= Keplerian cluster radius evolution under stellar capture
{c}
{title2=$\dfrac{\dot R}R\simeq(\xi-1)\dfrac\Gamma N-\dfrac{m\Gamma}{M_H}$}
For a homologous <black hole>-dominated cluster, write $E=-bGM_HNm/(2R)$, and let a captured star's specific orbital energy be $\epsilon_{\rm cap}=\xi E/(Nm)$. Removing negative orbital energy raises the remaining cluster energy, while growth $\dot M_H=m\Gamma$ deepens its potential. The energy budget gives the displayed radius response. Preferentially removing strongly bound stars can drive expansion; representative-energy removal instead gives the adiabatic contraction due to black-hole growth. The sign is not fixed by the <loss cone> angle alone.
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