Strong first-order phase transition in a rotating neutron star core and the associated energy release

Aims. We calculate the energy release associated with a strong first-order phase transition, from normal phase N to an “exotic” superdense phase S, in a rotating neutron star. Such a phase transition N−→S, accompanied by a density jump ρ N −→ ρ S , is characterized by ρ S /ρ N > 3 2 (1+P0/ρNc ), where P0 is the pressure, at which phase transition occurs. Configurations with small S-phase cores are then unstable and collapse into stars with large S-phase cores. The energy release is equal to the difference in mass-energies between the initial (normal) configuration and the final configuration containing an S-phase core, total stellar baryon mass and angular momentum being kept constant. Methods. The calculations of the energy release are based on precise numerical 2-D calculations. Polytropic equations of state (EOSs) as well as realistic EOS with strong first-order phase transition due to kaon condensation are used. For polytropic EOSs, a large parameter space is studied. Results. For a fixed “overpressure”, δP , defined as the relative excess of central pressure of collapsing metastable star over the pressure of equilibrium first-order phase transition, the energy release Erel does not depend on the stellar angular momentum. It coincides with that for nonrotating stars with the same δP . Therefore, results of 1-D calculations of Erel(δP ) for non-rotating stars can be used to predict, with very high precision, the outcome of much harder to perform 2-D calculations for rotating stars with the same δP . This result holds also for δPmin < δP < 0, corresponding to phase transitions with climbing over the energy barrier separating metastable N-phase configurations from those with an S-phase core. Such phase transitions could be realized in the cores of newly born, hot, pulsating neutron stars.