= Accretion output relative to galactic binding energy
{title2=$E_{\rm rad}/|W|\sim[\eta/(1-\eta)]\alpha(c/\sigma)^2$}
If a hole gains mass $\Delta M_{\rm BH}$ at constant radiative efficiency $\eta=L/(\dot M_{\rm in}c^2)$, the radiated energy is $\eta\Delta M_{\rm BH}c^2/(1-\eta)$. For negligible seed mass, final hole mass $\alpha M$, and total three-dimensional <galaxy> dispersion $\sigma$, its ratio to $|W|\simeq M\sigma^2$ is $\eta\alpha(c/\sigma)^2/(1-\eta)$. The net virial unbinding energy is half $|W|$ when surface terms are negligible.
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