1. Challenges in the Measurement of Neutron Star Radii Cole Miller University of Maryland 1 Collaborators: Romain Artigue, Didier Barret, Sudip Bhattacharyya, Stratos Boutloukos, Novarah Kazmi, Fred Lamb, Ka Ho Lo

2. Outline Radii from X-ray bursts Radii from cooling neutron stars Radii from X-ray light curves The promise of gravitational waves 2 NS masses are known up to 2 M sun. What about radii? Key point: all current NS radius estimates are dominated by systematics. None are reliable. But hope exists for the future.

3. Measuring stellar radii Ordinary star, like the Sun Too far for angular resolution But can get luminosity L If we assume blackbody, R 2 =L/(4  T 4 ) 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

4. 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 4

5. 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 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! 5

6. 6 Inferred relative emitting areas, for 102 16-s segments near the peak of the 1820 superburst: Miller et al., in prep

7. 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

8. 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

9. RXJ 1856.5–3754 Specific isolated NS Argument: BB most efficient emitter, thus R>=R BB True for bolometric but not for given band Example: Ho et al. condensed surface fit Different R constraints for different models 9 Klähn et al. 2006

10. RXJ 1856.5–3754 Specific isolated NS Argument: BB most efficient emitter, thus R>=R BB True for bolometric but not for given band Example: Ho et al. condensed surface fit Different R constraints for different models 10 Klähn et al. 2006

11. Baryonic vs. Grav. Mass Pulsar B in the double pulsar system M grav =1.249+-0.001 M sun If this came from e capture on Mg and Ne, M bary =1.366-1.375 M sun for core But what about fallback? Or could mass be lost after collapse? 11

12. Ray Tracing and Light Curves Rapidly rotating star 300- 600 Hz v surf ~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 12

13. 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:1203.4352 13 High-freq modeling, too

14. 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., 208 Pb skin thickness)?

15. 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! 15 Bogdanov 2012

16. High inclinations allow tight constraints on M and R Spot and observer inclinations = 90°, high background 16

17. Low inclinations produce looser constraints Amplitude similar to the previous slide, but low spot and observer inclinations, low background 17

18. Independent knowledge of the observer’s inclination can increase the precision Observer inclination unknown spot and observer inclinations = 90°, high background 18

19. Observer inclination known to be 90° Independent knowledge of the observer’s inclination can increase the precision spot and observer inclinations = 90°, high background 19

20. Incorrect modeling of the spot shape increases the uncertainties Actual spot elongated E-W by 45° spot and observer inclinations = 90°, medium background 20

21. 21 Fits Using New Models 64-second segment at peak temperature This model has F=0.95F Edd 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=0.95F Edd Model from Suleimanov et al. 2010 Yes! New models from Suleimanov et al. 2010 do seem to fit the data quite well.

22. Keplerian Constraints Suppose we observe periodic variations in the radial velocity of star 1, with period P b and amplitude v rad. 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 m 1 of the observed star. 22

23. Post-Keplerian Parameters With high-precision timing, can break degeneracies: If both objects are pulsars, also get mass ratio. Allows mass measurements, GR tests 23

24. Artigue et al. 2013 24  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