= Dynamical upper bound on black-hole fuelling
For a <singular isothermal sphere> of dispersion $\sigma$ and gas fraction $f_g$, placing all gas inside radius $R$ onto a hole in time $R/\sigma$ gives $\dot M_{\rm dyn}\sim2f_g\sigma^3/G$. This is an optimistic supply bound that omits <angular momentum> transport, <star formation>, and <active-galactic-nucleus feedback>. A numerical comparison with the <Eddington accretion rate> requires a gas fraction, reference radiative efficiency, opacity, and crossing-time convention.
Back to article page
