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

Abstract

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 of the extra pair(s) of images created. In this Letter, we develop a new formalism for 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 minimum total magnification extends 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 superposed along the line of sight or a multiple star configuration. These two possibilities can be differentiated by multiband observations.