  We characterize the Gaia-Enceladus-Sausage kinematic structure recently
discovered in the Galactic halo using photometric metallicities from the
SkyMapper survey, and kinematics from Gaia radial velocities measurements. By
examining the metallicity distribution functions (MDFs) of stars binned in
kinematic/action spaces, we find that the $\sqrt{J_R}$ vs $L_z$ space allows
for the cleanest selection of Gaia-Enceladus-Sausage stars with minimal
contamination from disc or halo stars formed in situ or in other past mergers.
Stars with $30 \leq \sqrt{J_R} \leq 50$ (kpc km s$^{-1})^{1/2}$ and $-500 \leq
L_z \leq 500$ kpc km s$^{-1}$ have a narrow MDF centered at [Fe/H] $= -1.17$
dex with a dispersion of 0.34 dex. This [Fe/H] estimate is more metal-rich than
literature estimates by $0.1-0.3$ dex. Based on the MDFs, we find that
selection of Gaia-Enceladus-Sausage stars in other kinematic/action spaces
without additional population information leads to contaminated samples. The
clean Gaia-Enceladus-Sausage sample selected according to our criteria is
slightly retrograde and lies along the blue sequence of the high $V_T$ halo CMD
dual sequence. Using a galaxy mass-metallicity relation derived from
cosmological simulations and assuming a mean stellar age of 10 Gyr we estimate
the mass of the Gaia-Enceladus-Sausage progenitor satellite to be
$10^{8.85-9.85}$ M$_{\odot}$, which is consistent with literature estimates
based on disc dynamic and simulations. Additional information on detailed
abundances and ages would be needed for a more sophisticated selection of
purely Gaia-Enceladus-Sausage stars.
