The Pristine Dwarf Galaxy Survey -- VII. The metallicity distributions of 12 Milky Way faint satellites
Spectroscopic studies of ultra-faint dwarf galaxies are typically limited to small samples of stars due to the scarcity of sufficiently bright targets. The small number statistics and possible presence of contaminants still hamper solid determinations of their metallicity distribution function. In this work, we characterise the metallicity distributions of 12 Milky Way faint satellites by exploiting deep narrow-band CaHK photometry from the Pristine dwarf galaxy survey. In order to derive accurate stellar photometric metallicities, we combined it with deep broad-band g and r photometry from Mu\~noz et al. (2018) and Pan-STARRS1, covering each system out to 5-8 times their half-light radius Rh, and reaching magnitudes as faint as g~23. Membership probabilities were determined incorporating the available spatial, photometric, astrometric, and spectroscopic information, further refined using the derived photometric metallicities. We identified 3917 probable member stars across the 12 systems, more than doubling the numbers recovered by previous spectroscopic studies. We deliver complete metallicity distributions that yield robust average metallicities and dispersions previously inaccessible for most of the systems examined in this study. We identify 170 candidate extremely metal-poor stars distributed across all systems, and confirm a departure from the linear luminosity-metallicity relation in the ultra-faint regime, with systems scattering around [Fe/H]~-2.3 dex. Given the extensive mass coverage of our sample, we were able to investigate the presence of metallicity gradients, finding clear evidence of radial variations in massive systems, but none in the ultra-faint dwarfs within 2.5xRh. The photometric strategy presented in this paper will continue to serve as an effective complement to future spectroscopic surveys.