deletions | additions       diff --git a/sectionDiscussion_an.tex b/sectionDiscussion_an.tex  index 21f1d24..738ed3b 100644  --- a/sectionDiscussion_an.tex  +++ b/sectionDiscussion_an.tex 
...
The rotation periods listed above are minimum periods for our stellar model. Calculations of rotation rates including magnetic torques \citep{Heger_2005,wheeler:14} typically yield rotation periods several times larger. Magnetic torques may therefore be the dominant AM transport mechanism responsible for extracting AM from massive stellar cores, although it is possible that both mechanisms play a significant role. If IGW are able to spin down cores to slower rotation rates, as we have speculated, then they could be the dominant AM redistribution mechanism during a massive star's life. It may seem surprising that AM transport via IGW can act on the short stellar evolution timescales of massive stars. However, the huge convective luminosities inside of red supergiants ensures large fluxes of IGWs (QS12, SQ14) that can transport energy and EM on short timescales. 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 IGW/magnetic torques. Such a spindown spin-down  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 $300 \, {\rm s} \lesssim P \lesssim 10^4  \, {\rm s}$. We thus find it extremely unlikely that magnetic torques can enforce very large pre-collapse spin periods as claimed by \cite{spruit:98}. If AM is conserved during the supernova, stochastic wave torques entail that most NS are born with $P \lesssim 1 {\rm s}$. Although there is significant uncertainty, our best estimates yields entail typical IGW spin-up entails  NSspin periods at  birth periods  of $P \sim $20  {\rm few} \times 100 \, ms} \lesssim P \lesssim 400  {\rm ms}$. ms}$, albeit with significant uncertainty.  This is comparable to spin periods of some young, slowly rotating NSs (\citealt{lai:96,gotthelf:13}), and for the broad inferred birth spin period distribution of $P \lesssim 500 \, {\rm ms}$ for ordinary pulsars (\citealt{faucher:06,popov:10,gullon:14}). Therefore, stochastic wave spin-up could be the dominant mechanism in determining the rotation periods of pre-collapse SN cores and newborn NSs. There is ample evidence that {\it some} CC events occur with rapidly rotating cores. In particular, long GRBs almost certainly require a rapidly rotating central engine \citep{Woosley_1993,Yoon_2006,Woosley_2006,Metzger_2011}, and the picture advanced above must break down in certain (although somewhat rare) circumstances. It is not immediately clear what factors contribute to the high spin rate in GRB progenitors, as our analysis was restricted to ``typical" NS progenitors with $10 M_\odot \lesssim M \lesssim 20 M_\odot$, which explode to produce type-IIp supernovae during a red supergiant phase \citep[See e.g.][]{Smartt_2009}. We speculate that GRB progenitors have {\it never} undergone a red supergiant phase, as torques via magnetic fields and/or waves are likely to spin-down the helium core by coupling it with the huge AM reservoir contained in the slowly rotating convective envelope. Alternatively, it may be possible that stars with very massive He cores, which exhibit more vigorous pre-SN burning phases, can generate stochastic wave spin-up strong enough to produce a GRB.