Local Group Analogs in $Λ$CDM cosmological simulations
We use semi-analytic galaxy catalogs based on two high-resolution cosmological $N$-body simulations, Millennium-WMAP7 and Millennium-II, to investigate the formation of the Local Group (LG) analogs. Unlike previous studies, we use the observed stellar masses to select the LG member (Milky Way (MW) and M31) analogs, and then impose constrains using the observed separation, isolation, and kinematics of the two main member galaxies. By comparing radial and low-ellipticity orbits between the MW and M31, we find higher tangential velocity results in higher total mass, which are 4.4$^{+2.4}_{-1.5}\times$10$^{12}\rm M_{\odot}$ and 6.6$^{+2.7}_{-1.5}\times$10$^{12}\rm M_{\odot}$ for radial and low-ellipticity orbits. The orbits also influence the individual mass distribution of MW and M31 analogs. For radial orbits, the typical host halo masses of the MW and M31 are 1.5$^{+1.4}_{-0.7}\times$10$^{12}\rm M_{\odot}$ and 2.5$^{+1.3}_{-1.1}\times$10$^{12}\rm M_{\odot}$; for low-ellipticity orbits, the masses are 2.5$^{+2.2}_{-1.4}\times$10$^{12}\rm M_{\odot}$ and 3.8$^{+2.8}_{-1.8}\times$10$^{12} \rm M_{\odot}$. The LG is located primarily in filaments with tails extending toward higher densities up to $δ\sim4.5$. The dark matter velocity anisotropy parameters $β$ of both the MW and M31 analogs are close to zero in the center, increasing to 0.2--0.3 at 50--80 kpc and decreasing slowly outward. The slope is much flatter than computed from the MW satellites, and the amplitude is smaller than traced by halo stars. Values of $β$ from different tracers agree at $\sim$120 kpc where $β\sim$ 0.2. We also find that model predictions agree broadly with observations in the radial distribution and luminosity function of satellites around the MW and M31.