Photo-dynamical characterisation of the K2-138 resonant chain: Estimation of a mass–radius relationship for resonant sub-Neptunes⋆
Journal article, 2026
Context. The K2-138 system consists of a K-dwarf transited by six planets in the sub-Neptune regime, with radii ranging from 1.5 to 3.4 R⊕ and orbital periods of between 2.3 and 42 days. The five innermost planets form a chain of zero-order three-body resonances, while the outermost planet is suspected to be linked to the chain through a first-order three-body resonances. The transit timing variations induced by the resonant configuration enable a precise determination of the system’s architecture. The fine-tuning and fragility of K2-138 and other resonant chains ensure that no significant scattering or collision event has taken place since the formation and migration of the planets in the protoplanetary disc, and hence provide important anchors for planet formation models. Aims. We aim to improve the characterisation of the architecture of this system, in particular the planetary masses and its resonant configuration. In addition, we place this system in context with other resonant chains, and expand on the recent finding that resonant sub-Neptunes are puffier than non-resonant ones by deriving a mass-radius relationship for each population. Methods. We performed a global analysis of all available photometry and radial velocity data for K2-138 using photo-dynamical modelling of the light curve. We also tried different sets of priors on the masses and eccentricity, as well as different stellar activity models, to study their effects on the masses estimated by transit timing variations and radial velocities. Results. We show that our joint photo-dynamical and radial velocity analysis resulted in a robust mass determination for planets b to f, with a precision of ∼15% for the mass of planet f, and better than 10% for planets b to e. We also show that K2-138 is indeed currently locked in the resonant configuration, the five inner planets librating around an equilibrium of the chain; however, existing data are not sufficient to verify if the outer triplet is librating in a first-order three-body resonance. Finally, we demonstrate that the mass-radius relationship of resonant sub-Neptunes is well described by M = 2.54 R0.84, which is less dense than the non-resonant population, for which we found M = 2.78 R1.32. We also found that the resonant population has a smaller spread around its mass-radius relationship than the non-resonant population, pointing towards an inter-system similarity in the composition of the resonant sub-Neptunes.
methods: data analysis
celestial mechanics
planets and satellites: detection
Author
A. Leleu
University of Bern
University of Geneva
A. Alnajjarine
Paris Observatory
J. B. Delisle
University of Geneva
A. Brandeker
Stockholm University
A. Correia
University of Coimbra
S.G. Sousa
University of Porto
T.G. Wilson
The University of Warwick
N. Billot
University of Geneva
C. Broeg
University of Bern
M. Rosenqvist
University of Geneva
Judith Korth
University of Geneva
A. Bonfanti
Institut fur Weltraumforschung
C. Pezzotti
University of Liège
B. Akinsanmi
University of Geneva
Y. Alibert
University of Bern
R. Alonso
Instituto de Astrofísica de Canarias
University of La Laguna
T. Bárczy
Admatis
D. Barrado
European Space Agency (ESA)
S.C.C. Barros
University of Porto
W. Baumjohann
Institut fur Weltraumforschung
W. Benz
University of Bern
M. Bergomi
Istituto nazionale di astrofisica (INAF)
L. Borsato
Istituto nazionale di astrofisica (INAF)
A. Castro-González
University of Geneva
A. Collier Cameron
University of St Andrews
C. Corral Van Damme
European Space Agency (ESA)
Szilard Csizmadia
German Aerospace Center (DLR)
P. E. Cubillos
Istituto nazionale di astrofisica (INAF)
Institut fur Weltraumforschung
Melvyn B. Davies
Lund University
M. Deleuil
Laboratoire d'Astrophysique de Marseille
A. Deline
University of Geneva
O. Demangeon
University of Porto
B.O. Demory
University of Bern
A. Derekas
Eötvös Loránd University (ELTE)
Billy Edwards
Netherlands Institute for Space Research (SRON)
D. Ehrenreich
University of Geneva
Anders Erikson
German Aerospace Center (DLR)
A. Fortier
University of Bern
L. Fossati
Institut fur Weltraumforschung
Malcolm Fridlund
Leiden University
Chalmers, Space, Earth and Environment, Astronomy and Plasmaphysics
D. Gandolfi
University of Turin
K. Gazeas
University of Athens
Michaël Gillon
University of Liège
M. Gudel
University of Vienna
Maximilian N. Günther
European Space Agency (ESA)
A. Heitzmann
University of Geneva
Ch. Helling
Technische Universität Graz
Institut fur Weltraumforschung
K. Isaak
European Space Agency (ESA)
Tatiana Keller
University of Bern
L. L. Kiss
Eötvös Loránd University (ELTE)
Hungarian Academy of Sciences
D. Kitzmann
University of Bern
E. Kopp
German Aerospace Center (DLR)
K. W.F. Lam
German Aerospace Center (DLR)
J. Laskar
Paris Observatory
A. L. des Etangs
Institut d 'Astrophysique de Paris
M. Lendl
University of Geneva
A. Luntzer
University of Vienna
D. Magrin
Istituto nazionale di astrofisica (INAF)
P. Maxted
Keele University
Bruno Merín
European Space Agency (ESA)
C. Mordasini
University of Bern
Valerio Nascimbeni
Istituto nazionale di astrofisica (INAF)
G. Olofsson
Stockholm University
H. P. Osborn
University of Bern
Swiss Federal Institute of Technology in Zürich (ETH)
R. Ottensamer
University of Vienna
I. Pagano
Istituto nazionale di astrofisica (INAF)
Enric Palle
Instituto de Astrofísica de Canarias
University of La Laguna
G. Peter
German Aerospace Center (DLR)
D. Piazza
University of Bern
Giampaolo P. Piotto
Istituto nazionale di astrofisica (INAF)
University of Padua
Don L. Pollacco
The University of Warwick
D. Queloz
Swiss Federal Institute of Technology in Zürich (ETH)
University of Cambridge
Roberto Ragazzoni
Istituto nazionale di astrofisica (INAF)
University of Padua
N. Rando
European Space Agency (ESA)
H. Rauer
German Aerospace Center (DLR)
Freie Universität Berlin
I. Ribas
Spanish National Research Council (CSIC)
Centre Tecnològic de Telecomunicacions de Catalunya (CTTC)
N. C. Santos
University of Porto
Gaetano Scandariato
Istituto nazionale di astrofisica (INAF)
D. Segransan
University of Geneva
A.E. Simon
University of Bern
A. M.S. Smith
German Aerospace Center (DLR)
M. Stalport
University of Liège
S. Sulis
Laboratoire d'Astrophysique de Marseille
G.M. Szabó
Eötvös Loránd University (ELTE)
S. Udry
University of Geneva
S. Ulmer-Moll
Leiden University
University of Liège
V. Van Grootel
University of Liège
J. Venturini
University of Geneva
E. Villaver
Instituto de Astrofísica de Canarias
University of La Laguna
N. A. Walton
University of Cambridge
Astronomy and Astrophysics
0004-6361 (ISSN) 1432-0746 (eISSN)
Vol. 711 A221Subject Categories (SSIF 2025)
Astronomy, Astrophysics, and Cosmology
DOI
10.1051/0004-6361/202558317