Predicting infall time of Milky Way satellites via machine learning

The properties of dwarf galaxies provide essential insight into galaxy formation and evolution in a hierarchical universe. Among various physical quantities, identifying their infall times to host galaxies is crucial, as these times encode key information such as star formation histories. However, estimating infall times remains challenging due to the complex interplay between different physical processes and the lack of consensus among existing methods. We propose a fast and interpretable method to predict the infall time of dwarf satellites using LightGBM, a gradient-boosting decision tree algorithm. Our model is trained on satellites from 30 Milky Way (MW)-like host galaxies generated by A-SLOTH, a semi-analytic model calibrated using observational constraints, including those from the MW and its satellites. To balance predictive ability and observational applicability, we adopt $\tau _{90}$, [Fe/H], and $M_{\star }$ as input features. Since satellites with prior group membership hinder accurate MW infall predictions, we exclude them from the training data. As a result, the model achieves the best average mean squared error (MSE) of 5.04 in the A-SLOTH dataset. Our model also shows good agreement with existing observational studies of MW satellites, although some discrepancies remain due to a few outliers such as CVn II and UMa I. In addition, for satellites experiencing prior infall events before MW-like host infall, the model predicts the timing of the first infall with a significantly lower MSE of 1.66, indicating the importance of the earliest infall in the quenching process of satellite galaxies.