Measuring the masses and radii of neutron stars in low-mass X-ray binaries: Effects of the atmospheric composition and touchdown radius

Context. X-ray bursts (XRBs) are energetic explosive events which have been observed in low-mass X-ray binaries (LMXBs). Some Type-I XRBs show photospheric radius expansion (PRE) and these PRE XRBs are used to simultaneously estimate the mass and the radius of a neutron star in LMXB. Aims. The mass and radius estimation depends on a few model parameters most of which are still uncertain. Among them, we focus on the effects of the chemical composition of the photosphere which determines the opacity during the PRE phase and the touchdown radius which can be larger than the neutron star radius. We investigate how these two model parameters affect the mass and radius estimation in a systematic way and whether there is any statistical trend for these two parameters including a correlation between them. 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.