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Within the minimum model of neutron stars (NS) consisting of neutrons,protons and electrons, a new approach is proposed for inferring the symmetryenergy of super-dense neutron-rich nucleonic matter above twice the saturationdensity $\rho_0$ of nuclear matter directly from integrating iterativelybarotropic pressures in both neutron stars and heavy-ion reactions.Simultaneously, the proton fraction of NSs at $\beta$ equilibrium is extractedas a function of baryon density from the same procedure. An application of thisapproach using the NS pressure from GW170817 and the pressure in cold symmetricnuclear matter (SNM) extracted earlier by analyzing nuclear collective flowdata in relativistic heavy-ion collisions provides a useful constraining bandfor the symmetry energy above $2\rho_0$.

Symmetry energy of super-dense neutron-rich matter from integrating barotropic pressures in neutron stars and heavy-ion reactions