Microlensing of Extremely Magnified Stars near Caustics of Galaxy Clusters

Recent observations of lensed galaxies at cosmological distances have detected individual stars that are extremely magnified when crossing the caustics of lensing clusters. In idealized cluster lenses with smooth mass distributions, two images of a star of radius R approaching a caustic brighten as t(-1/2) and reach a peak magnification similar to 10(6)(10 R-circle dot/R)(1/2) before merging on the critical curve. We show that a mass fraction (kappa(star) greater than or similar to 10(-4.5)) in microlenses inevitably disrupts the smooth caustic into a network of corrugated microcaustics and produces light curves with numerous peaks. Using analytical calculations and numerical simulations, we derive the characteristic width of the network, caustic-crossing frequencies, and peak magnifications. For the lens parameters of a recent detection and a population of intracluster stars with kappa(star) similar to 0.01, we find a source-plane width of 20 pc for the caustic network, which spans 0.2 arcsec on the image plane. A source star takes similar to 2 x 10(4) years to cross this width, with a total of similar to 6 x 10(4) crossings, each one lasting for similar to 5 hr (R/10 R-circle dot) with typical peak magnifications of similar to 10(4)(R/10 R-circle dot)(-1/2). The exquisite sensitivity of caustic-crossing events to the granularity of the lens-mass distribution makes them ideal probes of dark matter components, such as compact halo objects and ultralight axion dark matter.