= Angular-momentum estimate of a self-gravitating galactic disk
{title2=$R_d/R_h=f_j^2/(\kappa f_d),\quad v_d/v_h=\kappa f_d/f_j$}
Let a disk contain fraction $f_d$ of its host mass and let its edge <specific angular momentum> be $f_jR_hv_h$. With halo relation $v_h^2=GM_h/R_h$ and disk geometry coefficient $\kappa=v_d^2R_d/(GM_d)$, combining centrifugal balance and the edge <angular momentum> gives the displayed estimates. The coefficient records the radial mass profile and thickness: <enclosed mass does not determine a disc rotation curve>. Treating $\kappa=1$ as a monopole estimate must not be mistaken for an exact thin-disk theorem.
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