Imaging dark matter at the smallest scales with <i>z</i>  ≈ 1 lensed stars

Recent observations of caustic-crossing galaxies at redshift 0.7 ≲ z ≲ 1 show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicts such events should be common near the critical curves (CCs) of galaxy clusters (“near region”), but some are found relatively far away from these CCs (“far region”). We consider the possibility that substructure on milliarcsecond scales (few parsecs in the lens plane) is boosting the microlensing signal in the far region. We study the combined magnification from the macrolens, millilenses, and microlenses (“3M lensing”), when the macromodel magnification is relatively low (common in the far region). After considering realistic populations of millilenses and microlenses, we conclude that the enhanced microlensing rate around millilenses is not sufficient to explain the high fraction of observed events in the far region. Instead, we find that the shape of the luminosity function (LF) of the lensed stars combined with the amount of substructure in the lens plane determines the number of microlensing events found near and far from the CC. By measuring β (the exponent of the adopted power law LF, dN / dL = ϕ ( L )∝(1/ L ) β ), and the number density of microlensing events at each location, one can create a pseudoimage of the underlying distribution of mass on small scales. We identify two regimes: (i) positive-imaging regime where β &gt; 2 and the number density of events is greater around substructures, and (ii) negative-imaging regime where β &lt; 2 and the number density of microlensing events is reduced around substructures. This technique opens a new window to map the distribution of dark-matter substructure down to ∼10 3 M ⊙ . We study the particular case of seven microlensing events found in the Flashlights program in the Dragon arc ( z = 0.725). A population of supergiant stars having a steep LF with β = 2.55 −0.56 +0.72 fits the distribution of these events in the far and near regions. We also find that the new microlensing events from JWST observations in this arc imply a surface mass density substructure of Σ ∗ = 54 M ⊙ pc −2 , consistent with the expected population of stars from the intracluster medium. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of ∼1.3 × 10 8 M ⊙ (within its Einstein radius) in the galaxy cluster.