Virial velocity of a spherical-overdensity halo
= Virial velocity of a spherical-overdensity halo
{title2=$v_{\rm vir}=H(z)R_h\sqrt{\Delta_v/2}$}
For halo mean density $\Delta_v$ times the <critical density> at its epoch, the circular virial velocity obeys $v_{\rm vir}^2=GM_h/R_h=(\Delta_v/2)H^2R_h^2$. Thus $v_{\rm vir}=HR_h\sqrt{\Delta_v/2}$. Specifying whether overdensity is relative to mean matter or <critical density> is necessary for numerical inference.