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

Deconfinement to Quark Matter in Neutron Stars - The Influence of Strong Magnetic Fields

We use an extended version of the hadronic SU(3) non-linear realization of the sigma model that also includes quarks to study hybrid stars. Within this approach, the degrees of freedom change naturally as the temperature/density increases. Different prescriptions of charge neutrality, local and global, are tested and the influence of strong magnetic fields and the anomalous magnetic moment on the particle population is discussed.Comment: To appear in the proceedings of conference XII HADRON PHYSICS April, 22-27, 2012, Bento Goncalves, Wineyards Valley Region, Rio Grande do Sul, Brazil Revised version with corrections made to the text in page

The Star Cluster Population in the Tidal Tails of NGC 6872

We present a photometric analysis of the rich star cluster population in the tidal tails of NGC 6872. We find star clusters with ages between 1 - 100 Myr distributed in the tidal tails, while the tails themselves have an age of less than 150 Myr. Most of the young massive ($10^{4} \le M/M_{\odot} \le 10^{7}$) clusters are found in the outer regions of the galactic disk or the tidal tails. The mass distribution of the cluster population can be well described by power-law of the form $N(m) \propto m^{-\alpha}$, where $\alpha = 1.85 \pm 0.11$, in very good agreement with other young cluster populations found in a variety of different environments. We estimate the star formation rate for three separate regions of the galaxy, and find that the eastern tail is forming stars at $\sim 2$ times the rate of the western tail and $\sim 5$ times the rate of the main body of the galaxy. By comparing our observations with published N-body models of the fate of material in tidal tails in a galaxy cluster potential, we see that many of these young clusters will be lost into the intergalactic medium. We speculate that this mechanism may also be at work in larger galaxy clusters such as Fornax, and suggest that the so-called ultra-compact dwarf galaxies could be the most massive star clusters that have formed in the tidal tails of an ancient galactic merger.Comment: 12 pages, 10 figures, accepted A&

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

Some properties of convection in hybrid stars

It is shown that the unusual thermodynamic properties of matter within the region of two-phase coexistence in hybrid stars result in a change of the standard condition for beginning of convection. In particular, the thermal flux transported by convection may be directed towards the stellar center. We discuss favorable circumstances leading to such an effect of "inverse convection" and its possible influence on the thermal evolution of hybrid stars.Comment: 13 pages, 3 figures. The discussion is extended according to referees suggestions. New references added. Accepted to MNRA

Mass, radius, and composition of the outer crust of nonaccreting cold neutron stars

The properties and composition of the outer crust of nonaccreting cold neutron stars are studied by applying the model of Baym, Pethick, and Sutherland, which was extended by including higher order corrections of the atomic binding, screening, exchange and zero-point energy. The most recent experimental nuclear data from the atomic mass table of Audi, Wapstra, and Thibault from 2003 is used. Extrapolation to the drip line is utilized by various state-of-the-art theoretical nuclear models (finite range droplet, relativistic nuclear field and non-relativistic Skyrme Hartree-Fock parameterizations). The different nuclear models are compared with respect to the mass and radius of the outer crust for different neutron star configurations and the nuclear compositions of the outer crust.Comment: 5 pages, 2 figures, submitted to J. Phys. G, part of the proceedings of the Nuclear Physics in Astrophysics III conference in Dresde

Dynamical Systems On Three Manifolds Part II: 3-Manifolds,Heegaard Splittings and Three-Dimensional Systems

The global behaviour of nonlinear systems is extremely important in control and systems theory since the usual local theories will only give information about a system in some neighbourhood of an operating point. Away from that point, the system may have totally different behaviour and so the theory developed for the local system will be useless for the global one. In this paper we shall consider the analytical and topological structure of systems on 2- and 3- manifolds and show that it is possible to obtain systems with 'arbitrarily strange' behaviour, i.e., arbitrary numbers of chaotic regimes which are knotted and linked in arbitrary ways. We shall do this by considering Heegaard Splittings of these manifolds and the resulting systems defined on the boundaries.Comment: 15 pages with 9 pictures. Accepted by Int. J. of Bifurcation and Chao