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We developed a parametric Galactic model toward the Galactic bulge by fittingto spatial distributions of the Gaia DR2 disk velocity, VVV proper motion,BRAVA radial velocity, OGLE-III red clump star count, and OGLE-IV star countand microlens rate, optimized for use in microlensing studies. We include theasymmetric drift of Galactic disk stars and the dependence of velocitydispersion on Galactic location in the kinematic model, which has been ignoredin most previous models used for microlensing studies. We show that our modelpredicts a microlensing parameter distribution significantly different fromthose typically used in previous studies. We estimate various fundamental modelparameters for our Galaxy through our modeling, including the initial massfunction (IMF) in the inner Galaxy. Combined constraints from star counts andthe microlensing event timescale distribution from the OGLE-IV survey, inaddition to a prior on the bulge stellar mass, enable us to successfullymeasure IMF slopes using a broken power-law form over a broad mass range,$\alpha_{\rm bd}=0.22^{+0.20}_{-0.55}$ for $M<0.08\,M_{\odot}$, $\alpha_{\rmms} = 1.16^{+0.08}_{-0.15}$ 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 abreak mass at $M_{\rm br} = 0.90^{+0.05}_{-0.14} \, M_{\odot}$. This issignificantly different from the Kroupa IMF for local stars, but similar to theZoccali IMF measured from a bulge luminosity function. We also estimate thedark matter mass fraction in the bulge region of $28\pm7$\% which could belarger than a previous estimate. Because our model is purely parametric, it canbe universally applied using the parameters provided in this paper.

A Parametric Galactic Model toward the Galactic Bulge Based on Gaia and Microlensing Data