Principal Component Abundance Analysis of Microlensed Bulge Dwarf and
  Subgiant Stars
  Elemental abundance patterns can provide vital clues to the formation and
enrichment history of a stellar population. Here we present an investigation of
the Galactic bulge, where we apply principal component abundance analysis
(PCAA)---a principal component decomposition of relative abundances [X/Fe]---to
a sample of 35 microlensed bulge dwarf and subgiant stars, characterizing their
distribution in the 12-dimensional space defined by their measured elemental
abundances. The first principal component PC1, which suffices to describe the
abundance patterns of most stars in the sample, shows a strong contribution
from alpha-elements, reflecting the relative contributions of Type II and Type
Ia supernovae. The second principal component PC2 is characterized by a Na--Ni
correlation, the likely product of metallicity-dependent Type II supernova
yields. The distribution in PC1 is bimodal, showing that the bimodality
previously found in the [Fe/H] values of these stars is robustly and
independently recovered by looking at only their relative abundance patterns.
The two metal-rich stars that are alpha-enhanced have outlier values of PC2 and
PC3, respectively, further evidence that they have distinctive enrichment
histories. Applying PCAA to a sample of local thin and thick disk dwarfs yields
a nearly identical PC1; in PC1, the metal-rich and metal-poor bulge dwarfs
track kinematically selected thin and thick disk dwarfs, respectively,
suggesting broadly similar alpha-enrichment histories. However, the disk PC2 is
dominated by a Y--Ba correlation, likely indicating a greater contribution of
s-process enrichment from long-lived asymptotic giant branch stars that is
absent from the bulge PC2 because of its rapid formation.
