Neutron star masses from electron-capture supernovae under equation-of-state uncertainties
Electron-capture supernovae (ECSNe) are a promising formation channel for low-mass neutron stars, but the minimum gravitational mass of the neutron stars they produce depends on both the progenitor core structure and the neutron-star matter equation of state (EOS). We compute the electron-capture (EC) threshold gravitational mass ($M^\star_{WD}$) of cold white-dwarf-like O--Ne--Mg cores with representative compositions and map the baryon number onto cold neutron-star configurations constructed from a Bayesian ensemble of unified crust--core EOSs. Although the EC threshold density is sensitive to the concentrations of the O--Ne--Mg mixture, the threshold baryon number of the O--Ne--Mg core varies only weakly, producing a narrow remnant-mass window. In the baseline case with no baryonic mass loss during the transition from the EC threshold mass O--Ne--Mg core to the remnant neutron star, standard ECSNe yield remnant neutron stars with gravitational masses of $1.24$--$1.265\, M_\odot$, with only a small EOS-induced spread. Small baryonic mass losses of $0.01$--$0.02\, M_\odot$ shift this range modestly downward, but the $1.174\, M_\odot$ companion of PSR J0453+1559 would require an extreme mass loss close to $0.10\, M_\odot$, which is not favored by current ECSN simulations. We find that the residual EOS dependence of the remnant mass is controlled mainly by the pressure around nuclear saturation density, while the corresponding tidal deformability remains sensitive to the remnant radius and compactness. Thus, low-mass double neutron star systems can in principle connect ECSN-like formation channels with gravitational-wave constraints on the EOS. Our results show that ECSNe naturally form low-mass neutron stars, but within a restricted mass range; the lightest observed neutron stars likely require low-mass iron-core collapse, ultra-stripped supernovae, or other nonstandard channels.