Live Fast, Die $\alpha$-Enhanced: The Mass-Metallicity-$\alpha$ Relation of the Milky Way's Disrupted Dwarf Galaxies

The Milky Way's satellite galaxies ("surviving dwarfs") have been studied for decades as unique probes of chemical evolution in the low-mass regime. Here we extend such studies to the "disrupted dwarfs", whose debris constitutes the stellar halo. We present abundances ([Fe/H], [$\alpha$/Fe]) and stellar masses for nine disrupted dwarfs with $M_{\star}\approx10^{6}-10^{9}M_{\odot}$ from the H3 Survey (Sagittarius, $Gaia$-Sausage-Enceladus, Helmi Streams, Sequoia, Wukong/LMS-1, Cetus, Thamnos, I'itoi, Orphan/Chenab). The surviving and disrupted dwarfs are chemically distinct: at fixed mass, the disrupted dwarfs are systematically metal-poor and $\alpha$-enhanced. The disrupted dwarfs define a mass-metallicity relation (MZR) with a similar slope as the $z=0$ MZR followed by the surviving dwarfs, but offset to lower metallicities by $\Delta$[Fe/H]$\approx0.3-0.4$ dex. Dwarfs with larger offsets from the $z=0$ MZR are more $\alpha$-enhanced. In simulations as well as observations, galaxies with higher $\Delta$[Fe/H] formed at higher redshifts -- exploiting this, we infer the disrupted dwarfs have typical star-formation truncation redshifts of $z_{\rm{trunc}}{\sim}1-2$. We compare the chemically inferred $z_{\rm{trunc}}$ with dynamically inferred accretion redshifts and find almost all dwarfs are quenched only after accretion. The differences between disrupted and surviving dwarfs are likely because the disrupted dwarfs assembled their mass rapidly, at higher redshifts, and within denser dark matter halos that formed closer to the Galaxy. Our results place novel archaeological constraints on low-mass galaxies inaccessible to direct high-$z$ studies: (i) the redshift evolution of the MZR along parallel tracks but offset to lower metallicities extends to $M_{\star}\approx10^{6}-10^{9}M_{\odot}$; (ii) galaxies at $z\approx2-3$ are $\alpha$-enhanced with [$\alpha$/Fe]$\approx0.4$.