Color Superconductivity in Compact Stars and Gamma Ray Bursts

We study the effects of color superconductivity on the structure and formation of compact stars. We show that it is possible to satisfy most of recent observational boundaries on masses and radii if a diquark condensate forms in a hybrid or a quark star. Moreover, we find that a huge amount of energy, of the order of $10^{53}$ erg, can be released in the conversion from a (metastable) hadronic star into a (stable) hybrid or quark star, if the presence of a color superconducting phase is taken into account. Accordingly to the scenario proposed in Astrophys.J.586(2003)1250, the energy released in this conversion can power a Gamma Ray Burst. This mechanism can explain the recent observations indicating a delay, of the order of days or years, between a few Supernova explosions and the subsequent Gamma Ray Burst.Comment: 15 pages, 4 figures, 1 tabl

Conditions for Phase Equilibrium in Supernovae, Proto-Neutron and Neutron Stars

We investigate the qualitative properties of phase transitions in a general way, if not the single particle numbers of the system but only some particular charges like e.g. baryon number are conserved. In addition to globally conserved charges we analyze the implications of locally conserved charge fractions, like e.g. local electric charge neutrality or locally fixed proton or lepton fractions. The conditions for phase equilibrium are derived and it is shown, that the properties of the phase transition do not depend on the locally conserved fractions. Finally, the general formalism is applied to the liquid-gas phase transition and the hadron-quark phase transition for typical astrophysical environments like in supernovae, proto-neutron or a neutron stars. We demonstrate that the Maxwell construction known from cold-deleptonized neutron star matter with two locally charge neutral phases requires modifications and further assumptions concerning the applicability for hot lepton-rich matter. All possible combinations of local and global conservation laws are analyzed, and the physical meaningful cases are identified. Several new kinds of mixed phases are presented, as e.g. a locally charge neutral mixed phase in proto-neutron stars which will disappear during the cooling and deleptonization of the proto-neutron star.Comment: 18 page

Formation of Quark Phases in compact stars and their connection to Gamma-Ray-Bursts

We analyse the occurrence of quiescent times in the temporal structure of the Gamma-Ray-Bursts (GRBs) light curves. We show that if a long quiescent time is present, it is possible to divide the total duration of GRBs into three periods: the pre-quiescence emission, the quiescent time and the post-quiescence emission. We then discuss a model of the GRBs inner engine based on the formation of quark phases during the life of an hadronic star. Within this model the pre-quiescence emission is interpreted as due to the deconfinement of quark inside an hadronic star and the formation of 2SC quark matter. The post-quiescence emission is due to the conversion of 2SC into the Color-Flavor-Locking (CFL) phase. The temporal delay between these two processes is connected with the nucleation time of the CFL phase in the 2SC phase and it can be associated with the observed quiescent times in the GRBs light curves. The stability of CFL cores in compact stars is also discussed.Comment: 6 pages, 3 figures, to appear in the proceedings of 3th International Conference on Nuclear Physics in Astrophysics (NPAIII), 26 - 31 March 2007 Dresden, German

Propagator poles and an emergent stable state below threshold: general discussion and the E(38) state

In the framework of a simple quantum field theory describing the decay of a scalar state into two (pseudo)scalar ones we study the pole(s) motion(s) of its propagator: besides the expected pole on the second Riemann sheet, we find -- for a large enough coupling constant -- a second, additional pole on the first Riemann sheet below threshold, which corresponds to a stable state. We then perform a numerical study for a hadronic system in which a scalar particle couples to pions. We investigate under which conditions a stable state below the two-pion threshold can emerge. In particular, we study the case in which this stable state has a mass of 38 MeV, which corresponds to the recently claimed novel scalar state E(38). Moreover, we also show that the resonance $f_{0}(500)$ and the stable state E(38) could be two different manifestation of the same `object'. Finally, we also estimate the order of magnitude of its coupling to photons.Comment: 9 pages, 4 figure

Focusing inversion techniques applied to electrical resistance tomography in an experimental tank

We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in using a priori information about targets to reduce the ambiguity and the instability of the solution. By using the minimum gradient support (MGS) stabilizing functional, we introduce the following geometrical prior information in the reconstruction process: anomalies have sharp boundaries. The presented work is embedded in a project (L.A.R.A.) which aims at the estimation of hydrogeological properties from geophysical investigations. L.A.R.A. facilities include a simulation tank (4 m x 8 m x 1.35 m); 160 electrodes are located all around the tank and used for 3-D ERT. Because of the large number of electrodes and their dimensions, it is important to model their effect in order to correctly evaluate the electrical system response. The forward modelling in the presented algorithm is based on the so-called complete electrode model that takes into account the presence of the electrodes and their contact impedances. In this paper, we compare the results obtained with different regularizing functionals applied on a synthetic model.Comment: 4 pages, 7 figures, to appear in the Proceedings of Int. Assoc. for Mathematical Geology XI International Congres

A new possible quark-hadron mixed phase in protoneutron stars

The phase transition from hadronic matter to quark matter at high density might be a strong first order phase transition in presence of a large surface tension between the two phases. While this implies a constant-pressure mixed phase for cold and catalyzed matter this is not the case for the hot and lepton rich matter formed in a protoneutron star. We show that it is possible to obtain a mixed phase with non-constant pressure by considering the global conservation of lepton number during the stage of neutrino trapping. In turn, it allows for the appearance of a new kind of mixed phase as long as neutrinos are trapped and its gradual disappearance during deleptonization. This new mixed phase, being composed by two electric neutral phases, does not develop a Coulomb lattice and it is formed only by spherical structures, drops and bubbles, which can have macroscopic sizes. The disappearance of the mixed phase at the end of deleptonization might lead to a delayed collapse of the star into a more compact configuration containing a core of pure quark phase. In this scenario, a significant emission of neutrinos and, possibly, gravitational waves are expected.Comment: 4 pages, 4 figure

Focusing inversion techniques applied to electrical resistance tomography in an experimental tank

We present an algorithm for focusing inversion of electrical resistivity tomography (ERT) data. ERT is a typical example of ill-posed problem. Regularization is the most common way to face this kind of problems; it basically consists in using a priori information about targets to reduce the ambiguity and the instability of the solution. By using the minimum gradient support (MGS) stabilizing functional, we introduce the following geometrical prior information in the reconstruction process: anomalies have sharp boundaries. The presented work is embedded in a project (L.A.R.A.) which aims at the estimation of hydrogeological properties from geophysical investigations. L.A.R.A. facilities include a simulation tank (4 m x 8 m x 1.35 m); 160 electrodes are located all around the tank and used for 3-D ERT. Because of the large number of electrodes and their dimensions, it is important to model their effect in order to correctly evaluate the electrical system response. The forward modelling in the presented algorithm is based on the so-called complete electrode model that takes into account the presence of the electrodes and their contact impedances. In this paper, we compare the results obtained with different regularizing functionals applied on a synthetic model