THEORY OF PIXEL LENSING

Pixel lensing, gravitational microlensing of unresolved stars, is pote ntially much more sensitive and much more widely applicable than is ge nerally recognized. I give explicit expressions for the pixel noise in duced by a time-variable PSF, by photometric and geometric misalignmen t, and by discrete pixelization, and I show that these can al be reduc ed below the photon noise. Pixel lensing can be divided into two regim es. In the ''semiclassical'' regime, it is similar to classical lensin g in that it measures the timescale of individual events. In the ''spi ke'' regime, it measures the total optical depth but not individual ti mescales. I present simple expressions for the boundary between the tw o regimes and for the event rate in the latter one. These expressions can be used to quickly classify all potential pixel lensing experiment s. Pixel lensing can measure the luminosity function as well as the ma ss function of stars in target galaxies to a distance of a few megapar secs. Future space-based pixel lensing could be similar to 5 times mor e effective in the infrared than in the optical, depending on developm ents in detector technology. Pixel techniques can also be applied to n onpixel-lensing problems including the search for unresolved variable stars and follow-up observations of lensing events found in classical lensing searches. To benefit fully from pixel-lensing techniques, foll ow-up observations should have resolutions of at least 5 pixels per FW HM.