= Isothermal-galaxy momentum-balance shell threshold
{title2=$M_{\rm BH,crit}\propto f(1-f)\sigma^4$}
A swept gas shell of fraction $f$ at radius $R$ in a <galaxy> of one-dimensional dispersion $\sigma$ has mass $2f\sigma^2R/G$. Interior non-gas gravity supplies weight $4f(1-f)\sigma^4/G$. Fully intercepted single-scattering Eddington <momentum> overcomes it when $M_{\rm BH}>f(1-f)\sigma^4\sigma_T/(\pi m_pG^2)$. This neglects shell <self-gravity>, central-hole gravity and stored outward <kinetic energy>; weaker coupling raises the required <luminosity>.
Back to article page
