SIMBAD references

We present new free-form and hybrid mass reconstructions of the galaxy cluster lens MACS J0416.1$-$2403 at $z=0.396$ using the lens inversion method GRALE. The reconstructions use 237 spectroscopically confirmed multiple images from Bergamini et al. (2023) as the main input. Our primary model reconstructs images to a positional accuracy of 0.191 arcsec, thus representing one of the most precise reconstructions of this lens to date. Our models find broad agreement with previous reconstructions, and identify two $\sim 10^{12}\, {\rm M}_{\odot }$ light-unaffiliated substructures. We focus on two highly magnified arcs: Spock and Mothra. Our model features a unique critical curve structure around the Spock arc with 2 crossings. This structure enables sufficient magnification across this arc to potentially explain the large number of transients as microlensing events of supergiant stars. Additionally, we develop a model of the millilens substructure expected to be magnifying Mothra, which may be a binary pair of supergiants with $\mu \sim 6000$. This model accounts for flexibility in the millilens position while preserving the observed flux and minimizing image position displacements along the Mothra arc. We constrain the millilens mass and core radius to $\lesssim 10^6 {\rm M}_{\odot }$ and $\lesssim 17$ pc, respectively, which would render it one of the smallest and most compact substructures constrained by lensing. If the millilens is dominated by wave dark matter, the axion mass is constrained to be $\lesssim 3.0 \times 10^{-21}$ eV. Further monitoring of this lens with JWST will uncover more transients, permitting tighter constraints on the structure surrounding these two arcs.