The Pristine Inner Galaxy Survey (PIGS) IV: A photometric metallicity analysis of the Sagittarius dwarf spheroidal galaxy

We present a comprehensive metallicity analysis of the Sagittarius dwarf spheroidal galaxy (Sgr dSph) using $Pristine\,CaHK$ photometry. We base our member selection on $Gaia$ EDR3 astrometry applying a magnitude limit at $G_{0} = 17.3$, and our population study on the metallicity-sensitive photometry from the $Pristine$ Inner Galaxy Survey (PIGS). Working with photometric metallicities instead of spectroscopic metallicities allows us to cover an unprecedented large area ($\sim 100$ square degrees) of the dwarf galaxy, and to study the spatial distribution of its members as function of metallicity with little selection effects. Our study compares the spatial distributions of a metal-poor population of 9719 stars with [Fe/H] $< -1.3$ and a metal rich one of 30115 stars with [Fe/H] $> -1.0$. The photometric Sgr sample also allows us to assemble the largest sample of 1150 very metal-poor Sgr candidates ([Fe/H] $< -2.0$). By investigating and fitting the spatial properties of the metal-rich and metal-poor population, we find a negative metallicity gradient which extends up to 12 degrees from the Sgr center (or $\sim 5.5$ kpc at the distance of Sgr), the limit of our footprint. We conclude that the relative number of metal-poor stars increases in the outer areas of the galaxy, while the central region is dominated by metal-rich stars. These finding suggest an outside-in formation process and are an indication of the extended formation history of Sgr, which has been affected by the tidal interaction between Sgr and the Milky Way.