Determining Neutron Star Properties by Fitting Oblate-Star Waveforms To X-ray Burst Oscillations

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.