Astrometric Methods for Detecting Exomoons Orbiting Imaged Exoplanets: Prospects for Detecting Moons Orbiting a Giant Planet in <i>α</i> Centauri A’s Habitable Zone

Abstract Nearby giant exoplanets offer an opportunity to search for moons (exomoons) orbiting them. Here, we present a simulation framework for investigating the possibilities of detecting exomoons via their astrometric signal in planet-to-star relative astrometry. We focus our simulations on α Centauri A, orbited by a hypothetical giant planet consistent with candidate detections in Very Large Telescope and James Webb Space Telescope observations. We consider a variety of observatory architectures capable of searching for exomoons, including upcoming facilities and also a hypothetical dedicated facility—e.g., a purpose-built space telescope with diameter = 3 m, central observing wavelength of 500 nm, and contrast-limited performance of ∼10 −9 in 1 hr observations. We find that such a facility would be capable of detecting ∼Earth-mass moons in a 5 yr campaign, assuming a Saturn-mass planet. More generally, we simulate expected detection limits for a variety of levels of astrometric precision. We find that moons as small as ∼0.2 M ⊕ on orbital periods of 4−30 days can be detected with astrometric precision of 0.1 mas and observing cadence of 1 hr over a 5 yr campaign. Additionally, we find that a 39 m ground-based telescope can detect Earth-sized exomoons orbiting the same hypothetical planet with a more modest observing cadence of 1 day. We discuss these results as motivation for a dedicated space observatory as well as a more detailed study of the physical parameters of a greater variety of star–planet–moon systems.