High density behavior of nuclear symmetry energy is studied on the basis of the stiffest density dependence of asymmetric contribution to energy per nucleon in charge neutral n + p + e + [Formula: see text] matter under beta equilibrium. The density dependence of nuclear symmetry energy obtained in this way is neither very stiff nor soft at high densities and is found to be in conformity with recent observations of neutron stars.
The frequencies and damping times of the axial w-mode oscillations of neutron stars are investigated using a nuclear equation of state (EOS) partially constrained by the available terrestrial laboratory data. It is found that the nuclear symmetry energy E sym (ρ), especially its high density behavior, plays an important role in determining both the eigen-frequencies and the damping times of these oscillations.