Determining the minimal mass of a proto-neutron star with chirally constrained nuclear equations of state

The minimal masses and radii of proto-neutron stars during different stages of their evolution are investigated. In our work we focus on two stages, directly after the supernova shock wave moves outwards, where neutrinos are still captured in the core and the lepton per baryon ratio is fixed to $Y_L = 0.4$, and a few seconds afterwards, when all neutrinos have left the star. All nuclear equations of state used for this purpose fulfill the binding energy constraints from chiral effective field theory for neutron matter at zero temperature. We find for the neutrino-trapped case higher minimal masses than for the case when neutrinos have left the proto-neutron star. Thermal effects, here in the form of a given constant entropy per baryon $s$, have a smaller effect on increasing the minimal mass. The minimal proto-neutron star mass for the first evolutionary stage with $Y_L = 0.4$ and $s = 1$ amounts to $M_{min} \sim 0.62M_{\odot}$ and for the stage without neutrinos and $s = 2$ to $M_{min} \sim 0.22M_{\odot}$ rather independent on the nuclear equation of state used. We also study the case related to an accretion induced collapse of a white dwarf where the initial lepton fraction is $Y_L = 0.5$ and observe large discrepancies in the results of the different tables of nuclear equations of state used. Our finding points towards a thermodynamical inconsistent treatment of the nuclear liquid-gas phase transition for nuclear equations of state in tabular form demanding a fully generalized three-dimensional Gibbs construction for a proper treatment. Finally, we demonstrate that there is a universal relation for the increase of the proto-neutron star minimal mass with the lepton fraction for all nuclear equations of state used.