The Oblate Schwarzschild Approximation for Light Curves of Rapidly Rotating Neutron Stars

We present a simple method for including the oblateness of a rapidly rotating neutron star when fitting X-ray light curves. In previous work we showed that the oblateness induced by rotation at frequencies above 300 Hz produces a geometric effect which needs to be accounted for when modelling light curves to extract constraints on the neutron star's mass and radius. In our model X-rays are emitted from the surface of an oblate neutron star and propagate to the observer along geodesics of the Schwarzschild metric for a spherical neutron star. Doppler effects due to rotation are added in the same manner as in the case of a spherical neutron star. We show that this model captures the most important effects due to the neutron star's rotation. We also explain how the geometric oblateness effect can rival the Doppler effect for some emission geometries.Comment: 8 pages, 4 figures. v2: minor changes. Accepted by the Astrophysical Journa

Light Curves for Rapidly-Rotating Neutron Stars

We present raytracing computations for light emitted from the surface of a rapidly-rotating neutron star in order to construct light curves for X-ray pulsars and bursters. These calculations are for realistic models of rapidly-rotating neutron stars which take into account both the correct exterior metric and the oblate shape of the star. We find that the most important effect arising from rotation comes from the oblate shape of the rotating star. We find that approximating a rotating neutron star as a sphere introduces serious errors in fitted values of the star's radius and mass if the rotation rate is very large. However, in most cases acceptable fits to the ratio M/R can be obtained with the spherical approximation.Comment: Accepted by the Astrophysical Journal. 13 pages & 7 figure

Limits on Mass and Radius for the ms-Period X-ray Pulsar SAX J1808.4-3658

SAX J1808.4-3658 has a 2.5 millisecond neutron star rotation period and exhibits X-ray pulsations due to its rotating hot spot. Here we present an analysis of the pulse shapes of SAX J1808 during its 1998 outburst. The modeling of the pulse shape includes several effects, including gravitational light-bending, doppler effects and two spectral components with different emissivity. In addition we include the new effects of light-travel time-delays and the neutron star's oblate shape. We also consider two different data sets, with different selection in time period (1 day versus 19 days of data combined) and different energy binning and time resolution. We find that including time-delays and oblateness results in stronger restriction on allowed masses and radii. A second result is that the choice of data selection strongly affects the allowed masses and radii. Overall, the derived constraints on mass and radius favor compact stars and a soft equation of state.Comment: 10 pages, 4 figures. Accepted by ApJ. Analysis in v2 only uses data from the 1998 outburst. More details of the analysis included in v