Stellar convective instability

Stellar convective instability occurs when an adiabatic process displaces a fluid element and buoyancy amplifies the displacement. For uniform composition the Schwarzschild criterion gives instability when the actual temperature gradient exceeds the adiabatic temperature gradient; composition gradients instead require the Ledoux criterion.

A uniform-density perfect-gas sphere supported by decreasing pressure has buoyancy frequency squared $N^2=-2{\omega }_d^2{r}^2/[\gamma (R^2-r^2)]$ in the interior. Its specific entropy decreases outward and adiabatic displacements are buoyantly unstable. For the nonradial polynomial family, the product of the two normalized squared mode frequencies is $-l(l+1)$, displaying one growing branch even when radial compression modes are stable.