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| - Measuring the masses and radii of neutron stars in low-mass X-ray binaries: Effects of the atmospheric composition and touchdown radius
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| - Context. X-ray bursts (XRBs) are energetic explosive events that have been observed in low-mass X-ray binaries (LMXBs). Some Type-I XRBs exhibit 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 several model parameters, most of which are still uncertain. Here, 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 as well as whether there is a possible correlation between them. Methods. We used both a Monte Carlo (MC) sampling and a Bayesian analysis to examine the effects of the photospheric composition and the touchdown radius. We applied these two methods to six LMXBs exhibiting PRE XRBs. With both methods, we solved the Eddington flux equation and the apparent angular area equation, both of which include the correction terms. For the MC sampling, we 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, it is most likely that the radii of the neutron stars in these six LMXBs are less than 12.5 km. This value is similar to that of the bounds placed on the neutron star radius based on the tidal deformability measured from the gravitational wave signal.
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