= Constant-radius accretion energy budget
{title2=$E_{\rm acc}=G(M^2-M_s^2)/(2r_0)$}
Integrating $L_{\rm acc}=GM\dot M/r_0$ at fixed radius gives this result. With negligible seed <mass> it supplies the radiative requirement of monatomic cloud collapse only if $\Omega_f=-GM^2/r_0$ under the adopted zero-initial-energy approximation. A different density-profile coefficient, retained <accretion> heat, a wind or a changing radius modifies the budget. Positive binding-energy magnitude and negative potential <energy> must not be interchanged silently.
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