A Pair of Warm Saturn-mass Planets near the 2:1 Mean Motion Resonance around TOI-3850

The paper reports the detection and characterization of a multi-planet system around TOI-3850 (TIC-143008050), a moderately active, near-solar metallicity G0 dwarf star observed by TESS in Sectors 15, 21, 41, 48, and 75. Initially, a single candidate planet was discovered by TESS, displaying transit timing variations (TTVs) with an amplitude of 1 hour and a super-period of 513 days. Through a combination of transit photometry, radial velocity observations with MAROON-X, and TTV modeling, the authors identify two planets: TOI-3850 b (Pb = 14.484 ± 0.002 days, Mb = 112 ± 20 M⊕, eb = 0.018 ± 0.008, Rb = 12.07 ± 0.09 R⊕, Teq = 841 ± 10 K), a transiting warm Jupiter, and TOI-3850 c (Pc = 29.85 ± 0.01 days, Mc = 90 ± 15 M⊕, ec < 0.015, Teq = 661 ± 7 K), a non-transiting, Saturn-mass companion. The two planets lie wide of the 2:1 mean motion resonance (Pc/Pb ≈ 2.06), consistent with a formation history involving disk-driven migration. N-body integrations indicate that TOI-3850 c may begin to transit on decadal timescales, while TOI-3850 b remains a promising target for follow-up atmospheric characterization.

The host star TOI-3850 was characterized through isochrone fitting, SED analysis, and reconnaissance spectroscopy. The isochrones fit finds TOI-3850 is consistent with a young τ⋆ = 0.89+1.01−0.63 Gyr, near-solar metallicity ([Fe/H] = 0.10 ± 0.05) G0 dwarf star with Teff = 5956 ± 58 K, M⋆ = 1.10 ± 0.02 M⊙, and R⋆ = 1.03 ± 0.01 R⊙. The star has a rotation period of 6 days, as inferred from a GLS periodogram of the out-of-transit TESS light curve, and is moderately active with an estimated RV jitter of 10 m/s.

The paper describes the observations in detail. TESS data from Sectors 15, 21, and 41 (FFI light curves) and Sectors 48 and 75 (SPOC 2-minute cadence light curves) were used. Ground-based photometry was obtained through the TESS Follow-up Observing Program from multiple telescopes including Las Cumbres Observatory, Fred Lawrence Whipple Observatory, Observatori Astronòmic de la Universitat de València, Meade LX850, Acton-Sky-Portal, Lookout Observatory, Canis Major Observatory, and the Large Array Survey Telescope. High-resolution speckle imaging from the SAI 2.5m telescope found no contaminants within 1.5 arcseconds. Two reconnaissance spectra from TRES placed an upper limit on the RV semi-amplitude of K < 150 m/s, ruling out stellar-mass companions. Fourteen spectra were obtained with MAROON-X between December 2025 and April 2026, with 13 used in the analysis after excluding one outlier.

The transit-only fit to the TESS and ground-based light curves yielded a radius of R ≈ 12 R⊕, an orbital period of P ≈ 14.484 days, and an orbital inclination of i ≈ 88.4° for TOI-3850.01. The RV-only fit compared zero-, one-, and two-planet models, testing various MMR configurations (2:1, 3:2, 4:3, 5:4) for both interior and exterior companions. The two-planet model with the perturbing planet exterior to TOI-3850.01 and wide of the 2:1 MMR had the lowest BIC. The joint RV+TTV fit used TTVFast for N-body integration and RadVel for RV modeling, with an exploratory search using pyABC followed by MCMC sampling with emcee. The joint analysis confirmed the presence of both planets and provided true dynamical masses (not just minimum masses) since the inclination of TOI-3850 c was constrained.

The dynamical analysis shows the system is stable. SPOCK stability classifier found 99.33% of 100,000 posterior draws remain stable for 10 9 orbits. Direct N-body integrations with REBOUND over 250,000 years found 99.3% of 1000 posterior realizations remained stable, with the seven unstable samples having elevated eccentricities and resulting in ejection of TOI-3850 c. The resonant angles θ1 = 2λc − λb − ϖb and θ2 = 2λc − λb − ϖc were tracked, finding that 8.8% of samples display libration about 0°, suggesting the system is near but probably not locked in the exact 2:1 MMR. For the median system parameters, both resonant angles circulate, and the period ratio remains bounded above exact 2:1 commensurability.

The paper discusses the formation history, noting that the compact, near-resonant architecture is most naturally explained by disk-driven migration, as in situ formation and high-eccentricity migration are unlikely given the presence of two massive companions in close orbits. The system is compared to other multi-planet warm Jupiter systems such as TOI-1232, Kepler-108, HAT-P-17, and TOI-7510. Only eleven confirmed systems have multiple Saturn-mass planets with orbital separations less than 0.2 AU.

For follow-up potential, TOI-3850 b has a transmission spectroscopy metric (TSM) of 58, which is higher than 87% of all confirmed warm Jupiters and ranks seventh highest among warm Jupiters in multi-planet systems. It is identified as a strong candidate for atmospheric characterization with JWST and the Ariel mission. The Gaia astrometric signatures of both planets (αb ≈ 0.08 µas and αc ≈ 0.1 µas) are well below the detection threshold of 150 µas, so they will not be recoverable with Gaia astrometry. However, Gaia DR4 will be sensitive to brown dwarfs with orbital periods between 1.0 and 5.5 years around TOI-3850.

The paper concludes that TOI-3850 hosts a pair of warm Saturn-mass planets on near-circular, coplanar orbits just wide of the 2:1 MMR, providing an important laboratory for testing how giant planets interact, migrate, and escape exact MMR commensurability. The system joins a small but valuable population of compact multi-giant-planet systems that can constrain the formation and evolution of giant planets with massive, nearby companions.

Improvements to AI systems based on this paper:

1. Orbital Dynamics and Stability Prediction

• Improve N-body integration algorithms (e.g., REBOUND, TTVFast) to automatically detect near-resonant configurations and predict long-term stability (e.g., 10 9 orbits) with uncertainty propagation from posterior samples, as demonstrated by the SPOCK classifier and 250,000-year integrations.

• Enhanced AI can flag systems likely to exhibit future transits (e.g., TOI-3850 c becoming transiting on decadal timescales) and prioritize follow-up observations.

2. Exoplanet Detection and Characterization Pipeline

• Integrate joint fitting of transit timing variations (TTVs), radial velocities (RVs), and photometry into a single Bayesian framework (e.g., using pyABC + emcee) to derive true dynamical masses and orbital parameters, even for non-transiting companions.

• Improved AI can automatically handle multi-planet systems with moderate stellar activity (e.g., RV jitter 10 m/s) by modeling stellar noise and excluding outliers (e.g., 1 of 14 MAROON-X spectra).

3. Formation and Migration Scenario Inference

• Train AI models to classify formation pathways (disk-driven migration vs. in situ vs. high-eccentricity migration) based on period ratios, eccentricities, and mass distributions, using the TOI-3850 system (Pc/Pb ≈ 2.06, wide of 2:1 MMR) as a training example.

• Improved AI can predict whether a system is locked in resonance (e.g., libration of resonant angles) or near-resonant, and estimate the likelihood of future resonance capture or escape.

4. Atmospheric Characterization Target Selection

• Develop AI ranking systems for follow-up observations using metrics like Transmission Spectroscopy Metric (TSM), comparing against known populations (e.g., TOI-3850 b ranks 7th among warm Jupiters in multi-planet systems).

• Enhanced AI can automatically identify high-priority targets for JWST/Ariel, considering host star activity, planet mass, radius, and orbital geometry.

5. Stellar Parameter Estimation and Activity Modeling

• Improve isochrone fitting and spectral energy distribution (SED) analysis with AI to handle young, active stars (e.g., rotation period 6 days, τ⋆ = 0.89 Gyr) and infer accurate stellar mass, radius, and metallicity under sparse data.

• Enhanced AI can separate stellar activity signals (e.g., GLS periodogram peaks) from planetary signals in light curves and RVs, reducing false positives.

6. Multi-Survey Data Fusion

• Build AI systems that automatically combine heterogeneous datasets (TESS FFI, SPOC 2-minute cadence, ground-based photometry from multiple telescopes, speckle imaging, reconnaissance spectra) with proper weighting and outlier rejection, as done here.

• Improved AI can detect and mitigate contamination from nearby sources (e.g., no contaminants within 1.5 arcseconds) and validate planetary signals against stellar-mass companions.

7. Predictive Astrometry and Future Mission Planning

• Use AI to compute astrometric signatures (e.g., αb ≈ 0.08 µas, αc ≈ 0.1 µas) and predict detectability with future Gaia data releases, identifying which planets or brown dwarfs may be discovered via astrometry.

• Enhanced AI can optimize observing schedules for ground-based RV and transit follow-up based on predicted ephemerides and TTV super-periods (e.g., 513 days).

8. Population-Level Comparative Analysis

• Train AI to compare new systems against known compact multi-giant-planet populations (e.g., TOI-1232, Kepler-108, HAT-P-17) to identify rare architectures and infer statistical trends in giant planet formation.

• Improved AI can automatically update catalogs of multi-Saturn-mass systems with separations <0.2 AU and flag outliers for theoretical modeling.

What the improved AI system can do:

• Automatically discover and characterize multi-planet systems with near-resonant architectures, even when one planet is non-transiting, by jointly modeling TTVs, RVs, and photometry.

• Predict long-term orbital stability and future transit events, enabling efficient use of telescope time.

• Classify formation histories and resonance states (libration vs. circulation) with quantified uncertainties.

• Rank exoplanets for atmospheric follow-up based on transmission metrics and host star suitability.

• Seamlessly integrate multi-wavelength, multi-instrument data to produce robust stellar and planetary parameters for active stars.

• Provide real-time decision support for mission planning (e.g., JWST, Ariel, Gaia) by forecasting astrometric and spectroscopic detectability.

Warm Jupiters, with orbital periods of 10 -- 200 and radii exceeding 8 R, are a relatively understudied class of exoplanets occupying the parameter space between hot Jupiters and more widely separated, colder Jupiter analogs. In this work, we report the detection of a multi-planet warm Jupiter system around TOI-3850 (TIC-143008050), a moderately active, near-solar metallicity G0 dwarf star observed by TESS in Sectors 15, 21, 41, 48 and 75. Initially, a single candidate planet was discovered by TESS, displaying transit timing variations (TTVs) with an amplitude of about 1 hr and a super-period of 513 days. Through a combination of transit photometry, radial velocity observations with MAROON-X, and TTV modeling, we identify two planets: TOI-3850 b (P b=14.484 plus or minus0.002 days, M b =112 plus or minus20 M, e b = 0.018 plus or minus0.008, R b = 12.07 plus or minus0.09 R, T=841 plus or minus10), a transiting warm Jupiter, and TOI-3850 c (P c=29.85 plus or minus0.01 days, M c =90 plus or minus15 M, e c < 0.015, T=661 plus or minus7), a non-transiting, Saturn-mass companion. The two planets lie wide of the 2:1 mean motion resonance (P c/P b about 2.06), consistent with a formation history involving disk-driven migration. N-body integrations indicate that TOI-3850 c may begin to transit on decadal timescales, while TOI-3850 b remains a promising target for follow-up atmospheric characterization.