Rotation curves: a consistency check

Schommer et al. (1992) summarizes the derived rotation curve for clusters, planetary nebulae and HI including the Meatheringham et al. results (see Schommer et al. Fig. 8). Using a luminosity function derived for an exponential disk and typical velocity dispersion in halo with a flat rotation curve, one finds that the circular velocity V_c is roughly 20-30% larger than the rotation value V_o. For a rotation curve with $V_o\approx75$ km/s, one finds a mass within 10.8 kpc of $M\mathrel{\hbox to 0pt{\lower 3pt\hbox{$\mathchar''218$}\hss} \raise 2.0pt\hbox{$\mathchar''13E$}}2\times10^{10}{\rm\,M_\odot}$ which is nicely consistent with the tidal radius estimate. See Schommer et al. for more extensive discussion of these arguments.