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A phase of strong interacting matter with deconfined quarks is expected inthe core of massive neutron stars. We investigate the quark deconfinement phasetransition in cold (T = 0) and hot beta-stable hadronic matter. Assuming afirst order phase transition, we calculate and compare the nucleation rate andthe nucleation time due to quantum and thermal nucleation mechanisms. We showthat 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 metastableto 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 of10^{53}~erg, which causes a powerful neutrino burst, likely accompanied byintense gravitational waves emission, and possibly by a second delayed (withrespect to the supernova explosion forming the HS) explosion which could be theenergy source of a powerful gamma-ray burst (GRB). This stellar conversionprocess populates the QS branch of compact stars, thus one has in the Universetwo coexisting families of compact stars: pure hadronic stars and quark stars.We introduce the concept of critical mass M_{cr} for cold HSs andproto-hadronic stars (PHSs), and the concept of limiting conversion temperaturefor PHSs. We show that PHSs with a mass M < M_{cr} could survive the earlystages of their evolution without decaying to QSs. Finally, we discuss thepossible evolutionary paths of proto-hadronic stars.

Quark matter nucleation in neutron stars and astrophysical implications