The stellar mass of the Gaia-Sausage/Enceladus accretion remnant

The \textit{Gaia}-Sausage/Enceladus (GS/E) structure is an accretion remnant which comprises a large fraction of the Milky Way's stellar halo. We study GS/E using high-purity samples of kinematically selected stars from APOGEE DR16 and \textit{Gaia}. Employing a novel framework to account for kinematic selection biases using distribution functions, we fit density profiles to these GS/E samples and measure their masses. We find that GS/E has a shallow density profile in the inner Galaxy, with a break between 15--25~kpc beyond which the profile steepens. We also find that GS/E is triaxial, with axis ratios 1:0.55:0.45 (nearly prolate), and the major axis is oriented about 80~degrees from the Sun--Galactic centre line and 16 degrees above the plane. We measure a stellar mass for GS/E of $1.45\,^{+0.92}_{-0.51}\,\mathrm{(stat.)}\,^{+0.13}_{-0.37} \mathrm{(sys.)}\ \times10^{8}$~\Msun. Our mass estimate is lower than others in the literature, a finding we attribute to the excellent purity of the samples we work with. We also fit a density profile to the entire Milky Way stellar halo, finding a mass in the range of $6.7-8.4 \times 10^{8}$~\Msun, and implying that GS/E could make up as little as 15-25~per~cent of the mass of the Milky Way stellar halo. Our lower stellar mass combined with standard stellar-mass-to-halo mass relations implies that GS/E constituted a minor 1:8 mass-ratio merger at the time of its accretion.