EXPANDING THE REALM OF MICROLENSING SURVEYS WITH DIFFERENCE IMAGE PHOTOMETRY

We present a new technique for monitoring microlensing activity even i n highly crowded fields, and use this technique to place limits on low -mass MACHOs in the haloes of M31 and the Galaxy. Unlike present Galac tic microlensing surveys, we employ a technique in which a large fract ion of the stellar sample is compressed into a single CCD field, rathe r than spread out in a way requiring many different telescope pointing s. We implement the suggestion by Crotts [ApJ, 399, L43 (1993)] that c rowded fields can be monitored by searching for changes in flux of var iable objects by subtracting images of the same field, taken in time s equence, positionally registered, photometrically normalized, then sub tracted from one another (or a sequence average). The present work tac kles the most difficult part of this task, the adjustment of the point spread function among images in the sequence so that seeing variation s play an insignificant role in determining the residual after subtrac tion. The interesting signal following this process consists of positi ve and negative point sources due to variable sources. The measurement of changes in flux determined in this way we dub ''difference image p hotometry'' [also called ''pixel lensing''; Gould, preprint (1996)]. T he matching of the image point spread function (PSF) is accomplished b y 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 th is method is difficult in a typical telescope and wide field imaging c amera due to a subtle interplay between the spatial variation of the P SF associated with the optical design and the inevitable time variabil ity of the telescope focus. Such effects lead to complexities in match ing the PSF over an entire frame. We demonstrate the realization of th e difference image approach with two separate solutions to these probl ems-a software algorithm to determine the match of the spatially varyi ng PSF between frames using a limited number of stars and also a simpl e optical corrector for a wide field imager to simplify the PSF matchi ng 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 de tected 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 facilit ate the PSF matching problem. Of the KPNO sources discovered, 85 overl ap 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 o f the VATT objects over 14 nights confirm the short timescale variabil ity of these sources. Although some fraction of the sources are bright enough to be considered resolved in the raw data more than half the s ources are fainter than the surface brightness fluctuations associated with the unresolved stars in the galaxy and cannot be identified in t he raw data. However, the light curves of these sources appear to be f amiliar variables such as Cepheids and eclipsing binaries. We assess t he limitations and sensitivities of the techniques and demonstrate tha t we can achieve photometric errors of faint unresolved variables that are within a factor of three of the ultimate photon noise limit. Usin g this we show how the KPNO data over two good nights, and sensitive t o 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 sp herical halo), we can conclude that in two nights we have eliminated t he possibility at the 95% confidence level that the Galactic halo is c omprised of a single mass population of MACHOs in the sub-Earth mass r ange. Based on estimates of the M31 and Galactic MACHO tau=(5 - 10)x 1 0(-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 resol ved stars, which greatly expands the power of these surveys. Applicati on to surveys of more general kinds of variability is clear. We also s uggest other applications, such as to proper motion surveys. (C) 1996 American Astronomical Society.