Pseudo Rotation Curve connecting the Galaxy, Dark Halo, and Local Group

Abstract

We construct a Galacto-Local Group rotation curve, combining the Galactic rotation curve with a diagram, where galacto-centric radial velocities of outer globular clusters and member galaxies of the Local Group are plotted against their galacto-centric distances. The high-velocity ends of this pseudo rotation curve within a radius R ~ 150 kpc are well traced by a rotation curve calculated for the NFW (Navaro, Frenk, White) and Burkert dark halo models. The NFW model indicates that the Galaxy's mass within 385 kpc, half distance to M31, is ~ 4 x 10^{11}M_{sun}. High-velocity ends of the pseudo rotation curve for the entire Local Group up to 1.5 Mpc indicate isothermal nature with a terminal velocity of ~ 200 km/s. In order for the Local Group to be gravitationally bound, an order of magnitude larger mass than those of the Galaxy and M31 is required. This fact indicates that the Local Group contains dark matter of mass ~ 5 x 10^{12}M_{sun} filling the space between the Galaxy and M31. The mass density of the Galactic dark halo becomes equal to that of the Local Group's dark matter at R ~ 100 kpc, beyond which the intracluster dark matter dominates. If we define the Galaxy's radius at this distance, the enclosed Galactic mass is ~ 3 x 10^{11}M_{sun}. We comment on the barionic matter fraction of galaxies in the Local Group.