Understanding caustic crossings in giant arcs: characteristic scales,
  event rates, and constraints on compact dark matter
  The recent discovery of fast transient events near critical curves of massive
galaxy clusters, which are interpreted as highly magnified individual stars in
giant arcs due to caustic crossing, opens up the possibility of using such
microlensing events to constrain a range of dark matter models such as
primordial black holes and scalar field dark matter. Based on a simple analytic
model, we study lensing properties of a point mass lens embedded in a high
magnification region, and derive the dependence of the peak brightness,
microlensing time scales, and event rates on the mass of the point mass lens as
well as the radius of a source star that is magnified. We find that the lens
mass and source radius of the first event MACS J1149 Lensed Star 1 (LS1) are
constrained, with the lens mass range of $0.1~M_\odot \lesssim M \lesssim
4\times 10^3M_\odot$ and the source radius range of $40~R_\odot \lesssim R
\lesssim 260~R_\odot$. In the most plausible case with $M\approx 0.3~M_\odot$
and $R\approx 180~R_\odot$, the source star should have been magnified by a
factor of $\approx 4300$ at the peak. The derived lens properties are fully
consistent with the interpretation that MACS J1149 LS1 is a microlensing event
produced by a star that contributes to the intra-cluster light. We argue that
compact dark matter models with high fractional mass densities for the mass
range $10^{-5}M_\odot \lesssim M\lesssim 10^2M_\odot$ are inconsistent with the
observation of MACS J1149 LS1 because such models predict too low
magnifications. Our work demonstrates a potential use of caustic crossing
events in giant arcs to constrain compact dark matter.
