Estimating physical quantities for an observed galactic microlensing event

Abstract

For a given spatial distribution of the lenses and distribution of the transverse velocity of the lens relative to the line-of-sight, a probability distribution for the lens mass for a single observed event is derived. In addition, similar probability distributions are derived for the Einstein radius and the separation of the lens objects and their rotation period for a binary lens. These probability distributions are distinct from the distributions for the lens population, as investigated e.g. by the mass moment method of De Rujula, Jetzer, and Masso (1991). However, it is shown that the expectation value for the mass from the probability distribution coincides with the value from the mass moment method applied to a single observed event. The special cases of a Maxwellian velocity distribution and of a constant velocity are discussed in detail. For a rudimentary model of the Galactic halo, the probability distributions are shown and the relations between the expectation values of the physical quantities and the event timescale are given. For this model, it is shown that within a 95.4%-interval around the expectation value, the mass varies by a factor of 800.