Rotational Corrections to Neutron-Star Radius Measurements from Thermal Spectra

TL;DR

This paper models how neutron star rotation affects thermal spectrum measurements, providing correction formulas to improve radius estimates from observational data.

Contribution

It introduces a detailed Hartle-Thorne approximation method to accurately account for rotational effects in neutron star radius measurements.

Findings

Rotational effects cause a 1-4% flux underestimate for 10 km stars at 600 Hz.

For 15 km stars, corrections range from 2% to 12% depending on inclination.

Inferred radii are about 4% larger when rotational corrections are applied.

Abstract

We calculate the rotational broadening in the observed thermal spectra of neutron stars spinning at moderate rates in the Hartle-Thorne approximation. These calculations accurately account for the effects of the second-order Doppler boosts as well as for the oblate shapes and the quadrupole moments of the neutron stars. We find that fitting the spectra and inferring the bolometric fluxes under the assumption that a star is not rotating causes an underestimate of the inferred fluxes and, thus, radii. The correction depends on the stellar spin, radius, and observer's inclination. For a 10 km neutron star spinning at 600 Hz, the rotational correction to the flux is ~1-4%, while for a 15 km neutron star with the same spin period, the correction ranges from 2% for pole-on sources to 12% for edge-on sources. We calculate the inclination-averaged corrections to inferred radii as a function of the neutron-star radius and mass and provide an empirical formula for the corrections. For realistic neutron star parameters (1.4 M$_\odot$, 12 km, 600 Hz), the stellar radius is on the order of 4% larger than the radius inferred under the assumption that the star is not spinning.