Systematic Errors in Neutron Star Radius Measurements. Cole Miller University of Maryland and Joint Space-Science Institute

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1 Systematic Errors in Neutron Star Radius Measurements Cole Miller University of Maryland and Joint Space-Science Institute 1

2 Outline Key point: M max >2 M s is solid, but all current NS radius estimates are susceptible to systematics. Will focus on radii. Evidence of possible systematic errors Estimates from energy-dependent X-ray waveforms Using NICER in particular! Prospects for the future 2

3 Challenges Can we measure NS radii without significant systematic errors? What can we do with future X-ray satellites? What can we do with gravitational radiation? See Thurs. talk by Lackey 3

4 Important point: for most existing methods, there is no direct way, using observations, that we can tell if the model being used is the correct one. Thus we rely heavily on theoretical confidence, which could be a problem! 4

5 M and R from X-ray Bursts Thermonuclear explosions on accreting NS (Galloway) Assume known spectrum, uniform emission over surface Only with RXTE ( ) are there enough data ASTROSAT and NICER to the rescue! Original ideas: van Paradijs 1979 (M/R) Sztajno (M and R) Many elaborations since At this conference: Brown, Lattimer, Nättilä, Steiner 5

6 Spectral Models are Validated Models from Suleimanov et al. (2012) fit the best data extremely well. 64-second segment at peak temperature; 1820 superburst 4U superburst, nearly 20 million counts For full data set, best fit has χ 2 /dof=5238/5098 B-E best: χ 2 /dof=5770/4998 Fits are spectacularly good! I consider this to be strong observational validation of models Boutloukos, Miller, Lamb 2010 Pure He, log g = 14.3, F=0.95F Edd Model from Suleimanov et al. 2010

7 Use of Suleimanov et al. Models So is it a simple matter of applying the models? Unfortunately, no Fitted emitting area in 4U 1820 superburst changes systematically (must be area fraction, not radius) Assumption of constant emitting fraction throughout burst is not correct in this case; might also be incorrect in shorter bursts that we can t measure as well Inferred relative emitting areas, for s segments near the peak of the 1820 superburst: Miller et al. 2013

8 Axisymmetrization of Emission Sequence of frames from movie by Anatoly Spitkovsky of burning including Coriolis effect In this model, burning becomes more axisymmetric with time, but latitudinal variations remain 8

9 Radius Bias with T Variation Example of the bias toward low radii from single-temp fits to surface with varying temperature. Temperature varies smoothly from 2 kev (equator) to 0.2 kev (pole). Assume perfect energy response, zero N H Fit is good, but R is 13% low. With narrower T profile, larger correction

10 Area Normalization Ratio More generally (Kajava et al. 2014), the expected evolution of the blackbody area normalization is not seen in most bursts. Focus on the limited set that do seem consistent gives larger radii than an analysis of a broader sample of bursts.

11 Questions for Discussion Can we understand spectral contamination enough to model? Note: persistent emission probably changes through burst (talks by Bhattacharyya and Galloway) Are there independent ways to constrain the surface emitting fraction (e.g., energydependent waveforms)? What is needed for the model to be consistent with bursts and thus for inferred masses and radii to be trustworthy? 11

12 Ray Tracing and Waveforms Rapidly rotating star Hz v surf ~ c SR+GR effects Waveform is informative about both M and R Either spots or modes Must deal carefully with degeneracies Will now focus on the results by Lo et al and Miller+Lamb 2015 Figure from Anatoly Spitkovsky (synthetic data only) Hot spot during an X-ray burst Bogdanov: J0437, R>10.7km

13 Spot Waveform Parameters Model parameters: M, R, spot and observer inclination, distance, spot angular radius, spot temperature Must include arbitrary phase-indep background spectrum Nonzero spot angular radius must be included; does not introduce computational difficulties or compromise constraints Use oblate Schwarzschild approximation (Morsink, Cadeau); very accurate! 13

14 Bayesian Analyses of Waveforms 10 6 spot counts, 9x10 6 background 600 Hz θ= Hz θ=90 Miller+Lamb 2015 Top left: spot, obs on equator. 3%-7% precision possible in M, R. 600 Hz θ= Hz θ=60 Bottom right: data generated w/ temp gradient, fit with const temp. No statistically significant bias. M=1.6 M sun, R eq =11.8 km or 15 km No simple formula for precision.

15 J0437: Prospects with NICER Only temperature at infinity known Conservative: 6x10 5 photons from spot 4x10 5 photons from unmodulated surface emission 2x10 5 photons from unmodulated power law 15

16 J0437: Prospects with NICER Temperature and observer inclination known 16

17 J0437: Prospects with NICER Temperature, observer inclination, and spot inclination known 17

18 J0437: Prospects with NICER Temperature, observer inclination, and spot inclination known, and mass constrained to M sun (3σ) 18

19 Key Point: Systematic Errors May Not Be A Problem In addition to the optimal 3%-7% precisions possible with NICER or LOFT observations, systematic deviations examined so far aren t as problematic as in other methods Examples: spot shape, spectrum, beaming pattern, temperature distribution, modulated power law, incorrect background No substantial bias for statistically good fit and tight constraints for these examples

20 Questions for Discussion Promising so far, but are there other significant systematic errors to explore? Looking into rapid rotation Current data are unconstraining. Optimism for NICER, but will this model be extendable to isolated pulsars with multiple spots and thus extra parameters? 20

21 Conclusions Many methods of radius estimation have been proposed. To me, it seems that waveform fitting and, in the near future, gravitational wave analysis are most promising. But systematics must be explored carefully!