1. Measuring neutron star parameters from mixed H/He thermonuclear bursts May 2009, Santa Fe Duncan Galloway Monash University Matt Amthor GANIL, Fr Jerzy Madej U. Warsaw Alex Heger U. Minnesota Richard Linossi Monash

2. Özel (2006) approach To resolve the degeneracies implicit in measurements of neutron star parameters, we need to independently measure three quantities, from –Radiation radius (blackbody normalisation) –Eddington flux (radius-expansion bursts) –Distance (NOT from the Eddington flux) –Redshift (spectral lines? Perhaps not) Then you can solve for the “interesting” parameters (mass and radius) Özel 2006, Nature 441, 1115 Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts”

3. The blackbody normalisation For the vast majority of bursts the X-ray spectra throughout are consistent with a Planck (blackbody) spectrum Such spectra are characterised by two parameters: the temperature and the radius of the emitting object We observe a flux at the earth which depends also upon the distance (assuming isotropy) The spectrum also is distorted slightly so we must correct based on assumptions about the photosphere Blackbody normalisation R bb measured throughout tail… not always constant, or consistent…

4. Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts” See also poster by Tolga Guver

5. Another way to measure distance Observed/predicted lightcurve comparisons allow constraints on the distance: The 1-d (KEPLER) code assumes the NS radius and redshift to calculate the burst lightcurve The full constraint (for 1826-24) has the form i.e. the distance also depends upon the assumed radius & redshift AND the anisotropy parameter ξ b (Heger et al. 2007, ApJL 671, L141)

6. Combining our two constraints We can combine the burst lightcurve comparison with the blackbody normalisation to give the redshift in terms of the observables; the anisotropy & distance drop out: lightcurve

7. Regular bursts from KS 1731-26 Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts”

8. Lightcurve comparison for KS 1731-26 As we did with 1826-24, we calculate model burst lightcurves with the same recurrence time and try to match the burst lightcurve Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts” Bursts from KS 1731-26 are shorter, brighter and more frequent than those in 1826- 24 We requre slightly sub-solar H-fraction (X~0.6) to match with the lightcurve

9. The only remaining bugbear is… The spectral correction factor f c This correction is determined from model calculations, assuming the atmospheric composition (Madej et al. 2004, ApJ 602, 904) Since we already have a model describing the physics of the fuel layer, which can be also matched to the atmospheric composition, we can uniquely determine this value in a consistent manner We extract temperature-density profiles from the nuclear burning model and match them at low density with the atmosphere models Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts”

10. T_eff log g T_c/T_bb 2.25E+07 14.40 1.586 2.30E+07 14.40 1.644 2.35E+07 14.40 1.704 & X=0.6, as for the burst model

11. Results - KS 1731-26 14 bursts with a consistent blackbody radius 0.68 ± 0.02 (km/kpc) 2 Distance comparison (with lightcurves from a sub-solar X~0.6 model) gives (7.39 ± 0.11)  b 1/2 kpc And a spectral correction of f ∞ = 1.64 from the temperature profile for log g = 14.4 Giving a redshift of 1+z = 1.421 ± 0.014 (after re-doing the lightcurve comparison with a higher initial trial value)

12. Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts” GS 1826-24 1+z = 1.34±0.03 KS 1731-26 1+z = 1.421±0.014 Blackbody radius measurements in both systems are consistent from burst to burst, even those spanning years

13. More for KS 1731-26 Detection of radius-expansion bursts allow a consistency check on the distance… –Implied range is 7.2 ± 1.0 kpc, which brackets the value determined from lightcurve comparison …as well as determination of the NS mass –Here we compare the predicted Eddington flux as a function of the assumed mass –With the measured mean peak flux of the radius-expansion bursts (43±6)  10 -8 erg/cm 2 /s –To obtain an “allowed” region in the M-R plane

14. Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts” GS 1826-24 1+z = 1.34±0.03 KS 1731-26 1+z = 1.421±0.014

15. Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts” Variation of f c with g will tend to steepen these M-R relations… BUT KS 1731-26 results are self-consistent for log g = 14.4

17. Results - GS 1826-24 For 57 bursts observed between 1997-2007, we find a consistent blackbody radius of 0.96 ± 0.07 (km/kpc) 2 We adopt a distance of (6.07 ± 0.18)  b 1/2 kpc from comparison of model predicted and observed burst lightcurves And a spectral correction of f ∞ = 1.58 (T eff is similar to that in 1731-26) Giving a redshift of (1+z) = 1.29 ± 0.03 (neglecting the uncertainty in f ∞ )

18. All radius expansion bursts reach the same peak flux -> No. Perhaps intrinsically the same, but 14% standard deviation is typical Blackbody radii from all bursts from the same source are consistent -> Not in general (e.g. EXO 1745-248!) Spectral hardening factor in the burst tails is 1.4 -> No! that’s too low for KS 1731-26; likely radius- expansion bursts reach higher temperatures (AND it depends on the surface gravity) Galloway, “Measuring neutron star parameters from mixed H/He thermonuclear bursts”

19. Takeaway messages for Bob For the EOS aficionados: There is reason to be optimistic about these new constraints from bursts BUT beware of the systematics which can dominate these kinds of calculations (more work is required to understand these in some cases) For the modelers: Large libraries of burst lightcurves would help for these kinds of analyses; uniqueness of lightcurve matching? Sensitivity to inputs -> uncertainty?