Equation of State of Hyperonic Nuclear Matter at Zero and Finite Temperatures with the Variational Method

Abstract

A new equation of state (EOS) for uniform nuclear matter including Λ hyperons at zero and finite temperatures is constructed with the variational many-body theory using the Argonne v18 twonucleon potential, Urbana IX three-nucleon potential, and the ΛN and ΛΛ interactions that reproduce the experimental data on single-and double-Λ hypernuclei. At zero temperature, we calculate the energy per baryon of hyperonic nuclear matter in the two-body cluster approximation supplemented by the three-nucleon-force contribution. The mass-radius relation of neutron stars calculated with the obtained EOS is consistent with that of the observationally suggested data, and the maximum mass of neutron stars with the EOS including an effective three-baryon repulsive force is consistent with recently observed masses of heavy neutron stars. At finite temperature, the free energy per baryon of hyperonic nuclear matter is calculated by extending the variational method proposed by Schmidt and Pandharipande. The obtained free energies and related thermodynamic quantities for various densities, temperatures, and particle fractions are reasonable. The composition of hyperon-mixed supernova matter under an appropriate equilibrium condition is investigated using the obtained EOS for hot hyperonic nuclear matter. It is found that the Λ hyperon mixing is enhanced when supernova matter becomes hotter and more neutron-rich.