[Paper Review] First Doppler Limits on Binary Planets and Exomoons in the HR 8799 System

Andrew Vanderburg, Joseph E. Rodriguez|arXiv (Cornell University)|Oct 27, 2021

Stellar, planetary, and galactic studies69 references14 citations

TL;DR

This study presents the first radial velocity constraints on exomoons and binary planets using Doppler monitoring of directly imaged exoplanets in the HR 8799 system. Despite low spectral resolution (λ/Δλ ≈ 4000) and moderate signal-to-noise, the analysis rules out edge-on Jupiter-mass exomoons with orbital periods shorter than 5 days around HR 8799 c, and half-Jupiter-mass moons with periods under 1 day, setting stringent upper limits at 95% confidence.

ABSTRACT

We place the first constraints on binary planets and exomoons from Doppler monitoring of directly imaged exoplanets. We model radial velocity observations of HR 8799 b, c, and d from Ruffio et al. (2021) and determine upper limits on the $m\sin{i}$ of short-period binary planets and satellites. At 95% confidence, we rule out companions orbiting the three planets more massive than $m\sin{i} = 2 M_J$ with orbital periods shorter than 5 days. We achieve our tightest constraints on moons orbiting HR 8799 c, where with 95% confidence we rule out out edge-on Jupiter-mass companions in periods shorter than 5 days and edge-on half-Jupiter-mass moons in periods shorter than 1 day. These radial velocity observations come from spectra with resolution 20 times lower than typical radial velocity instruments and were taken using a spectrograph that was designed before the first directly imaged exoplanet was discovered. Similar datasets from new and upcoming instruments will probe significantly lower exomoon masses.

Motivation & Objective

• To place the first radial velocity-based upper limits on the presence of exomoons and binary planets around directly imaged exoplanets.
• To test the feasibility of detecting massive exomoons using Doppler spectroscopy on low-resolution, moderate-sensitivity instruments.
• To explore the parameter space of short-period exomoons and binary planets around distant, massive planets.
• To assess the potential of future high-resolution spectrographs for detecting rocky exomoons.

Proposed method

• Utilized radial velocity measurements of HR 8799 b, c, and d from Ruffio et al. (2021), obtained with the Keck OSIRIS spectrograph over a 10-year baseline.
• Applied Lomb-Scargle periodograms to detect periodic signals indicative of orbiting companions in the radial velocity time series.
• Conducted Markov Chain Monte Carlo (MCMC) simulations to explore plausible short-period orbits and derive upper limits on companion masses (m sin i).
• Modelled radial velocity signals assuming edge-on orbits and computed 95% confidence upper limits on m sin i for companions with periods < 5 days.
• Used a Bayesian framework to assess the significance of potential signals and rule out false positives.
• Compared the sensitivity of radial velocity and astrometry for detecting exomoons, noting complementary scaling with orbital period.

Experimental results

Research questions

• RQ1 Can radial velocity monitoring of directly imaged exoplanets detect massive exomoons or binary planets?
• RQ2 What are the upper limits on the mass and orbital period of exomoons around HR 8799 b, c, and d?
• RQ3 How sensitive is low-resolution Doppler spectroscopy to short-period exomoons despite low signal-to-noise?
• RQ4 What are the prospects for detecting exomoons with future high-resolution instruments on 30-meter telescopes?
• RQ5 How do radial velocity and astrometric methods compare in sensitivity to exomoons at different orbital periods?

Key findings

• At 95% confidence, the study rules out edge-on Jupiter-mass companions (m sin i > 2 MJ) in orbits with periods shorter than 5 days around HR 8799 c.
• For HR 8799 c, the analysis sets a tighter limit: edge-on half-Jupiter-mass moons (m sin i > 1 MJ) are ruled out for orbital periods shorter than 1 day.
• The constraints are strongest for HR 8799 c, with 95% confidence upper limits of m sin i < 2 MJ for companions with periods < 5 days.
• The study demonstrates that even moderate-resolution spectrographs (λ/Δλ ≈ 4000), such as OSIRIS, can yield meaningful constraints on exomoons despite low spectral resolution.
• The radial velocity semi-amplitude for a Jupiter-mass companion in a 10-day orbit around HR 8799 planets is ≈2.4 km s⁻¹, comparable to the best single-point OSIRIS uncertainties.
• The results suggest that future high-resolution instruments (e.g., KPIC, GMTNIRS, HIRES/ELT) could reduce radial velocity uncertainties by a factor of 30, enabling detection of rocky exomoons.