Rotating neutron stars with nonbarotropic thermal profile

Abstract

Neutron stars provide an excellent laboratory for physics under the most\nextreme conditions. Up to now, models of axisymmetric, stationary,\ndifferentially rotating neutron stars were constructed under the strong\nassumption of barotropicity, where a one-to-one relation between all\nthermodynamic quantities exists. This implies that the specific angular\nmomentum of a matter element depends only on its angular velocity. The physical\nconditions in the early stages of neutron stars, however, are determined by\ntheir violent birth processes, typically a supernova or in some cases the\nmerger of two neutron stars, and detailed numerical models show that the\nresulting stars are by no means barotropic. Here, we construct models for\nstationary, differentially rotating, non-barotropic neutron stars, where the\nequation of state and the specific angular momentum depend on more than one\nindependent variable. We show that the potential formulation of the\nrelativistic Euler equation can be extended to the non-barotropic case, which,\nto the best of our knowledge, is a new result even for the Newtonian case. We\nimplement the new method into the XNS code and construct equilibrium\nconfigurations for non-barotropic equations of state. We scrutinize the\nresulting configurations by evolving them dynamically with the numerical\nrelativity code BAM, thereby demonstrating that the new method indeed produces\nstationary, differentially rotating, non-barotropic neutron star\nconfigurations.\n