Download FERMI GBM detections of four AXPs at soft gamma-rays

FERMI GBM detections of four AXPs
at soft gamma-rays
Felix ter Beek
Thesis for the degree
Master of Science
in Astronomy & Astrophysics
University of Amsterdam
November 2012
Supervisor: Prof. dr. W. Hermsen
Daily supervisor: Dr. L. Kuiper
2
Abstract
Anomalous X-ray Pulsars (AXPs) are believed to be magnetars, i.e. neutron stars powered by the decay of extremely strong magnetic fields (1013 -1015
Gauss), as they show outbursts and persistent emission with luminosities exceeding the rotational energy loss. Distinct spectral features of their persistent
emission are: a (mostly thermal) component at soft X-rays that can be described by the magnetar model, and a non-thermal component peaking at
soft gamma-rays. There is no consensus on the underlying emission process of
this second component. More observations at hard X-rays and soft gammarays are required to constrain the models aiming to describe this non-thermal
emission. The Fermi Gamma-ray Burst Monitor (GBM) is the most suitable
instrument for detecting the pulsed emission of AXPs above 100 keV. We
analyzed the CTIME data from the GBM NaI detectors (8 keV - 2 MeV) to
measure the pulsed emission of four AXPs ; 4U 0142+614, 1RXS J1708-4009,
1E 1841-045 and 1E 1547.0-5408. The flux values derived from these observations are consistent with published INTEGRAL ISGRI (20-300 keV) and
RXTE PCA/HEXTE (15-250 keV) measurements in the overlapping energy
range and are further constraining the spectral shape. We found evidence for
a spectral break below 300 keV for 4U 0142+614, 1E 1841-045 and 1E 1547.05408. The new spectral findings are shortly discussed in the framework of the
magnetar model.
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4
TABLE OF CONTENTS
Table of Contents
1 Introduction
1.1 The pulsar class . . . . . . . . . . . . . . . .
1.1.1 Rotation powered pulsars . . . . . .
1.1.2 Accretion powered pulsars . . . . . .
1.1.3 Magnetars . . . . . . . . . . . . . . .
1.2 Basic pulsar parameters . . . . . . . . . . .
1.2.1 Magnetic field strength at the surface
1.2.2 Characteristic age . . . . . . . . . . .
1.2.3 The [P, Ṗ ]-diagram . . . . . . . . . .
1.3 Magnetar spectral energy distribution . . . .
1.3.1 1RXS J1708-4009 . . . . . . . . . . .
1.3.2 1E 1841-045 . . . . . . . . . . . . . .
1.3.3 4U 0142+614 . . . . . . . . . . . . .
1.3.4 1E 1547.0-5408 . . . . . . . . . . . .
1.4 Candidate models and emission processes . .
1.4.1 Synchrotron radiation . . . . . . . .
1.4.2 Thermal bremsstrahlung . . . . . . .
1.4.3 Inverse Compton scattering . . . . .
2 Instrumentation and Event Selection
2.1 The FERMI mission . . . . . . . . .
2.2 FERMI GBM . . . . . . . . . . . . .
2.3 Event selection . . . . . . . . . . . .
2.4 Flux determination . . . . . . . . . .
3 Data reduction and results
3.1 Timing Analysis . . . . . .
3.1.1 1RXS J1708-4009 .
3.1.2 1E 1841-045 . . . .
3.1.3 4U 0142+614 . . .
3.1.4 1E 1547.0-5408 . .
3.2 Spectral analysis . . . . .
3.2.1 1RXS J1708-4009 .
3.2.2 1E 1841-045 . . . .
3.2.3 4U 0142+614 . . .
3.2.4 1E 1547.0-5408 . .
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4 Summary and Conclusions
49
References
51
5
LIST OF TABLES
List of Figures
1
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The (P, dP/dT )-diagram. . . . . . . . . . . . . . . . . . . . . . . . . .
The soft X-ray spectrum of 1RXS J1708-4009 . . . . . . . . . . . . . .
The X-ray spectrum of 1RXS J1708-4009 . . . . . . . . . . . . . . . .
The X-ray spectrum of 1E 1841-045 . . . . . . . . . . . . . . . . . . .
The X-ray spectrum of 4U 0142+614 . . . . . . . . . . . . . . . . . .
The X-ray spectrum of 1E 1547.0-5408 . . . . . . . . . . . . . . . . .
Sketch drawing of a twisted magnetic loop. . . . . . . . . . . . . . . .
Simulated inverse Compton spectrum. . . . . . . . . . . . . . . . . .
Simulated magnetar spectra. . . . . . . . . . . . . . . . . . . . . . . .
The response function (cm2 ) of the GBM detectors. . . . . . . . . . .
The orientation of the GBM detectors. . . . . . . . . . . . . . . . . .
Energy dependence of the GBM NaI effective area (cm2 ) per channel.
Angular dependence of the GBM NaI effective area (cm2 ) in ch. 1-2. .
Angular dependence of the GBM NaI effective area (cm2 ) in ch. 3-7. .
Observed light curve (120 phase bins) of 1RXS J1708-4009. . . . . . .
Pulse profile of 1RXS J1708-4009 summed over channels 2-4. . . . . .
Pulse profiles of 1RXS J1708-4009 in channels 2-4. . . . . . . . . . . .
Pulse profile of 1E 1841-045 summed over channels 2-4. . . . . . . . .
Pulse profiles of 1E 1841-045 in channels 2-4. . . . . . . . . . . . . . .
Pulse profile of 4U 0142+614 summed over channels 2-4. . . . . . . .
Pulse profiles of 4U 0142+614 in channels 2-4. . . . . . . . . . . . . .
Pulse profile of 1E 1547.0-5408 summed over channels 2-4. . . . . . .
Pulse profiles of 1E 1547.0-5408 in channels 2-4. . . . . . . . . . . . .
Updated high-energy spectrum of 1RXS J1708-4009. . . . . . . . . . .
Updated high-energy spectrum of 1E 1841-045. . . . . . . . . . . . . .
Updated high-energy spectrum of 4U 0142+614. . . . . . . . . . . . .
Updated high-energy spectrum of 1E 1547.0-5408. . . . . . . . . . . .
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List of Tables
1
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Pointing angles of GBM detectors in spacecraft coordinates.
List of FERMI GBM observations used in this work. . . . .
Phase-coherent timing models. . . . . . . . . . . . . . . . . .
Pulsed count rates of 1RXS J1708-4009 in channels 1-7. . . .
Pulsed count rates of 1E 1841-045 in channels 1-7. . . . . . .
Pulsed count rates of 4U 0142+614 in channels 1-7. . . . . .
Pulsed count rates of 1E 1547.0-5408 in channels 1-7. . . . .
Best-fit parameters for fitting spectral models. . . . . . . . .
The observed pulsed flux of 1RXS J1708-4009. . . . . . . . .
The observed pulsed flux of 1E 1841-045. . . . . . . . . . . .
The observed pulsed flux of 4U 0142+614. . . . . . . . . . .
The observed pulsed flux of 1E 1547.0-5408. . . . . . . . . .
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LIST OF TABLES
List of Acronyms
AXP Anomalous X-ray Pulsar
SGR Soft Gamma Repeater
GRB gamma-ray burst
SAA South Atlantic Anomaly
FERMI FERMI Gamma-Ray Space Telescope
GLAST Gamma-ray Large Area Space Telescope
LAT Large Area Telescope
GBM Gamma-ray Burst Monitor
CGRO Compton Gamma-Ray Observatory
COMPTEL COMPton TELescope
INTEGRAL INTErnational Gamma-Ray Astrophysics Laboratory
IBIS Imager on Board INTEGRAL Satellite
ISGRI INTEGRAL Soft Gamma-Ray Imager
SPI SPectrometer on INTEGRAL
RXTE Rossi X-Ray Timing Explorer
PCA Proportional Counter Array
HEXTE High Energy X-ray Timing Experiment
Suzaku Suzaku
XIS X-ray Imaging Spectrometer
XMM-Newton X-ray Multi-mirror Mission - Newton
EPIC European Photon Imaging Camera
Chandra Chandra X-ray Observatory
ACIS Advanced Ccd Imaging Spectrometer
SWIFT SWIFT gamma-ray burst mission
XRT X-Ray Telescope
7
LIST OF TABLES
8
1
1.1
Introduction
The pulsar class
Pulsars are a class of astronomical objects from which pulsed emission is observed.
The pulsar class can be divided in three main subclasses, based on the energy source
and emission mechanism of the pulsar.
1.1.1
Rotation powered pulsars
The first pulsar detection took place in 1967 with the Mullard Radio Astronomy
Observatory (Hewish et al. 1968), and was soon followed by detections of other
pulsars at different locations (Pilkington et al. 1968).
These pulsars where suggested to be rotating magnetized neutron stars by Pacini
(1968), Gold (1968), but this theory was met with skepticism from other scientists
who believed the pulsars to be white dwarfs instead. However, the discovery of
the Crab pulsar with a pulse period of 33 ms disproved the white dwarf interpretation, and after Richards & Comella (1969) observed the spin-down rate of the Crab
pulsar to be as predicted by Pacini (1968) the skepticism against the neutron star
interpretation faded.
Historically, all known radio pulsars were consistent with being rotation powered.
These pulsars are rotating magnetized (B ∼ 1012 Gauss) neutron stars with magnetic
dipole emission. As the emission is powered by the loss of rotational energy, the total
luminosity is constrained by the spin-down luminosity, which can be derived from
the period and period derivative.
Ṗ
Ṗ
d IΩ2
= 4π 2 I 3 = 3.95 × 1046 3 [erg · s−1 ]
(1)
Ė = −
dt
2
P
P
where Ė is the spin-down luminosity, I = 1045 g · cm2 is the moment of inertia for a
typical neutron star, Ω = 2π/P is the angular velocity and P is the rotation period
of the pulsar in s.
1.1.2
Accretion powered pulsars
Accretion powered pulsars are accreting neutron stars, producing pulsed emission
because of their orbital motion in a binary system. The energy source of this class
of objects is the gravitational potential energy of the accreted matter.
GM ṁ
= 1.9 × 1020 · ṁ [erg · s−1 ]
(2)
R
where Ė is the accretion luminosity, M = 2.8 × 1033 g and R = 106 cm are the mass
and radius of a typical neutron star and ṁ is the rate of mass accretion in g · s−1 .
The accretion luminosity of these objects is limited by the Eddington luminosity,
the luminosity at which the radiation pressure is equal to the gravitational pressure.
Ė =
4πcGmp
M = 2.1 × 1038 [erg · s−1 ]
(3)
σT
where LEdd is the Eddington luminosity and M = 2.8 × 1033 g is the mass of a
typical neutron star.
LEdd =
1.1.3
Magnetars
Magnetars are neutron stars that are formed in such conditions that efficient
helical dynamo action takes place during the first seconds after gravitational collapse
9
1 INTRODUCTION
of a star (Duncan & Thompson 1992, Thompson et al. 2002), and therefore have
very high magnetic field strength (B > 1013 Gauss). Because of their high magnetic
field strength, magnetars quickly lose most of their rotational energy to magnetic
dipole braking.
Internal magnetic stresses cause the stellar crust of the magnetar to undergo
sudden adjustments, also called starquakes, inducing twists to the magnetic dipole
field. These starquakes can be observed as outbursts and timing glitches. The
untwisting of the strong magnetic field leads to a current of charged particles along
the magnetic field lines which heats the stellar surface.
Historically there are two types of magnetar candidates, Soft Gamma Repeaters
(SGRs) and Anomalous X-ray Pulsars (AXPs).
SGRs
The first observed Soft Gamma Repeater (SGR) burst originated from SGR
1806-20 and was detected on 7 January, 1979 by one of the KONUS experiments
(Mazets & Golenetskii 1981, Laros et al. 1986). Soon after that an extraordinary
bright burst was observed on 5 March, 1979 (Mazets et al. 1979). The burst had a
very bright (L ∼ 1045 erg · s−1 ) spike, followed by a ∼ 3-minute decay, during which
∼ 8-second pulsations were visible. One day later, on 6 March, 1979 Mazets et al.
(1979) observed another, much weaker, burst from the same source. After these first
observations several other sources with repeated bursts in the X- and γ-rays were
detected. Several years later, in 1994, SGRs were discovered to show persistent
X-ray emission by Vasisht et al. (1994), Rothschild et al. (1994), Murakami et al.
(1994).
A breakthrough in SGR and magnetar physics was reached when Kouveliotou et al.
(1998) measured the period and period derivative of SGR 1806-20. From these
measurements, they found that the observed persistent X-ray flux of this SGR is
two orders of magnitude higher than what can be explained from rotational energy
loss, indicating that SGR 1806-20 is not rotation-powered. Moreover, they derived
a magnetic field strength of ∼ 8 × 1014 Gauss by assuming that the rotational
energy loss is due to magnetic dipole braking (to be discussed in section 1.2.1).
From these observations, Kouveliotou et al. (1998) argue that SGRs are powered
by the decay of their huge magnetic fields, as described in the magnetar model
(Duncan & Thompson 1992). As the already developed magnetar model could give
an explanation for the observed glitches, bursts, and X-ray luminosity, the magnetar
interpretation of SGRs was quickly accepted.
It is noteworthy that SGRs have both active and dormant periods. During an
active period an SGR can show several hundreds of bursts in a week, while during
a dormant period it can occur that no bursts are detected for several years.
AXPs
The first Anomalous X-ray Pulsar (AXP) to be discovered was 1E 2259+586
(Fahlman & Gregory 1981), a bright X-ray pulsar with a ∼ 7-second period and ∼
2×1035 erg · s−1 luminosity in the 2 - 4 keV band. The period derivative was derived
to be 5 × 10−13 s · s−1 (Koyama et al. 1987), indicating a spin-down luminosity of
∼ 6 × 1031 erg · s−1 , much lower than the observed X-ray luminosity.
A few more sources with similar characteristics were found, and were eventually
categorized as AXPs because of their high X-ray luminosities. AXPs cannot be powered by rotation because their observed luminosities are several orders of magnitude
larger than the derived rotational energy loss, but it is also unlikely that they are
powered by accretion because of the lack of observed bright optical counterparts or
10
1.2 Basic pulsar parameters
orbital modulation.
Their luminosities, inferred magnetic field strengths, rotational periods and period derivatives (all similar to values observed for SGRs) made AXPs magnetar
candidates, but the magnetar interpretation was not readily accepted because of
the lack of observed glitches and bursts from these sources. Only after AXPs were
observed to show glitches (Kaspi et al. 2000, Kaspi & Gavriil 2003, Dall’Osso et al.
2003) and SGR-like bursts (Kaspi et al. 2003, Gavriil et al. 2004) the magnetar interpretation of AXPs became widely accepted.
1.2
Basic pulsar parameters
By measuring the period P and period derivative Ṗ of a pulsar it is possible to
give an estimate of the age and magnetic field strength at the surface if we assume
that the pulsar does not accrete mass and that the rotational energy loss is due to
magnetic dipole breaking.
1.2.1
Magnetic field strength at the surface
In general a non-accreting pulsar will gradually lose kinetic energy due to magnetic dipole braking, slowing down the rotation of the neutron star.
Ṗ
d IΩ2
= 4π 2 I 3
(4)
Ė = −
dt
2
P
where Ė is the rate of energy loss, I is the moment of inertia, Ω is the angular
velocity and P is the rotation period.
An estimate for the rate of energy loss follows from the magnetic dipole model
(Pacini 1967; 1968, Ostriker & Gunn 1969).
Ė =
2 |m|2 Ω4 sin2 α
3c3
(5)
where Ė is the rate of energy emission through magnetic braking, |m| is the magnetic
dipole moment, Ω = 2π/P is the angular velocity and α is the angle between the
rotation axis and the dipole axis.
Since α is usually an unknown parameter it is common practice to set 2 |m| sin α =
BR3 , where B is the magnetic field strength on the surface at the equator and R is
the radius of the neutron star.
Ė =
r
8π 4 B 2 R6
3c3 P 4
r
(6)
3c3 P 4
3c3 I
×
Ė
=
P Ṗ
(7)
8π 4 R6
2π 2 R6
By filling in typical values for I (1045 g · cm2 ) and R (106 cm) we obtain an
expression for the magnetic field strength of a pulsar at the equator, assuming that
the emission process for the bulk of the emission is dipole radiation.
p
(8)
B = 3.2 × 1019 P Ṗ [Gauss]
B=
where P is the period of the pulsar in s and Ṗ is the period derivative in s · s−1 .
Noteworthy is that for some pulsars the magnetic field strength at the surface
surpasses the critical magnetic field strength BQED = 4.413 × 1013 Gauss, above
which quantum electrodynamic physics start playing a significant role.
11
1 INTRODUCTION
1.2.2
Characteristic age
By assuming a spin-down formula for dipole emission ν̇ ∝ ν 3 and solving for
τ = t − t0 one finds an expression for the age of a pulsar.
"
"
2 #
2 #
−ν
P
ν
P0
τ=
1−
=
(9)
1−
2ν̇
ν0
P
2Ṗ
If one assumes the rotation period at birth of the neutron star (P0 ) to be much
smaller than the current rotation period one can derive the commonly used expression for the characteristic age of a pulsar.
P
(10)
2Ṗ
It should be noted that the characteristic age is only a first order estimate of
the true age of a pulsar, and that deviations from this estimate due to temporal
variations can be significant.
τ=
Figure 1:
The [P, Ṗ ]-diagram. Displayed in this diagram are all known pulsars
with measured [P, Ṗ ] in black dots, lines of equal characteristic age τ in dark blue
and lines of equal magnetic field strength B in dark red. The critical magnetic field
strength for electrons BQED = 4.413 × 1013 Gauss is shown as a bright red line. AXPs
and AXP candidates are marked with boxes, SGRs and SGR candidates are marked
with triangles. Data from http://www.physics.mcgill.ca/˜pulsar/magnetar/main.html
and http://www.atnf.csiro.au/research/pulsar/psrcat/ were used for making this diagram.
1.2.3
The [P, Ṗ ]-diagram
The [P, Ṗ ]-diagram is a valuable tool in displaying the basic characteristics of
the pulsar population. Figure 1 displays all known pulsars with measured [P, Ṗ ]. In
this figure three main groups can be identified:
The largest group has B ∼ 1012 Gauss, and the majority of the pulsars in this
group are radio pulsars, powered by the loss of rotational energy.
The next group has Ṗ < 10−17 s s−1 and P < 50 ms, and includes millisecond
pulsars and other recycled pulsars.
12
1.3 Magnetar spectral energy distribution
The group of most interest for this work is the group with P > 1.0 s and B >
BQED , where BQED = 4.413 × 1013 Gauss is the critical magnetic field strength for
electrons. This group includes all currently known AXPs and SGRs plus AXP and
SGR candidates, with the possible exception of SGR 0418+5729 (Rea et al. 2010).
Note that all pulsars in this group are ’young’ pulsars, with τ ∼ 104 year.
Figure 2: The phase-averaged soft X-ray spectrum of 1RXS J1708-4009 as measured
with XMM-Newton EPIC-PN (Rea et al. 2005). The black line shows an empirical fit
with an absorbed black body plus power law.
1.3
Magnetar spectral energy distribution
In this work we aim to increase the knowledge on the spectral energy distribution
of the persistent magnetar emission. We will first present a short overview of the
observations before this work in this section and of the possible emission processes
for these observed spectra in section 1.4 before discussing our own observations.
A typical soft X-ray (0.5 - 10 keV) spectrum of an AXP (Fig. 2) can be fit
empirically with a black body (kT ∼ 3 - 4 keV) plus soft power-law (Γ ∼ −4 - −3,
defined as F ∝ E Γ ), or with a double black body model (Rea et al. 2005).
The magnetar model (Thompson et al. 2002) explains the observed soft X-ray
spectra as thermal X-ray spectra from the stellar surface with non-thermal tails due
to resonant cyclotron scattering against charged particles in the twisted magnetosphere. The non-thermal spectral tail is harder for more strongly twisted magnetospheres because the current through the magnetosphere increases with the magnetic
twist, leading to a higher density of charged particles and thus a higher optical dept
to resonant cyclotron scattering.
As the magnetar model could give an explanation for the observed luminosities,
spectra below 10 keV, glitches and outbursts of AXPs and SGRs, it was thought
for a short while that the observable characteristics of AXPs were fully understood. But in 2004 a new spectral component was discovered when persistent hard
X-ray (> 10 keV) emission was observed from 1E 1841-045 (Molkov et al. 2004,
Kuiper et al. 2004), 1RXS J1708-4009 (Revnivtsev et al. 2004) and 4U 0142+614
13
1 INTRODUCTION
(den Hartog et al. 2004). It is not unlikely that other AXPs and SGRs have similar hard X-ray emission, at a luminosity lower than detection limits of currently
available instruments.
For this work we studied four AXPs: 1RXS J1708-4009, 1E 1841-045, 1E 1841045 and 1E 1547.0-5408. In the following subsections the X-ray characteristics of
these AXPs will be shortly presented.
Figure 3: X-ray spectra of 1RXS J1708-4009 (den Hartog et al. 2008b). In this figure are
displayed: pulsed flux measurements by XMM-Newton EPIC-PN in black, RXTE PCA in
blue, RXTE HEXTE in aqua and INTEGRAL IBIS-ISGRI in red with triangle markers;
total flux measurements by XMM-Newton EPIC-PN (< 12 keV) in black, INTEGRAL
IBIS-ISGRI in black with triangle markers, INTEGRAL SPI in grey with triangle markers
and CGRO COMPTEL (> 1000 keV) in black; and empirical fits to the total spectra with
a power law in grey and with a logparabola (log F = a log2 E + b log E + c) in blue.
1.3.1
1RXS J1708-4009
1RXS J1708-4009 was discovered during the ROSAT all sky survey (Voges et al.
1999), and was measured to have a period and period derivative of P = 11 s and
Ṗ = 1.9 × 10−11 s · s−1 (Kaspi et al. 1999, Gavriil & Kaspi 2002). 1RXS J1708-4009
was the first AXP that was observed to glitch (Kaspi et al. 2000, Kaspi & Gavriil
2003, Dall’Osso et al. 2003).
The X-ray pulse profile of this AXP has been observed to change significantly with energy above E = 4 keV (Sugizaki et al. 1997, Israel et al. 2001,
Gavriil & Kaspi 2002). Subsequent phase-resolved spectral analysis confirmed this
observation (Israel et al. 2001, Rea et al. 2003; 2005). Moreover, the soft X-ray
(0.5 - 10 keV) spectrum of 1RXS J1708-4009 has been observed to be time variable
(Rea et al. 2005), with an increased flux and a harder spectral tail near the glitch
epochs. The recent soft X-ray observations with XMM-Newton EPIC-PN can be fit
empirically with a black body with temperature kT ∼ 0.46 keV plus a power law
with index Γ ∼ −2.8 (Rea et al. 2005).
During an INTEGRAL hard X-ray survey, Revnivtsev et al. (2004) discovered
a point source with emission in the 18 - 60 keV energy band at the position of
1RXS J1708-4009.
In more recent publications by den Hartog et al. (2008b) (Fig. 3) using data
from INTEGRAL IBIS-ISGRI, RXTE PCA/HEXTE and XMM-Newton EPIC-PN,
the hard X-ray emission (> 10 keV) is found to be stable within instrumental uncertainties over almost a decade of observations. den Hartog et al. (2008b) observes
14
1.3 Magnetar spectral energy distribution
Figure 4: X-ray spectra of 1E 1841-045 (Kuiper et al. 2008). In this figure are displayed:
pulsed flux measurements by RXTE PCA, RXTE HEXTE and INTEGRAL IBIS-ISGRI;
total flux measurements by XMM-Newton EPIC-PN (AXP plus supernova remnant),
Chandra ACIS (only AXP) model fit, INTEGRAL IBIS-ISGRI and CGRO COMPTEL;
and an empirical fit to the pulsed spectra at E > 15 keV with a power law. Note that the
observed pulsed spectrum is harder than the observed total spectrum. The measurements
are consistent with 100% pulsed emission at E > 100 keV.
that the pulse profile changes significantly with energy at 2 - 10 keV, and then
remains stable up to ∼ 300 keV. The spectral index of the hard X-ray emission
is determined to be Γ ∼ −1.1. Indication for a spectral break of the hard X-ray
emission, other than constraining upper limits set by non-simultaneous (April 1991
to May 2000) observations with CGRO COMPTEL in the MeV band (Kuiper et al.
2006), was not found.
1.3.2
1E 1841-045
1E 1841-045 was discovered as an ∼ 11.8 s X-ray pulsar by Vasisht & Gotthelf
(1997) with ASCA, and was later observed to have a period derivative of Ṗ =
4.1 × 10−11 s · s−1 (Gotthelf et al. 2002). The soft X-ray spectrum as observed with
Chandra ACIS can be described as a black body with temperature kT ∼ 0.44 keV
plus a power law with index Γ ∼ −2.0 (Morii et al. 2003).
Hard X-ray (> 10 keV) emission from 1E 1841-045 was first detected during an
INTEGRAL hard X-ray survey (Molkov et al. 2004), and was later confirmed to be
originating from the AXP 1E 1841-045 through detection of pulsed hard X-ray emission with observations by RXTE PCA/HEXTE (Kuiper et al. 2004). Kuiper et al.
(2004) observes that the shape of the pulse profile changes significantly at 2 - 10 keV,
and then remains stable within observational uncertainties up to ∼ 100 keV. The
pulsed hard X-ray emission (Fig. 4) is observed to have a spectral index of 0.94±0.16
up to ∼ 150 keV. Moreover, the observations are consistent with a pulsed fraction of 100% at ∼ 100 keV. Emission in the MeV band was not found with
non-simultaneous (April 1991 to May 2000) observations with CGRO COMPTEL
(Kuiper et al. 2006).
15
1 INTRODUCTION
Figure 5: X-ray spectra of 4U 0142+614 (den Hartog et al. 2008a). In this figure are
displayed: total flux measurements by XMM-Newton EPIC-PN (< 11.5 keV) in black,
INTEGRAL IBIS-ISGRI (20 - 300 keV in black with square markers, INTEGRAL SPI
(20 - 1000 keV in red and CGRO COMPTEL (> 750 keV) in black; and empirical fits
to the total spectra with a power law in grey and with the sum of three logparabola
(log F = a log2 E + b log E + c) in blue.
1.3.3
4U 0142+614
4U 0142+614 was discovered by the Uhuru X-ray observatory in the seventies
(Forman et al. 1978). The period and period derivative of the AXP have been measured at P = 8.7 s and Ṗ = 2.0 × 10−12 s · s−1 , respectively (Gavriil & Kaspi 2002).
Subsequent soft X-ray (< 10 keV) observations with ASCA (White et al. 1996),
Chandra (Patel et al. 2003) and XMM-Newton (Göhler et al. 2005) indicate that
the spectrum of 4U 0142+614 can be described as a black body with temperature
kT ∼ 0.4 keV plus a power law with index Γ ∼ −3.5.
Hard X-ray (> 10 keV) emission from 4U 0142+614 was first detected by
den Hartog et al. (2004) using INTEGRAL observations. After the first discovery of non-thermal hard X-ray emission from 4U 0142+614 a more detailed spectral
analysis was done with combined multi-year observations with INTEGRAL, RXTE,
XMM-Newton, ASCA and CGRO COMPTELl (den Hartog et al. 2008a) (Fig. 5).
In this analysis, it is found that the pulse profile of 4U 0142+614 changes significantly with energy at 0.3 - 15 keV, and then remains stable within observational
uncertainties for higher energies. The observed hard X-ray spectrum has a spectral
index Γ = −0.93 ± 0.06 up to ∼ 200 keV, and is expected to show a spectral break
in the range 200 - 750 keV, imposed by upper limits from INTEGRAL SPI and nonsimultaneous (April 1991 to May 2000) CGRO COMPTELL (Kuiper et al. 2006)
observations.
1.3.4
1E 1547.0-5408
1E 1547.0-5408 was first discovered as an X-ray source by Lamb & Markert
(1981) with the Einstein observatory. Based on X-ray observations with XMM-Newton
and Chandra Gelfand & Gaensler (2007) proposed 1E 1547.0-5408 to be a magnetar,
though no X-ray pulsations were detected.
Soon thereafter, Camilo et al. (2007) confirmed 1E 1547.0-5408 to be a pulsar
through radio observations. The pulsar was measured to have period P = 2.069 s
and period derivative Ṗ = (2.318 ± 0.005) × 10−11 s · s−1 . From these numbers a
16
1.3 Magnetar spectral energy distribution
Figure 6: Spectral evolution of 1E 1547.0-5408 (Kuiper et al. 2012) from October 2008 to
December 2010. The figure displays pulsed flux measurements by RXTE PCA (filled circle
markers) and RXTE HEXTE (filled square markers), divided in several time segments.
surface magnetic field strength (Eq. 8) of B ∼ 2.2 × 1014 Gauss can be derived.
Halpern et al. (2008) first detected X-ray pulsations from 1E 1547.0-5408 in 2007
in a period of increased activity, and concluded that the AXP was recovering from
an outburst that would have taken place in 2006-2007.
Strong SGR-like bursting activity was detected from 1E 1547.0-5408 on 3 October
2008 (Krimm et al. 2008, Israel et al. 2010, Kaneko et al. 2010) and 22 January 2009
(Gronwall et al. 2009). Based on a 100 ks follow-up observation with INTEGRAL
2 days after the 22 January outburst, Baldovin et al. (2009) reported a detection
in the hard X-rays with a spectral index Γ = −1.8 ± 0.2. After a consecutive
300 ks observation (Kuiper et al. 2009, den Hartog et al. 2009), the spectral index
was measured at Γ ∼ −1.5.
The initial discovery of transient hard X-ray emission was followed by observations with Suzaku (Enoto et al. 2010), Chandra (Ng et al. 2011, Bernardini et al.
2011), XMM-Newton (Bernardini et al. 2011), INTEGRAL (Bernardini et al. 2011),
RXTE (Ng et al. 2011) and SWIFT (Bernardini et al. 2011, Scholz & Kaspi 2011)
over a timespan of 1.5 years following the outburst of 22 January 2009.
Making use of the large amount of 1E 1547.0-5408 observations with SWIFT,
RXTE and INTEGRAL, Kuiper et al. (2012) studied the spectral and temporal
evolution of the AXP during the recovery from the outburst in January 2009. They
find that the pulsed hard X-ray (> 10 keV) emission is highly variable in time,
reaching a maximum 70 ± 30 days after the outburst, followed by a gradual decay.
The observed pulsed spectra are displayed in Figure 6.
As 1E 1547.0-5408 is very noisy in the period following the January 2009 outburst
there are constraints in the availability of phase-coherent timing solutions which we
need for our further analysis. As a result, we only analysed 1E 1547.0-5408 at
MJD 54855-54890, a timespan overlapping with segment 3 and segment 4 in Figure
6. During this timespan, the pulsed hard X-ray (> 10 keV) emission is near its
maximum.
17
1 INTRODUCTION
1.4
Candidate models and emission processes
The magnetar model (Thompson et al. 2002), where AXPs and SGRs are modelled
as highly magnetized (B > 1014 Gauss) neutron stars with twisted magnetic fields,
offers a viable explanation for the observed soft X-ray (< 10 keV) spectra, bursts
and glitching behaviour, but no consensus has yet been reached on an emission
process for the observed hard X-ray (> 10 keV) emission.
The proposed emission processes include ’fast-mode breakdown’ magnetohydrodynamic waves (Heyl & Hernquist. 2005a;b), synchrotron radiation at ∼ 100 km
above the stellar surface (Thompson & Beloborodov 2005), thermal bremsstrahlung
near the stellar surface (Thompson & Beloborodov 2005, Beloborodov & Thompson
2007), inverse Compton scattering in a twisted magnetosphere (Baring & Harding
2007, Beloborodov 2011; 2012), resonant cyclotron scattering in a twisted multipole
magnetosphere (Pavan et al. 2009) and comptonization in a fallback accretion disk
(Trümper et al. 2010).
We will focus on the work of Thompson and Beloborodov, who have been modelling emission processes for hard X-ray (> 10 keV) emission within the magnetar
framework and have been continually updating their modelling in response to observational results.
Thompson & Beloborodov (2005), Beloborodov & Thompson (2007), Beloborodov
(2011; 2012) theorized that particles are injected in a magnetic loop from the stellar
surface (where B > 4.4 × 1013 Gauss) and are accelerated to relativistic speeds. Due
to the high magnetic field strength (B > 1013 Gauss) in the inner part of the loop,
these relativistic particles cause cascades of electron-positron pair production, forming a corona of e± plasma. The e± density in the corona is self-regulated because
the plasma shields the electric field, acting as a bottleneck to e± pair creation. As
electrical currents flow through the corona, the magnetic field gradually untwists.
Magnetic field lines with small radii untwist on a shorter time scale than those with
larger radii (Beloborodov 2011), leading to a shrinking ’j-bundle’ of electric currents
concentrated near the magnetic axis. Under certain circumstances it is possible to
reach a quasi-stable configuration of the j-bundle, self-regulated near a threshold of
MHD instability.
Using this scenario as a basis, there are several possible emission processes. The
following sections will introduce synchrotron radiation, thermal bremsstrahlung and
inverse Compton scattering as possible emission processes for high energy (E >
15 keV) emission of magnetars.
1.4.1
Synchrotron radiation
Thompson & Beloborodov (2005) theorized that cyclotron resonant scattering
causes a strong radiative drag on charged particles, causing a strong electric field at
a height of ∼ 100 km above the stellar surface, where the electron cyclotron energy
is in the keV range. As a result, electrons and positrons injected in this region
undergo runaway acceleration caused by the radiative drag force and up-scatter
photons above the threshold for e± pair creation. The e± pairs emit synchrotron
radiation with a spectral peak at ∼ 1 MeV and a spectral index dependent on the
strength of the magnetic twist.
1.4.2
Thermal bremsstrahlung
Thompson & Beloborodov (2005), Beloborodov & Thompson (2007) theorized
that the persistent hard X-ray emission is produced in a thin transition layer between
the relatively cool stellar surface and the hot magnetar corona. The layer is heated
18
1.4 Candidate models and emission processes
to kT ∼ 100 keV by incoming charged particles which are accelerated in the corona,
and emits thermal bremsstrahlung. The resulting emission has a spectral index
Γ ∼ −1 with a spectral break at ∼ 100 keV. the pulsed fraction through this
emission process can be very high (up to 100%) if the magnetosphere is only locally
twisted.
1.4.3
Inverse Compton scattering
Beloborodov (2011; 2012) theorized that the soft X-ray (E < 15 keV) emission is
up-scattered against the highly relativistic e± plasma in the j-bundle. In the inner
part of the j-bundle, where B > 1013 Gauss, all energy is processed through e±
pair creation and no radiation can escape. In the outer part of the j-bundle, where
B < 1013 Gauss, the bulk of the energy is radiated away. As inverse Compton
scattering in general is strongly beamed along the flow direction of the particles, the
resulting X-ray emission is expected to be anisotropic. In the outermost part of the
twisted magnetosphere, on the equatorial plane with respect to the magnetic dipole
axis, the electrons and positrons collide and annihilate, causing an emission line at
E = 511 keV with luminosity equal to ∼ 10% of the total luminosity. See Figure 7
for a sketch of a magnetic loop.
h νsc
γ>
>
10
e +−
keV
γ∼1
keV
>
γ>
10
e+− hνsc
Figure 7: Sketch of a twisted magnetic loop. The inner zone (where B > 1013 Gauss) is
shaded in blue and the annihilation zone is shaded in pink. The figure is from Beloborodov
(2012).
Detailed radiative transfer calculations (Beloborodov 2012) indicate that the
emission is indeed highly anisotropic (Fig. 8), and that the pulsed fraction and
the shape of the pulse profile can be highly variable with photon energy (Fig. 9).
Because of the high anisotropy with respect to the magnetic dipole axis, the modelled
spectra for the total and the pulsed emission are highly dependent on the orientation
of the rotation axis and the magnetic dipole axis with respect to the line of sight and
on the azimuthal extension (i.e. axisymmetric or confined to a certain azimuthal
range) of the j-bundle with respect to the magnetic dipole axis.
19
1 INTRODUCTION
Figure 8: Simulated magnetar spectra in the hard X-rays for four different angles
between the line of sight and the magnetic dipole axis. The figure is from Beloborodov
(2012).
Figure 9: Simulated magnetar spectra for an orthogonal rotator, i.e. a magnetar with
angle α = 90◦ between the rotation axis and the magnetic dipole axis, with an axisymmetric j-bundle. The left figure displays spectra for an angle β = 20◦ between the rotation
axis and the line of sight, the right figure displays spectra for β = 90◦ . The solid lines
indicate the total simulated spectra, while the dashed lines display the difference between
the maximum and the minimum emission of the pulsed signal. Many different configurations of the rotation axis and the magnetic dipole axis are possible. The figures are from
Beloborodov (2012).
20
2
2.1
Instrumentation and Event Selection
The FERMI mission
The FERMI Gamma-Ray Space Telescope (FERMI), formerly known as Gammaray Large Area Space Telescope (GLAST), was launched in June 2008, and has
since then been orbiting the Earth in a low orbit of 550 km above the Earth surface.
The mission is aimed toward bringing γ-ray astronomy to a new level by detecting
and observing γ-rays from a wide range of point sources and phenomena. During
the first 11 months after launch, FERMI detected 1451 sources in the 100 MeV 100 GeV range with a > 4σ significance (Abdo et al. 2010).
The primary instrument on board of the FERMI spacecraft is the Large Area
Telescope (LAT), a pair conversion telescope sensitive over an energy range of ∼
20 MeV to > 300 GeV. The secondary instrument is the Gamma-ray Burst Monitor
(GBM), consisting of scintillation detectors, with an energy range of ∼ 8 keV to
∼ 40 MeV. The FERMI spacecraft orbits the Earth once every 95 minutes. While
in scanning mode, the satellite tilts 35◦ north and south on alternating orbits. As
the instruments on board FERMI have very wide field of view (∼ 2.4 sr for the
LAT), the whole sky is covered at least once every two orbits (Atwood et al. 2009).
The role of the GBM is to extend the energy range of the LAT to the hard X-ray
band, and to detect gamma-ray bursts (GRBs). When a GRB is detected, the burst
mode is triggered. During this mode the time resolution is increased and the LAT
is pointed in the direction of the GRB.
For this work we only used observation data from the GBM as the energy range
of this instrument is most suited for observing hard X-ray (10 - 1000 keV) emission.
2.2
FERMI GBM
The FERMI GBM (Meegan et al. 2009) consists of 12 NaI detectors (8 keV to
2 MeV) and two BGO detectors (200 keV to 40 MeV). The instrument provides
three main data products: CTIME, CSPEC and TTE.
CTIME provides the counts accumulated every 0.256s (0.064s in burst mode) in
8 energy channels for each detector. CSPEC provides the counts accumulated every
4.096s (1.024s in burst mode) in 128 energy channels. TTE (Time Tagged Events)
provides event data with a time resolution of 2µs in 128 energy channels during
bursts only.
The FERMI GBM is designed to detect only the general direction of all incoming
bursts and to measure X-ray spectra of these bursts. Therefore the detectors have
very wide angular response functions (Fig. 10) and are pointed in different directions
(Fig. 11, Table 1). These characteristics make this instrument unsuitable for fine
imaging or pointed observations. These same characteristics, however, make the
FERMI GBM a suitable instrument for detecting persistent pulsed emission with
period P > 0.512s.
For our work we used the CTIME data product because the time resolution of
the CSPEC data product is too low for a timing analysis on AXPs and the TTE
data product is only provided during burst mode. Although at first sight the energy
range of the BGO detectors appears interesting for our work, we chose to only use
observations by the NaI detectors because the angular response function (Fig. 10)
of the NaI detectors offers the possibility for a much better background suppression
through event selection than what would be possible for the BGO detectors.
21
2 INSTRUMENTATION AND EVENT SELECTION
140
32 keV
simulated
measured
100
Photopeak Effective Area (cm2)
Photopeak Effective Area (cm2)
120
279 keV
simulated
measured
80
662 keV
simulated
measured
60
40
20
0
-200
-150
-100
-50
0
50
100
Source Position (degrees)
150
200
120
100
80
279 keV
simulated
measured
60
898 keV
simulated
measured
40
1836 keV
simulated
measured
20
-200
-150
-100
-50
0
50
100
Source Position (degrees)
150
200
Figure 10: The effective area (cm2 ) of the GBM NaI (left) and BGO (right) detectors
as a function of the angle between the detector pointing vector and the source direction.
The figures are from Meegan et al. (2009).
Table 1: Measured (Meegan et al.
2009) orientation of GBM NaI detectors
in spacecraft coordinates.
Detector Azimuth Zenith
ID
[◦ ]
[◦ ]
NaI−0
45.9
20.6
NaI−1
45.1
45.3
NaI−2
58.4
90.2
NaI−3
314.9
45.2
NaI−4
303.2
90.3
NaI−5
3.4
89.8
NaI−6
224.9
20.4
NaI−7
224.6
46.2
NaI−8
236.6
90.0
NaI−9
135.2
45.6
NaI−10
123.7
90.4
NaI−11
183.7
90.3
Figure 11: The orientation of the GBM detectors. Note that in this drawing the LAT
is located below the GBM, therefore none of the detectors are pointed in that direction.
The image is from Meegan et al. (2009).
22
2.3 Event selection
2.3
Event selection
After it’s launch, FERMI has been collecting and archiving observation data since
August 2008. For our timing analysis, we used the archive data from August 2008
until December 2010 for 1RXS J1708-4009, 1E 1841-045 and 1E 1841-045, and we
used archive data from 24 Januari 2009 until 28 Februari 2009 for 1E 1547.0-5408.
Due to the wide angular response functions (Fig. 10) the GBM is expected to
observe X-rays from the whole sky simultaneously. As a result, AXP pulsations
should be present in our full data set, but the background radiation is very high.
We applied a number of selection criteria to our data set in order to maximize the
signal-to-noise ratio.
• Widening the OFF-period during the passage over the South Atlantic Anomaly (SAA). Once every orbit, FERMI passes through the
SAA, an area where the Van Allen radiation belt of the Earth dips down
to an altitude of ∼ 200 - 550 km. The instruments on board of FERMI are
deactivated during the SAA passage (the OFF-period) to protect them from
cosmic particles. We found that the background level of the GBM is significantly increased just before and just after the SAA passage, and thus we
widened the OFF-period with 300 s before and after.
• Screen the data for bursts and flares. The scientific goal of the GBM is
to monitor bursts and flares, but for our data analysis these phenomena are
considered as background radiation. For this reason we discarded those parts
of our data set where bursts and flares are visible.
• Compute the angle α between the Earth zenith and the source direction, and discard events for which α > 110◦ . Since the Earth is opaque
to X-ray radiation, we need to ensure that the source we want to observe is
not blocked from view by the Earth. With a radius of ∼ 6370 km and an
atmosphere height of ∼ 100 km the Earth is observed to have a radius ∼ 70◦
from FERMI.
• Compute the angle β between the Earth zenith and the detector
pointing, and discard events for which β > 128◦. The Earth atmosphere
is a significant X-ray source, therefore we discard events collected during time
periods for which the Earth enters significantly in the field of view. By testing
our selection procedure on Hercules X-1, an X-ray binary with strong pulsed
emission with a period of 1.24 s in the X-ray band, we found that using a
selection criterion of β < 128◦ leads to the best signal-to-noise ratio.
• Compute the angle γ between the detector pointing and the source
direction, and select γ < 58◦ for channel 2 and lower, or γ < 84◦
for channel 3 and higher. At high source angle γ the detector effective
area for radiation from the source direction decreases significantly (Fig. 10),
therefore events recorded at high source angle γ are more likely to originate
from background radiation than events recorded at low source angle γ. We
suppress the background radiation by discarding events for which the source
angle γ exceeds a certain threshold value. By testing our selection procedure
on Hercules X-1 we found that using a threshold value of 84◦ for channel 3
and higher (> 50.617 keV) and 58◦ for channel 2 and lower (< 50.617 keV)
leads to the best signal-to-noise ratio.
23
2 INSTRUMENTATION AND EVENT SELECTION
We applied these selection criteria to all events in our data set. Table 2 lists the
time window and the total screened exposure, summed over all NaI detectors for
each of the four AXPs that are analyzed for this work.
Table 2: List of FERMI GBM observations used in this work. The screened exposure is
summed over all NaI detectors.
Source
4U 0142+614
1RXS J1708-4009
1E 1841-045
1E 1547.0-5408
Start
[MJD]
End
[MJD]
54690
54690
54690
54855
55496
55516
55524
54890
Screened exposure
(Ms)
ch.0,1,2
133.48
147.99
126.00
5.8288
24
Screened exposure
(Ms)
ch.3,4,5,6,7
244.39
262.28
221.75
10.184
2.4 Flux determination
2.4
Flux determination
−
+
n
The measured count rate ∆c
of a detector in channel n with energy interval [Em
, Em
]
∆t
can be used to compute the flux Fn in that channel if the effective area Ǎn for that
channel is known.
Fn =
∆cn
∆t
Ǎn · ∆Em
(11)
In the case of the FERMI GBM, the effective area Ai (Eγ , θ, φ) of detector i is a
function of the direction of incoming photons (θ, φ) and of the photon energy Eγ .
We also need to take into account the redistribution matrix Ri (Eγ .Em , θ, φ), which
gives the chance that a photon of energy Eγ is detected with energy Em . The first
step is to average (Ai (Eγ , θ, φ) · Ri (Eγ .Em , θ, φ)) over all detectors i and photon
directions (θ, φ), using the observed exposure per detector per direction Ti (θ, φ) as
a weight.
P
Ti (θ, φ) · (Ai (Eγ , θ, φ) · Ri (Eγ .Em , θ, φ))
P
hA(Eγ ) · R(Eγ , Em )i =
(12)
Ti (θ, φ)
Then we integrate hA(Eγ ) · R(Eγ , Em )i over Em to obtain the effective area per
channel Ǎn (Eγ ) (Fig. 12).
Ǎn (Eγ ) =
Z
+
Em
hA(Eγ ) · R(Eγ , Em )i · dEm
(13)
−
Em
And finally we compute the weighted average of Ǎn (Eγ ) over Eγ by assuming a
spectral shape f (Eγ ) for the source.
Ǎn =
R∞
0
f (Eγ ) · Ǎn (Eγ ) · dEγ
+
R Em
− f (Eγ ) · dEγ
Em
(14)
Figure 12: The energy dependence of the effective area (cm2 ) of the GBM NaI detectors per energy channel, averaged over different detectors and source positions using the
recorded exposure as weight. For this figure the recorded exposure of 1RXS J1708-4009
was used.
25
2 INSTRUMENTATION AND EVENT SELECTION
We based our flux reconstruction of FERMI GBM observations on data from
instrument response simulations (Kippen et al. 2007, Bissaldi et al. 2009), consisting
of a set of response matrices R(Eγ , Em ); one for each of 272 different source positions,
for each of 12 NaI detectors. See Figure 13, 14 for the angular dependence of the
detector effective area.
For our estimate of the spectral shape f (Eγ ) in Equation 14 we initially assumed
f (Eγ ) = Eγ−1 , and then took an iterative approach by using the result of an empirical
spectral fit for the spectral shape f (Eγ ) in the next iteration of flux reconstruction.
Figure 13: The angular dependence of the effective area (cm2 ) of the NaI detectors
in 11.710 - 50.617 keV, assuming a F ∝ E −1 spectrum. The cross indicates the detector
pointing, and the dashed line marks the boundary where the source angle γ equals 58◦ . The
[φ, θ] coordinates are in FERMI spacecraft coordinates. The above figures were obtained by
integrating response matrices from (Kippen et al. 2007, Bissaldi et al. 2009) over measured
energy and photon energy (using f (Eγ ) = Eγ−1 as weight) and interpolating at 2◦ × 2◦
intervals.
26
2.4 Flux determination
Figure 14: The angular dependence of the effective area (cm2 ) of the NaI detectors
in 50.617 - 2000.0 keV, assuming a F ∝ E −1 spectrum. The cross indicates the detector
pointing, and the dashed line marks the boundary where the source angle γ equals 84◦ . The
[φ, θ] coordinates are in FERMI spacecraft coordinates. The above figures were obtained by
integrating response matrices from (Kippen et al. 2007, Bissaldi et al. 2009) over measured
energy and photon energy (using f (Eγ ) = Eγ−1 as weight) and interpolating at 2◦ × 2◦
intervals.
27
2 INSTRUMENTATION AND EVENT SELECTION
28
3
3.1
Data reduction and results
Timing Analysis
The GBM is a non-imaging instrument with a very wide field of view. The instrument is not designed to accurately locate individual events from a point source.
We can, however, use the GBM to measure the pulsed flux component of our
target AXPs by applying a timing analysis.
We chose to use a method of timing analysis known as ’epoch folding’. After
barycentering all events (i.e. convert for each event the arrival time at the FERMI
spacecraft to the arrival time at the center of mass of the solar system) we used a
set of phase-coherent timing models (Table 3, derived from RXTE PCA monitoring
data) to compute the phase for each event.
The epoch-folded events are then binned into a fixed number of phase bins, and
are divided by the exposure per phase bin to obtain the phase-folded light curve.
For our analysis we used a number of nbins = 120 phase bins for intermediate results.
Sampling effects
For a pulsar period of P ∼ 10 s each of the phase bins in the intermediate results
has a width of ∆t ∼ 0.08 s (120 phase bins), much smaller than the 0.256 s (scanning
mode) time resolution of the GBM CTIME data. As the intermediate results are
clearly oversampled, we expected these light curves to be dominated by noise.
Figure 15: (Left) Observed light curve (120 phase bins) of 1RXS J1708-4009 using
FERMI GBM CTIME data. The oscillation in the data is of a much higher frequency
than the pulse frequency of 1RXS J1708-4009. (Right) Fourier strength Sn , defined as
2
2
Sn2 = (An /∆AP
n ) + (Bn /∆Bn ) where An and Bn are the best fit values for fitting a
Fourier series
An cos(2nπφ) + Bn sin(2nπφ) to the observed light curve. The strong
oscillations at n = 43 and n = 34 are due to the ∼ 0.256 s binning period of the CTIME
data.
The light curve of 1RXS J1708-4009 (Fig. 15), however, displays an unexpected
strong oscillation. The time scale of the oscillation is much shorter than the expected
pulse period (P ∼ 11.005 s) of 1RXS J1708-4009 and the amplitude is much larger
than the Poisson error bars (χ2 = 908.901 for 119 degrees of freedom).
To better understand the cause
P of this artifact, we fit the observed light curve
with a discrete Fourier series
An cos(2nπφ) + Bn sin(2nπφ), and define Sn as
29
Source
4U 0142+614
4U 0142+614
1RXS J1708-4009
1RXS J1708-4009
1RXS J1708-4009
1E 1841-045
1E 1841-045
1E 1547.0-5408
Start
[MJD]
54682
55203
54623
54899
55202
54657
55168
54855
End
[MJD]
55315
55496
54899
55202
55516
55169
55539
54890
t0 , Epoch
[MJD,TDB]
54713.0
55329.0
54623.0
54899.0
55202.0
54860.0
55168.0
54856.0
ν
[Hz]
0.1150900037859
0.1150885887349
0.0908705155243
0.0908666965249
0.0908624449122
0.0848432394597
0.0848356784588
0.4825951820243
ν̇
[Hz/s]
−2.74516 × 10−14
−2.60829 × 10−14
−1.69097 × 10−13
−1.60190 × 10−13
−1.62015 × 10−13
−2.83664 × 10−13
−2.83056 × 10−13
−4.90615 × 10−12
ν̈
[Hz/s2 ]
−3.60 × 10−23
0
9.78 × 10−22
−8.10 × 10−23
−1.37 × 10−22
0
−9.42 × 10−23
−2.30 × 10−19
Φ0
0.751
0.526
0.208
0.431
0.153
0.445
0.482
0.071
30
3 DATA REDUCTION AND RESULTS
Table 3: Phase-coherent timing models as derived from RXTE PCA monitoring data. Φ = ν · (t − t0 ) + 21 ν̇ · (t − t0 )2 + 61 ν̈ · (t − t0 )3 − Φ0
3.1 Timing Analysis
follows:
Sn =
s
An
∆An
2
+
Bn
∆Bn
2
(15)
Bn
An
and ∆B
to be normally distributed
Under the null hypothesis we expect ∆A
n
n
with zero mean and unit variance for all n, so that the resulting Sn2 is expected to
follow the chi-square distribution with 2 degrees of freedom (Abramowitz & Stegun
1972). In the case of a pulsar observation we expect Sn2 to deviate from the χ22
distribution for low n.
The Sn diagram of 1RXS J1708-4009 (Fig. 15) displays distinct peaks at n = 43
(P ∼ 0.25593 s) and n = 34 (P ∼ 0.32368 s). The explanation for these strong
Fourier modes is that they originate from the 0.256 s sampling of the CTIME data,
and that these sampling effects survived through our timing analysis because the
period of 1RXS J1708-4009 is a near-integer multiple of the sampling period of the
GBM CTIME data. In this interpretation the second harmonic (P = 0.128 s) of
the GBM CTIME sampling effect is reflected against the Nyquist frequency of the
binning used for our timing analysis, and is observed as an oscillation with period
P ∼ 0.32368 s. We checked this hypothesis by repeating the epoch folding analysis
using a number of nbins = 100 phase bins, in which case we found strong Fourier
components at n = 43 and at n = 14.
After closer inspection, we found similar - but much weaker - artifacts in the
observed light curves of 1E 1841-045 and 4U 0142+614. We could not detect similar features for 1E 1547.0-5408, possibly due to the worse signal-to-noise ratio for
observations on 1E 1547.0-5408 when compared to the other observations.
Considering that the cause of the sampling effects are well understood and are
limited to specific Fourier modes we correct for the sampling effects by fitting these
specific Fourier modes and subtracting them from the observed light curves. All
light curves of 4U 0142+614, 1RXS J1708-4009 and 1E 1841-045 shown hereafter are
corrected for these sampling effects.
Significance test
A frequently used test to estimate the significance of a pulse detection is the Zn2
test. Through analysis of a limited number of Fourier modes a statistical variable,
Zn2 , is obtained which is distributed according to the χ22n distribution under the null
hypothesis.
For our work, however, the Zn2 test as described by Buccheri et al. (1983) is
unsuitable because it assumes an equal exposure per phase bin. For this reason we
will use an alternative for the Zn2 for significance testing.
First we perform a least Chi Square
Pnfit on the observed light curve with a limited
number of Fourier components f = i=1 Ai cos(2iπφ) + Bi sin(2iπφ), and then we
define a statistic Tn2 .
Tn2
2 2
n X
Ai
Bi
=
+
∆A
∆Bi
i
i=1
(16)
Bi
Ai
and ∆B
are all normally distributed with zero
Under the null hypothesis ∆A
i
i
2
mean and unit variance, so that Tn follows a χ22n distribution (Abramowitz & Stegun
1972). This property allows us to use the Tn2 statistic to estimate the significance
of a pulse detection in a way very similar to how the Zn2 statistic is used in other
works.
31
3 DATA REDUCTION AND RESULTS
Based on previous observations, we expect that 2 harmonics are needed to adequately describe the AXP pulse shape. Therefore we will use the T22 statistic for
estimating the significance of FERMI GBM pulsar detections.
32
3.1 Timing Analysis
3.1.1
1RXS J1708-4009
Figure 16: Pulse profile of 1RXS J1708-4009 using FERMI GBM data. The detection
has a 7.6σ significance, following from a T22 test. The light curve is re-binned to 12 phase
bins for display purposes. The smooth line displays the template light curve observed with
INTEGRAL IBIS-ISGRI, 29-Jan-2003 to 05-Oct-2006, at 20-210 keV (den Hartog et al.
2008b).
The light curve of 1RXS J1708-4009 as observed by the FERMI GBM, summed
over channels 2-4 (27.0-295.3 keV), is displayed in Fig. 16. By applying a T22
test, we detected pulsed emission with a 7.6σ significance. The light curve observed with FERMI GBM shows strong resemblance to a light curve observed with
INTEGRAL IBIS-ISGRI, Revs 37-485 (29-Jan-2003 to 05-Oct-2006), at 20-210 keV
(den Hartog et al. 2008b). This resemblance indicates that the hard X-ray pulse profile of 1RXS J1708-4009 is stable, within instrumental uncertainties, over a timespan
of at least 7 years.
The observed light curves in channels 2, 3 and 4 (27.0-50.6 keV, 50.6-101.9 keV
and 101.9-295.3 keV) are displayed in Fig. 17. The observations are consistent with
1RXS J1708-4009 having a pulse profile that does not change in shape for different
photon energies.
We performed a linear χ2 fit with the IBIS-ISGRI template light curve on the
observed FERMI GBM light curves to derive the pulsed count rates of 1RXS J17084009 in channels 1-7 (Table 4).
33
3 DATA REDUCTION AND RESULTS
Table 4:
List of FERMI GBM count rates
of 1RXS J1708-4009, obtained by fitting the
observed light curves with a template light
curve observed with INTEGRAL IBIS-ISGRI,
29-Jan-2003 to 05-Oct-2006, at 20-210 keV
(den Hartog et al. 2008b).
Ch.
#
1
2
3
4
5
6
7
2-4
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
989.34
26.982
E+
Count rate
[keV]
[10−3 × 1s ]
26.982
3.7 ± 1.9
50.617
4.7 ± 1.4
101.88
4.4 ± 0.9
295.29
6.2 ± 0.9
539.85
0.5 ± 0.4
989.34 −0.2 ± 0.5
2000.0
0.4 ± 0.5
295.29
15.2 ± 1.9
χ2
ν=10
15.3
6.7
17.4
16.2
9.8
12.6
9.2
12.9
Figure 17:
Pulse profiles of 1RXS J1708The light
4009 using FERMI GBM data.
curves are re-binned to 12 phase bins for display purposes.
The smooth line shows the
template light curve observed with INTEGRAL
IBIS-ISGRI, 29-Jan-2003 to 05-Oct-2006, at 20210 keV (den Hartog et al. 2008b).
34
3.1 Timing Analysis
3.1.2
1E 1841-045
Figure 18: Pulse profile of 1E 1841-045 using FERMI GBM data. The detection has a
7.1σ significance, following from a T22 test. The light curve is re-binned to 12 phase bins for
display purposes. The smooth line shows the template profile observed with INTEGRAL
IBIS-ISGRI, 10-Mar-2003 to 30-Sep-2009, at 50-150 keV.
The light curve of 1E 1841-045 as observed by the FERMI GBM, summed over
channels 2-4 (27.0-295.3 keV), is displayed in Fig. 18. By applying a T22 test, we
detected pulsed emission with a 7.1σ significance. The light curve observed with
FERMI GBM shows strong resemblance to a light curve observed with INTEGRAL
IBIS-ISGRI, Revs 49-850 (10-Mar-2003 to 30-Sep-2009), at 20-210 keV (unpublished, updated from Kuiper et al. (2004)). The resemblance to this IBIS-ISGRI
template light curve and to the earlier published (Kuiper et al. 2004) light curve indicates that the hard X-ray pulse profile of 1E 1841-045 is stable, within instrumental
uncertainties, over a timespan of at least 6 years.
The observed light curves in channels 2, 3 and 4 (27.0-50.6 keV, 50.6-101.9 keV
and 101.9-295.3 keV) are displayed in Fig. 19. The observations are consistent
with 1E 1841-045 having a pulse profile that has a constant shape over different
photon energies up to ∼ 100 keV. In channel 4 (101.9-295.3 keV) the observed pulse
profile seems to deviate (χ210 = 24.3) from the IBIS-ISGRI template profile, but the
statistical significance σ = 2.7 of the deviation is low.
We performed a linear χ2 fit with the IBIS-ISGRI template light curve on the
observed FERMI GBM light curves to derive the pulsed count rates of 1E 1841-045
in channels 1-7 (Table 5).
35
3 DATA REDUCTION AND RESULTS
Table 5:
List of FERMI GBM count rates
of 1E 1841-045, obtained by fitting the observed
light curves with a template light curve observed
with INTEGRAL IBIS-ISGRI, 10-Mar-2003 to
30-Sep-2009, at 50-150 keV.
Ch.
#
1
2
3
4
5
6
7
2-4
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
989.34
26.982
E+
count rate
[keV] [10−3 × 1s ]
26.982
5.1 ± 3.0
50.617 12.2 ± 2.3
101.88
8.0 ± 1.4
295.29
3.2 ± 1.4
539.85 −0.3 ± 0.7
989.34 −0.2 ± 0.8
2000.0
0.0 ± 0.8
295.29 23.4 ± 3.0
χ2
ν=10
23.3
8.9
21.0
24.3
10.4
5.1
6.5
8.6
Figure 19: Pulse profiles of 1E 1841-045 using FERMI GBM data. The light curves are
re-binned to 12 phase bins for display purposes.
The smooth line shows the template light curve
observed with INTEGRAL IBIS-ISGRI, 10-Mar2003 to 30-Sep-2009, at 50-150 keV.
36
3.1 Timing Analysis
3.1.3
4U 0142+614
Figure 20: Pulse profile of 4U 0142+614 using FERMI GBM data. The detection has a
4.8σ significance, following from a T22 test. The light curve is re-binned to 12 phase bins for
display purposes. The smooth line shows the template profile observed with INTEGRAL
IBIS-ISGRI, 12-Dec-2003 to 13-Aug-2006, at 20-160 keV (den Hartog et al. 2008a).
The light curve of 4U 0142+614 as observed by the FERMI GBM, summed over
channels 2-4 (27.0-295.3 keV), is displayed in Fig. 20. By applying a T22 test, we
detected pulsed emission with a 4.8σ significance. The light curve observed with
FERMI GBM shows resemblance to a light curve observed with INTEGRAL IBISISGRI, Revs 142-468 (12-Dec-2003 to 13-Aug-2006), at 20-160 keV (den Hartog et al.
2008a). The light curve observed with FERMI GBM is consistent with 4U 0142+614
having a stable hard X-ray pulse profile over a timespan of 6.5 years.
The observed light curves in channels 2, 3 and 4 (27.0-50.6 keV, 50.6-101.9 keV
and 101.9-295.3 keV) are displayed in Fig. 21. The observations are consistent with
4U 0142+614 having a pulse profile that is constant over different photon energies.
We performed a linear χ2 fit with the IBIS-ISGRI template light curve on the
observed FERMI GBM light curves to derive the pulsed count rates of 4U 0142+614
in channels 1-7 (Table 6).
37
3 DATA REDUCTION AND RESULTS
Table 6: List of FERMI GBM count rates of
4U 0142+614, obtained by fitting the observed
light curves with a template light curve observed
with INTEGRAL IBIS-ISGRI, 12-Dec-2003 to
13-Aug-2006, at 20-160 keV (den Hartog et al.
2008a).
Ch.
#
1
2
3
4
5
6
7
2-4
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
989.34
26.982
E+
count rate
[keV] [10−3 × 1s ]
26.982
0.4 ± 3.0
50.617
5.7 ± 2.3
101.88
4.8 ± 1.5
295.29
3.5 ± 1.5
539.85 −0.3 ± 0.7
989.34 −0.2 ± 0.8
2000.0
0.0 ± 0.8
295.29 14.1 ± 3.1
χ2
ν=10
12.1
19.7
11.4
13.3
17.8
7.8
8.8
24.5
Figure 21:
Pulse profiles of 4U 0142+614
using FERMI GBM data. The light curves
are re-binned to 12 phase bins for display purposes. The smooth line shows the template light
curve observed with INTEGRAL IBIS-ISGRI,
12-Dec-2003 to 13-Aug-2006, at 20-160 keV
(den Hartog et al. 2008a).
38
3.1 Timing Analysis
3.1.4
1E 1547.0-5408
Figure 22: Pulse profile of 1E 1547.0-5408 using FERMI GBM data. The detection has
a 2.7σ significance, following from a T22 test. The light curve is re-binned to 12 phase bins
for display purposes. The smooth line shows the template profile observed with RXTE
PCA and RXTE HEXTE at 28-80 keV (Kuiper et al. 2012).
The light curve of 1E 1547.0-5408 as observed by the FERMI GBM, 24-Jan2009 to 28-Feb-2009, summed over channels 2-4 (27.0-295.3 keV), is displayed in
Fig. 22. By applying a T22 test, we detected pulsed emission with a weak 2.7σ
significance, but the significance of the detection increases to 3.2σ (T22 ) if we only
consider the observations at 101.9-295.3 keV. The light curve observed with FERMI
GBM shows resemblance to a light curve observed (Kuiper et al. 2012) with RXTE
PCA and RXTE HEXTE at 28-80 keV during the peak of the hard X-ray luminosity,
06-Feb-2009 to 03-May-2009.
The observed light curves in channels 2, 3, 4 and 5 (27.0-50.6 keV, 50.6-101.9 keV,
101.9-295.3 keV and 295.3-539.9 keV) are displayed in Fig. 23. The error margins
on the FERMI GBM observations are too large to search for changes in the pulse
profile.
We performed a linear χ2 fit with the RXTE template light curve on the observed
FERMI GBM light curves to derive the pulsed count rates of 1E 1547.0-5408 in
channels 1-7 (Table 7).
39
3 DATA REDUCTION AND RESULTS
Table 7: List of FERMI GBM count rates of
1E 1547.0-5408, obtained by fitting the observed
light curves with a template light curve observed
with RXTE PCA and RXTE HEXTE at 2880 keV (Kuiper et al. 2012).
Ch.
#
1
2
3
4
5
6
7
2-4
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
989.34
26.982
E+
count rate
[keV] [10−3 × 1s ]
26.982
9.2 ± 6.2
50.617
8.0 ± 4.8
101.88
1.2 ± 3.0
295.29 10.7 ± 3.0
539.85
3.0 ± 1.5
989.34
1.0 ± 1.5
2000.0 −2.8 ± 2.0
295.29 19.8 ± 6.4
χ2
ν=10
6.2
4.5
8.9
8.0
7.9
12.7
9.9
8.4
Figure 23: Pulse profiles of 1E 1547.0-5408 using FERMI GBM data. The light curves are rebinned to 12 phase bins for display purposes. The
smooth line shows the template light curve observed with RXTE PCA and RXTE HEXTE at
28-80 keV (Kuiper et al. 2012).
40
3.2 Spectral analysis
3.2
Spectral analysis
In order to differentiate between the different emission models for AXP hard X-ray
(E > 15 keV) emission we need to measure the spectral shape. We used earlier observations with IBIS ISGRI (20-300 keV) and RXTE PCA/HEXTE (15-250
keV) (Kuiper et al. private communication), and added new observations with
FERMI GBM to obtain updated knowledge of the spectral energy distribution of
1RXS J1708-4009, 1E 1841-045, 4U 0142+614 and 1E 1547.0-5408. We fit the pulsed
emission above ∼ 15 keV with three empirical models: a power law (Eq. 17), a
power law with sharp, super-exponential, spectral break (Eq. 18) and a power law
with fixed index (Γ = −1) and exponential break (Eq. 19).
F (E) = F0 · (E/E0 )Γ
(17)
F (E) = F0 · (E/E0 )Γ · exp(−(E/Ec )2 )
(18)
F (E) = F0 · (E/E0 )−1 · exp(−E/Ec )
(19)
The power law model serves as a null hypothesis, the model with power law plus
sharp spectral break can be used to fit spectra that resemble the simulated inverse
Compton spectra by Beloborodov (2011; 2012), and the power law plus exponential
spectral break can be used to fit thermal Bremsstrahlung emission spectra. We
report the best fit values for fitting the observed spectra with Eq. 17, 18 and
19. We perform the F-test on the fit results with Eq. 17 and 18 to find the false
positive probability for spectral break detections. From the derived values for the
spectral index Γ and spectral break energy Ec we attempt to discriminate between
the different emission mechanisms described in Section 1.4. The fit results can be
found in Table 8.
3.2.1
1RXS J1708-4009
Using earlier observations with RXTE PCA/HEXTE and INTEGRAL IBISISGRI (Kuiper et al. private communication) in addition to new observations with
FERMI GBM (Table 9, Fig. 24), we find no indication for a spectral break in
the pulsed emission above 15 keV. Assuming a power law with super-exponential
spectral break (Eq. 18) we find a spectral index Γ = −1.33 ± .06 and a 2σ lower
limit to the spectral break energy Ec at 450 keV, while the non-simultaneous CGRO
COMPTEL observations in the MeV band set an upper limit to Ec at ∼ 1 MeV.
The thermal bremsstrahlung model (Eq. 19) fits the observed spectrum adequately, but the spectral break energy Ec−brems = 411 ±105
keV is much higher
58
than the Ec−brems ∼ 100 keV predicted by the thermal bremsstrahlung model for
magnetars (Section 1.4.2). Therefore, we do not favour the thermal bremsstrahlung
model. Both the synchrotron radiation model (Section 1.4.1) and the inverse Compton model (Section 1.4.3) are consistent with the observed spectrum of 1RXS J17084009.
When comparing the best fit pulsed spectrum with the total emission spectrum
as measured with INTEGRAL IBIS-ISGRI we find that the pulsed fraction is 25-30%
at 35-200 keV.
3.2.2
1E 1841-045
Using earlier observations with RXTE PCA/HEXTE and INTEGRAL IBISISGRI (Kuiper et al. private communication) in addition to new observations with
41
E0
[keV]
)Γ
F (E) = F0 · (E/E0
F (E) = F0 · (E/E0 )Γ · exp(−(E/Ec )2 )
F (E) = F0 · (E/E0 )−1 · exp(−E/Ec )
100.587
100.587
100.587
F (E) = F0 · (E/E0 )Γ
F (E) = F0 · (E/E0 )Γ · exp(−(E/Ec )2 )
F (E) = F0 · (E/E0 )−1 · exp(−E/Ec )
68.4908
68.4908
68.4908
F (E) = F0 · (E/E0 )Γ
F (E) = F0 · (E/E0 )Γ · exp(−(E/Ec )2 )
F (E) = F0 · (E/E0 )−1 · exp(−E/Ec )
79.9548
79.9548
79.9548
F (E) = F0 · (E/E0 )Γ
165.202
F0
[cm−2 s−1 MeV−1 ]
1RXS J1708-4009
0.00076 ± 0.00003
0.00076 ± 0.00005
0.00112 ± 0.00005
1E 1841-045
0.00131 ± 0.00008
0.00246 ± 0.00022
0.00219 ± 0.00013
4U 0142+614
0.00083 ± 0.00009
0.00242 ± 0.00033
0.00251 ± 0.00013
1E 1547.0-5408
0.00054 ± 0.00013
Γ
−1.32 ± 0.04
−1.32 ± 0.06
−1.36 ± 0.05
−0.78 ± 0.10
−1.27 ± 0.07
−0.34 ± 0.17
−1.19 ± 0.21
Ec
[keV]
χ2 (ν)
> 450
411±105
58
21.2(17)
21.2(16)
21.0(17)
155 ± 23
233±52
41
39.0(23)
16.0(22)
22.2(23)
142 ± 22
464±300
148
40.8(19)
15.1(18)
28.8(19)
7.0(5)
p(F ∗ )
100.0%
X
0.001%
X
0.003%
X
X
42
3 DATA REDUCTION AND RESULTS
Table 8: Best-fit parameters for fitting the spectra with a power law (Eq. 17), a power law with super-exponential break (Eq. 18) and a power law
with fixed index (Γ = 1) and exponential break (Eq. 19). Also shown are χ2ν and the number of degrees of freedom ν for each fit. Also listed is the
probability p(F ∗ ) that the observed χ2 difference is caused by statistical fluctuations. A p(F ∗ ) ∼ 0% indicates that a spectral break is required to fit the
flux observations adequately.
3.2 Spectral analysis
FERMI GBM (Table 10, Fig. 25) we find evidence for a spectral break in the pulsed
emission above 15 keV. Assuming a power law with super-exponential spectral
break (Eq. 18) we derived the break energy Ec = 155 ± 23 keV and spectral index
Γ = −0.78 ± 0.10 keV for energies lower than the spectral break energy Ec .
As we detected a spectral break at 155 ± 23 keV, we reject the synchrotron
radiation model as described in Section 1.4.1 for this AXP. The observed pulsed
spectrum can be fit with the thermal bremsstrahlung model (Eq. 19) reasonably
well, but the derived spectral break energy Ec−brems = 233 ±52
41 keV is significantly
higher than the Ec−brems ∼ 100 keV predicted by the thermal bremsstrahlung model
for magnetars (Section 1.4.2). The inverse Compton model (Section 1.4.3) appears
to be consistent with our observations on 1E 1841-045. Note the resemblance up to
∼ 300 keV between the observed pulsed spectrum of 1E 1841-045 (Fig. 25) and the
simulated pulsed spectrum in Figure 9, left.
When comparing the best fit pulsed spectrum with the total emission spectrum
as measured with INTEGRAL IBIS-ISGRI we find that the pulsed fraction is 20-30%
at 20-200 keV.
3.2.3
4U 0142+614
Using earlier observations with RXTE PCA/HEXTE and INTEGRAL IBISISGRI (Kuiper et al. private communication) in addition to new observations with
FERMI GBM (Table 11, Fig. 26) we find evidence for a spectral break in the pulsed
emission above 15 keV. Assuming a power law with super-exponential spectral break
(Eq. 18) we derived the spectral break energy Ec = 142 ± 22 keV and spectral index
Γ = −0.34 ± 0.17 keV for energies lower than the spectral break energy Ec .
Because of our detection of a break in the spectrum of 4U 0142+614 at 142 ±
22 keV we reject the synchrotron radiation model as described in Section 1.4.1
for 4U 0142+614. The thermal bremsstrahlung model (Eq. 19) does not fit the
data properly (see Table 8). Therefore we reject the thermal bremsstrahlung model
(Section 1.4.2). The inverse Compton model (Section 1.4.3) appears to be consistent
with our observations. Note the resemblance up to ∼ 300 keV between the observed
pulsed spectrum of 1E 1841-045 (Fig. 26) and the simulated pulsed spectrum in
Figure 9, left.
When comparing the best fit pulsed spectrum with the total emission spectrum
as measured with INTEGRAL IBIS-ISGRI we find that the pulsed fraction is 20-30%
at 20-200 keV.
3.2.4
1E 1547.0-5408
Using only the FERMI GBM observations (Table 12, Fig. 27) - because of the
high temporal variability of 1E 1547.0-5408 - we find a spectral index Γ = −1.19 ±
0.21 keV for pulsed emission above 10 keV. We did not attempt to find the spectral
break energy Ec because we judged that we had an insufficient number of significant
F
flux measurements to do so, but we do note that we observed a ∆F
= 2.1 pulsation
in the 295.29-539.85 keV band (see the pulse profile in Fig. 23), while Kuiper et al.
(2012) reports νFν maxima in the 90-105 keV range with an uncertainty of 20 keV.
F
The ∆F
= 2.1 observation at 295.29-539.85 keV renders the thermal bremsstrahlung
interpretation as described in Section 1.4.2 unlikely for the hard X-ray emission of
1E 1547.0-5408. Both the synchrotron radiation model (Section 1.4.1) and the inverse Compton model (Section 1.4.3) are consistent with our observations on this
AXP.
43
3 DATA REDUCTION AND RESULTS
Table 9: The observed pulsed flux of 1RXS J1708-4009 in five energy bands.
Ch.
#
1
2
3
4
5
6-7
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
E+
[keV]
26.982
50.617
101.88
295.29
539.85
2000.0
F
[cm−2 s−1 MeV−1 ]
(4.2 ± 2.1) × 10−3
(2.5 ± 0.8) × 10−3
(1.2 ± 0.2) × 10−3
(3.8 ± 0.5) × 10−4
(5.2 ± 4.6) × 10−5
< 5.3 × 10−5
Figure 24: The high-energy spectrum of 1RXS J1708-4009. Displayed in this figure are:
pulsed flux measurements by XMM-Newton EPIC-PN, RXTE PCA, RXTE HEXTE,
INTEGRAL IBIS-ISGRI and FERMI GBM; total flux measurements by XMM-Newton
EPIC-PN, INTEGRAL IBIS ISGRI and CGRO COMPTEL; and a fit to the pulsed emission above 15 keV with a power law (Eq. 17). There is no indication of a spectral break if
only pulsed flux measurements are taken into account, but as the pulsed flux can never be
higher than the total flux, the COMPTEL observations put an upper limit to the spectral
break energy at Ec < 1 MeV. Assuming a sharp spectral break (Eq. 18), we found a 2σ
lower limit to the spectral break energy Ec at 450 keV.
44
3.2 Spectral analysis
Table 10: The observed pulsed flux of 1E 1841-045 in five energy bands.
Ch.
#
1
2
3
4
5
6-7
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
E+
[keV]
26.982
50.617
101.88
295.29
539.85
2000.0
F
[cm−2 s−1 MeV−1 ]
(5.3 ± 3.1) × 10−3
(6.4 ± 1.2) × 10−3
(2.3 ± 0.4) × 10−3
(2.7 ± 1.2) × 10−4
< 2.2 × 10−4
< 4.9 × 10−5
Figure 25: The high-energy spectrum of 1E 1841-045. Displayed in this figure are:
pulsed flux measurements by Suzaku XIS, RXTE PCA, RXTE HEXTE, INTEGRAL
IBIS-ISGRI and FERMI GBM; total flux measurements by Chandra ACIS, INTEGRAL
IBIS ISGRI and CGRO COMPTEL; and a fit to the pulsed emission above 15 keV with a
power law plus super-exponential break (Eq. 18). We found evidence for a spectral break
at Ec = 155 ± 23 keV.
45
3 DATA REDUCTION AND RESULTS
Table 11: The observed pulsed flux of 4U 0142+614 in five energy bands.
Ch.
#
1
2
3
4
5
6-7
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
E+
[keV]
26.982
50.617
101.88
295.29
539.85
2000.0
F
[cm−2 s−1 MeV−1 ]
< 5.8 × 10−3
(3.0 ± 1.2) × 10−3
(1.4 ± 0.4) × 10−3
(3.1 ± 1.3) × 10−4
< 1.6 × 10−4
< 1.1 × 10−4
Figure 26: The high-energy spectrum of 4U 0142+614. Displayed in this figure are:
pulsed flux measurements by XMM-Newton EPIC-PN, RXTE PCA, RXTE HEXTE,
INTEGRAL IBIS-ISGRI and FERMI GBM; total flux measurements by Chandra ACIS,
INTEGRAL IBIS ISGRI and CGRO COMPTEL; and a fit to the pulsed emission above
15 keV with a power law plus super-exponential break (Eq. 18). We found evidence for a
spectral break at Ec = 142 ± 22 keV
46
3.2 Spectral analysis
Table 12: The observed pulsed flux of 1E 1547.0-5408 in five energy bands.
Ch.
#
1
2
3
4
5
6-7
E−
[keV]
11.710
26.982
50.617
101.88
295.29
539.85
E+
[keV]
26.982
50.617
101.88
295.29
539.85
2000.0
F
[cm−2 s−1 MeV−1 ]
(1.0 ± 0.7) × 10−2
(4.2 ± 2.5) × 10−3
< 1.8 × 10−3
(5.9 ± 1.7) × 10−4
(2.9 ± 1.4) × 10−4
< 9.6 × 10−5
Figure 27: The high-energy spectrum of 1E 1547.0-5408. Displayed in this figure are:
pulsed flux measurements by RXTE PCA, RXTE HEXTE and FERMI GBM; total flux
measurements by SWIFT XRT and INTEGRAL IBIS ISGRI; and a power law (Eq. 17)
fit to the FERMI GBM observations. The displayed FERMI GBM flux measurements are
from an observation with time window from 24-Jan-2009 to 28-Feb-2009, while the displayed RXTE and INTEGRAL flux measurements are from observations with time window
from 06-Feb-2009 to 03-May-2009. As 1E 1547.0-5408 has been shown (Kuiper et al. 2012)
to be variable in hard X-ray luminosity, the non-overlapping time window explains why
the GBM observations yield lower fluxes than the other displayed observations.
47
3 DATA REDUCTION AND RESULTS
48
4
Summary and Conclusions
Using archive data of FERMI GBM, the instrument with the highest sensitivity
to photons in the E > 100 keV range, we succeeded in detecting pulsed emission
from 1RXS J1708-4009, 1E 1841-045, 4U 0142+614 and 1E 1547.0-5408 in hard Xrays (> 15 keV). We extracted count rates for the pulsed emission by fitting the
epoch-folded FERMI GBM data with template profiles, and reconstructed the flux
for these observations. In order to correctly reconstruct the fluxes, we averaged the
FERMI GBM effective area over photon direction and over all NaI detectors using
the observed exposure as weight.
In an attempt to further constrain the spectral shape of the hard X-ray emission
of 1RXS J1708-4009, 1E 1841-045, 4U 0142+614 and 1E 1547.0-5408 we used updated pulsed flux observations with INTEGRAL IBIS-ISGRI and RXTE PCA/HEXTE
(Kuiper et al. private communication) in addition to the new pulsed flux measurements with FERMI GBM, and performed a chi-square fit with three empirical
models:
• A power law: F (E) = F0 · (E/E0 )Γ
Since there is no spectral break in this model, it can be used as a null hypothesis
for detecting a spectral break.
• A power law with sharp spectral break: F (E) = F0 · (E/E0 )Γ · exp(−(E/Ec )2 )
The spectral break in this model resembles the spectral break in simulated
inverse Compton spectra by Beloborodov (2012).
• A thermal bremsstrahlung model: F (E) = F0 · (E/E0 )−1 · exp(−E/Ec )
This model has a fixed spectral index (Γ = −1) and an exponential spectral
break.
While we did not attempt to fit the pulsed flux measurements of 1E 1547.05408 with a model that includes a spectral break due to a lack of contemporary
measurements, our fit results (Table 8) indicate that the pulsed flux measurements
of 1RXS J1708-4009, 1E 1841-045 and 4U 0142+614 can be fit properly with the
model with power law and spectral break. By performing an F-test with the power
law model as null hypothesis, we found evidence for a spectral break for 1E 1841-045
and 4U 0142+614 below 200 keV. For 1RXS J1708-4009 we found a 2σ lower limit
to the break energy of the hard X-ray spectrum at 450 keV. The best-fit values for
Γ, the spectral index at energies lower than the spectral break energy Ec , vary from
Γ ∼ −1.3 for 1RXS J1708-4009 to Γ ∼ −0.3 for 4U 0142+614.
The pulsed flux measurements on 1RXS J1708-4009 and 1E 1841-045 can also
be fit with the thermal bremsstrahlung model, but in both cases the spectral break
52
energy, Ec−brems = 411±105
58 keV for 1RXS J1708-4009 and Ec−brems = 233±41 keV for
1E 1841-045, is significantly higher than the spectral break energy of Ec ∼ 100 keV
predicted by Thompson & Beloborodov (2005).
By comparing the best fit model for the pulsed flux with published observations
of the total emission spectra of 1RXS J1708-4009 (den Hartog et al. 2008b), 1E 1841045 (Kuiper et al. 2008) and 4U 0142+614 (den Hartog et al. 2008a), we found that
the pulsed flux fraction, defined as the phase-averaged pulsed flux divided by the
total flux, is in the 20%-30% range up to energies of 200 keV - as opposed to
the reported consistency with ∼ 100% pulsed fraction for energies above 100 keV
reported in earlier publications (den Hartog et al. 2008b, Kuiper et al. 2008).
49
4 SUMMARY AND CONCLUSIONS
As it is unlikely - though not impossible - that the four AXPs studied in this
work have different underlying emission processes for the production of hard Xray emission, we will assume one unified explanation for the observed persistent
spectral characteristics of all four AXPs. From this point of view we reject the
thermal bremsstrahlung model (Section 1.4.2, Thompson & Beloborodov (2005),
Beloborodov & Thompson (2007)).
Based on the detection of spectral breaks below 200 keV for 1E 1841-045
and 4U 0142+614 we also reject the synchrotron radiation model (Section 1.4.1,
Thompson & Beloborodov (2005)) as a significant contributor to the observed persistent pulsed emission. It is, however, still possible that synchrotron radiation
produced at a large height above the stellar surface results in more non-pulsed hard
X-ray emission.
Only the more recent inverse Compton model (Section 1.4.3, Beloborodov (2011;
2012)) is consistent with the observed pulsed emission from each of the four AXPs
that were studied in this work. In this interpretation the different orientation of
the rotation axes and magnetic axes with respect to the observer could explain the
differences in spectral shape between the four observed AXPs.
Considering that the pulsed fractions of 1RXS J1708-4009, 1E 1841-045 and
4U 0142+614 are observed to be in the 20%-30% range up to energies of 200 keV, an
emission process for the non-pulsed hard X-ray emission (70%-80% of the total hard
X-ray emission) needs to be proposed. One possible explanation follows from the
inverse Compton model by Beloborodov (2012): If the twist in the magnetosphere is
axisymmetric with respect to the magnetic dipole axis, then there are configurations
where a considerable part of the produced emission is non-pulsed (example: Fig. 9
(left)). Another possible explanation for non-pulsed hard X-ray emission can be
found in the synchrotron radiation model by Thompson & Beloborodov (2005).
More observational evidence at E > 100 keV is required to reach more constraining conclusions. Possible results that would be especially helpful in testing the
discussed models include:
• A significant energy dependency of the pulse profile shape. Such an observation
would suggest that radiation at different photon energies would be produced
at different locations in the magnetosphere.
• A spectral line at 511 keV due to e± annihilation. Beloborodov (2012) predicts
a spectral line at 511 keV with luminosity equal to 10% of the total luminosity
of the magnetar.
• The spectral break of 1RXS J1708-4009, as well as the shape of the spectral
break of 1E 1841-045 and 4U 0142+614.
• An upturn in the pulsed spectra at energies higher than the spectral break energies found in this work. In this work we detected spectral breaks in the
persistent pulsed spectra of 1E 1841-045 and 4U 0142+614 at 155 ± 23 keV
and 142 ± 22 keV, respectively. But there is a possibility that these detected
spectral breaks are followed by spectral upturns at even higher energies, similar to what is visible in the simulated inverse Compton spectrum in Figure 9
(left).
50
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