On the Minimum Magnification between Caustic Crossings for Microlensing by Binary and Multiple Stars

The total magnification in gravitational microlensing by star(s) is known to have a lower bound of one. However, when the source is inside the caustics, the total magnification must be larger because the extra pair(s) of images created. In this paper, we develop a new formalism in studying the magnifications for lensing by double lenses. We prove analytically that when a source is inside the caustics the sum of five image magnifications times their corresponding parities is one and the minimum total magnification is three. For a source located on the binary axis, the total magnification can be obtained analytically without directly solving the lens equation. For multiple (number #>=# 3) stars, the minmum total magnification reaches below three. We give an explanation why this is so. Any caustic crossing event found in the ongoing microlensing experiments that has a minimum magnification smaller than three between the caustic peaks requires either an unlensed component superimposed along the line of sight or a multiple star configuration. These two possibilities can be differentiated by multi-band observations. (orig.)