Effects of the treatment of the mass quadrupole moment on ray-tracing applications for rapidly-rotating neutron stars

TL;DR

This study compares various spacetime metrics for ray tracing around rapidly rotating neutron stars, assessing their accuracy and practicality in modeling pulse profiles to improve neutron star equation of state constraints.

Contribution

It provides a systematic comparison of exact and approximate metrics for neutron star ray tracing at high rotation rates, highlighting their differences and potential for constraining spacetime properties.

Findings

Small metric differences at rotation frequencies above ~700 Hz.

Potential to constrain quadrupole moments using metric differences.

Assessment of metric practicality for large-scale pulse-profile modeling.

Abstract

The Neutron Star Interior Composition Explorer (NICER) mission has provided a unique opportunity to constrain the equation of state of neutron stars by using the technique of pulse-profile modelling. This technique requires accurate and efficient ray tracing, that in turn requires a robust representation of the spacetime around a neutron star. Several exact and approximate metrics have been proposed, and used, to perform ray tracing around neutron stars, with both moderate and fast rotation. In this paper, we perform a comparison between several of these metrics, when used for ray tracing. We calculate the shape of the neutron star as seen by a distant observer using two different surface formulae, the thermal spectrum and pulse profiles from circular and crescent-shaped hotspots, for four configurations of pulsars with rotation rates ranging from 622 to 1000 Hz, and using both a moderate and a stiff equation of state to include realistic and extreme cases. We find small differences between the metrics for rotation frequencies starting at ~700 Hz that could theoretically be used for constraining the quadrupole moment or the spacetime models. We also determine the practicality of use of each metric in larger-scale applications such as pulse-profile