Variational study of the supernova equation of state with hyperons

We report on a new equation of state (EOS) of nuclear matter containing Lambda hyperons constructed with the variational many-body theory for core-collapse supernova simulations. Bare baryon interactions, including the Argonne v18 two-nucleon and Urbana IX three-nucleon potentials are adopted, and the energy per baryon at zero temperature is calculated with the cluster variational method. The free energy per baryon at finite temperature is calculated with an extension of the variational method proposed by Schmidt and Pandharipande. The resulting thermodynamic quantities of hyperonic nuclear matter for various densities, temperatures, and proton fractions under the equilibrium condition mu(n) = mu(Lambda) are reasonable as compared with those of the Shen EOS. It is also observed that the fraction of Lambda hyperons in hot dense matter increases as the proton fraction decreases or the temperature increases. Furthermore, due to the smaller symmetry energy with our EOS, the Lambda fraction of our EOS for neutron-rich matter is less than that of the Shen EOS.