Equation of state of hot neutron star matter using finite range simple effective interaction

The equation of state (EoS) of hot neutron star matter (NSM) of n+p+e+μ composition in β-equilibrium is studied for both neutrino-free isothermal and neutrino-trapped isoentropic conditions, using the formalism where the thermal evolution is built upon its zero-temperature predictions in a self-consistent manner. The accuracy of the parabolic approximation, often used in the finite temperature calculation of hot NSM, is verified by comparing with the results obtained from the exact evaluation in the neutrino-free NSM. The EoS of neutrino-trapped isoentropic matter at low entropic condition, relevant to the core-collapsing supernovae, is formulated. In the isoentropic matter, the particle fractions and EoS have marginal variance as entropy per particle vary between 1 and 3 (in the unit of kB), but the temperature profile shows marked variation. The isentropes are found to be much less sensitive to the nuclear matter incompressibility, but have large dependence on the slope parameter L. The bulk properties of the neutron stars predicted by the isoentropic EoSs for different entropy are calculated. A model calculation for the early stage evolution of protoneutron star to neutron star configuration is also given.