The Low-Mass Stellar Initial Mass Function in Nearby Ultra-Faint Dwarf Galaxies

The stellar initial mass function (IMF) describes the distribution of stellar masses that form in a given star-formation event. The long main-sequence lifetimes of low-mass stars mean that the IMF in this regime (below ∼ 1 M_⊙) can be investigated through star counts. Ultra-faint dwarf galaxies are low luminosity systems with ancient, metal poor stellar populations. We investigate the low-mass IMF in four such systems (Reticulum II, Ursa Major II, Triangulum II, and Segue 1), using Hubble Space Telescope imaging data that reaches to ≲ 0.2 M_⊙ in each galaxy. The analysis techniques that we adopt depend on the number of low-mass stars in each sample. We use Kolmogorov-Smirnov tests for all four galaxies to determine whether their observed apparent magnitude distributions can reject a given combination of IMF parameters and binary fraction for the underlying population. We forward model a thousand synthetic populations for each combination of parameters, and reject those parameters only if each of the thousand realizations reject the null hypothesis. We find that all four galaxies reject a variety of IMFs, and the IMFs that they cannot reject include those that are identical, or similar, to that of the stellar populations of the Milky Way. We determine the best-fit parameter values for the IMF in Reticulum II and Ursa Major II and find that the IMF in Reticulum II is generally consistent with that of the Milky Way, while the IMF in Ursa Major II is more bottom-heavy. The interpretation of the results for Ursa Major II is complicated by possible contamination from two known background galaxy clusters.