Dead man tells tales: metallicity distribution of the Milky Way stellar halo reveals the past of the GSE progenitor galaxy

The Gaia-Sausage-Enceladus~(GSE) stands out as the largest known ancient accretion event in the Milky Way~(MW) history. Despite this significance, the parameters of its progenitor galaxy are still poorly constrained. We identify GSE stars from the APOGEE DR17 using Gaussian mixture models and recover a negative radial metallicity gradient for the GSE debris within the MW stellar halo, with a magnitude of $\approx -0.014^{-0.002}_{-0.022}$ dex/kpc. We argue that this gradient reflects the radial metallicity gradient of the GSE galaxy progenitor before it was disrupted by the MW. By investigating the cosmological HESTIA simulations and $N$-body models of galaxy mergers, we constrain the radial metallicity gradient of the GSE-progenitor to be $\approx -0.1^{-0.06}_{-0.15}$ dex/kpc. We, therefore, propose that a chemical tagging of accreted stars using their integrals of motion, although they are not conserved during mergers, provide essential information about the structure and the past of systems accreted onto the MW.