Exotic Baryons in Hot Neutron Stars

We study the nuclear isentropic equation of state for a stellar matter composed of nucleons, hyperons, and $\Delta$-resonances. We investigate different snapshots of the evolution of a neutron star, from its birth as a lepton-rich protoneutron star in the aftermath of a supernova explosion to a lepton-poor regime when the star starts cooling to a catalyzed configuration. We use a relativistic model within the mean-field approximation to describe the hot stellar matter and adopt density-dependent couplings adjusted by the DDME2 parameterization. We use baryon-meson couplings for the spin-$1/2$ baryonic octet and spin-$3/2$ decuplet determined in a unified manner relying on $\text{SU}(6)$ and $\text{SU}(3)$ symmetry arguments. We observe that $\Lambda$ is the dominant exotic particle in the star at different entropies for both neutrino-free and neutrino-trapped stellar matter. For a fixed entropy, the inclusion of new particles (hyperons and/or delta resonances) in the stellar matter decreases the temperature. Also, an increase in entropy per baryon ($1\;\text{to}\; 2$) with decreasing lepton number density ($0.4\;\text{to}\; 0.2$) leads to an increase in stellar radii and a decrease in its mass due to neutrino diffusion. In the neutrino transparent matter, the radii decrease from entropy per baryon $2$ to $T\,=\,0$ without a significant change in stellar mass.