Stellar buoyancy frequency ($N^2=g\left(\frac{1}{\gamma p}\frac{dp}{dr}-\frac{1}{\rho }\frac{d\rho }{dr}\right)$)

In a spherically symmetric stellar model with inward gravity magnitude $g$, the squared buoyancy frequency isPositive $N^2$ gives stable stratification. Regular central profiles have $g=O(r)$ and logarithmic pressure and density gradients of order $r$, so $N^2=O(r^2)$ near the center.