Eddington-regulated galactic gas balance
= Eddington-regulated galactic gas balance
{c}
{title2=$M_{s,\max}=\Phi/A$}
For an Eddington-luminous hole with $M_{\rm BH}=\beta M_s$ and wind mass flux $\lambda L$, define $A=\lambda\beta(4\pi Gm_pc/\sigma_T)$. The gas budget $\dot M_g=\Phi-\epsilon M_g-A M_s$ has positive instantaneous balance only for $M_s<\Phi/A$. A positive constant-gas trajectory is incompatible with ongoing $\dot M_s=\epsilon M_g$ unless the secular black-hole coupling is neglected.