= Virial pressure-radius curve with uniform-sphere binding energy
{title2=$p_{\rm ext}=A/r^3-B/r^4$}
For fixed cloud <mass> $M$ and isothermal sound speed $c_s$, approximate the binding <energy> by $-3GM^2/(5r)$. The boundary-pressure <virial theorem> gives $A=3Mc_s^2/(4\pi)$ and $B=3GM^2/(20\pi)$. The required external <pressure> peaks at $r_c=4B/(3A)$. A homologous radial displacement is restoring on the branch $dp_{\rm ext}/dr<0$, or $r>r_c$; the smaller-radius positive-pressure branch is unstable. This is a one-radius virial model, not the exact hydrostatic isothermal-sphere sequence.
Back to article page
