Estimating physical quantities for an observed galactic microlensing event

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 Rújula et al. (1991). It is shown that the expectation value for the mass of a certain event as derived in this paper coincides with the estimated average mass of the underlying mass spectrum as found with the mass moment method when only one event is considered. 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. For the observed events towards the LMC — including the binary lens models for MACHO LMC#1 (Dominik & Hirshfeld 1996) and MACHO LMC#9 (Bennett et al. 1996) — the results are shown explicitly. I discuss what information can be extracted and how additional information from the ongoing microlensing observations influences the results.