Blending of Light in Gravitational Microlensing Events

When there is more than one source of light along the line of sight to a gravitationally lensed object, the characteristics of the observed light curve are influenced by the presence of the light that is not lensed. In this paper we develop a formalism to quantify the associated effects. We find it useful to introduce the concept of a ``blended Einstein radius" and an ``effective Einstein 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 lead to generic predictions about the results of gravitational microlensing experiments. One example is that the optical depth for the lensing of giants is greater than that for the lensing of main sequence stars; for any given population of sources and lenses this effect can be quantified. We test and sharpen these predictions by performing a series of Monte Carlo simulations. We also outline general methods to (1) test whether specific events which fail to be 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 be possible if there were no blending, and (3) include the effects of blending when inferring properties of underlying populations through the statistical study of lensing events.