Measuring Masses and Radii of Neutron Stars in Low-Mass X-ray Binaries: Effects of Atmospheric Composition and Touchdown Radius

TL;DR

This study investigates how atmospheric composition and touchdown radius affect neutron star mass and radius measurements in low-mass X-ray binaries, using Monte Carlo and Bayesian methods to analyze observational data.

Contribution

It demonstrates that photospheric composition and touchdown radius significantly influence mass-radius estimates and introduces an efficient iterative Monte Carlo method for solving related equations.

Findings

H-poor photosphere and larger touchdown radius are statistically favored.

Most neutron star radii are estimated to be less than 12.5 km.

A correlation exists between photospheric composition and touchdown radius.

Abstract

Methods. We use both a Monte Carlo (MC) sampling and a Bayesian analysis to find the effects of the photospheric composition and the touchdown radius. We apply these two methods to six LMXBs that show PRE XRBs. In both methods, we solve the Eddington flux equation and the apparent angular area equation both of which include the correction terms. For the MC sampling, we have developed an iterative method in order to solve these two equations more efficiently. Results. We confirm that the effects of the photospheric composition and the touchdown radius are similar in the statistical and analytical estimation of mass and radius even when the correction terms are considered. Furthermore, in all of the six sources, we find that a H-poor photosphere and a large touchdown radius are favored statistically regardless of the statistical method. Our Bayesian analysis also hints that touchdown can occur farther from the neutron star surface when the photosphere is more H-poor. This correlation could be qualitatively understood with the Eddington flux equation. We propose a physical explanation for this correlation between the photospheric composition and the touchdown radius. Our results show that when accounting for the uncertainties of the photospheric composition and the touchdown radius, most likely radii of the neutron stars in these six LMXBs are less than 12.5 km, which is similar to the bounds for the neutron star radius placed with the tidal deformability measured from the gravitational wave signal.