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It has been suggested based on analytic theory that even in non-rotatingsupernova progenitors stochastic spin-up by internal gravity waves (IGWs)during the late burning stages can impart enough angular momentum to the coreto result in neutron star birth spin periods below 100ms, and a relatively firmupper limit of 500ms for the spin period. We here investigate this processusing a 3D simulation of oxygen shell burning in a $3M_\odot$ He star. Ourmodel indicates that stochastic spin-up by IGWs is less efficient thanpreviously thought. We find that the stochastic angular momentum flux carriedby waves excited at the shell boundary is significantly smaller for a givenconvective luminosity and turnover time than would be expected from simpledimensional analysis. This can be explained by noting that the waves launchedby overshooting convective plumes contain modes of opposite angular wave numberwith similar amplitudes, so that the net angular momentum of excited wavepackets almost cancels. We find that the wave-mediated angular momentum fluxfrom the oxygen shell follows a random walk, but again dimensional analysisoverestimates the random walk amplitudes since the correlation time is only afraction of the convective turnover time. Extrapolating our findings over theentire life time of the last burning stages prior to collapse, we predict thatthe core angular momentum from stochastic spin-up would translate into longbirth spin periods of several seconds for low-mass progenitors and no less than100ms even for high-mass progenitors.

Stochastic Core Spin-Up in Massive Stars -- Implications of 3D Simulations of Oxygen Shell Burning