We study the consequences of the hadron-quark deconfinement phase transition in stellar compact objects when finite size effects between the deconfined quark phase and the hadronic phase are taken into account. We show that above a threshold value of the central pressure (gravitational mass) a neutron star is metastable to the decay (conversion) to a hybrid neutron star or to a strange star. The mean-life time of the metastable configuration dramatically depends on the value of the stellar central pressure. We explore the consequences of the metastability of "massive" neutron stars and of the existence of stable compact quark stars (hybrid neutron stars or strange stars) on the concept of limiting mass of compact stars. We discuss the implications of our scenario on the interpretation of the stellar mass and radius extracted from the spectra of several X-ray compact sources. Finally, we show that our scenario implies, as a natural consequence a two step-process which is able to explain the inferred "delayed" connection between supernova explosions and GRBs, giving also the correct energy to power GRBs.

We study the hydrodynamical transition from an hadronic star into a quark or a hybrid star. We discuss the possible mode of burning, using a fully relativistic formalism and realistic Equations of State in which hyperons can be present. We take into account the possibility that quarks form a diquark condensate. We also discuss the formation of a mixed phase of hadrons and quarks, and we indicate which region of the star can rapidly convert in various possible scenarios. An estimate of the final temperature of the system is provided. We find that the conversion process always corresponds to a deflagration and never to a detonation. Hydrodynamical instabilities can develop on the front. We estimate the increase in the conversion's velocity due to the formation of wrinkles and we find that, although the increase is significant, it is not sufficient to transform the deflagration into a detonation in essentially all realistic scenarios. Concerning convection, it does not always develop. In particular the system does not develop convection if hyperons are not present in the initial phase and if the newly formed quark phase is made of ungapped (or weakly gapped) quarks. At the contrary, the process of conversion from ungapped quark matter to gapped quarks always allows the formation of a convective layer. Finally, we discuss possible astrophysical implications of our results.

We show that r-mode instabilities severely constrain the composition of a compact star rotating with a submillisecond period. In particular, the only viable astrophysical scenario for such an object, present inside the lowmass X-ray binary associated with the X-ray transient XTE J1739Ϫ285, is that it has a strangeness content. Since previous analyses indicate that hyperonic stars or stars containing a kaon condensate are not good candidates, the only remaining possibility is that such an object is either a strange quark star or a hybrid quark-hadron star. We also discuss under which conditions submillisecond pulsars are rare. The possibility has been widely discussed in the literature that r-mode instabilities can very efficiently drag angular momentum from a rotating compact star if its temporal evolution on the Q-T plane (angular velocity and temperature) enters the r-mode instability window; see, e.g., Andersson (1998) and Friedman & Morsink (1998). Therefore huge regions of the Q-T plane are excluded. Moreover, the size and position of that window are strictly related to the composition of the star, since it is strongly dependent on the value of the bulk and shear viscosity. It is particularly important to recall that for stars containing strangeness, such as hyperon stars (Lindblom & Owen 2002), hybrid stars (Drago et al. 2005), and strange quark stars (Madsen 2000), there is also a contribution to the bulk viscosity associated with the formation of strangeness. Due to this, the instability window splits into two parts: one which starts at temperatures larger than (7 ‫ע‬ 3) # 10 9 K (high-temperature instability window, HTIW) and a lower temperature window at temperatures smaller than (5 ‫ע‬ 4) # 10 8 K (low-temperature instability window, LTIW). 3 Concerning the left border of the LTIW, its position is regulated by the shear viscosity and by the so-called viscous boundary layers located at the interface between the crust and the fluid composing the inner part of the star (Bildsten & Ushomirsky 2000). In particular, in bare quark stars (composed by either normal or superconducting quark matter), due to the absence of a significant crust, the left border of the LTIW extends to much lower temperatures and the LTIW has a minimum corresponding to a significantly lower temperature than in the case of stars containing a crust.

We study the role played by neutrino trapping on the hadron star (HS) to quark star (QS) conversion mechanism proposed recently by Berezhiani and collaborators. We find that the nucleation of quark matter (QM) drops inside hadron matter (HM), and therefore the conversion of a HS into a QS is strongly inhibited by the presence of neutrinos.