We present a model for describing nuclear matter at finite density based on quarks interacting with chiral fields, sigma and pi and with vector mesons introduced as massive gauge fields. The chiral Lagrangian includes a logarithmic potential, associa
ted with the breaking of scale invariance. We provide results for the soliton in vacuum and at finite density, using the Wigner-Seitz approximation. We show that the model can reach higher densities respect to the linear-sigma model and that the introduction of vector mesons allows to obtain saturation. This result was never obtained before in similar approaches.
We discuss new limits on masses and radii of compact stars and we conclude that they can be interpreted as an indication of the existence of two classes of stars: normal compact stars and ultra-compact stars. We estimate the critical mass at which the first configuration collapses into the second.
In millisecond pulsars the existence of the Coriolis force allows the development of the so-called Rossby oscillations (r-modes) which are know to be unstable to emission of gravitational waves. These instabilities are mainly damped by the viscosity
of the star or by the existence of a strong magnetic field. A fraction of the observed millisecond pulsars are known to be inside Low Mass X-ray Binaries (LMXBs), systems in which a neutron star (or a black hole) is accreting from a donor whose mass is smaller than 1 $M_odot$. Here we show that the r-mode instabilities can generate strong toroidal magnetic fields by inducing differential rotation. In this way we also provide an alternative scenario for the origin of the magnetars.
We describe possible scenarios of quark deconfinement in compact stars and we analyze their astrophysical implications. The quark deconfinement process can proceed rapidly, as a strong deflagration, releasing a huge amount of energy in a short time a
nd generating an extra neutrino burst. If energy is transferred efficiently to the surface, like e.g. in the presence of convective instabilities, this burst could contribute to revitalize a partially failed SN explosion. We discuss how the neutrino observations from SN1987A would fit in this scenario. Finally, we focus on the fate of massive and rapidly rotating progenitors, discussing possible time separations between the moment of the core collapse and the moment of quark deconfinement. This mechanism can be at the basis of the interpretation of gamma ray bursts in which lines associated with heavy elements are present in the spectrum.
