Title: Microlensing of Extremely Magnified Stars near Caustics of Galaxy Clusters,
Abstract: 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 $\sim 10^{6}\, (10\,
R_{\odot}/R)^{1/2}$ before merging on the critical curve. We show that a mass
fraction ($\kappa_\star \gtrsim \, 10^{-4.5}$) 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 $\kappa_\star
\sim 0.01$, we find a source-plane width of $\sim 20 \, {\rm pc}$ for the
caustic network, which spans $0.2 \, {\rm arcsec}$ on the image plane. A source
star takes $\sim 2\times 10^4$ years to cross this width, with a total of $\sim
6 \times 10^4$ crossings, each one lasting for $\sim 5\,{\rm
hr}\,(R/10\,R_\odot)$ with typical peak magnifications of $\sim 10^{4} \left(
R/ 10\,R_\odot \right)^{-1/2}$. 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.