Early evolution of newly born proto-neutron stars

A proto-neutron star (PNS) is the first phase of life of a neutron star, and is likely to origin from a core-collapse supernova. After about 200 ms from core-collapse, the PNS evolution may be modeled as a sequence of quasi-stationary configurations. These configurations depend on the PNS thermodynamic profiles, whose evolution largely depends upon the neutrino diffusion. We developed a new PNS evolutionary code that solves by iteration the neutrino number and energy transport equations together with the relativistic stellar structure equations assuming spherical symmetry. The neutrino cross sections are determined consistently with the underlying equation of state (EoS). To include the EoSs in the evolution, we devised and tested a new fitting formula for the interacting part of the baryon free-energy, valid at finite temperature and arbitrary degeneracy. Using our code, we provide estimates for the neutrino signal in the Super-Kamiokande III detector and the frequencies of the gravitational waves due to stellar oscillations, for three stellar masses and three nucleonic EoSs. For the first time we evolve a PNS with a nuclear many-body theory EoS in a consistent way, that is, we take into account realistic nuclear interactions in the computation of the neutrino cross sections. By including rotation in an effective way, we have also determined the time variation of the rotation frequency due to PNS contraction and neutrino angular momentum loss, and the gravitational wave signal due to rotation. We find that the mass shedding limit restricts the initial angular momentum. Consequently, the final rotation frequency has to be smaller than about 300 Hz for a PNS of about 1.6 solar masses whose EoS is described by the GM3 mean-field model.