Implications of rapid rotation for pulse profile models of millisecond-period x-ray pulsars.

摘要

The rapid rotation of recycled neutron stars in accretion-powered millisecond-period X-ray pulsars has important consequences for models of their pulsed emission, and by extension, the analysis of observations of these objects. We begin by considering the problem of calculating the time-varying bolometric flux arising due to emission from a bright spot on the surface of a rapidly rotating neutron star, with rotational period on the order of a millisecond. We restrict to the case of isotropic emission from an infinitesimal emission zone, but carry out the calculations with sufficient generality to incorporate a precisely solved spacetime metric and stellar structure. The geodesic equation is integrated numerically.;We also consider the consequences that result when approximate pulse profiles are used to obtain neutron star parameters such as mass, radius, emission inclination, and observer inclination via least squares fitting. Specifically, we look at fitting light curves calculated using the Schwarzschild metric and a spherical star to a light curve calculated using a precisely-solved metric and stellar structure. We are able to conclude that, in an idealised case where there is no random noise component and all light curves are for bolometric fluxes from isotropic emission, neglecting photon times-of-flight or stellar oblateness in model light curves used for fitting can introduce errors at the level of several tens of percent on the determination of mass and radius individually. However, these errors will often offset each other such that the fitted parameters will yield better determinations of the compactness.;To facilitate the inclusion of oblateness effects in other codes, we give a single polynomial which describes the oblate shape of stars for a range of masses and rotation periods for three separate equations of state.;Using the computer code developed for this work, we investigate the effect that commonly-used simplifying approximations have on the shape of the pulse profile compared to the full calculation. In particular, we consider the effect of neglecting the phase-dependent travel time of photons, approximating the exterior metric as either Schwarzschild or Kerr, and neglecting the rotation-induced oblateness of the neutron star.