We investigate remnant neutron star masses (in particular, the minimum allowed mass) by performing advanced stellar evolution calculations and neutrino-radiation hydrodynamics simulations for core-collapse supernova explosions. We find that, based on standard astrophysical scenarios, low-mass carbon-oxygen cores can have sufficiently massive iron cores that eventually collapse, explode as supernovae, and give rise to remnant neutron stars that have a minimum mass of 1.17 M$_odot$ --- compatible with the lowest mass of the neutron star precisely measured in a binary system of PSR J0453+1559.
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