deletions | additions       diff --git a/IGW_are_generated_by.tex b/IGW_are_generated_by.tex  index 5c3c5a7..507d48b 100644  --- a/IGW_are_generated_by.tex  +++ b/IGW_are_generated_by.tex 
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For simplicity, we only focus on cases in which a convectively burning shell overlies the radiative core, irradiating it with IGW. A full understanding of the effects of IGW should also include the effects of IGW emitted during core convective phases, and the combined effects of IGW emitted by multiple convective shells. We focus on convective shell-generated IGWs because they are generated 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 a factor of a few larger than those presented here.   Figure \ref{fig:Massivehist} 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 have smaller, higher density cores. 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. \begin{table*}