Reconstructing the Accretion History of the Galactic Stellar Halo from
  Chemical Abundance Ratio Distributions
  Observational studies of halo stars during the last two decades have placed
some limits on the quantity and nature of accreted dwarf galaxy contributions
to the Milky Way stellar halo by typically utilizing stellar phase-space
information to identify the most recent halo accretion events. In this study we
tested the prospects of using 2-D chemical abundance ratio distributions
(CARDs) found in stars of the stellar halo to determine its formation history.
First, we used simulated data from eleven "MW-like" halos to generate satellite
template sets of 2-D CARDs of accreted dwarf satellites which are comprised of
accreted dwarfs from various mass regimes and epochs of accretion. Next, we
randomly drew samples of $\sim10^{3-4}$ mock observations of stellar chemical
abundance ratios ([$\alpha$/Fe], [Fe/H]) from those eleven halos to generate
samples of the underlying densities for our CARDs to be compared to our
templates in our analysis. Finally, we used the expectation-maximization
algorithm to derive accretion histories in relation to the satellite template
set (STS) used and the sample size. For certain STS used we typically can
identify the relative mass contributions of all accreted satellites to within a
factor of 2. We also find that this method is particularly sensitive to older
accretion events involving low-luminous dwarfs e.g. ultra-faint dwarfs -
precisely those events that are too ancient to be seen by phase-space studies
of stars and too faint to be seen by high-z studies of the early Universe.
Since our results only exploit two chemical dimensions and near-future surveys
promise to provide $\sim6-9$ dimensions, we conclude that these new
high-resolution spectroscopic surveys of the stellar halo will allow us to
recover its accretion history - and the luminosity function of infalling dwarf
galaxies - across cosmic time.
