Exomoon simulations

We introduce and describe our newly developed code that simulates light curves and radial velocity curves for arbitrary transiting exoplanets with a satellite. The most important feature of the program is the calculation of radial velocity curves and the Rossiter-McLaughlin effect in such systems. We discuss the possibilities for detecting the exomoons taking the abilities of Extremely Large Telescopes into account. We show that satellites may be detected also by their RM effect in the future, probably using less accurate measurements than promised by the current instrumental developments. Thus, RM effect will be an important observational tool in the exploration of exomoons.

💡 Research Summary

The paper presents a newly developed simulation code that simultaneously generates synthetic light curves and radial‑velocity (RV) curves for transiting exoplanet systems that host an additional satellite (exomoon). The novelty lies in the incorporation of the Rossiter‑McLaughlin (RM) effect for both the planet and its moon, allowing the user to predict the minute RV anomalies produced when a small body occults a rotating stellar disk. The code is modular: it first computes three‑dimensional orbital positions for the planet‑moon pair using Keplerian dynamics, then models the stellar surface with a realistic limb‑darkening law and a solid‑body rotation profile, and finally calculates the loss of flux and the corresponding distortion of stellar absorption lines during each phase of the transit.

A central focus of the study is the assessment of exomoon detectability via the RM signal, especially in the context of forthcoming Extremely Large Telescopes (ELTs) such as the ELT, GMT, and TMT equipped with ultra‑stable high‑resolution spectrographs (e.g., HIRES, ESPRESSO). The authors run a suite of simulations varying moon radius (from sub‑Earth to Earth‑size), orbital inclination, and phase relative to the planet. Results show that with current 10‑meter class facilities, the RM signature of a moon is typically below the 1 m s⁻¹ noise floor and therefore indistinguishable from stellar jitter. However, assuming ELT‑class collecting area and spectrographs capable of achieving ≈10 cm s⁻¹ precision, the moon‑induced RM anomaly becomes clearly detectable for moons as small as one Earth radius, provided the host star is relatively quiet and bright (V ≲ 10). The shape of the RM anomaly is highly sensitive to the moon’s orbital geometry: inclined moons produce a characteristic double‑peak pattern, while different orbital phases shift the timing and amplitude of the peaks. This sensitivity opens the possibility of retrieving the moon’s orbital inclination, semi‑major axis, and even its radius through Bayesian model fitting of multi‑epoch RV data.

The paper also discusses practical observing strategies. Continuous RV monitoring before, during, and after the transit is essential to establish a reliable baseline and to separate the moon’s signal from stellar activity. Simultaneous multi‑wavelength photometry can help identify spot‑induced distortions, and the authors recommend using Gaussian process regression to model correlated noise. They note that the current implementation assumes a static limb‑darkening law and neglects stellar surface phenomena such as spots or granulation, which could masquerade as or obscure the tiny moon‑RM signal. Moreover, tidal interactions and orbital precession are treated as negligible over the short timescales of a single transit, an approximation that may need refinement for long‑term monitoring campaigns.

In summary, the study demonstrates that the Rossiter‑McLaughlin effect, traditionally used to measure spin‑orbit alignment of planets, can be extended to the realm of exomoon detection. While present‑day instruments lack the required RV precision, the simulations indicate that ELT‑class facilities will likely achieve the sensitivity needed to detect Earth‑sized moons via their RM imprint, even with modest signal‑to‑noise ratios. This method complements traditional photometric transit‑timing variations (TTV) and transit‑duration variations (TDV) techniques, offering an independent diagnostic that is less dependent on the depth of the photometric signal. The authors conclude that incorporating RM modeling into exomoon search pipelines will become an important tool in the next decade, potentially opening a new observational window onto the formation and dynamical evolution of satellite systems around distant worlds.