Symmetry energy, neutron star crust, neutron skin thickness, and the r-mode instability

We analyze different aspects of the nuclear symmetry energy by using both microscopic and phenomenoliogical approaches to the nuclear equation of state. Microscopic includes Brueckner-Hatree-Fock, the variational form due to Akmal, Pandharipande, and Ravenhall, and a parametrization of recent Auxiliary Field Diffusion Monte Carlo. For phenomenological approaches we use Skyrme forces and relativistic mean field models. Specifically, we study correlations of symmetry energy parameters, the slope L and the curvature K_symm, with the neutron slin thinkness (in neutron rich isotopes) and the crust-core transition point (in neutron stars). We confirm that there is an inverse correlations between the neutron slin thinkness and the transition density. The role of L in the r-mode instability of neutron stars is also studied. The r-mode instablity region is smaller for models which give larger values of L. Using the measured spin frequency and estimated core temperature of the pulsar in the low mass X-ray binary 4U 1608-52, we show that observational data seem to favor L values larger than ~50 MeV.