Coire Cadeau

Light Curves for Rapidly Rotating Neutron Stars

We present ray-tracing 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 that 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. Approximating a rotating neutron star as a sphere introduces serious errors in fitted values of the stars 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.

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 that needs to be accounted for when modeling light curves to extract constraints on the neutron stars 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 stars rotation. We also explain how the geometric oblateness effect can rival the Doppler effect for some emission geometries.

Limits on Mass and Radius for the Millisecond-Period X-Ray Pulsar SAX J1808.4–3658

SAX J1808.4–3658 has a 2.5 ms 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 J1808.4–3658 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 stars oblate shape. We also consider two different data sets, with different selections in time period (1 vs. 19 days of data combined) and different energy binning and time resolution. We find that including time delays and oblateness results in a 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.

Pulse Shapes from Rapidly Rotating Neutron Stars: Equatorial Photon Orbits

We demonstrate that fitted values of the stellar radius obtained by fitting theoretical light curves to observations of millisecond-period X-ray pulsars can significantly depend on the method used to calculate the light curves. The worst-case errors in the fitted radius are evaluated by restricting ourselves to the case of light emitted and received in the equatorial plane of a rapidly rotating neutron star. First, using an approximate flux that is adapted to the one-dimensional nature of such an emission region, we show how pulse shapes can be constructed using an exact spacetime metric and fully accounting for time-delay effects. We compare this to a method that approximates the exterior spacetime of the star by the Schwarzschild metric, inserts special relativistic effects by hand, and neglects time-delay effects. By comparing these methods, we show that there are significant differences in these methods for some applications—for example, pulse timing and constraining the stellar radius. In the case of constraining the stellar radius, we show that fitting the approximate pulse shapes to the full calculation yields errors in the fitted radius of as much as approximately ±10%, depending on the rotation rate and size of the star as well as the details describing the emitting region. However, not all applications of pulse shape calculations suffer from significant errors; we also show that the calculation of the soft-hard phase lag for a 1 keV blackbody does not strongly depend on the method used for calculating the pulse shapes.

Time delays, Doppler effects and oblateness: results for the ms pulsar SAXJ1808‐3658

A method is presented for including the time‐delays, Doppler effects and oblateness of a rapidly rotating neutron star when fitting X‐ray light curves. Doppler effects and time‐delays are previously known to be essential. We find 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 stars mass and radius. The method is applied to model the light curves of the ms pulsar: SAXJ1808‐3658. The results of the modeling are discussed and the resulting constraints on mass and radius of the neutron stars.