Microlensing Within the Local Group

Broadly speaking, there are two types of strong lensing: macrolensing and microlensing. In the former case, the multiple images of the source can be spatially resolved, while in the latter case, they cannot. In this chapter, we investigate microlensing of stars within the Local Group of galaxies. In both Chaps. 2 and 4, we solved the lens equation to find the image positions, with the understanding that they could be observed individually. In this chapter, we assume only that the centroid (i.e., center of light) and total magnification of the images can be measured. We begin by considering microlensing of a point source. The simplest such case is for a lens consisting of a single point mass (Sect. 5.1). We then turn to the case of lensing by several point masses (Sect. 5.2). After formulating the problem in terms of complex variables (Sect. 5.2.1), we specialize to the binary lensing (Sect. 5.2.2) of a source by two stars close together or by a single star orbited by a planet. Extended sources are considered in Sect. 5.3. Putting microlensing theory into practice requires the statistical approach presented in Sect. 5.4. Applications of microlensing are discussed in Sect. 5.5.