The pasta phases are expected to appear in hot supernova matter and cold neutron stars.In supernova matter,the pasta phases with a series of geometric shapes are studied using the compressible liquid-drop(CLD)mod-el,where nuclear matter separates into a dense liquid phase of nucleons and a dilute gas phase of nucleons and a particles.The equilibrium conditions for two coexisting phases are derived by minimization of the total free energy including the surface and Coulomb contributions.Compared to the results considering only spherical nuclei,the in-clusion of pasta phases can delay the transition to uniform matter and enlarge the region of nonuniform matter in the phase diagram.It is found that the density ranges of various pasta shapes depend on both the temperature and the proton fraction.The thermodynamic quantities obtained with the pasta phases using the CLD model are consistent with those in the realistic equation of state table for astrophysical simulations using the Thomas-Fermi approxima-tion.The hadron-quark pasta phases occurring in the interior of massive neutron stars are studied using the energy minimization(EM)method,which is analogous to the CLD method for nuclear pasta.It was found that the hadron-quark pasta phases could be significantly affected by the model parameters used.
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