= High-density core bound from TOV compactness
{title2=$a<\frac1{\sqrt{3\pi\rho_0}}$}
Let $\rho_0>0$ be a density threshold and let $a,\mu$ be the radius and enclosed mass where a monotonically decreasing stellar density reaches that threshold. Then $\mu\geq4\pi\rho_0a^3/3$. A local compactness bound $\mu/a<4/9$ implies $a<(3\pi\rho_0)^{-1/2}$ and $\mu<4/(9\sqrt{3\pi\rho_0})$, independently of the <equation of state> above the threshold. A total-mass bound also requires suitable control of the known low-density envelope.
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