# Orbits of massive satellite galaxies: II. Bayesian Estimates of the Milky Way and Andromeda masses using high precision astrometry and cosmological simulations

## TL;DR

This paper introduces a Bayesian method using high-precision astrometry and cosmological simulations to estimate the masses of the Milky Way and Andromeda galaxies more reliably by focusing on the conserved orbital angular momentum of their satellites.

## Contribution

The study presents a novel Bayesian inference approach that leverages satellite orbital angular momentum to improve galaxy mass estimates, reducing bias and uncertainty.

## Key findings

- Orbital angular momentum (j) provides a more stable mass constraint than current position and velocity.
- Estimated masses: MW ≈ 1.02×10^{12} M_⊙, M31 ≈ 1.37×10^{12} M_⊙.
- M33's orbital history suggests M31's virial mass is around 10^{12} M_⊙.

## Abstract

Space observatories like the Hubble Space Telescope and Gaia are providing unprecedented 6D phase space information of satellite galaxies. Such measurements can shed light on the structure and assembly history of the Local Group, but improved statistical methods are needed to use them efficiently. Here we illustrate such a method using analogs of the Local Group's two most massive satellite galaxies, the Large Magellanic Cloud (LMC) and Triangulum (M33), from the Illustris dark-matter-only cosmological simulation. We use a Bayesian inference scheme combining measurements of positions, velocities, and specific orbital angular momenta ( j ) of the LMC/M33 with importance sampling of their simulated analogs to compute posterior estimates of the Milky Way (MW) and Andromeda's (M31) halo masses. We conclude the resulting host halo mass is more susceptible to bias when using measurements of the current position and velocity of satellites, especially when satellites are at short-lived phases of their orbits (i.e. at pericentre). Instead, the j value of a satellite is well-conserved over time and provides a more reliable constraint on host mass. The inferred virial mass of the MW (M31) using j of the LMC (M33) is $\rm M_{vir, MW}=1.02^{+0.77}_{-0.55}\times10^{12}\; M_{\odot}$ ($\rm M_{vir, M31}=1.37^{+1.39}_{-0.75}\times10^{12}\; M_{\odot}$). Choosing simulated analogs whose j values are consistent with the conventional picture of a previous (< 3 Gyr ago), close encounter (< 100 kpc) of M33 about M31 results in a very low virial mass for M31 ($\rm\sim\!10^{12}\; M_{\odot}$). This supports the new scenario put forth in Patel et al. (2017), wherein M33 is on its first passage about M31 or on a long period orbit. We conclude that this Bayesian inference scheme, utilising satellite j, is a promising method to reduce the current factor of two spread in the mass range of the MW and M31 moving forward.