Matteo Cantiello edited sectionDiscussion_an.tex  over 9 years ago

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We have shown that convectively generated internal gravity waves (IGW) in massive stars are capable of redistributing angular momentum (AM) on short time scales. In particular, inwardly propagating IGW launched from shell burning convective zones can likely slow down the core to much slower spin rates than it would obtain in the absence of other AM transport mechanisms. For our $12 M_\odot$ model, IGW generated at the base of the convective zone during the core He burning red supergiant phase can slow the core to minimum spin periods of $P \sim 2 \, {\rm days}$. IGW launched during subsequent shell burning phases can remove more AM from the core, and we calculate a minimum iron core rotation period before CC of $P \gtrsim 130 \, {\rm s}$. We therefore expect the majority of NS-spawning supernovae to be in the regime of slow rotation. If AM is conserved during the supernova, we expect minimum NS rotation periods of $P \sim 7 \, {\rm ms}$.   The rotation periods listed above are minimum periods for our stellar model. Interestingly, calculations of rotation rates including magnetic torques \citep{heger:00,wheeler:14} \citep{heger_05,wheeler:14}  yield similar figures. It is possible that both mechanisms play a significant role within massive stars. If IGW are able to spin down cores to slower rotation rates, as we have speculated, than they may be the dominant AM redistribution mechanism during a massive star's life. This is especially true during the final stages of evolution (O burning and onward) when evolution time scales become so short that magnetic torques become ineffective \citep{heger:00,wheeler:14}. \citep{heger_05,wheeler:14}.  However, the increasingly large wave fluxes allow IGW to continue to act on time scales shorter than evolution time scales. We therefore encourage efforts to incorporate the effects of IGW in stellar evolution codes focusing on the final stages of massive star evolution. Stochastic influxes of IGW also lead to minimum core rotation rates, which may be realized given very efficient prior core spin down via waves/magnetic torques. Such a spindown is not unreasonable, especially given that the cores of low mass red giant stars rotate slower than can be accounted for using hydrodynamic mechanisms or magnetic torques via the Tayler-Spruit dynamo \citep{cantiello:14}. It is thus quite plausible that massive star cores are efficiently spun down via waves/magnetic torques, after which they are stochasticly spun up via waves launched during O/Si burning. If this mechanism determines the core spin rate before death, it entails a Maxwellian distribution in spin frequency, with typical spin periods of $P \sim 2 \times 10^3 \, {\rm s}$. We thus find it extremely unlikely that magnetic torques can enforce very large pre-collapse spin periods as claimed by \cite{spruit:98}.