Interplay between Symmetry Energy and Excluded Volume Corrections under the Direct Urca Cooling Constraint in Neutron Stars

Both the symmetry energy part and excluded volume corrections to the equation of state play an important role for the neutron star interior structure and composition, namely for the profile of the baryon density and the proton fraction. While the symmetry energy uniquely determines the proton fraction, excluded volume effects control the maximum density values inside neutron stars. Observations of cooling neutron stars indicate that the fast direct Urca cooling is not operative for the typical, low mass stars, pointing at proton fractions that lie below the threshold for the onset of direct Urca cooling process. This in turn, restricts the density range admissible in neutron star interiors and may require an excluded volume correction. In this contribution we discuss the interplay between fast cooling, symmetry energy and excluded volume corrections to the equation of state that would be required to fulfil the direct Urca cooling constraint.