Stochastical distributions of lens and source properties for observed galactic microlensing events

Abstract

A comprehensive new approach is presented for deriving probability densities of physical properties characterizing lens or source that constitute an observed galactic microlensing event. While previously encountered problems are overcome, constraints from event anomalies and model parameter uncertainties can be incorporated into the estimate. Probability densities for given events need to be carefully distinguished from the statistical distribution of the same parameters among the underlying population from which the actual lenses and sources are drawn. Using given model distributions of the mass spectrum, the mass density, and the velocity distribution of Galactic disk and bulge constituents, probability densities of lens mass, distance, and the effective lens-source velocities are derived, where the effect on the distribution that arises from additional observations of annual parallax or finite-source effects, or the absence of significant effects, is shown. The presented formalism can also be used to calculate probabilities for the lens to belong to one or another population and to estimate parameters that characterize anomalies. Finally, it is shown how detection efficiency maps for binary-lens companions in the physical parameters companion mass and orbital semi-major axis arise from values determined for the mass ratio and dimensionless projected separation parameter, including the deprojection of the orbital motion for elliptical orbits. Compared to the naive estimate based on 'typical values', the detection efficiency for low-mass companions is increased by mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller masses of the primary).