Finite temperature effects on anisotropic pressure and equation of state of dense neutron matter in an ultrastrong magnetic field

Spin polarized states in dense neutron matter with recently developed Skyrme effective interaction (BSk20 parametrization) are considered in the magnetic fields $H$ up to ${10}^{20}$ G at finite temperature. In a strong magnetic field, the total pressure in neutron matter is anisotropic, and the difference between the pressures parallel and perpendicular to the field direction becomes significant at $H>H_{th}\sim {10}^{18}$ G. The longitudinal pressure decreases with the magnetic field and vanishes in the critical field ${10}^{18}<H_c\lesssim {10}^{19}$ G, resulting in the longitudinal instability of neutron matter. With increasing the temperature, the threshold $H_{th}$ and critical $H_c$ magnetic fields also increase. The appearance of the longitudinal instability prevents the formation of a fully spin polarized state in neutron matter and only the states with moderate spin polarization are accessible. The anisotropic equation of state is determined at densities and temperatures relevant for the interiors of magnetars. The entropy of strongly magnetized neutron matter turns out to be larger than the entropy of the nonpolarized matter. This is caused by some specific details in the dependence of the entropy on the effective masses of neutrons with spin up and spin down in a polarized state.