Download Cole Miller: Challenges in the measurements of neutron star radii

Challenges in the Measurement
of Neutron Star Radii
Cole Miller
University of Maryland
Collaborators: Romain Artigue, Didier Barret,
Sudip Bhattacharyya, Stratos Boutloukos, Novarah
Kazmi, Fred Lamb, Ka Ho Lo
1
Outline
NS masses are known up to 2 Msun.
What about radii?
• Radii from X-ray bursts
• Radii from cooling neutron stars
• Radii from X-ray light curves
• The promise of gravitational waves
Key point: all current NS radius estimates
are dominated by systematics. None are
reliable. But hope exists for the future. 2
Measuring stellar radii
•
•
•
•
•
•
Ordinary star, like the Sun
Too far for angular resolution
But can get luminosity L
If we assume blackbody, R2=L/(4psT4)
But for NS, usually gives ~5 km!
Why? Spectral shape is ~Planck, but
inefficient emission
• Need good spectral models
• But data usually insufficient to test
3
M and R from X-ray Bursts
•
•
•
•
van Paradijs (1979) method
XRB: thermonuclear explosions on accreting NS
Assume known spectrum, emission over whole surf.
Only with RXTE (1995-2011) is there enough data
4
http://cococubed.asu.edu/images/binaries/images/xray_burst3_web.jpg
4U 1820 Bursts: Soft EOS?
Guver et al. 2010; known dist (globular)
Uses most optimistic
assumption: no systematics,
only statistical uncertainties
But small errors are
misleading; only ~10-8
of prior prob. space gives
M, R in real numbers!
(Guver et al., Steiner et al.)
Spectral model is
terrible fit to best data!
• Fits of good spectral models to hours-long bursts
show that fraction of emitting area changes! 5
Inferred relative emitting areas, for 102 16-s segments near
the peak of the 1820 superburst: Miller et al., in prep
6
Emission from Cooling NS
• Old, transiently accreting NS
• Deep crustal heating (e.g., e capture)
• If know average accretion rate,
emission provides probe of cooling; can
we use to fit radius?
• Predictions of simple model:
Minimum level of emission
Spectrum should be thermal
No variability: steady, slow decay
7
Cooling NS Observations
• Oops!
• All the predictions fail
L sometimes below minimum
Large power law component
Significant variability
• Excuses exist, but failure of basic model means
we can’t use these observations to get R
• Also: is surface mainly H? He? C? Makes 10s
of percent difference to R
• Magnetic field can also alter spectrum
• Again, wide variety of models fit data, thus can’t
use data to say which model is correct
8
RXJ 1856.5–3754
• Specific isolated NS
• Argument: BB most
efficient emitter, thus
R>=RBB
• True for bolometric
but not for given band
• Example: Ho et al.
condensed surface fit
• Different R constraints
for different models
Klähn et al. 2006
9
RXJ 1856.5–3754
• Specific isolated NS
• Argument: BB most
efficient emitter, thus
R>=RBB
• True for bolometric
but not for given band
• Example: Ho et al.
condensed surface fit
• Different R constraints
for different models
Klähn et al. 2006
10
Baryonic vs. Grav. Mass
• Pulsar B in the double pulsar system
• Mgrav=1.249+-0.001 Msun
• If this came from e capture on Mg and
Ne, Mbary=1.366-1.375 Msun for core
• But what about fallback?
• Or could mass be lost after collapse?
11
Ray Tracing and Light Curves
• Rapidly rotating star 300600 Hz
vsurf~0.10.2c
SR+GR effects
• Light curve informative
about M, R
Bogdanov 2012; MSP
• Must deal carefully with
degeneracies
• Lo et al., arXiv:1304.2330
(synth data); no systematic
that gives good fit, tight
constraints, and large bias Weinberg, Miller, and Lamb 2001
12
Phase Accumulation from GWs
• aLIGO/Virgo: >=2015
• Deviation from point mass
in NS-NS inspiral:
accumulated tidal effects
• For aLIGO, can measure
tidal param (Del Pozzo+
2013: distinguish R~11, 13
km?)
• Recent analytics confirmed
by numerical relativity
(Bernuzzi et al. 2012)
• High-freq sensitivity key
High-freq modeling, too
Damour et al., arXiv:1203.4352
13
Conclusions
Current radius estimates are all dominated by systematics
Light curve fitting shows promise:
No deviations we have tried from our models produce
significant biases while fitting well and also giving apparently
strong constraints. LOFT, AXTAR, NICER
Future measurements of M and R using gravitational waves
may be competitive in their precision with X-ray based
estimates, and will have very different systematics
Open question: how can we best combine astronomical
information with laboratory measurements (e.g., 208Pb skin
thickness)?
Ray Tracing from MSP
• S. Bogdanov 2012
• Binary millisecond
pulsar J0437-4715
• Two spots, H atm
• Multitemp plus
Comptonized spect
• Qs about beaming,
spectrum; intriguing
results, though!
Bogdanov 2012
15
High inclinations allow tight constraints on M and R
Spot and observer inclinations = 90°, high background
16
Low inclinations produce looser constraints
Amplitude similar to the previous slide, but low spot and
observer inclinations, low background
17
Independent knowledge of the observer’s inclination
can increase the precision
spot and observer inclinations = 90°, high
background
Observer inclination unknown
18
Independent knowledge of the observer’s inclination
can increase the precision
spot and observer inclinations = 90°, high
background
Observer inclination known to be 90°
19
Incorrect modeling of the spot shape
increases the uncertainties
spot and observer inclinations = 90°, medium
background
Actual spot elongated E-W by 45°
20
Fits Using New Models
Yes! New models from
Suleimanov et al. 2010 do seem
to fit the data quite well.
64-second segment at peak
temperature
This model has F=0.95FEdd
Best fit: 2/dof=42.3/48
Best B-E fit: 2/dof=55.6/50
For full 102-segment data set,
best fit has 2/dof=5238/5098
B-E best: 2/dof=5770/4998
Fits are spectacularly good!
Much better than B-E, so
further info can be derived
Pure He, log g = 14.3, F=0.95FEdd
Model from Suleimanov et al. 2010
21
Keplerian Constraints
Suppose we observe periodic variations in the
radial velocity of star 1, with period Pb and
amplitude vrad. Then we can construct the
mass function
This is a lower limit to the mass of star 2, but
depends on the unknown inclination i and the
unknown mass m1 of the observed star.
22
Post-Keplerian Parameters
With high-precision timing, can break degeneracies:
If both objects are pulsars, also get mass ratio.
23
Allows mass measurements, GR tests
Artigue et al. 2013
Analysis of bursts from 4U 1636-536; previously
claimed to contradict rotating spot model
2/dof for all five bursts combined: 1859/1850 (44%)
2/dof for far left burst only: 401.8/372 (14%)
Hot spot model fits very well
24