DETERMINING NEUTRON STAR PROPERTIES BY FITTING OBLATE-STAR WAVEFORM MODELS TO X-RAY BURST OSCILLATIONS

Abstract

We describe sophisticated new Bayesian analysis methods that make it possible to estimate quickly the masses and radii of rapidly rotating, oblate neutron stars by fitting oblate-star waveform models to energy-resolved observations of the X-ray oscillations produced by a hot spot on such stars. We conclude that models that take the oblate shape of the star into account should be used for stars with large radii and rotation rates $>300$ Hz. We find that a 25% variation of the temperature of the hot spot with latitude does not significantly bias estimates of the mass $M$ and equatorial radius $R_{\rm eq}$ derived by fitting a model that assumes a uniform-temperature spot. Our results show that fits of oblate-star waveform models to waveform data can simultaneously determine $M$ and $R_{\rm eq}$ with uncertainties $\lesssim\,$7% if (1) the star's rotation rate is $\gtrsim\,$$600$ Hz; (2) the spot center and observer's sightline are both within $30^\circ$ of the star's rotational equator; (3) the oscillations have a fractional rms amplitude $\gtrsim\,$10%; and (4) $\gtrsim$$10^7$ counts are collected from the star. This is a realistic fractional amplitude, and this many counts could be obtained from a single star by the accepted NICER and proposed LOFT and AXTAR space missions by combining data from many X-ray bursts. These uncertainties are small enough to improve substantially our understanding of cold, ultradense matter.