Internal structures from the suite of 1 M_⊙ main-sequence models with different rotation rates (0 ≤ Ω ≤ 0.5Ω_K) shown in Table 1. Upper panel: temperature and density profiles near the bottom of the convective envelope. The models towards the left-hand side are the fastest rotators. Middle panel: temperature gradient for the same models. The curves that reach the highest ∇ are the fastest rotators and the fastest is denoted by a thick line. Lower panel: ratio of the temperature gradients as a function of enclosed mass and radial coordinate. The denominator in the ratio of the temperature gradients ∇_ad + Ω is the right-hand side of inequality (11) instead of the true adiabatic temperature gradient ∇_ad. The requirement for convective instability in the models with rotation is ∇_rad/∇_ad + Ω >  1. The curves furthest to the right are the fastest rotators and the fastest is denoted by a thick line. Convectively unstable regions are shown in red and stable regions in blue.