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

TL;DR

This work places the first astrometric limits on exomoons and binary planets around β Pictoris b by combining GRAVITY VLTI and SPHERE data within a two-planet framework augmented by a potential moon. The authors construct a rigorous likelihood formalism that accounts for correlated astrometric uncertainties, and they fit both a Two Planet model and a Two Planet & Moon model using edmcmc and PocoMC with informative priors from RV analyses. No evidence for a moon is found; they derive 3σ upper limits on moon mass across orbital periods from ≈50 to ≈1100 days, with the strongest constraints at long periods (m_moon ≲ 30–50 M⊕). The results demonstrate the sensitivity of interferometric astrometry to exomoon signals and outline a path toward improved detections via GRAVITY+, longer baselines, and multi-technique synergy. These limits illuminate the feasibility of astrometric exomoon searches in nearby, directly imaged planetary systems and set the stage for future discoveries.

Abstract

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 $β$ 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 $β$ 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 $β$ 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 $3σ$ confidence. At intermediate periods near 300 days, we exclude moons more massive than $\approx 65~M_{\oplus}$ ($0.2~M_{\text{Jup}}$) at $3σ$ 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 $3σ$ confidence). These results place the first astrometric constraints on moons and binary planets in the $β$ Pictoris system and demonstrate the sensitivity of interferometric observations for exomoon studies.

Figures (4)

• Figure 1: Relationship between the K-band brightness ratio of $\beta$ Pic b and a hypothetical moon as a function of the moon's mass. At lower moon masses, the K-band brightness contribution of the hypothetical moon is minimal compared to its host planet, motivating our assumption that any moons in the system are dark compared to the host planet.
• Figure 2: The predicted separation of both $\beta$ Pic b and c in our best-fit 2-planet model (solid grey curves), along with the actual observed separations. The dark purple points represent GRAVITY observations, while the lighter purple points represent SPHERE observations.
• Figure 3: Right ascension and declination residuals for the GRAVITY observations of $\beta$ Pictoris b and c with respect to our best-fit two-planet model. The top row presents the residuals for $\beta$ Pictoris b, while the bottom row displays the corresponding residuals for $\beta$ Pictoris c. The gray lines represent 1000 randomly selected posterior draws from our "Two Planet & Moon" fit. We see no correlated residuals to the "Two Planet" model indicative of an un-modeled signal, and we see no coherent pattern to the posterior draws for planet b, which includes hypothetical lunar perturbations. We note that the posterior samples of $\beta$ Pic c show some evidence for bimodality due to the relatively sparse sampling of the planet's orbit with GRAVITY.
• Figure 4: Upper mass limits for a potential lunar companion to $\beta$ Pic b as a function of orbital period. The color is proportional to the density of MCMC posterior samples, and the solid curves indicate the 68%, 95%, and 99.7% confidence intervals. The upper panel covers longer orbital periods ($\lesssim 1450$ days, within the dynamical stability limit), where companions more massive than $\sim 0.5~M_{\text{Jup}}$ ($\sim 60~M_{\oplus}$) are excluded. The dashed line marks the Earth–Moon mass ratio scaled to $\beta$ Pic b, and the solid green curve shows the moon/binary planet boundary from Sternlevison, which marks the theoretical separation between large moons and binary planetary systems based on mass ratios and orbital stability criteria. The lower panel zooms in on short orbital periods ($\lesssim 50$ days), where the constraints are weaker. The dashed line indicates the Pluto–Charon mass ratio, while the solid green curve again shows the Sternlevison moon/binary planet boundary.