Blending of Light in Gravitational Microlensing Events

When there is more than one source of light along the line of sight to agravitationally lensed object, the characteristics of the observed light curveare influenced by the presence of the light that is not lensed. In this paperwe develop a formalism to quantify the associated effects. We find it useful tointroduce the concept of a ``blended Einstein radius" and an ``effectiveEinstein radius", to describe the probability that a mass will serve as a lens,or that a source will be lensed in an observable way. These considerations leadto generic predictions about the results of gravitational microlensingexperiments. One example is that the optical depth for the lensing of giants isgreater than that for the lensing of main sequence stars; for any givenpopulation of sources and lenses this effect can be quantified. We test andsharpen these predictions by performing a series of Monte Carlo simulations. Wealso outline general methods to (1) test whether specific events which fail tobe fit by point-mass light curves are viable candidates for blended events, (2)use the effects of blending to learn more about the lensing event than would bepossible if there were no blending, and (3) include the effects of blendingwhen inferring properties of underlying populations through the statisticalstudy of lensing events.Comment: 8 pages, uuencoded, compressed postscript including figure