Delta-resonances and hyperons in proto-neutron stars and merger remnants

The equation of state (EoS) and composition of dense and hot $\Delta$-resonance admixed hypernuclear matter is studied under conditions that are characteristic of neutron star binary merger remnants and supernovas. The cold, neutrino free regime is also considered as a reference for the astrophysical constraints on the EoS of dense matter. Our formalism uses the covariant density functional (CDF) theory successfully adapted to include the full $J^P=1/2^+$ baryon octet and non-strange members of $J^P=3/2^+$ decouplet with density-dependent couplings that have been suitably adjusted to the existing laboratory and astrophysical data. The effect of $\Delta$-resonances at finite temperatures is to soften the EoS of hypernuclear matter at intermediate densities and stiffen it at high densities. At low temperatures, the heavy baryons $\Lambda$, $\Delta^-$,$\Xi^-$, $\Xi^0$ and $\Delta^0$ appear in the given order if the $\Delta$-meson couplings are close to those for the nucleon-meson couplings. As is the case for hyperons, the thresholds of $\Delta$-resonances move to lower densities with the increase of temperature indicating a significant fraction of $\Delta$'s in the low-density subnuclear regime. We find that the $\Delta$-resonances comprise a significant fraction of baryonic matter, of the order of $10\%$ at temperatures of the order of several tens of MeV in the neutrino-trapped regime and, thus, may affect the supernova and binary neutron star dynamics by providing, for example, a new source for neutrino opacity or a new channel for bulk viscosity via the direct Urca processes. The mass-radius relation of isentropic static, spherically symmetric hot compact stars is discussed.