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.