\label{fig:Massivestruc} Internal structure of our \(12 M_\odot\) stellar model, at the phases labeled in Figure \ref{fig:MassiveIGWhist}. At all stages shown, the star is a red supergiant with radius \(R \sim 10^3 R_\odot\). The He-burn stage is core helium burning, while the C-burn, O-burn, and Si-burn stages are shell carbon, oxygen, and silicon burning phases, respectively. Vertical shaded bars are drawn near the base of the surface convection zone for the He-burn stage, and near the base of the convective shell burning region of the other stages. Top: Density profiles \(\rho\) of the inner regions of our models. The envelope density profile is similar for each model, but central densities vary by orders of magnitude. Middle: Enclosed mass profiles. For C/O/Si-burning, the models are chosen such that the mass internal to the convective shell burning region is \(M_c \sim 1.2 M_\odot\). Bottom: The Brunt-Väisälä frequency, \(N\), of our models. We have also plotted horizontal dashed lines at the convective turnover frequencies \(\omega_c\) below the relevant convective zone. IGW propagate in the regions where \(\omega_c < N\), shown by the horizontal extent of the dashed lines.