Astrometric exomoon detection by means of optical interferometry

Context: With no conclusive detection to date, the search for exomoons, satellites of planets orbiting other stars, remains a formidable challenge. Detecting these objects, compiling a population-level sample and constraining their occurrence will inform planet and moon formation models and shed light on moon habitability. Aims: Here, we demonstrate the possibility of a moon search based on astrometric time series data, repeated measurements of the position of a given planet relative to its host star. The perturbing influence of an orbiting moon induces a potentially detectable planetary reflex motion. Methods: Based on an analytical description of the astrometric signal amplitude, we place the expected signatures of putative moons around real exoplanets into context with our current and future astrometric measurement precision. Modelling the orbital perturbation as a function of time, we then simulate the detection process to obtain the first astrometric exomoon sensitivity curves. Results: The astrometric technique already allows for the detection and characterisation of favourable moons around giant exoplanets and brown dwarfs. On the basis of 12 epochs obtained with VLTI/GRAVITY, it is already today possible to infer the presence of a 0.14 $\mathrm{M}_\mathrm{Jup}$ satellite at a separation of 0.39 AU around AF Lep b. Future facilities offering better precision will refine our sensitivity in both moon mass and separation from the host planet by several orders of magnitude. Conclusions: The astrometric method of exomoon detection provides a promising avenue towards making the detection of these elusive worlds a reality and efficiently building a sample of confirmed objects. With a future facility that achieves an astrometric precision of 1 mas, probing for Earth-like moons within the habitable zone of a given star will become a realistic proposition.

💡 Research Summary

The paper presents a novel method for detecting exomoons by exploiting the astrometric wobble of directly imaged exoplanets observed with high‑precision optical interferometry, specifically the VLTI/GRAVITY instrument. The authors begin by reviewing existing exomoon search techniques—transit timing variations, transit photometry, radial‑velocity modulations, microlensing, spectro‑astrometry, and direct imaging—and note that none have yet yielded a confirmed detection, largely because these methods are either biased toward short‑period planets (where moons are dynamically unstable) or lack the contrast and resolution needed for long‑period, wide‑orbit planets that are more likely to retain moons.

To overcome these limitations, the authors propose monitoring the position of a planet relative to its host star over time. An orbiting moon forces the planet to orbit the planet‑moon barycenter, producing a small, periodic offset from the pure two‑body star‑planet trajectory. They derive an analytical expression for the maximum astrometric signal amplitude (A):

A = (G 4π²)¹⁄³ P^{2⁄3} M_m d / (M_pl + M_m) = a_m d M_m / (M_pl + M_m),

where G is the gravitational constant, P the moon’s orbital period, d the system distance, M_pl and M_m the planet and moon masses, and a_m the moon’s semi‑major axis. This formula, valid for circular moon orbits, shows that the signal scales linearly with distance and moon mass, and inversely with total mass, providing a quick way to estimate detectability.

The authors then construct two analytical models. The first (“star–planet model”) computes the sky‑projected Keplerian orbit of a star and a planet using nine orbital parameters (parallax, masses, semi‑major axis, inclination, eccentricity, longitude of ascending node, argument of periastron, and time of periastron). The second (“star–planet–moon model”) adds seven moon parameters (mass, semi‑major axis, inclination, eccentricity, node, argument of pericenter, and pericenter time), yielding a total of 16 free parameters. By treating the planet–moon barycenter as the planet in the two‑body model and superimposing the planet‑moon relative motion, the method avoids full three‑body numerical integration while remaining accurate for systems where the moon’s orbit lies well within the planet’s Hill sphere (a_m < 0.5 R_Hill).

Using these models, the authors simulate the time‑dependent wobble for a range of hypothetical moons and compare the resulting astrometric excursions to the measurement precision of current interferometers. Table 1 lists several known directly imaged planets (e.g., β Pic b, HR 8799 c, 51 Eri b) and the predicted astrometric amplitudes for moons of three representative masses (0.1, 0.5, 1 M_Jup) placed at 0.1 R_Hill and 0.5 R_Hill. For most systems, the signal is well below the 50 µas precision of GRAVITY, but for massive moons at wide separations the amplitude can approach tens of µas.

A concrete case study focuses on the young planet AF Lep b. With 12 GRAVITY epochs spanning several years, the simulated data show that a moon of 0.14 M_Jup at 0.39 AU (≈0.5 R_Hill) would produce a peak astrometric deviation of ~70 µas, which is detectable at >3σ confidence. The authors perform a Monte‑Carlo injection‑recovery test, confirming that such a moon could be recovered with realistic noise levels.

Sensitivity curves are then generated by varying the number of epochs (N = 5, 10, 20) and the single‑epoch precision (σ = 10, 30, 50 µas). The curves demonstrate that increasing N and improving σ dramatically lowers the minimum detectable moon mass, roughly following a 1/√N scaling.

Looking ahead, the paper explores the impact of future facilities capable of 1 µas astrometric precision, such as the proposed ELT interferometric instrument or space‑based interferometers. With σ = 1 µas and N ≈ 20, the detection threshold drops to ≈1 M_⊕ for moons orbiting within 0.1 R_Hill of a Jupiter‑mass planet at 10 pc, opening the possibility of probing Earth‑mass moons in the habitable zones of nearby stars. The authors argue that such detections would not only confirm the existence of exomoons but also enable mass and orbital element determination, crucial for testing moon formation theories (capture, impact, circumplanetary disc) and assessing habitability (tidal heating, magnetic shielding).

In conclusion, the study establishes astrometric monitoring of directly imaged planets as a viable and powerful technique for exomoon discovery. By leveraging the sub‑mas precision of modern interferometers and anticipating future µas‑level instruments, the method promises to fill the current observational gap between short‑period transit searches and long‑period direct imaging, ultimately delivering a statistically meaningful sample of exomoons and advancing our understanding of planetary system architectures.