A Ray-Tracing Algorithm for Spinning Compact Object Spacetimes with Arbitrary Quadrupole Moments. II. Neutron Stars

TL;DR

This paper presents a ray-tracing algorithm based on the Hartle-Thorne metric to accurately compute the apparent surface area of spinning neutron stars, aiding in constraining their equation of state by analyzing observable surface area changes.

Contribution

It introduces a novel analytic ray-tracing method for spinning neutron stars using the Hartle-Thorne metric, independent of the equation of state details.

Findings

Apparent surface area increases with spin for ~10 km radius neutron stars.

Apparent surface area decreases with spin for ~15 km radius neutron stars.

Surface area changes are less than 5%, minimally affecting radius measurements.

Abstract

A moderately spinning neutron star acquires an oblate shape and a spacetime with a significant quadrupole moment. These two properties affect its apparent surface area for an observer at infinity, as well as the lightcurve arising from a hot spot on its surface. In this paper, we develop a ray-tracing algorithm to calculate the apparent surface areas of moderately spinning neutron stars making use of the Hartle-Thorne metric. This analytic metric allows us to calculate various observables of the neutron star in a way that depends only on its macroscopic properties and not on the details of its equation of state. We use this algorithm to calculate the changes in the apparent surface area, which could play a role in measurements of neutron star radii and, therefore, in constraining their equation of state. We show that whether the spinning neutron star appears larger or smaller than its non-rotating counterpart depends primarily on its equatorial radius. For neutron stars with radii ~10 km, the corrections to the Schwarzschild spacetime cause the apparent surface area to increase with spin frequency. In contrast, for neutron stars with radii ~15 km, the oblateness of the star dominates the spacetime corrections and causes the apparent surface area to decrease with increasing spin frequency. In all cases, the change in the apparent geometric surface area for the range of observed spin frequencies is < 5% and hence only a small source of error in the measurement of neutron star radii.