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 we 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-circle dot less than or similar to M less than or similar to 4 x 10(3) M-circle dot and the source radius range of 40R(circle dot) less than or similar to R 260R(circle dot). In the most plausible case with M approximate to 0.3 M-circle dot and R approximate to 180R(circle dot), the source star should have been magnified by a factor of approximate to 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 intracluster light. We argue that compact dark matter models with high fractional mass densities for the mass range 10(-5) M-circle dot less than or similar to M less than or similar to 10(2) M-circle dot 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.