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We discuss the observation that under neutron star conditions of chargeneutrality and $\beta-$equilibrium the contribution from the symmetry energy tothe equation of state (EoS) follows a universal behaviour. We call thisbehaviour the conjecture of a Universal Symmetry Energy Contribution (USEC). Wefind 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 valuesbelow the threshold for the direct Urca (DU) cooling process. The absence of DUcooling in typical mass neutron stars appears to be supported by thephenomenology of neutron star cooling data and allows to constrain thebehaviour of $E_s(n)$ at high densities. Two classes of symmetry energyfunctions are investigated more in detail to elucidate the USEC. We derive ananalytic formula for the USEC to the neutron star EoS based on the result forthe symmetry energy extracted from isobaric analog states of nuclei.

Universal symmetry energy contribution to the neutron star equation of state