First Astrometric Limits on Binary Planets and Exomoons orbiting $\beta$ Pictoris b

The search for exomoons, or moons in other star systems, has attracted significant interest in recent years, driven both by advancements in detection sensitivity and by the expanding population of known exoplanets. The $\beta$ Pictoris system is a particularly favorable target, as its proximity and directly imaged planets allow for precise astrometric monitoring. We present astrometric constraints on the presence of binary planets and exomoons in the $\beta$ Pictoris system using archival observations from the GRAVITY interferometer and SPHERE instruments. We calculate these limits by modeling the motion of the two orbiting planets and introducing an additional perturbation to the model that simulates the astrometric motion caused by an exomoon orbiting the planet $\beta$ Pictoris b. We find that for short orbital periods ($\approx50$ days), a lunar companion is only allowed if its mass remains below $\approx 180~M_{\oplus}$ ($0.6~M_{\text{Jup}}$) at $3\sigma$ confidence. At intermediate periods near 300 days, we exclude moons more massive than $\approx 65~M_{\oplus}$ ($0.2~M_{\text{Jup}}$) at $3\sigma$ confidence. At longer orbital periods, we place the tightest constraints, ruling out any potential exomoon above $\approx 50~M_{\oplus}$ ($0.15~M_{\text{Jup}}$) at $700$ days and $\approx 30~M_{\oplus}$ ($0.1~M_{\text{Jup}}$) at $1,100$ days (both at $3\sigma$ confidence). These results place the first astrometric constraints on moons and binary planets in the $\beta$ Pictoris system and demonstrate the sensitivity of interferometric observations for exomoon studies.