiation alone can lead
to significant warping; see Petterson 1977; Pringle 1996; Maloney et al. 1996). For an
unwarped disk, the subtended semi-angle would be set by the disk’s scale height at
the relevant radius (∼ 1010 cm). By employing an analysis similar to that in Perna,
Hernquist & Narayan (1999), we estimate that the re-emitted optical flux in such a
model would be (just) below the optical flux limits for the Cas A source.
Thus, the optical limits strongly constrain accretion models, but do not yet conclusively eliminate them. By comparing the predictions of the models with the X-ray
observations, specifically the small effective area ∼ km2 of the emission, we conclude
that models with accreting NSs are more promising than those with BHs.
E.4.4
Comparison with AXPs, SGRs, and Radio-quiet Point
Sources
It is interesting to compare the properties of the Cas A point source with three
classes of objects whose nature remains puzzling: AXPs, SGRs, and the radio-quiet
non-plerionic X-ray point sources in SNRs. Both AXPs and SGRs pulse with slow
spin periods despite being young objects (based on their association with SNRs). We
summarize the X-ray properties of these objects in Table E-3.
The X-ray spectrum of most AXPs is best characterized by a two-component
257
spectrum consisting of a ∼ 0.5 keV BB and a steep (Γ = 3–4) power law extending
out to 10 keV, with comparable luminosity in both components. The BB components
∞
34
35
erg s−1 , quite similar to the BB fit for the
have R∞
bb = 1–4 km and Lbb ∼ 10 –10
Cas A point source. (We note that, due to poor photon statistics in the present data,
we would be unable to detect the presence of an additional power-law component
with this BB fit if the Cas A point source has an AXP-like two-component spectrum.)
While four of the AXPs have large pulsed fractions (30–70%), two have much lower
pulsed fractions (10–15%) which are consistent with the non-detection of pulsations in
Cas A. However, the X-ray luminosity of the Cas A source is at least a factor of three to
ten lower than that of the AXPs, in spite of its relative youth. Overall, the properties
of the Cas A point source are roughly consistent with being an underluminous AXP.
This possibility can be tested by a deeper search for long-period X-ray pulsations.
The quiescent emission of SGRs may be fit with a power law with Γ = 1.1–2.5
and a 2–10 keV luminosity of (3–100)×1034 erg s−1 . These spectral parameters are
also consistent with those measured for Cas A. However, we note that the proposed
associations between SGRs and SNRs are somewhat tenuous, in contrast to those
proposed for AXPs (Gaensler 2000). Moreover, no soft gamma-ray bursts have ever
been detected from the direction of Cas A.
Finally, there are the three radio-quiet X-ray point sources that each lie near the
center of an SNR and have no evidence for a plerion. The X-ray properties of these
sources are summarized in Table E-3. The X-ray emission from these objects is well
characterized by a BB spectrum with kT ∞ ≈ 0.2–0.6 keV and Rbb ≈ 0.6–3 km,
comparable to what we measure in Cas A. From a spectral point of view, these four
sources form a remarkably homogeneous group. A marginal detection of pulsations
(P = 75.3 ms) was reported from the source in Pup A with a pulsed fraction of
20% (Pavlov, Zavlin, & Trümper 1999a), below the limit placed in Cas A. However,
the point source in RCW 103 has shown order of magnitude variability in its flux
(Gotthelf, Petre, & Vasisht 1999a). This is in stark contrast to the Cas A point
source, which shows no evidence for strong variability on either short (see TableE-1)
258
or long (Pavlov & Zavlin 1999; Pavlov et al. 1999b) time scales.
E.5
Conclusions
At present, we do not have a unique model to account for the observed properties of
the X-ray point source in Cas A. Thermal emission from an isolated, cooling NS can
account for the data, but only if unconventional modifications are incorporated into
spectral models in order to satisfy the requirement that the emitting area be small.
Localized hot spots can, in principle, be produced on the surface of a NS by horizontal
chemical abundance gradients in the liquid envelope (Pavlov et al. 1999b). Alternatively, hot spots could be formed by particle bombardment of the polar caps through
magnetospheric activity, as may be occurring in some middle-aged radio pulsars (e.g.
Becker & Trumper 1997). Whether or not this second possibility is reasonable for the
Cas A point source in view of the absence of detectable radio emission is questionable. In any event, hot spots should give rise to a significant pulsed component to the
emission, in general, and such models will likewise be constrained by future limits or
detections of X-ray modulation. Accretion onto a BH does not appear promising, but
NS accretion provides a viable mechanism for explaining the characteristics of the Xray emission. If the NS is very weakly magnetized, the observed emission could arise
from a boundary layer. Otherwise, the X-rays could be produced by magneticallychanneled accretion onto the NS. In the latter case, we expect pulsed emission, so
again, future timing limits test this interpretation.
The point source in Cas A is similar in many respects to the AXPs and quiescent
SGRs, which have been interpreted as ultramagnetized neutron stars (“magnetars”;
Duncan & Thompson 1992; Thompson & Duncan 1996; Heyl & Hernquist 1997a,
1997b) or as neutron stars with normal magnetic fields of order 1012 –1013 G accreting
from fallback disks (Chatterjee et al. 1999; Alpar 1999). It is important to note the
detailed thermal emission from neutron stars with magnetic fields B ∼ 1014 –1015 has
yet to be calculated. Conceivably, X-ray spectra in this regime could account for the
259
small emitting areas of the Cas A point source and the AXPs without requiring small
polar hot spots.
Regardless of the eventual resolution to the puzzling aspects of the point source in
Cas A, it is already clear that the mere existence of this and similar objects demands
a dramatic revision of our generally accepted notions of the nature of compact objects
found in supernova remnants. The discovery of radio pulsars in the 1960s led to a
paradigm in which supernovae generally leave behind strongly magnetized, rapidly
rotating neutron stars. The subsequent failure to locate radio pulsars in the majority
of SNRs has been a long-standing problem for this point of view (Kaspi 2000, Gotthelf & Vasisht 2000). The unanticipated properties of the Cas A point source and
the relative youth of the Cas A SNR imply that the birthrate of “unusual” compact
objects is likely to be at least roughly comparable to that of radio pulsars, potentially
resolving the difficulties posed by SNR/pulsar associations. In this sense, the identification of the point source in Cas A may be as significant to our understanding of
neutron stars as was the original discovery of radio pulsars.
Acknowledgements
We are grateful to Fred Baganoff, Mark Bautz, Bryan Gaensler, Vicky Kaspi, Herman
Marshall, Rosalba Perna, Dimitrios Psaltis, and Norbert Schulz for advice and useful
discussions. We also thank Frank Marshall for allowing us to use his proprietary
RXTE data to verify our pulse timing of PSR B0540–69, as well as Fred Seward and
Arnold Rots for help with retrieving data from the Chandra Data Archive. The ASCA
data for SNR E0102–72 was obtained from the High Energy Astrophysics Science
Archive Research Center (HEASARC) at NASA Goddard Space Flight Center.
E.6
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