Halo density estimate of formation redshift
= Halo density estimate of formation redshift
{title2=$1+z_f\simeq[\rho_h/(\Delta_{\rm vir}\bar\rho_{m,0})]^{1/3}$}
If a halo retains the mean density acquired at collapse, $3M/(4\pi R^3)=\Delta_{\rm vir}\bar\rho_{m,0}(1+z_f)^3$ estimates its formation redshift. In the non-dissipative <spherical-collapse model> during matter domination, $\Delta_{\rm vir}=18\pi^2$. Subsequent mass growth, profile evolution and the reference-density convention limit this inference.