(a) Schematic of our three-dimensional spherical-shell simulation domain. The yellow region depicts the CZ with bulk overturning fluid motions represented by circular arrows. The CZ lies atop a thin stably stratified region (green) with significant nonlinear effects from overshoot and a deep stably stratified RZ (purple) where the motion is essentially linear, represented by curvy “radiation” arrows. (b) Schematic of the reference state that enforces the geometry of panel (a). Convection is forced in roughly the bottom third of the CZ by a prescribed internal heating ﹩{\tilde{Q}}_{{\rm{rad}}}^{* }﹩, which causes an accompanying “nonradiative” energy flux ﹩4\pi r{* }^{2}{\tilde{F}}_{{\rm{nr}}}^{* }﹩ that convection and conduction must carry in a steady state to maintain thermal equilibrium (see N. A. Featherstone & B. W. Hindman 2016). The stable stratification is enforced through the background positive squared buoyancy frequency ﹩{\widetilde{N}}^{* 2}﹩ in the RZ. These are the shapes of the profiles used for cases 0, 3, 4, and 6 and have been normalized to all lie on the same scale. The dashed circle (panel (a)) and dashed vertical line (panel (b)) mark the location of the true solar surface.