Event Rate and Einstein Time Evaluation in Pixel Microlensing

Abstract

It has been shown that a flux--weighted full width at half maximum timescale of a microlensing event can be used in an unbiased estimator of the optical depth. For the first time, this allows a physical parameter to be easily estimated from pixel microlensing data. We derive analytic expressions for the observed rate of pixel lensing events as a function of the full width at half maximum timescale. This contrasts work in the literature which express rates in terms of an ``event duration'' or Einstein time, which require knowledge of the magnification, which is difficult to determine in a pixel event. The full width at half maximum is the most directly measured timescale. We apply these results to possible pixel lensing surveys, using HST for M87, and CFHT for M31. We predict M87 microlensing rates for the HST Advanced Camera and for NGST, and demonstrate that one will be able to probe the stellar IMF. Next, we describe a new method by which a crude measurement of the magnification can be made in the regime of magnifications A~10-100. This in turn gives a crude measurement of the Einstein time. This program requires good photometry and sampling in the low magnification tails of an event, but is feasible with today's technology.