  The advent of the Gaia era has led to potentially revolutionary understanding
of dark matter (DM) dynamics in our galaxy, which has important consequences
for direct detection (DD) experiments. In this paper, we study how the
empirical DM velocity distribution inferred from Gaia-Sausage, a dominant
substructure in the solar neighborhood, affects the interpretation of DD data.
We survey different classes of operators in the non-relativistic effective
field theory that could arise from several relativistic benchmark models and
emphasize that the Gaia velocity distribution could modify both the total
number of events as well as the shape of the differential recoil spectra, the
two primary observables in DD experiments. Employing the euclideanized signal
method, we investigate the effects of the Gaia distribution on reconstructing
DM model parameters and identifying the correct DM model given a positive
signal at future DD experiments. We find that for light DM with mass ~10 GeV,
the Gaia distribution poses an additional challenge for characterizing DM
interactions with ordinary matter, which may be addressed by combining
complementary DD experiments with different targets and lowering the detection
threshold. Meanwhile, for heavy DM with mass above ~30 GeV, depending on the
type of DM model, there could be a (moderate) improvement in the sensitivity at
future DD experiments.
