A simulation-based inference of the Milky Way merger history

Abstract

Accreted stars in the Milky Way (MW) preserve information about the progenitor galaxies where they formed in their chemical and kinematic properties. In this study, we use the chemo-dynamical signatures in the merger debris to approximate the posterior distribution of disrupted satellite properties at the time of infall. Adopting a simulation-based inference framework, we train an ensemble of normalizing flows using samples of merger debris from the Auriga suite of simulations of MW-like galaxies. Applying this methodology to a local sample of accreted stars in the MW, we infer the lookback times, stellar and halo masses, and halo mass merger ratios of several known accretion events in the Galaxy: Gaia Enceladus-Sausage (GES), Helmi streams, Heracles, I'itoi, LMS-1/Wukong, Sagittarius (Sgr), Sequoia and Thamnos. Our predictions align with the accretion time and mass estimates from the literature, and the expected relation between the progenitor stellar masses and debris metallicities across redshifts. The total stellar mass accreted from these events is predicted to be $2.2^{+1.1}_{-0.6}\times10^{9}~\rm{M_{\odot}}$, with GES and Sgr being the largest contributors. The predicted stellar mass accreted from fully disrupted progenitors in the stellar halo is $1.3^{+1.0}_{-0.5}\times10^{9}~\rm{M_{\odot}}$, which is consistent with previous mass measurements of this component. We provide a prediction for the evolution of the MW halo mass until the accretion of Sgr ($z\approx1$): specifically, we find that the mass growth of the Galaxy from the time of its first merger ($z\approx5$) to $z\approx2$ exceeds the total mass of the known progenitors accreted during that interval, suggesting the presence of unidentified substructures. Our estimate of the Galaxy halo mass after the Sgr merger, but prior to the accretion of the Magellanic Clouds, is $5.9^{+1.4}_{-1.1}\times10^{11}~\rm{M_{\odot}}$.

Figures (12)

• Figure 1: Distribution of the orbital properties ($E$ and $L_{z}$) of the accreted stars in the solar neighbourhood of the MW. The accreted stars are grouped by the proposed progenitor galaxy in which they formed, according to the criteria of Horta_2023, and are plotted on top of the overall distribution of stars in the APOGEE sample from which they were selected.
• Figure 2: Chemical abundance ratios ([Mg/Fe] and [Fe/H]) distribution for the same samples of stars plotted in Fig. \ref{['fig:IoM']}.
• Figure 3: Relations between data, $\bm{x}$, and parameters, $\bm{\theta}$ for the the model, $\mathcal{M}$, describing the relation between merger and debris properties, and the calibration model, $\mathcal{C}$, describing the difference between simulated and observed stellar properties. The parameters referring to each model are indicated by dashed boxes.
• Figure 4: Chemo-dynamical properties of the accreted star particles from the Auriga simulations used to train the posterior estimator (blue) and of the stars in the MW parent sample obtained from the APOGEE and Gaia surveys (red). The distribution of the MW stars belonging to the accreted substructures considered is also shown (pink). The distributions are normalised by the total amount of samples.
• Figure 5: Outline of the pipeline used for the modelling of the posterior distribution of the properties of merger events, $\bm{\theta}$, from the observed $z=0$ chemo-dynamical properties of their debris, $\bm{\hat{x}}$.