Accurate nuclear symmetry energy at finite temperature within a Brueckner-Hartree-Fock approach

We compute the free energy of asymmetric nuclear matter in a Brueckner-Hartree-Fock approach at finite temperature, paying particular attention to the dependence on isospin asymmetry. The first- and second-order symmetry energies are determined as functions of density and temperature and useful parametrizations are provided. We find small deviations from the quadratic isospin-asymmetry dependence and very small corresponding effects on (proto)neutron star structure.