Angular-momentum-conserving self-gravitating disc radius
= Angular-momentum-conserving self-gravitating disc radius
{title2=$R_h/R_d=C_df_d/q^2$}
Let a disc contain fraction $f_d$ of total halo mass, take its edge gravity to be $v_d^2=C_dGM_d/R_d$, and equate its edge specific angular momentum to $qR_hv_{\rm vir}$. With $v_{\rm vir}^2=GM_h/R_h$, these conditions give $R_h/R_d=C_df_d/q^2$. The structural coefficient $C_d$ is essential: disc mass alone does not uniquely determine its edge rotation curve.