Matteo Cantiello edited sectionSpin_Evolutio.tex  over 9 years ago

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\section{Spin Evolution}  Using our spin-down time scales derived above, we can begin to speculate on the spin evolution of the cores of typical NS progenitors. We have focused on a low mass ($12 M_\odot$), solar metallicity model at red supergiant stages of evolution. These stars invariably contain an extended, slowly spinning convective zone that is a nearly unlimited AM sink. The core spin rate can therefore be changed without any significant change in envelope rotation rate. In what follows, we ignore magnetic torques, which may substantially slow core rotation rates \citep{heger:00,wheeler:14}. \citep{Heger_2005,wheeler:14}.  We therefore consider our results to represent maxim maximum  expected spin rates, which will be enforced regardless of the efficacy of magnetic torques. Our results (see Figure \ref{fig:MassiveIGWtime}) indicate that the entire helium core ($M \lesssim 4 M_\odot$) likely to be substantially spun down by IGW excited at the base of the surface convection zone. The IGW may not penetrate into the inner $\sim 1.5 M_\odot$ because this region contains the convective He-burning core. However, we expect the convective central core to couple relatively strongly to the overlying He outer core, either through IGW emitted by the convective core, through magnetic torques, or during subsequent burning phases. Figure \ref{fig:MassiveIGWtime} indicates that a plausible upper limit to the core during the He-burning stage is $\Omega_{\rm max} \sim \omega_* \sim 4 \times 10^{-5}{\rm Hz}$. The corresponding minimum rotation period is $P_{\rm min} \sim 2 \, {\rm days}$. In the absence of AM transport, using a typical main sequence equatorial rotation velocity of $v = 100 \, {\rm km}\,{\rm s}^{-1}$ \citep{demink:13}, the He-burning core would rotate at $P \sim 3 \,{\rm hr}$. IGW will therefore substantially spin down the core during the He core burning phase.