We discuss the possible impact of strange quark matter on the evolution of core-collapse supernovae with emphasis on low critical densities for the quark-hadron phase transition. For such cases the hot proto-neutron star can collapse to a more compac
t hybrid star configuration hundreds of milliseconds after core-bounce. The collapse triggers the formation of a second shock wave. The latter leads to a successful supernova explosion and leaves an imprint on the neutrino signal. These dynamical features are discussed with respect to their compatibility with recent neutron star mass measurements which indicate a stiff high density nuclear matter equation of state.
Explosive astrophysical systems, such as supernovae or compact star binary mergers, provide conditions where strange quark matter can appear. The high degree of isospin asymmetry and temperatures of several MeV in such systems may cause a transition
to the quark phase already around saturation density. Observable signals from the appearance of quark matter can be predicted and studied in astrophysical simulations. As input in such simulations, an equation of state with an integrated quark matter phase transition for a large temperature, density and proton fraction range is required. Additionally, restrictions from heavy ion data and pulsar observation must be considered. In this work we present such an approach. We implement a quark matter phase transition in a hadronic equation of state widely used for astrophysical simulations and discuss its compatibility with heavy ion collisions and pulsar data. Furthermore, we review the recently studied implications of the QCD phase transition during the early post-bounce evolution of core-collapse supernovae and introduce the effects from strong interactions to increase the maximum mass of hybrid stars. In the MIT bag model, together with the strange quark mass and the bag constant, the strong coupling constant $alpha_s$ provides a parameter to set the beginning and extension of the quark phase and with this the mass and radius of hybrid stars.
We explore the implications of the QCD phase transition during the postbounce evolution of core-collapse supernovae. Using the MIT bag model for the description of quark matter and assuming small bag constants, we find that the phase transition occur
s during the early postbounce accretion phase. This stage of the evolution can be simulated with general relativistic three-flavor Boltzmann neutrino transport. The phase transition produces a second shock wave that triggers a delayed supernova explosion. If such a phase transition happens in a future galactic supernova, its existence and properties should become observable as a second peak in the neutrino signal that is accompanied by significant changes in the energy of the emitted neutrinos. In contrast to the first neutronization burst, this second neutrino burst is dominated by the emission of anti-neutrinos because the electron-degeneracy is lifted when the second shock passes through the previously neutronized matter.
The effect of the QCD phase transition is studied for the mass-radius relation of compact stars and for hot and dense matter at a given proton fraction used as input in core-collapse supernova simulations. The phase transitions to the 2SC and CFL col
or superconducting phases lead to stable hybrid star configurations with a pure quark matter core. In supernova explosions quark matter could be easily produced due to $beta$-equilibrium, small proton fractions and nonvanishing temperatures. A low critical density for the phase transition to quark matter is compatible with present pulsar mass measurements.
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.
