The Local Group Mass in the Light of Gaia

High-accuracy proper motions (PMs) of M31 and other Local Group (LG) satellites have now been provided by the Gaia satellite. We revisit the timing argument to compute the total mass M of the LG from the orbit of the Milky Way and M31, allowing for the cosmological constant. We rectify a systematic effect caused by the presence of the Large Magellanic Cloud (LMC). The interaction of the LMC with the Milky Way induces a motion toward the LMC. This contribution to the measured velocity of approach of the Milky Way and M31 must be removed. We allow for cosmic bias and scatter by extracting correction factors tailored to the accretion history of the LG. The distribution of correction factors is centered around 0.63 with a scatter of ±0.2, indicating that the timing argument significantly overestimates the true mass. Adjusting for all these effects, the estimated mass of the LG is $M={3.4}_{-1.1}^{+1.4}\times {10}^{12}{M}_{\odot }$ (68% CL) when using the M31 tangential velocity, ${v}_{\tan }={82}_{-35}^{+38}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Lower tangential velocity models with ${v}_{\tan }={59}_{-38}^{+42}\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (derived from the same PM data with a flat prior on the tangential velocity) lead to an estimated mass of $M={3.1}_{-1.0}^{+1.3}\times {10}^{12}{M}_{\odot }$ (68% CL). By making an inventory of the total mass associated with the four most substantial LG members (the Milky Way, M31, M33, and the LMC), we estimate the known mass to be in the range ${3.7}_{-0.5}^{+0.5}\times {10}^{12}\,{M}_{\odot }$.