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 } M _ { \odot } and 6.6 ^ { +2.7 } _ { -1.5 } \times 10 ^ { 12 } 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 } M _ { \odot } and 2.5 ^ { +1.3 } _ { -1.1 } \times 10 ^ { 12 } M _ { \odot } ; for low-ellipticity orbits , the masses are 2.5 ^ { +2.2 } _ { -1.4 } \times 10 ^ { 12 } M _ { \odot } and 3.8 ^ { +2.8 } _ { -1.8 } \times 10 ^ { 12 } M _ { \odot } .
The LG is located primarily in filaments with tails extending toward higher densities up to \delta \sim 4.5 .
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 .