The existence of neutron stars with masses of $$\sim${}2{M}_{$\bigodot${}}$ requires a stiff equation of state at high densities. On the other hand, the necessary appearance also at high densities of new degrees of freedom, such as hyperons and $\mathrm{$\Delta${}}$ resonances, can lead to a strong softening of the equation of state with resulting maximum masses of $$\sim${}1.5{M}_{$\bigodot${}}$ and radii smaller than $$\sim${}10\text{ }\text{ }\mathrm{km}$. Hints for the existence of compact stellar objects with very small radii have been found in recent statistical analyses of quiescent low-mass X-ray binaries in globular clusters. We propose an interpretation of these two apparently contradicting measurements, large masses and small radii, in terms of two separate families of compact stars: hadronic stars, whose equation of state is soft, can be very compact, while quark stars, whose equation of state is stiff, can be very massive. In this respect an early appearance of $\mathrm{$\Delta${}}$ resonances is crucial to guarantee the stability of the branch of hadronic stars. Our proposal could be tested by measurements of radii with an error of $$\sim${}1\text{ }\text{ }\mathrm{km}$, which is within reach of the planned Large Observatory for X-ray Timing satellite, and it would be further strengthened by the discovery of compact stars heavier than $$\sim${}2{M}_{$\bigodot${}}$.

We propose a model to explain how a gamma-ray burst can take place days or years after a supernova explosion. Our model is based on the conversion of a pure hadronic star ( neutron star) into a star made at least in part of deconfined quark matter. The conversion process can be delayed if the surface tension at the interface between hadronic and deconfined quark matter phases is taken into account. The nucleation time (i.e., the time to form a critical-size drop of quark matter) can be extremely long if the mass of the star is small. Via mass accretion the nucleation time can be dramatically reduced and the star is finally converted into the stable configuration. A huge amount of energy, on the order of 10^(52)-10^(53) ergs, is released during the conversion process and can produce a powerful gamma-ray burst. The delay between the supernova explosion generating the metastable neutron star and the new collapse can explain the delay inferred in GRB 990705 and in GRB 011211

We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric $(q\leftrightarrow q^{-1})$ algebra and show that it can be built on the formalism of q calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semiclassical limit and the low-temperature regime and demonstrate that the nature of the q deformation gives rise to pure quantum statistical effects stronger than undeformed boson and fermion particles.

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.Comment: 47 pages, 23 figures New version after referee's comments. Two sections and two figures adde