A Deep Search for Exomoons Around WISE 0855 With JWST

JWST is collecting time-series observations of many free-floating planets (FFPs) to study their weather, but these light curves are the ideal datasets to search for exomoons that transit the FFP during observations. In this paper, we present observations of the planetary-mass Y dwarf ($T=250-285K$, $M = 6.5\pm3.5 M_{Jup}$, d = 2.3$\,$pc) WISE J085510.83-071442.5 (WISE 0855), whose proximity and brightness make it ideal for a transiting exomoon search. We examine 11 hours of time-series spectra from the JWST Near-Infrared Spectrograph (NIRSpec) whose sensitivity, in combination with Gaussian process (GP) modeling, allows for the disentanglement of exomoon transits from WISE 0855's variability. We do not find statistically significant evidence of an exomoon transit in this dataset. Using injection and recovery tests of artificial transits for depths ranging between 0.1-1% (0.35-1.12 $R_{\oplus}$) we explore the exomoon parameter space where we could successfully detect transits. For transit depths $\geq 0.5\%$ (1.96$\,R_{\text{Titan}}$), our detection rate is 96%, which, for WISE 0855, corresponds to a moon with a companion-to-host mass ratio similar to that of Titan and Saturn. Given our sensitivity, transit probabilities, and our observational duration, we determine a $\sim$91% probability of detecting a Titan mass analog exomoon after 18 such observations if every observed system hosts a Titan mass analog exomoon in a Galilean-like system. This suggests that JWST observations of dozens of FFPs could yield meaningful constraints on the occurrence rate of exomoons. This paper is the first demonstration that JWST is sensitive to Galilean moon mass analogs around FFPs.