The Energy Release–stellar Angular Momentum Independence in Rotating Compact Stars Undergoing First-order Phase Transitions

We present the general relativistic calculation of the energy release associated with a first order phase transition (PT) at the center of a rotating neutron star (NS). The energy release, Erel, is equal to the difference in mass-energies between the initial (normal) phase configuration and the final configuration containing a superdense matter core, assuming constant total baryon number and the angular momentum. The calculations are performed with the use of precise pseudo-spectral 2-D numerical code; the polytropic equations of state (EOS) as well as realistic EOSs (Skyrme interactions, Mean Field Theory kaon condensate) are used. The results are obtained for a broad range of metastability of initial configuration and size of the new superdense phase core in the final configuration. For a fixed “overpressure”, δP , defined as the relative excess of central pressure of a collapsing metastable star over the pressure of the equilibrium first-order PT, the energy release up to numerical accuracy does not depend on the stellar angular momentum and coincides with that for nonrotating stars with the same δP . When the equatorial radius of the superdense phase core is much smaller than the equatorial radius of the star, analytical expressions for the Erel can be obtained: Erel is proportional to (δP ) for small δP . At higher δP , the results of 1-D calculations of Erel(δP ) for non-rotating stars reproduce with very high precision exact 2-D results for fast-rotating stars. The energy release-angular momentum independence for a given overpressure holds also for the so-called “strong” PTs (that destabilise the star against the axi-symmetric perturbations), as well as for PTs with “jumping” over the energy barrier.