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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

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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 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.

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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, 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

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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 4

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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 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

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6 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 7

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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 8

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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

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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

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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

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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

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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:1203.4352 13 High-freq modeling, too

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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., 208 Pb skin thickness)?

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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! 15 Bogdanov 2012

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

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

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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 18

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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 19

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

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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.

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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

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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

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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

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