We explore the parameter space of the two-flavor thermal quark-meson model and its Polyakov loop-extended version under the influence of a constant external magnetic field $B$. We investigate the behavior of the pseudo critical temperature for chiral
symmetry breaking taking into account the likely dependence of two parameters on the magnetic field: the Yukawa quark-meson coupling and the parameter $T_0$ of the Polyakov loop potential. Under the constraints that magnetic catalysis is realized at zero temperature and the chiral transition at $B=0$ is a crossover, we find that the quark-meson model leads to thermal magnetic catalysis for the whole allowed parameter space, in contrast to the present picture stemming from lattice QCD.
We compute the mixed phase of nuclear matter and 2SC matter for different temperatures and proton fractions. After showing that the symmetry energy of the 2SC phase is, to a good approximation, three times larger than the one of the normal quark phas
e, we discuss and compare all the properties of the mixed phase with a 2SC component or a normal quark matter component. In particular, the local isospin densities of the nuclear and the quark component and the stiffness of the mixed phase are significantly different whether the 2SC phase or the normal quark phase are considered. If a strong diquark pairing is adopted for the 2SC phase, there is a possibility to eventually enter in the nuclear matter 2SC matter mixed phase in low energy heavy ions collisions experiments. Possible observables able to discern between the formation of the 2SC phase or the normal quark phase are finally discussed.
We discuss the impact of strange hadrons, in particular hyperons, on the gross features of compact stars and on core-collapse supernovae. Hyperons are likely to be the first exotic species which appears around twice normal nuclear matter density in t
he core of neutron stars. Their presence largely influences the mass-radius relation of compact stars, the maximum mass, the cooling of neutron stars, the stability with regard to the emission of gravitational waves from rotation-powered neutron stars and the possible early onset of the QCD phase transition in core-collapse supernovae. We outline also the constraints from subthreshold kaon production in heavy-ion collisions for the maximum possible mass of neutron stars.
The possibility of a hadron-quark phase transition in extreme astrophysical phenomena such as the collapse of a supernova is not discarded by the modern knowledge of the high-energy nuclear and quark-matter equations of state. Both the density and th
e temperature attainable in such extreme processes are possibly high enough to trigger a chiral phase transition. However, the time scales involved are an important issue. Even if the physical conditions for the phase transition are favorable (for a system in equilibrium), there may not be enough time for the dynamical process of phase conversion to be completed. We analyze the relevant time scales for the phase conversion via thermal nucleation of bubbles of quark matter and compare them to the typical astrophysical time scale, in order to verify the feasibility of the scenario of hadron-quark phase conversion during, for example, the core-collapse of a supernova.
We discuss a pulsar acceleration mechanism based on asymmetric neutrino emission from the direct quark Urca process in the interior of proto neutron stars. The anisotropy is caused by a strong magnetic field which polarises the spin of the electrons
opposite to the field direction. Due to parity violation the neutrinos and anti-neutrinos leave the star in one direction accelerating the pulsar. We calculate for varying quark chemical potentials the kick velocity in dependence of the quark phase temperature and its radius. Ignoring neutrino quark scattering we find that within a quark phase radius of 10 km and temperatures larger than 5 MeV kick velocities of 1000km s$^{-1}$ can be reached very easily. On the other hand taking into account the small neutrino mean free paths it seems impossible to reach velocities higher than 100km s$^{-1}$ even when including effects from colour superconductivity where the neutrino quark interactions are suppressed.
We discuss an acceleration mechanism for pulsars out of their supernova remnants based on asymmetric neutrino emission from quark matter in the presence of a strong magnetic field. The polarized electron spin fixes the neutrino emission from the dire
ct quark Urca process in one direction along the magnetic field. We calculate the magnetic field strength which is required to polarize the electron spin as well as the required initial proto-neutron star temperature for a successfull acceleration mechanism. In addition we discuss the neutrino mean free paths in quark as well as in neutron matter which turn out to be very small. Consequently, the high neutrino interaction rates will wash out the asymmetry in neutrino emission. As a possible solution to this problem we take into account effects from colour superconductivity.
