BUFFALO/Flashlights: Constraints on the abundance of lensed supergiant stars in the Spock galaxy at redshift 1

In this work, we present a constraint on the abundance of supergiant (SG) stars at redshift $z 1$, based on recent observations of a strongly lensed arc at this redshift. First we derived a free-form model of MACS J0416.1-2403 using data from the Beyond Ultra-deep Frontier Fields and Legacy Observations (BUFFALO) program. The new lens model is based on 72 multiply lensed galaxies that produce 214 multiple images, making it the largest sample of spectroscopically confirmed lensed galaxies on this cluster. The larger coverage in BUFFALO allowed us to measure the shear up to the outskirts of the cluster, and extend the range of lensing constraints up to $ 1$\,Mpc from the central region, providing a mass estimate up to this radius. As an application, we make predictions for the number of high-redshift multiply lensed galaxies detected in future observations with the James Webb Space Telescope (JWST). Then we focus on a previously known lensed galaxy at $z=1.0054$, nicknamed Spock, which contains four previously reported transients. We interpret these transients as microcaustic crossings of SG stars and explain how we computed the probability of such events. Based on simplifications regarding the stellar evolution, we find that microlensing (by stars in the intracluster medium) of SG stars at $z=1.0054$ can fully explain these events. The inferred abundance of SG stars is consistent with either (1) a number density of stars with bolometric luminosities beyond the Humphreys-Davidson (HD) limit max for red stars), which is below $ $, or (2) the absence of stars beyond the HD limit but with a SG number density of $ $ for stars with luminosities between $10^5\ and $6 This is equivalent to one SG star per $10 pc$^2$. Finally, we make predictions for future observations with JWST's NIRcam. We find that in observations made with the F200W filter that reach 29 mag AB, if cool red SG stars exist at $z 1$ beyond the HD limit, they should be easily detected in this arc.