The age distribution of stars in the Milky Way bulge
  The age and chemical characteristics of the Galactic bulge link to the
formation and evolutionary history of the Galaxy. Data-driven methods and large
surveys enable stellar ages and precision chemical abundances to be determined
for vast regions of the Milky Way, including the bulge. Here, we use the
data-driven approach of The Cannon, to infer the ages and abundances for
125,367 stars in the Milky Way, using spectra from Apache Point Observatory
Galaxy Evolution Experiment (APOGEE) DR14. We examine the ages and
metallicities of 1654 bulge stars within $R_{\text{GAL}}<3.5$ kpc. We focus on
fields with $b<12^\circ$, and out to longitudes of $l<15^\circ$. We see that
stars in the bulge are about twice as old ($\tau=8$ Gyrs), on average, compared
to those in the solar neighborhood ($\tau=4$ Gyrs), with a larger dispersion in
[Fe/H] ($\approx0.38$ compared to 0.23 dex). This age gradient comes primarily
from the low-$\alpha$ stars. Looking along the Galactic plane, the very central
field in the bulge shows by far the largest dispersion in [Fe/H]
($\sigma_{[Fe/H]}\approx0.4$ dex) and line of sight velocity
($\sigma_{vr}\approx90$ km/s), and simultaneously the smallest dispersion in
age. Moving out in longitude, the stars become kinematically colder and less
dispersed in [Fe/H], but show a much broader range of ages. We see a signature
of the X-shape within the bulge at a latitude of $b=8^\circ$, but not at
$b=12^\circ$. Future APOGEE and other survey data, with larger sampling,
affords the opportunity to extend our approach and study in more detail, to
place stronger constraints on models of the Milky Way.
