On the Microlensing Optical Depth of the Galactic Bar

Abstract

The microlensing probability (optical depth $\tau$) toward the Galactic center carries information about the mass distribution of the Galactic bulge/bar, so can be used to constrain the very uncertain shape parameters of the bar. We find $tau$ depends on the bar mass, radial profile, angle, axis scale lengths and boxyness by a few simple analytical formulae, which shows: (1) $\tau$ is proportional to the mass of the bar, $M$. (2) $\tau$ falls along the minor axis with a strong gradient. (3) An oblate bulge can have more optical depth than a triaxial bar if the bar angle $\alpha >45$ degress. (4) $\tau$ is the largest if the angle $\alpha$ and the axis ratio $y_0/x_0$ conspires so that $y_0/x_0=\tan \alpha$. (5) At a fixed field on the minor axis but away from the center, boxy bars with a flat density profile tend to give a larger optical depth than ellipsoidal bars with a steep profile. (6) Main sequence sources should have a significantly lower (20-50\% lower) optical depth than red clump giants if main sequence stars are not observed as deep as the bright clump giants. An application to four COBE-constrained models (Dwek et al. 1994) shows most models produce optical depth $2\sigma$ lower than MACHO and OGLE observed values even with both a massive bar $2.8\times 10^{10}{M}_{\odot }$ and a full disk. The high $\tau$ argues for a massive ($>2\times 10^{10}{M}_{\odot }$) boxy bar with $y_0/x0\approx \tan \alpha$ and $\alpha <20$ deg and with a flat radial profile up to corotation.

28 pages including 6 postscript figures in uuencoded compressed tar file. Submitted to MNRAS

Cited by in corpus (33)

• LCDM-based models for the Milky Way and M31 I: Dynamical Models
• Reddening and Extinction Toward the Galactic Bulge from OGLE-III: The Inner Milky Way's Rv ~ 2.5 Extinction Curve
• Microlensing optical depth towards the Galactic bulge from MOA observations during 2000 with Difference Image Analysis
• Stellar Contribution to the Galactic Bulge Microlensing Optical Depth
• Dark Matter distribution in the Milky Way: microlensing and dynamical constraints
• The MACHO project: Microlensing Optical Depth towards the Galactic Bulge from Difference Image Analysis
• Secular bar formation in galaxies with significant amount of dark matter
• The properties of the Galactic bar implied by gas kinematics in the inner Milky Way
• Microlensing Optical Depth towards the Galactic Bulge Using Clump Giants from the MACHO Survey
• Microlensing optical depth toward the Galactic Bulge using bright sources from OGLE-II
• Microlensing optical depth and event rate toward the Galactic bulge from 8 yr of OGLE-IV observations
• The Microlensing Event Rate and Optical Depth Toward the Galactic Bulge from MOA-II
• Models for the Gravitational Field of the Galactic Bar. An Application to Stellar Orbits in the Galactic Plane and Orbits of Some Globular Clusters
• Bulge Microlensing Optical Depth from EROS 2 observations
• The power spectrum of the Milky Way: Velocity fluctuations in the Galactic disk
• A Dynamical Model of the Inner Galaxy
• 3D outer bulge structure from near infrared star counts
• Theory of pixel lensing towards M31 I: the density contribution and mass of MACHOs
• Microlensing constraints on the Galactic Bulge Initial Mass Function
• Phase space transport in cuspy triaxial potentials: Can they be used to construct self-consistent equilibria?
• Blending in Gravitational Microlensing Experiments: Source Confusion And Related Systematics
• Possible Solution of the long-standing discrepancy in the Microlensing Optical Depth Toward the Galactic Bulge by correcting the stellar number count
• Galactic Bulge Microlensing Events from the MACHO Collaboration
• Mass distribution in our Galaxy
• The Maximum Optical Depth Towards Bulge Stars From Axisymmetric Models of the Milky Way
• An inner ring and the micro lensing toward the Bulge
• The Sagittarius dwarf galaxy as a microlensing target
• Probing the Milky Way stellar and brown dwarf initial mass function with modern microlensing observations
• Microlensing in the Galactic Bulge: Effects of the Disk Behind the Bulge
• The Magellanic Stream in Modified Newtonian Dynamics
• Microlensing Optical Depth Revisited with Recent Star Counts
• Deprojection of light distributions of nearby systems: perspective effect and non-uniqueness
• Effect of Binary Source Companions on the Microlensing Optical Depth Determination toward the Galactic Bulge Field