Ledoux criterion

The Ledoux criterion tests local adiabatic stellar convective stability in the presence of a composition gradient. Definewhere $\mu$ is the mean molecular weight and the partial derivatives describe the equation of state. For positive $\delta$, the stratification is stable to an infinitesimal composition-preserving adiabatic process displacement whenThe parcel adjusts its pressure to its surroundings, retains its composition and changes temperature along the adiabatic temperature gradient. Comparing its resulting mass density with the ambient value determines the restoring buoyancy. For positive $\varphi /\delta$, increasing mean molecular weight inward gives ${\nabla }_{\mu }>0$ and an additional stabilizing contribution. With uniform composition the condition reduces to the Schwarzschild criterion. Thermal or compositional diffusion introduces further instability questions beyond this adiabatic parcel test.