The Spin Periods and Rotational Profiles of Neutron Stars at Birth

We present results from an extensive set of one- and two-dimensional radiation-hydrodynamic simulations of the supernova core-collapse, bounce, and postbounce phases and focus on the proto-neutron star (PNS) spin periods and rotational profiles as a function of initial iron core angular velocity, degree of differential rotation, and progenitor mass. For the models considered, we find a roughly linear mapping between initial iron core rotation rate and PNS spin. The results indicate that the magnitude of the precollapse iron core angular velocities is the single most important factor in determining the PNS spin. Differences in progenitor mass and degree of differential rotation lead only to small variations in the PNS rotational period and profile. Based on our calculated PNS spins at ~200-300 ms after bounce and assuming angular momentum conservation, we estimate final neutron star rotation periods. We find periods of 1 ms and shorter for initial central iron core periods of ≲10 s. This is appreciably shorter than what previous studies have predicted and is in disagreement with current observational data from pulsar astronomy. After considering possible spin-down mechanisms that could lead to longer periods, we conclude that there is no mechanism that can robustly spin down a neutron star from ~1 ms periods to the "injection" periods of tens to hundreds of milliseconds observed for young pulsars. Our results indicate that, given current knowledge of the limitations of neutron star spin-down mechanisms, precollapse iron cores must rotate with periods of around 50-100 s to form neutron stars with periods generically near those inferred for the radio pulsar population.