Large spectroscopic surveys plus Gaia astrometry have shown us that the inner
stellar halo of the Galaxy is dominated by the debris of Gaia Enceladus/Sausage
(GES). With the richness of data at hand, there are a myriad of ways these
accreted stars have been selected. We investigate these GES selections and
their effects on the inferred progenitor properties using data constructed from
APOGEE and Gaia. We explore selections made in eccentricity, energy-angular
momentum (E-Lz), radial action-angular momentum (Jr-Lz), action diamond, and
[Mg/Mn]-[Al/Fe] in the observations, selecting between 144 and 1,279 GES stars
with varying contamination from in-situ and other accreted stars. We also use
the Auriga cosmological hydrodynamic simulations to benchmark the different GES
dynamical selections. Applying the same observational GES cuts to nine Auriga
galaxies with a GES, we find that the Jr-Lz method is best for sample purity
and the eccentricity method for completeness. Given the average metallicity of
GES (-1.28 < [Fe/H] < -1.18), we use the z=0 mass-metallicity relationship to
find an average Mββ of βΌ4Γ108Mββ. We
adopt a similar procedure and derive Mββ for the GES-like systems
in Auriga and find that the eccentricity method overestimates the true Mββ by βΌ2.6Γ while E-Lz underestimates by βΌ0.7Γ.
Lastly, we estimate the total mass of GES to be 1010.5β11.1Β Mββ using the relationship between the metallicity gradient and
the GES-to-in-situ energy ratio. In the end, we cannot just `pick and choose'
how we select GES stars, and instead should be motivated by the science
question.Comment: 20 pages, 14 figures, submitted to MNRA