Quark-hadron pasta in neutron stars

Pasta structures are studied for the quark-hadron phase transition. We find the useful correlation, which can provide the physical limits of the surface energy between quark and hadron matter, namely “σc-Pc relation”. Our hadron model is based on the relativistic mean field theory with a general formulation, which can reproduce the traditional Walecka-type model, non-linear Walecka-type model, etc. without changing the Lagrangian. The quark model is the string-flip model with the quasi-particle approximation and excluded volume effects. We also find that the analytic estimation derived from the liner-approximation is consistent with the numerical results. It means that we can roughly estimate the physical limit of the surface tension without any special numerical techniques, when we prepare uniform quark matter and hadron matter. We expect that the above behaviors can be help to reduce numerical costs to make huge EOS tables for astrophysical simulations, and would be a useful index to understand the quark-hadron phase transition.