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 the galacto-centric radial velocities of the outer globular clusters and the 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 of $R$$\sim$ 150 kpc are well traced by a rotation curve calculated for the NFW (Navaro, Frenk, White) and Burkert dark halo models. The NFW model indicates that the Galaxy’s mass within 385 kpc, half the distance to M 31, is $\sim$4$\times$10$^{11}M_\odot$. High-velocity ends of the pseudo rotation curve for the entire Local Group up to 1.5 Mpc indicate an isothermal nature with a terminal velocity of $\sim$200 kms$^{-1}$. In order for the Local Group to be gravitationally bound, an order-of-magnitude larger mass than those of the Galaxy and M 31 is required. This fact suggests that the Local Group contains dark matter of mass $\sim$5$\times$10$^{12}M_\odot$, filling the space between the Galaxy and M 31. The mass density of the Galactic dark halo becomes equal to that of the Local Group’s dark matter at $R$$\sim$ 100 kpc, beyond which the intracluster dark matter dominates. If we define the Galaxy’s radius at this distance, the enclosed Galactic mass is $\sim$3$\times$10$^{11}M_\odot$.