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 rho(N) -> rho(S), is characterized by rho(S)/rho(N) > 3/2 (1 + P-0/rho(N)c(2)), where P-0 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, the total stellar baryon mass and angular momentum being kept constant. Methods. The calculations of the energy release are based on precise numerical 2D calculations. Polytropic equations of state (EOSs) as well as realistic EOSs 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", delta P, defined as the relative excess of central pressure of a collapsing metastable star over the pressure of the equilibrium first-order phase transition, the energy release E-rel does not depend on the stellar angular momentum. It coincides with that for nonrotating stars with the same delta P. Therefore, results of 1D calculations of E-rel(delta P) for non-rotating stars can be used to predict, with very high precision, the outcome of much harder to perform 2D calculations for rotating stars with the same delta P. This result holds also for delta(P) over bar (min) < delta(P) over bar < 0, corresponding to phase transitions overcoming 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.