Sum of the masses of the Milky Way and M31: A likelihood-free inference approach

We use density estimation likelihood-free inference, $\mathrm{\ensuremath{\Lambda}}$ cold dark matter simulations of $\ensuremath{\sim}2M$ galaxy pairs, and data from Gaia the Hubble Space Telescope to infer sum masses Milky Way Andromeda (M31) galaxies, two main components local group. This method overcomes most approximations traditional timing argument, makes writing a theoretical likelihood unnecessary, allows nonlinear modeling observational errors that take into account correlations in non-Gaussian distributions. obtain an ${M}_{200}$ mass estimate ${M}_{\mathrm{MW}+\mathrm{M}31}=4.{6}_{\ensuremath{-}1.8}^{+2.3}\ifmmode\times\else\texttimes\fi{}{10}^{12}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ (68% C.L.), agreement with previous estimates both for individual masses. result is not only one reliable date, but also illustration inference problem parameter three points.