We present a new technique for monitoring microlensing activity even in highly crowded fields, and use this technique to place limits on low-mass MACHOs in the haloes of M31 and the Galaxy. Unlike present Galactic microlensing surveys, we employ a technique in which a large fraction of the stellar sample is compressed into a single CCD field, rather than spread out in a way requiring many different telescope pointings. We implement the suggestion by Crotts [ApJ, 399, L43 (1993)] that crowded fields can be monitored by searching for changes in flux of variable objects by subtracting images of the same field, taken in time sequence, positionally registered, photometrically normalized, then subtracted from one another (or a sequence average). The present work tackles the most difficult part of this task, the adjustment of the point spread function among images in the sequence so that seeing variations play an insignificant role in determining the residual after subtraction. The interesting signal following this process consists of positive and negative point sources due to variable sources. The measurement of changes in flux determined in this way we dub ''difference image photometry'' [also called ''pixel lensing''; Gould, preprint (1996)]. The matching of the image point spread function (PSF) is accomplished by a division of PSFs in Fourier space to produce a convolution kernel, in a manner explored for other reasons by Phillips & Davis [ASP Conf. Series 77, p. 297 (1995)]. In practice, we find the application of this method is difficult in a typical telescope and wide field imaging camera due to a subtle interplay between the spatial variation of the PSF associated with the optical design and the inevitable time variability of the telescope focus. Such effects lead to complexities in matching the PSF over an entire frame. We demonstrate the realization of the difference image approach with two separate solutions to these problems-a software algorithm to determine the match of the spatially varying PSF between frames using a limited number of stars and also a simple optical corrector for a wide field imager to simplify the PSF matching function. The former solution yielded light curves of 139 variable sources detected in a 16' by 16' field in M31 over four nights on the KPNO 4-m telescope in 1994 and the latter yielded over 2000 sources detected over 50 nights in a single 11' by 11' field in M31 observed at the VATT 1.8-m telescope in 1995 using an optical corrector to facilitate the PSF matching problem. Of the KPNO sources discovered, 85 overlap with the VATT field and 23 of these were found to have a positional coincidence of <1'' to sources found in the VATT data. Light curves of the VATT objects over 14 nights confirm the short timescale variability of these sources. Although some fraction of the sources are bright enough to be considered resolved in the raw data more than half the sources are fainter than the surface brightness fluctuations associated with the unresolved stars in the galaxy and cannot be identified in the raw data. However, the light curves of these sources appear to be familiar variables such as Cepheids and eclipsing binaries. We assess the limitations and sensitivities of the techniques and demonstrate that we can achieve photometric errors of faint unresolved variables that are within a factor of three of the ultimate photon noise limit. Using this we show how the KPNO data over two good nights, and sensitive to similar to 10(6) stars on a single CCD frame, yields 2 sigma optical depth limits of 5 X 10(-7) for Galactic MACHOs in the mass range 2 X 10(-7)M. (0.07 Earth masses). Given the estimate of the optical depth of the Galactic halo towards M31 of tau=1x10(-6) (assuming a simple spherical halo), we can conclude that in two nights we have eliminated the possibility at the 95% confidence level that the Galactic halo is comprised of a single mass population of MACHOs in the sub-Earth mass range. Based on estimates of the M31 and Galactic MACHO tau=(5 - 10)x 10(-6) we exclude the halo of these galaxies being composed of 8 X 10(-5)M. MACHOs at the >95% confidence level. These kind of techniques can extend present microlensing surveys into regimes not limited to resolved stars, which greatly expands the power of these surveys. Application to surveys of more general kinds of variability is clear. We also suggest other applications, such as to proper motion surveys. (C) 1996 American Astronomical Society.
