Challenges in the Measurement of Neutron Star Radii

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Challenges in the Measurement of Neutron Star Radii

Cole MillerUniversity of Maryland

Collaborators: Romain Artigue, Didier Barret,Sudip Bhattacharyya, Stratos Boutloukos, Novarah Kazmi, Fred Lamb, Ka Ho Lo

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Outline

• Radii from X-ray bursts• Radii from cooling neutron stars• Radii from X-ray light curves• The promise of gravitational waves

NS masses are known up to 2 Msun. What about radii?

Key point: all current NS radius estimatesare dominated by systematics. None arereliable. But hope exists for the future.

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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

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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

http://cococubed.asu.edu/images/binaries/images/xray_burst3_web.jpg

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4U 1820 Bursts: Soft EOS?

• Fits of good spectral models to hours-long bursts show that fraction of emitting area changes!

Guver et al. 2010; known dist (globular)Uses most optimisticassumption: no systematics,only statistical uncertainties

But small errors aremisleading; only ~10-8

of prior prob. space givesM, R in real numbers! (Guver et al., Steiner et al.)

Spectral model is terrible fit to best data!

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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 thermalNo 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 300-

600 Hz vsurf~0.1-0.2c 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 Damour et al., arXiv:1203.4352High-freq modeling, too

Conclusions

Current radius estimates are all dominated by systematicsLight 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 astronomicalinformation with laboratory measurements (e.g., 208Pb skinthickness)?

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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

Observer inclination unknown

spot and observer inclinations = 90°, high background

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Observer inclination known to be 90°

Independent knowledge of the observer’s inclination can increase the precision

spot and observer inclinations = 90°, high background

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Incorrect modeling of the spot shapeincreases the uncertainties

Actual spot elongated E-W by 45°

spot and observer inclinations = 90°, medium background

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Fits Using New Models64-second segment at peaktemperature

This model has F=0.95FEdd

Best fit: 2/dof=42.3/48Best B-E fit: 2/dof=55.6/50

For full 102-segment data set,best fit has 2/dof=5238/5098B-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

Yes! New models from Suleimanov et al. 2010 do seemto fit the data quite well.

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Keplerian ConstraintsSuppose we observe periodic variations in theradial velocity of star 1, with period Pb andamplitude vrad. Then we can construct themass function

This is a lower limit to the mass of star 2, butdepends on the unknown inclination i and theunknown mass m1 of the observed star.

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Post-Keplerian ParametersWith high-precision timing, can break degeneracies:

If both objects are pulsars, also get mass ratio.Allows mass measurements, GR tests

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Artigue et al. 2013

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

Analysis of bursts from 4U 1636-536; previously claimed to contradict rotating spot model