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

TL;DR

This paper introduces Bayesian methods for estimating neutron star masses and radii by fitting oblate-star waveform models to X-ray burst oscillation data, emphasizing the importance of star shape and observational conditions.

Contribution

It develops new Bayesian analysis techniques for rapid, accurate neutron star property estimation using oblate-star waveform models, accounting for star shape and observational factors.

Findings

Oblate-star models are essential for stars with large radii and >300 Hz rotation.

A 25% temperature variation does not bias mass and radius estimates significantly.

Mass and radius can be determined with <7% uncertainty under specific observational conditions.

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.