  The standard picture of galaxy formation motivates the decomposition of the
Milky Way into 3--4 stellar populations with distinct kinematic and elemental
abundance distributions: the thin disk, thick disk, bulge, and stellar halo. To
test this idea, we construct a Gaussian mixture model (GMM) for both simulated
and observed stars in the Solar neighborhood, using measured velocities and
iron abundances (i.e., an augmented Toomre diagram) as the distributions to be
decomposed. We compare results for the Gaia-APOGEE DR16 crossmatch catalog of
the Solar neighborhood with those from a suite of synthetic Gaia-APOGEE
crossmatches constructed from FIRE-2 cosmological simulations of Milky Way-mass
galaxies. We find that in both the synthetic and real data, the best-fit GMM
uses five independent components, some of whose properties resemble the
standard populations predicted by galaxy formation theory. Two components can
be identified unambiguously as the thin disk and another as the halo. However,
instead of a single counterpart to the thick disk, there are three intermediate
components with different age and alpha abundance distributions (although these
data are not used to construct the model). We use decompositions of the
synthetic data to show that the classified components indeed correspond to
stars with different origins. By analogy with the simulated data, we show that
our mixture model of the real Gaia-APOGEE crossmatch distinguishes the
following components: (1) a classic thin disk of young stars on circular orbits
(46%), (2) thin disk stars heated by interactions with satellites (22%), (3, 4)
two components representing the velocity asymmetry of the alpha-enhanced thick
disk (27%), and (5) a stellar halo consistent with early, massive accretion
(4%).
