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

Abstract

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 kinematic model, which has been ignored in most previous models used for microlensing studies. We show that our model predicts a microlensing parameter distribution that is significantly different from the one with a typically used model in the previous studies. Through our modeling, we estimate various fundamental model parameters for our Galaxy, 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, α bd = 0.22 +0.20 −0.55 for M < 0.08 M , α ms = 1.16 +0.08 −0.15 for 0.08 M ≤ M < M br , and α hm = 2.32 +0.14 −0.10 for M ≥ M br , as well as a break mass at M br = 0.90 +0.05 −0.14 M . 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 ± 7% 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.

OGLE-2014-BLG-0319: A Sub-Jupiter-Mass Planetary Event Encountered Degeneracy with Different Mass Ratios and Lens-Source Relative Proper Motions

“…This implies that the lenses for models B and C would be sub-stellar objects, which is unlikely for microlensing events with t E ∼ 35 day (Sumi et al 2011;Mróz et al 2017). To quantitatively demonstrate this, we compared the observed θ E and µ rel values with prior probabilities derived from a Bayesian analysis using a Galactic model optimized for use in microlensing studies (Koshimoto et al 2021a) detailed in the Section 4.3. Figure 5 shows the result and indicates that the observed θ E and µ rel values for models B and C are ∼ 3σ from the medians.…”