First Astrometric Limits on Binary Planets and Exomoons orbiting $β$ 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 $β$ 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 $\approx 180M_{\oplus}$ ($0.6M_{\text{Jup}}$) at $3σ$ confidence. At intermediate periods near 300 days, we exclude moons more massive than $\approx 65M_{\oplus}$ ($0.2M_{\text{Jup}}$) at $3σ$ confidence. At longer orbital periods, we place the tightest constraints, ruling out any potential exomoon above $\approx 50M_{\oplus}$ ($0.15M_{\text{Jup}}$) at $700$ days and $\approx 30M_{\oplus}$ ($0.1M_{\text{Jup}}$) 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.

💡 Research Summary

The paper presents the first astrometric constraints on the presence of binary planets and exomoons orbiting the directly imaged giant planet β Pictoris b, using archival high‑precision measurements from the GRAVITY interferometer on the VLTI and the SPHERE high‑contrast imager on the VLT. The authors combine 34 SPHERE astrometric points (spanning 2014–2020) with 12 GRAVITY points (2018–2021) that achieve uncertainties as low as 20 μas. After discarding earlier, lower‑precision NACO data, they calibrate the remaining measurements by applying a multiplicative “j‑factor” to the reported errors, thereby accounting for systematic under‑estimation of uncertainties in each instrument.

To search for moons, the authors first assess whether a luminous satellite could shift the measured photocenter of β Pic b. Using ATMO evolutionary models for 23 Myr‑old gas giants, they find that even a massive 2 MJup satellite would contribute less than 5 % of the total K‑band flux, corresponding to a planet‑to‑satellite mass ratio of ~20 %—well below the brightness of any Solar System moon. Consequently, they treat any exomoon as effectively dark and focus solely on its gravitational perturbation of the planet’s orbit.

The orbital motion of the two known planets (β Pic b and β Pic c) is modeled with the open‑source Orbitize! package, fitting seven orbital parameters (semi‑major axis, eccentricity, inclination, argument of periastron, longitude of ascending node, epoch of periastron passage, and planet mass) simultaneously for both planets via a Markov Chain Monte Carlo (MCMC) approach. A log‑likelihood function assumes Gaussian errors and incorporates the calibrated uncertainties. The best‑fit two‑planet solution reproduces the existing astrometry and serves as the baseline model.

An additional perturbation term is introduced to represent a putative moon orbiting β Pic b. The moon’s mass (M_moon) and orbital period (P_moon) are treated as free parameters; for each (M_moon, P_moon) pair the model predicts a small wobble in the planet’s sky‑projected position. By scanning a grid of periods from ~50 days to ~1 200 days and evaluating the increase in χ² relative to the baseline, the authors derive 3σ upper limits on the moon’s mass as a function of period.

The resulting constraints are:

• For short periods (~50 days), any moon must be lighter than ≈180 M⊕ (≈0.6 MJup).
• Near 300 days, the limit tightens to ≈65 M⊕ (≈0.2 MJup).
• At ~700 days, moons heavier than ≈50 M⊕ (≈0.15 MJup) are excluded.
• At ~1 100 days, the most stringent limit is ≈30 M⊕ (≈0.1 MJup).

These limits reflect the fact that short‑period moons induce larger astrometric signatures (because the planet–moon barycenter moves more rapidly), while long‑period moons produce slower, lower‑amplitude wobbles, allowing tighter mass constraints. The authors compare these limits with theoretical expectations for moon formation (co‑accretion, capture, impact‑generated debris) and conclude that any large, Neptune‑mass satellite around β Pic b is ruled out. This has implications for models of satellite formation around massive, young giant planets.

The paper also discusses future prospects. Upgrades to GRAVITY (GRAVITY+) and the advent of ELT‑MICADO or similar instruments promise sub‑10 μas astrometric precision, which would push detectable moon masses down to the Earth‑mass regime for similar orbital periods. The authors argue that the present work establishes a methodological framework for astrometric exomoon searches and demonstrates that interferometric astrometry is a viable path toward the first confirmed detection of an exomoon.

In summary, by leveraging the exquisite astrometric precision of GRAVITY and SPHERE, the authors place the first quantitative, period‑dependent upper limits on the mass of any satellite orbiting β Pictoris b, ruling out moons larger than roughly 30–180 Earth masses depending on orbital period. This study marks a significant step forward in the emerging field of exomoon detection via astrometry and sets the stage for future, more sensitive observations.