Transcript 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
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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
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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
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M and R from X-ray Bursts
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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
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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
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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
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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
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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
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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
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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?
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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
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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
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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
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High inclinations allow tight constraints on M and R
Spot and observer inclinations = 90°, high background
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Low inclinations produce looser constraints
Amplitude similar to the previous slide, but low spot and
observer inclinations, low background
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Independent knowledge of the observer’s inclination
can increase the precision
spot and observer inclinations = 90°, high
background
Observer inclination unknown
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Independent knowledge of the observer’s inclination
can increase the precision
spot and observer inclinations = 90°, high
background
Observer inclination known to be 90°
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Incorrect modeling of the spot shape
increases the uncertainties
spot and observer inclinations = 90°, medium
background
Actual spot elongated E-W by 45°
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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
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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.
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Post-Keplerian Parameters
With high-precision timing, can break degeneracies:
If both objects are pulsars, also get mass ratio.
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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
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