On the mass of the Local Group
  We use recent proper motion measurements of the tangential velocity of M31,
along with its radial velocity and distance, to derive the likelihood of the
sum of halo masses of the Milky Way and M31. This is done using a sample halo
pairs in the Bolshoi cosmological simulation of $\Lambda$CDM cosmology selected
to match properties and environment of the Local Group. The resulting
likelihood gives estimate of the sum of masses of $M_{\rm MW,200}+M_{\rm
M31,200}=$ $2.40_{-1.05}^{+1.95}\times10^{12}\,M_{\odot}$ ($90\%$ confidence
interval). This estimate is consistent with individual mass estimates for the
Milky Way and M31 and is consistent, albeit somewhat on the low side, with the
mass estimated using the timing argument. We show that although the timing
argument is unbiased on average for all pairs, for pairs constrained to have
radial and tangential velocities similar to that of the Local Group the
argument overestimates the sum of masses by a factor of $1.6$. Using similar
technique we estimate the total dark matter mass enclosed within $1$ Mpc from
the Local Group barycenter to be $M_{\rm LG}(r<1\, {\rm
Mpc})=4.2_{-2.0}^{+3.4}\times10^{12}\,M_{\odot}$ ($90\%$ confidence interval).
