Quark matter nucleation in neutron stars and astrophysical implications

A phase of strong interacting matter with deconfined quarks is expected in the core of massive neutron stars. We investigate the quark deconfinement phase transition in cold ((Formula presented.) and hot (Formula presented.) -stable hadronic matter. Assuming a first order phase transition, we calculate and compare the nucleation rate and the nucleation time due to quantum and thermal nucleation mechanisms. We show that above a threshold value of the central pressure a pure hadronic star (HS) (i.e. a compact star with no fraction of deconfined quark matter) is metastable to the conversion to a quark star (QS) (i.e. a hybrid star or a strange star). This process liberates an enormous amount of energy, of the order of 1053erg, which causes a powerful neutrino burst, likely accompanied by intense gravitational waves emission, and possibly by a second delayed (with respect to the supernova explosion forming the HS) explosion which could be the energy source of a powerful gamma-ray burst (GRB). This stellar conversion process populates the QS branch of compact stars, thus one has in the Universe two coexisting families of compact stars: pure hadronic stars and quark stars. We introduce the concept of critical mass (Formula presented.) for cold HSs and proto-hadronic stars (PHSs), and the concept of limiting conversion temperature for PHSs. We show that PHSs with a mass (Formula presented.) could survive the early stages of their evolution without decaying to QSs. Finally, we discuss the possible evolutionary paths of proto-hadronic stars.