We use a large sample of isolated dark matter halo pairs drawn from cosmological N-body simulations to identify candidate systems whose kinematics match that of the Local Group of Galaxies (LG). We find, in agreement with the timing argument and earl
ier work, that the separation and approach velocity of the Milky Way (MW) and Andromeda (M31) galaxies favour a total mass for the pair of $sim 5times 10^{12} ,M_{odot}$. A mass this large, however, is difficult to reconcile with the small relative tangential velocity of the pair, as well as with the small deceleration from the Hubble flow observed for the most distant LG members. Halo pairs that match these three criteria have average masses a factor of $sim 2$ times smaller than suggested by the timing argument, but with large dispersion. Guided by these results, we have selected $12$ halo pairs with total mass in the range $1.6$-$3.6 times 10^{12},M_{odot}$ for the APOSTLE project (A Project Of Simulating The Local Environment), a suite of hydrodynamical resimulations at various numerical resolution levels (reaching up to $sim10^{4},M_{odot}$ per gas particle) that use the subgrid physics developed for the EAGLE project. These simulations reproduce, by construction, the main kinematics of the MW-M31 pair, and produce satellite populations whose overall number, luminosities, and kinematics are in good agreement with observations of the MW and M31 companions. The APOSTLE candidate systems thus provide an excellent testbed to confront directly many of the predictions of the $Lambda$CDM cosmology with observations of our local Universe.
Current models of galaxy formation predict that galaxy pairs of comparable magnitudes should become increasingly rare with decreasing luminosity. This seems at odds with the relatively high frequency of pairings among dwarf galaxies in the Local Grou
p. We use literature data to show that ~30% of all satellites of the Milky Way and Andromeda galaxies brighter than M_V=-8 are found in likely physical pairs of comparable luminosity. Besides the previously recognised pairings of the Magellanic Clouds and of NGC 147/NGC 185, other candidate pairs include the Ursa Minor and Draco dwarf spheroidals, as well as the And I/And III satellites of M31. These pairs are much closer than expected by chance if the radial and angular distributions of satellites were uncorrelated; in addition, they have very similar line-of-sight velocities and luminosities that differ by less than three magnitudes. In contrast, the same criteria pair fewer than 4% of satellites in N-body/semi-analytic models that match the radial distribution and luminosity function of Local Group satellites. If confirmed in studies of larger samples, the high frequency of dwarf galaxy pairings may provide interesting clues to the formation of faint galaxies in the current cosmological paradigm.
