Type I X-ray bursts are thermonuclear explosions on the neutron star (NS) surface by mass accretion from a companion star. Observation of X-ray bursts provides valuable information on X-ray binary systems, e.g., binary parameters, the chemical composition of accreted matter, and the nuclear equation of state (EOS) of NSs. There have been several theoretical studies to constrain the physics of X-ray bursters. However, they were mainly focused on the burning layers above the NS surface. The effects of the EOS and the heating and cooling processes inside the NS are still unknown. In this study, we calculated a series of X-ray bursts using a general relativistic stellar-evolution code with several NS EOSs. We compared the X-ray burst models with the burst parameters of a clocked burster associated with GS 1826-24. We found a monotonic correlation between the NS radius and the light-curve profile. A larger radius shows a higher recurrence time and a large peak luminosity. In contrast, the dependence of light curves on the NS mass becomes more complicated, where the neutrino cooling suppress the efficiency of nuclear ignition. We also constrained the EOS and mass of GS~1826-24, i.e., stiffer EOSs, corresponding to larger NS radii, are unpreffered due to a too high peak luminosity. The EOS and the cooling and heating of NSs are important to discuss the theoretical and observational properties of X-ray bursts.
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