Event rate and Einstein time evaluation in pixel microlensing

In previous work it has been shown that a flux-weighted FWHM timescale of a microlensing event can be used as an unbiased estimator of the optical dep th. For the first time, this allows the optical depth, which is effectively the microlensing probability, to be easily estimated from pixel microlensi ng data. In this paper we derive analytic expressions for the observed rate of pixel lensing events as a function of the FWHM timescale. This contrast s works in the literature that 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 FWHM is the most directly meas ured timescale. We apply these results to possible pixel lensing surveys, u sing the Hubble Space Telescope (HST) for M87 and the Canada-France-Hawaii Telescope (CFHT) for M31. We predict M87 microlensing rates for the HST Adv anced Camera and for the Next-Generation Space Telescope (NGST), and demons trate that one will be able to probe the stellar initial mass function (IMF ). Next, we describe a new method by which a crude measurement of the magni fication can be made in the regime of magnifications A similar to 10-100. T his in turn gives a crude measurement of the Einstein time. This program re quires good photometry and sampling in the low-magnification tails of an ev ent, but is feasible with today's technology.