A Parametric Galactic Model toward the Galactic Bulge Based on Gaia and
  Microlensing Data
  We developed a parametric Galactic model toward the Galactic bulge by fitting
to spatial distributions of the Gaia DR2 disk velocity, VVV proper motion,
BRAVA radial velocity, OGLE-III red clump star count, and OGLE-IV star count
and microlens rate, optimized for use in microlensing studies. We include the
asymmetric drift of Galactic disk stars and the dependence of velocity
dispersion on Galactic location in the kinematic model, which has been ignored
in most previous models used for microlensing studies. We show that our model
predicts a microlensing parameter distribution significantly different from
those typically used in previous studies. We estimate various fundamental model
parameters for our Galaxy through our modeling, including the initial mass
function (IMF) in the inner Galaxy. Combined constraints from star counts and
the microlensing event timescale distribution from the OGLE-IV survey, in
addition to a prior on the bulge stellar mass, enable us to successfully
measure IMF slopes using a broken power-law form over a broad mass range,
$\alpha_{\rm bd}=0.22^{+0.20}_{-0.55}$ for $M<0.08\,M_{\odot}$, $\alpha_{\rm
ms} = 1.16^{+0.08}_{-0.15}$ for $0.08\,M_{\odot}\leq\,M<M_{\rm br}$, and
$\alpha_{\rm hm} = 2.32^{+0.14}_{-0.10}$ for $M\geq\,M_{\rm br}$, as well as a
break mass at $M_{\rm br} = 0.90^{+0.05}_{-0.14} \, M_{\odot}$. This is
significantly different from the Kroupa IMF for local stars, but similar to the
Zoccali IMF measured from a bulge luminosity function. We also estimate the
dark matter mass fraction in the bulge region of $28\pm7$\% which could be
larger than a previous estimate. Because our model is purely parametric, it can
be universally applied using the parameters provided in this paper.
