An approach to constrain models of accreting neutron stars with the use of an equation of state

We investigate X-ray bursts during the thermal evolution of an accreting neutron star which corresponds to the X-ray burster GS\ 1826-24. Physical quantities of the neutron star are included using an equation of state below and above the nuclear matter density. We adopt an equation of state and construct an approximate network that saves the computational time and calculates nuclear energy generation rates accompanying the abundance evolutions. The mass and radius of the neutron star are got by solving the stellar evolution equations from the center to the surface which involve necessary information such as the nuclear energy generation in accreting layers, heating from the crust, and neutrino emissions inside the stellar core. We reproduce the light curve and recurrence time of the X-ray burst from GS 1826-24 within the standard deviation of 1$\sigma$ for the assumed accretion rate, metallicity, and equation of state. It is concluded that the observed recurrence time is consistent with the theoretical model having metallicity of the initial CNO elements $Z_{\rm CNO}$ = 0.01. We suggest that the nuclear reaction rates responsible for the $rp$-process should be examined in detail, because the rates may change the shape of the light curve and our conclusion.