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Universal symmetry energy contribution to the neutron star equation of state

We discuss the observation that under neutron star conditions of charge neutrality and $β-$equilibrium the contribution from the symmetry energy to the equation of state (EoS) follows a universal behaviour. We call this behaviour the conjecture of a Universal Symmetry Energy Contribution (USEC). We find that an USEC holds provided the density dependence of the symmetry energy $E_s(n)$ follows a behaviour that limits the proton fraction $x(n)$ to values below the threshold for the direct Urca (DU) cooling process. The absence of DU cooling in typical mass neutron stars appears to be supported by the phenomenology of neutron star cooling data and allows to constrain the behaviour of $E_s(n)$ at high densities. Two classes of symmetry energy functions are investigated more in detail to elucidate the USEC. We derive an analytic formula for the USEC to the neutron star EoS based on the result for the symmetry energy extracted from isobaric analog states of nuclei.