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Constraints on the symmetry energy from neutron star equation of state

We develop an equation of state (EOS) for neutron star (NS) matter, which forbids the direct URCA cooling and satises the recent information on the mass and the radius, simultaneously. At sub-saturation densities, the symmetry energy of the EOS is well described by a function Esym ( ) = 31:6 ( = 0) with 0:70 0:77. This constraint on the density dependence of the symmetry energy is much severer than that obtained from the analysis of the isospin di¤usion date in heavy-ion collisions. Consequently, we can obtain the valuable information on nuclear matter from the astrophysical observations of NSs.