Local Group Analogs in $\Lambda$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
$\delta\sim4.5$. The dark matter velocity anisotropy parameters $\beta$ 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 $\beta$ from different tracers agree at $\sim$120 kpc
where $\beta \sim$ 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.
