The High-Density Symmetry Energy and Direct Urca
  The symmetry energy of nucleonic matter is usually assumed to be quadratic in the isospin density. While this may be justified at sub-saturation densities, there is no need to enforce this restriction at super-saturation densities. The presence of a quartic term can strongly modify the critical density for the direct Urca process which leads to faster cooling of neutron stars. Neutron star cooling predictions which lie below the observational data can, for some equations of state, be repaired with a quartic term which effectively turns off the direct Urca process. 
Andrew W. Steiner