Statistical Microlensing Toward Magnified High-Redshift Star Clusters
  We study light variability of gravitationally magnified high-redshift star
clusters induced by a foreground population of microlenses. This arises as the
incoherent superposition of light variations from a large number of source
stars traversing the random magnification pattern on the source plane. The
light curve resembles a scale-invariant, Gaussian process on timescales of
years to decades, while exhibits rapid and frequent micro-caustic crossing
flares of larger amplitudes on timescales of days to months. For a concrete
example, we study a young Lyman-continuum-leaking star cluster recently
discovered in the lensed Sunburst Arc at $z=2.37$. We show that one magnified
image happens to be intervened by a faint foreground galaxy, and hence should
exhibit a variable flux at the $1$--$2\%$ level, which is measurable in space
with $\sim 1$--$3\,$ks exposures on the Hubble Space Telescope and more easily
with the James Webb Space Telescope, or from the ground using a $\sim$4-meter
telescope without adaptive optics. Detailed measurement of this variability
will enable us to determine the absolute macro magnification and hence the
intrinsic mass and length scales of the star cluster, test synthetic models of
stellar population, and probe multiplicity of massive stars. We furthermore
suggest that monitoring the other lensed images of the star cluster, which are
free from significant intervention by foreground stellar microlenses, will
allow us to probe planetary to stellar mass compact objects constituting as
little as just a few percent of the dark matter. Given the typical surface
density of intracluster stars, we expect this phenomenon to be relevant for
many other gravitationally magnified star clusters at Cosmic Noon behind galaxy
cluster lenses.
