Microlensing of microlensing: effects of random stars on the double-source-plane gravitational lens

Microlensing, the influence of stars within a galactic gravitational lens, has emerged as a powerful probe of compact mass and, through differential magnification, sub-parsec scale sources at cosmological distances. The recent discovery of a double-source-plane gravitational lens system in which the most distant source is a quasar offers the prospect of compound microlensing, in which quasar light rays are influenced by compact masses within the two foreground lensing galaxies. Here, we present the first numerical simulations of this ‘microlensing of microlensing’. We consider the recently discovered ‘Einstein zig–zag’ lens, J1721+8842, as a fiducial case, and construct microlensing magnification maps for each of the six quasar images in this system. Due to the secondary microlensing effects of the myriad of initial microimages, the resulting maps contain more complex caustic features than seen in the case of single plane microlensing. This is reflected in the expected light curves seen for each of the images. Given the cosmological promise of time-delay lenses for measuring the Hubble constant, combined with more powerful constraints on the lensing potential in double-source-plane lenses, examining the statistical characteristics of compound microlensing is timely to maximize the cosmological output of double-source-plane time-delay lenses.