A protoneutron star (PNS) gets formed after a successful supernova when the stellar remnant decouples from the ejecta. In this study, we explore a relativistic framework for the finite-temperature $\beta$-equilibrium limit of equation of state (EOS), constrained via a Bayesian inference methodology. The EOS is obtained using a minimal number of constraints, including a few nuclear saturation properties, low-density pure neutron matter constraints from chiral effective field theory, and a neutron star (NS) maximum mass greater than $2.0M_{\odot }$. Two sets of EOS derived from the relativistic mean-field model for nucleonic and hyperonic matter constrained by a Bayesian inference calculation at the zero temperature limit are used. The thermal adiabatic index (${\mathrm{\Gamma }}_{\mathrm{Th}}$) is calculated as a function of the baryonic density across several temperatures for both the sets. Our results suggest that the maximum NS mass is of the order of $2.15M_{\odot }$ if hyperons are present. In addition, the present study suggests that an observation of NS with mass larger than $2.2M_{\odot }$ can indirectly indicate the absence of hyperons in its core. The deleptonization of hyperonic PNS reduces the stellar maximum mass rendering the PNS exceeding the zero temperature maximum stellar (baryonic) mass limit becomes metastable which is prone to collapse into a black hole while PNSs below such a mass threshold evolve to a stable NS.

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• Neutron star cooling
• Nuclear matter in neutron stars