Infimum Microlensing Amplification of the Maximum Number of Images ofn‐Point Lens Systems

The total amplification of a source inside a caustic curve of a binary lens is no less than 3. Here we show that the infimum amplification, 3, is satisfied by a family of binary lenses where the source position is at the midpoint of the lens positions, independent of the mass ratio that parameterizes the family. We present a new proof of an underlying constraint that the total amplification of the two positive images is larger than that of the three negative images by 1 inside a caustic. We show that a similar constraint holds for an arbitrary class of n-point lens systems for sources in the "maximal domains." We introduce the notions that a source plane consists of "graded caustic domains" and that the "maximal domain" is the area of the source plane where a source star produces the maximum number of images, n2 + 1. We show that the infimum amplification of a three-point lens is 7 and that the amplification is larger than n2 + 1 - n for n ≥ 4.