= Radiative energy of virialized gravitational collapse
{title2=$E_{\rm rad}\simeq3M\sigma^2/2$}
For an isolated final <stellar population> with isotropic one-dimensional <velocity dispersion> $\sigma$, kinetic energy is $K=3M\sigma^2/2$. The <virial theorem> gives $W=-2K$ and total energy $E=-K$. Collapse from a diffuse nearly unbound gas reservoir therefore requires removal of approximately $K$ of energy. The radiated fraction can differ if there are outflows, appreciable initial binding energy, or boundary stresses.
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