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Transit Timing Variations in HIP 41378: CHEOPS and TESS confirm a non-transiting sixth planet in the system

P. Leonardi, L. Borsato, L. Pagliaro, D. Kubyshkina, J. A. Egger, T. G. Wilson, A. Heitzmann, A. Brandeker, M. N. Günther, V. Nascimbeni, A. Leleu, S. G. Sousa, A. Bonfanti, G. Mantovan, G. Piotto, L. Fossati, D. Nardiello, T. Zingales, V. Adibekyan, C. Pezzotti, B. Akinsanmi, Y. Alibert, R. Alonso, T. Bárczy, D. Barrado, S. C. C. Barros, W. Baumjohann, W. Benz, N. Billot, C. Broeg, M. Buder, A. Collier Cameron, C. Corral van Damme, A. C. M. Correia, Sz. Csizmadia, P. E. Cubillos, M. B. Davies, M. Deleuil, A. Deline, O. D. S. Demangeon, B. -O. Demory, A. Derekas, B. Edwards, D. Ehrenreich, A. Erikson, J. Farinato, A. Fortier, M. Fridlund, D. Gandolfi, K. Gazeas, M. Gillon, M. Güdel, Ch. Helling, K. G. Isaak, L. L. Kiss, J. Korth, K. W. F. Lam, J. Laskar, A. Lecavelier des Etangs, M. Lendl, D. Magrin, P. F. L. Maxted, B. Merín, C. Mordasini, G. Olofsson, R. Ottensamer, I. Pagano, E. Pallé, G. Peter, D. Piazza, D. Pollacco, D. Queloz, R. Ragazzoni, N. Rando, H. Rauer, I. Ribas, N. C. Santos, G. Scandariato, D. Ségransan, A. E. Simon, A. M. S. Smith, M. Stalport, S. Sulis, Gy. M. Szabó, S. Udry, B. Ulmer, S. Ulmer-Moll, V. Van Grootel, J. Venturini, E. Villaver, N. A. Walton, S. Wolf

TL;DR

This study leverages an extensive, multi-instrument dataset to model transit timing variations in HIP 41378, combining CHEOPS, TESS, K2, Spitzer, HST, and HARPS data with TRADES-based N-body dynamics. The analysis robustly confirms a non-transiting sixth planet, HIP 41378 g, with a period near 64 days and a mass around 7 M⊕, suggesting a near 1:2:4 resonant configuration with the inner b and c planets. The work refines the masses, radii, and orbits of the inner sub-Neptunes and explores possible architectures for the outer planets, finding that the inner system exhibits a strong peas-in-a-pod-like regularity while the outer system remains dynamically unconstrained. Interior-structure modeling reveals degeneracies between water-rich envelopes and thin H/He layers, underscoring the need for atmospheric data (e.g., JWST) to resolve composition, while the dynamical analysis confirms long-term stability under the inferred configurations.

Abstract

In multiple-planet systems, gravitational interactions of exoplanets could lead to transit timing variations (TTVs), whose amplitude becomes significantly enhanced when planets are in or near mean-motion resonances (MMRs). In cases where both TTVs and radial velocity (RV) measurements are available, combined analysis can break degeneracies and provide robust planetary and system characterization, even detecting non-transiting planets. In this context, HIP 41378 hosts five confirmed transiting planets with periods ranging from 15 to over 542 days, providing a unique dynamical laboratory for investigating wide multi-planet systems analogous to the Solar System. In this study, we present an intensive space-based photometric follow-up of HIP 41378, combining 15 new CHEOPS observations with eight TESS sectors, alongside data from K2, Spitzer, HST, and HARPS. We dynamically modeled the TTVs and RV signals of the two inner sub-Neptunes via N-body integration. These planets, HIP 41378 b ($P_{b}$ = 15.57 days) and HIP 41378 c ($P_{c}$ = 31.71 days), are close to ($Δ\sim1.8$ %) a 2:1 period commensurability. We report a clear detection of TTVs with amplitudes of 20 mins for planet b and greater than 3 hrs for planet c. We dynamically confirm the planetary nature of HIP 41378 g, a non-transiting planet with a period of about 64 days and a mass of about 7 $M_{\oplus}$, close to a 2:1 commensurability with planet c, suggesting a possible MMR chain in the inner system. Our precise determination of the masses, eccentricities, and radii of HIP 41378 b and c enabled us to investigate their possible volatile-rich compositions. Finally, by leveraging on the last TESS sectors we constrained the period of HIP 41378 d to three possible aliases ($P_{d} =$ 278, 371, and 1113 days) suggesting that the system could be placed in a double quasi resonant chain, highlighting its complex dynamical architecture.

Transit Timing Variations in HIP 41378: CHEOPS and TESS confirm a non-transiting sixth planet in the system

TL;DR

This study leverages an extensive, multi-instrument dataset to model transit timing variations in HIP 41378, combining CHEOPS, TESS, K2, Spitzer, HST, and HARPS data with TRADES-based N-body dynamics. The analysis robustly confirms a non-transiting sixth planet, HIP 41378 g, with a period near 64 days and a mass around 7 M⊕, suggesting a near 1:2:4 resonant configuration with the inner b and c planets. The work refines the masses, radii, and orbits of the inner sub-Neptunes and explores possible architectures for the outer planets, finding that the inner system exhibits a strong peas-in-a-pod-like regularity while the outer system remains dynamically unconstrained. Interior-structure modeling reveals degeneracies between water-rich envelopes and thin H/He layers, underscoring the need for atmospheric data (e.g., JWST) to resolve composition, while the dynamical analysis confirms long-term stability under the inferred configurations.

Abstract

In multiple-planet systems, gravitational interactions of exoplanets could lead to transit timing variations (TTVs), whose amplitude becomes significantly enhanced when planets are in or near mean-motion resonances (MMRs). In cases where both TTVs and radial velocity (RV) measurements are available, combined analysis can break degeneracies and provide robust planetary and system characterization, even detecting non-transiting planets. In this context, HIP 41378 hosts five confirmed transiting planets with periods ranging from 15 to over 542 days, providing a unique dynamical laboratory for investigating wide multi-planet systems analogous to the Solar System. In this study, we present an intensive space-based photometric follow-up of HIP 41378, combining 15 new CHEOPS observations with eight TESS sectors, alongside data from K2, Spitzer, HST, and HARPS. We dynamically modeled the TTVs and RV signals of the two inner sub-Neptunes via N-body integration. These planets, HIP 41378 b ( = 15.57 days) and HIP 41378 c ( = 31.71 days), are close to ( %) a 2:1 period commensurability. We report a clear detection of TTVs with amplitudes of 20 mins for planet b and greater than 3 hrs for planet c. We dynamically confirm the planetary nature of HIP 41378 g, a non-transiting planet with a period of about 64 days and a mass of about 7 , close to a 2:1 commensurability with planet c, suggesting a possible MMR chain in the inner system. Our precise determination of the masses, eccentricities, and radii of HIP 41378 b and c enabled us to investigate their possible volatile-rich compositions. Finally, by leveraging on the last TESS sectors we constrained the period of HIP 41378 d to three possible aliases ( 278, 371, and 1113 days) suggesting that the system could be placed in a double quasi resonant chain, highlighting its complex dynamical architecture.

Paper Structure

This paper contains 28 sections, 2 equations, 11 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Observations extraction and reduction
  3. K2
  4. Spitzer
  5. TESS
  6. HST
  7. CHEOPS
  8. HARPS
  9. Stellar parameters
  10. Data analysis
  11. CHEOPS-only analysis
  12. Global transit light curve modeling
  13. Dynamical modeling with TRADES
  14. Two-planet model
  15. Three-planet model
  16. ...and 13 more sections

Figures (11)

  • Figure 1: Radial velocities of HIP 41378. Upper panel: RV plot minus the offset $\mathrm{\gamma}$. TRADES MAP model is shown as a black line with the shaded gray areas indicating the 1$\sigma$, 2$\sigma$, and 3$\sigma$ confidence intervals. HARPS observations are depicted as purple circles. Lower Panel: RV residuals after subtracting the model.
  • Figure 2: O-C diagrams of HIP 41378 b (left) and c (right). Each dataset is plotted with a different marker and color. Top: Best-fit two-planet TRADES model (black line with gray-shaded $1\sigma$, $2\sigma$, and $3\sigma$ confidence intervals). Bottom: Best-fit three-planet TRADES model. Lower panels in each plot show the residuals with respect to the corresponding model.
  • Figure 3: Mass-radius diagram including all confirmed planets with radii below 4 $R_{\oplus}$ with masses and radii measured to better than 30% precision (Gray points). Planet parameters are taken from the NASA Exoplanet Archive's confirmed planets table, as queried on January 20, 2025. The purple pentagon represents the position of HIP 41378 b, while the green diamond represents the postion of HIP 41378 c. The color-coded lines show different theoretical mass–radius relations corresponding to the planet compositions taken from zeng_2019 (solid lines) and lopez_fortney_2014 (dashed lines; 1 Gyr, solar metallicity and incident flux of 10 $S_{\oplus}$). Also shown are Earth, Uranus and Neptune, for reference.
  • Figure 4: Three-body Laplace resonant angles evolution for HIP 41378 b, c and g, for the $\mathrm{MAP_{HDI}}$ solutions. The top two panels show the evolution of the critical angles $\phi_{12}$ and $\phi_{23}$. The bottom panel shows the three-body angle, which is a linear combination of the mean longitudes of the planets.
  • Figure 5: Phase-folded light curves of HIP 41378 b & c, combining observations from K2, Spitzer, HST, CHEOPS, and TESS. The oversampled best-fit transit models are overlaid on the light curves.
  • ...and 6 more figures