Tracing stars in Milky Way satellites with A-SLOTH

We study the stellar mass-to-halo mass relation at $z=0$ in 30 Milky Way-like systems down to the ultra-faint ($M_* < 10^5 M_\odot$) regime using the semi-analytic model A-SLOTH. A new model allows us to follow star formation and the stochastic stellar feedback from individually sampled Pop II stars. Our fiducial model produces consistent results with the stellar mass-to-halo mass relation derived from abundance matching and the observed cumulative stellar mass function above the observational completeness. We find a plateau in the stellar mass-to-halo mass relation in the ultra-faint regime. The stellar mass of this plateau tells us how many stars formed before supernovae occur and regulate further star formation, which is determined by the Pop~II star formation efficiency. We also find that the number of luminous satellites increases rapidly as $M_*$ decreases until $M_* \approx 10^4 M_\odot$. Finally, we find that the relative streaming velocity between baryons and dark matter at high redshift is important in determining the number of ultra-faint dwarf galaxies at $z=0$. The new model in A-SLOTH provides a framework to study the stellar properties and the formation history of metal-poor stars in Milky Way and its satellites.