We study the hadron-quark mixed phase in protoneutron stars, where neutrinos are trapped and lepton number becomes a conserved quantity besides the baryon number and electric charge. Considering protoneutron-star matter as a ternary system, the Gibbs
conditions are applied together with the Coulomb interaction. We find that there no crystalline (pasta) structure appears in the regime of high lepton-number fraction; the size of pasta becomes very large and the geometrical structure becomes mechanically unstable due to the charge screening effect. Consequently the whole system is separated into two bulk regions like an amorphous state, where the surface effect is safely neglected. There, the local charge neutrality is approximately attained, so that the equation of state is effectively reduced to the one for a binary system. Hence, we conclude that there is no possibility for the density discontinuity to appear in protoneutron-star matter, which is a specific feature in a pure system. These features are important when considering astrophysical phenomena such as supernova explosions or radiation of the gravitational wave from protoneutron stars.
We study the quark-hadron mixed phase in proto-neutron stars with the finite-size effects. In the calculations of pasta structures appeared in the mixed phase, the Gibbs conditions require the pressure balance and chemical equilibrium between two pha
ses besides the thermal equilibrium. We find that the region of the mixed phase is limited due to thermal instability. Moreover, we study the effects of neutrinos to the pasta structures. As a result, we find that the existence of neutrinos make the pasta structures unstable, too. These characteristic features of the hadron-quark mixed phase should be important for the middle stage of the evolutions of proto-neutron stars.
We report the effects of quark-hadron phase transition on the structures of general relativistic stars with purely toroidal magnetic field. For the mixed phase, we take into account of the finite-size effects, which lead to non-uniform Pasta structur
es. Our study is based on axisymetric and stationary formalism including purely toroidal magnetic field. For hybrid stars, we find the characteristic distribution of magnetic field, which has a discontinuity originated in the quark-hadron mixed phase. These distributions of magnetic field will change astrophysical phenomena, such as cooling processes.
