deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index c462485..99c6955 100644  --- a/IGW_are_generated_by.tex  +++ b/IGW_are_generated_by.tex 
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IGW are generated by convective regions and propagate into neighboring stably stratified regions, carrying energy and AM. To estimate energy and AM fluxes carried by IGW, we use techniques similar to those of F14, QS12, and SQ14. We begin by constructing a sequence of stellar models using the MESA stellar evolution code (Paxton et al. 2011,2013). In what follows, we focus on a $M=12 M_\odot$, $Z=0.02$ model that has been evolved to CC. Details on the model can be found in Appendix \ref{model}. For our purposes, the most important model outputs are the local heat flux, convective mach numbers, and life time of convectively burning zones. As in SQ14, we find these quantities correlate most strongly the helium core mass. Stellar models of larger mass or with more mixing (due to overshoot or rotation) tend to have a higher He core mass and may exhibit different wave dynamics than our fiducial model. Our main goal here is simply to provide a rough estimate of IGW AM fluxes for a typical low-mass ($M \lesssim 20 M_\odot$) NS progenitor star.   A full understanding of AM transport by IGW should include the combined effects waves emitted from each convective zone. For simplicity, we focus on cases in which a convective shell overlies the radiative core, irradiating it with IGW. These convective shell phases typically occur after core burning phases and thus have the final impact for a given burning phase. We use mixing length theory (MLT), as described in F14, to calculate IGW frequencies and fluxes. Our MLT calculations yield convective velocities and Mach numbers that tend to be a factor of a few smaller than those seen in simulations (e.g., \citealt{Meakin_2006,meakinb:07,Meakin_2007,Arnett_2008}). This could be due to the larger mass of their stellar model or the inadequacy of the MLT approximation. We proceed with our MLT results, but caution that realistic wave frequencies and fluxes may be slightly larger than differ from  those presented here. used here by a factor of a few.  Figure \ref{fig:MassiveIGWhist} shows a Kippenhahn diagram for our stellar model, and Figure \ref{fig:Massivestruc} shows the density ($\rho$), mass [$M(r)$], and Brunt-V\"{a}is\"{a}l\"{a} frequency ($N$) profiles of our model during important convective shell phases. The first convective shell phase occurs during He-core burning, at which point the star has evolved into a red supergiant. At this stage, IGW are generated at the base of the surface convection zone and propagate toward the He-burning core. We have also shown profiles during shell C-burning, O-burning, and Si-burning, when the radiative core contains a mass of $M_c \sim 1 M_\odot$ and is being irradiated by IGW generated from the overlying convective burning shell. The basic features of each of these phases is quite similar, the main difference is that more advanced burning stages are more vigorous but shorter in duration. We find that the characteristics of the convective burning shells (convective luminosities, turnover frequencies, mach numbers, and lifetimes) are similar to those listed in QS12 and SQ13, although the shell burning phases are generally more vigorous and shorter-lived than the core burning examined in SQ13. Table 1 lists some of the parameters of our convective zones.