Profiles of mean thermodynamic states from representative runs. Top panel: time-averaged radial profiles of azimuthally averaged temperature (orange, left axis) and density (black, right axis) as functions of radius from the non-rotating run HD1. The inset shows the radial profile of the mean specific entropy s̄/c_P. Bottom: mean specific entropy s̄/c_P(r) from runs HD1, MHD1, MHD3, and MHD5 as indicated by the legend. The dots show a scatter plot of s̄(ϖ,θ) as a function of spherical radius r. The dotted vertical line indicates the upper boundary of the convective layer in the non-rotating run HD1.