JWST's PEARLS: 119 multiply imaged galaxies behind MACS0416, lensing properties of caustic crossing galaxies, and the relation between halo mass and number of globular clusters at $z=0.4$

We present a new lens model for the $z=0.396$ galaxy cluster MACS J0416.1$-$2403 based on a previously known set of 77 spectroscopically confirmed, multiply imaged galaxies plus an additional set of 42 candidate multiply imaged galaxies from past HST and new JWST data. The new galaxies lack spectroscopic redshifts but have geometric and/or photometric redshift estimates that are presented here. The new model predicts magnifications and time delays for all multiple images. The full set of constraints totals 343, constituting the largest sample of multiple images lensed by a single cluster to date. Caustic-crossing galaxies lensed by this cluster are especially interesting. Some of these galaxies show transient events, most of which are interpreted as micro-lensing of stars at cosmological distances. These caustic-crossing arcs are expected to show similar events in future, deeper JWST observations. We provide time delay and magnification models for all these arcs. The time delays and the magnifications for different arcs are generally anti-correlated, as expected from $N$-body simulations. In the major sub-halos of the cluster, the dark-matter mass from our lens model correlates well with the observed number of globular clusters. This confirms earlier results, derived at lower redshifts, which suggest that globular clusters can be used as powerful mass proxies for the halo masses when lensing constraints are scarce or not available.