= Stellar buoyancy frequency
{title2=$N^2=g\left(\frac1{\gamma p}\frac{dp}{dr}-\frac1\rho\frac{d\rho}{dr}\right)$}
In a spherically symmetric stellar model with inward gravity magnitude $g$, the squared buoyancy frequency is
$$
N^2=g\left(\frac1{\gamma p}\frac{dp}{dr}-\frac1\rho\frac{d\rho}{dr}\right).
$$
Positive $N^2$ 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.
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