How Many Components? Quantifying the Complexity of the Metallicity
  Distribution in the Milky Way Bulge with APOGEE
  We use data of $\sim$13,000 stars from the SDSS/APOGEE survey to study the
shape of the bulge MDF within the region $|\ell|\leq11^\circ$ and
$|b|\leq13^\circ$, and spatially constrained to ${\rm R_{GC}\leq3.5}$ kpc. We
apply Gaussian Mixture Modeling and Non-negative Matrix Factorization
decomposition techniques to identify the optimal number and the properties of
MDF components. We find the shape and spatial variations of the MDF (at ${\rm
[Fe/H]\geq-1}$ dex) are well represented as a smoothly varying contribution of
three overlapping components located at [Fe/H]=+$0.32$, $-0.17$ and $-0.66$
dex. The bimodal MDF found in previous studies is in agreement with our
trimodal assessment once the limitations in sample size and individual
measurement errors are taken into account. The shape of the MDF and its
correlations with kinematics reveal different spatial distributions and
kinematical structure for the three components co-existing in the bulge region.
We confirm the consensus physical interpretation of metal-rich stars as
associated with the secularly evolved disk into a boxy/peanut X-shape bar. On
the other hand, metal-intermediate stars could be the product of in-situ
formation at high redshift in a gas-rich environment characterized by violent
and fast star formation. This interpretation would help to link a present-day
structure with those observed in formation in the center of high redshift
galaxies. Finally, metal-poor stars may correspond to the metal-rich tail of
the population sampled at lower metallicity from the study of RR Lyrae stars.
Conversely, they could be associated with the metal-poor tail of the early
thick disc.
