Estimating the Mass of the Local Group using Machine Learning Applied to Numerical Simulations

We revisit the estimation of the combined mass of the Milky Way and Andromeda (M31), which dominate the mass of the Local Group. We make use of an ensemble of 30,190 halo pairs from the Small MultiDark simulation, assuming a $\Lambda$CDM (Cosmological Constant with Cold Dark Matter) cosmology, to investigate the relationship between the bound mass and parameters characterising the orbit of the binary and their local environment with the aid of machine learning methods (artificial neural networks, ANN). Results from the ANN are most successful when information about the velocity shear is provided, which demonstrates the flexibility of machine learning to model physical phenomena and readily incorporate new information as it becomes available. The resulting estimate for the Local Group mass, when shear information is included, is $4.9 \times 10^{12} M_\odot$, with an error of $\pm0.8 \times 10^{12} M_\odot$ from the 68% uncertainty in observables, and a 68% confidence interval of $^{+1.3}_{-1.4} \times 10^{12}M_\odot$ from the intrinsic scatter from the differences between the model and simulation masses. We also consider a recently reported large transverse velocity of M31 relative to the Milky Way, and produce an alternative mass estimate of $3.6\pm0.3\pm1.4 \times 10^{12}M_\odot$. Although different methods predict similar values for the most likely mass of the LG, application of ANN compared to the Timing Argument reduces the scatter in the log mass by over half when tested on samples from the simulation.