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An upper limit on late accretion and water delivery in the TRAPPIST-1 exoplanet system

Abstract

The TRAPPIST-1 system contains seven roughly Earth-sized planets locked in a multiresonant orbital configuration1,2, which has enabled precise measurements of the planets’ masses and constrained their compositions3. Here we use the system’s fragile orbital structure to place robust upper limits on the planets’ bombardment histories. We use N-body simulations to show how perturbations from additional objects can break the multiresonant configuration by either triggering dynamical instability or simply removing the planets from resonance. The planets cannot have interacted with more than ~5% of one Earth mass (M) in planetesimals—or a single rogue planet more massive than Earth’s Moon—without disrupting their resonant orbital structure. This implies an upper limit of 10−4 M to 10−2M of late accretion on each planet since the dispersal of the system’s gaseous disk. This is comparable to (or less than) the late accretion on Earth after the Moon-forming impact4,5, and demonstrates that the growth of the TRAPPIST-1 planets was complete in just a few million years, roughly an order of magnitude faster than that of the Earth6,7. Our results imply that any large water reservoirs on the TRAPPIST-1 planets must have been incorporated during their formation in the gaseous disk.

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Fig. 1: Response of the TRAPPIST-1 system when interacting with rogue planets.
Fig. 2: A possible growth history for the TRAPPIST-1 planets compared with constraints for Solar System objects.
Fig. 3: Late water delivery to the TRAPPIST-1 planets.

Data availability

All simulation data and model data that support the findings of this study or were used to make the plots are available from the corresponding author upon reasonable request.

Code availability

The Mercury N-body integrator12 is publicly available and can be downloaded at https://github.com/4xxi/mercury. We made trivial modifications to stop simulations in which two planets collided and to create an additional data dump any time a planetesimal was removed from the simulation. For water content calculations, the interior structure code is available from C.D. (cdorn@physik.uzh.ch) upon reasonable request, and the atmospheric code is based on polynomial fits from Turbet et al.24.

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Acknowledgements

We thank S. Rousseau and A. Collioud for managing the machines on which our simulations were run. S.N.R. is grateful to the ECLIPSE research team at the Laboratoire d’Astrophysique de Bordeaux and the ‘Zooming In On Rocky Planet Formation’ ISSI Team for helpful discussions, and to A. Guilbert-Lepoutre and A. Gkotsinas for input on the water contents of comets. S.N.R. and F.S. thank the CNRS’s PNP programme for support. A.I. and R.D. acknowledge NASA grant number 80NSSC18K0828 for financial support during the preparation and submission of this work. A.I. also thanks the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES), in the scope of the Program CAPES-PrInt, process number 88887.310463/2018-00, International Cooperation Project number 3266 and CNPq (313998/2018-3). P.B. acknowledges a St Leonard’s Interdisciplinary Doctoral Scholarship from the University of St Andrews. L.C. acknowledges support from the DFG Priority Programme SP1833 grant number CA 1795/3. E.A. and S.N.R. acknowledge support from from the Virtual Planetary Laboratory Team, a member of the NASA Nexus for Exoplanet System Science, funded via NASA Astrobiology Program grant number 80NSSC18K0829. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreement number 832738/ESCAPE. This work has been carried out within the framework of the National Centre of Competence in Research PlanetS supported by the Swiss National Science Foundation. M.T. and E.B. acknowledge the financial support of the SNSF. This work was performed using the High-Performance Computing (HPC) resources of Centre Informatique National de l’Enseignement Supérieur (CINES) under allocation number A0080110391 made by Grand Équipement National de Calcul Intensif (GENCI). M.T. thanks the Gruber Foundation for its support to this research. C.D. acknowledges support from the Swiss National Science Foundation under grant number PZ00P2_174028.

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Authors and Affiliations

Authors

Contributions

S.N.R. initiated the project after discussions with L.C., P.B. and A.I., and ran and analysed the simulations using codes optimized by A.I. and configurations of the system provided by S.L.G. and E.A. C.D. and M.T. performed the interior modelling to obtain constraints on the water contents of the TRAPPIST-1 planets. E.B. performed the analysis of the tidal effects. S.N.R. wrote the paper with feedback from A.I., E.B., C.D., F.S., M.T., E.A., P.B., L.C., R.D., M.G. and S.L.G.

Corresponding author

Correspondence to Sean N. Raymond.

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The authors declare no competing interests.

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Peer review information Nature Astronomy thanks Shigeru Ida and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Evolution of resonant angles for our fiducial Trappist-1 system with no added objects.

The top four panels each show one angle that characterizes the mean motion resonance between a pair of neighboring planets, as defined in Equations 1 and 2. The bottom three panels show angles that characterize the 3-body Laplace resonances between triplets of planets, as defined in Eq. 3.

Extended Data Fig. 2 Evolution of the resonant angles for three simulations that included our fiducial Trappist-1 system and 1000 rogue planetesimals.

Each system was stable for the full 10 Myr simulation. The resonant angles that are shown are the same ones presented in Extended Data Fig. 1. The total mass in planetesimals for each system was 0.0213 M (left panel; resonance maintained), 0.0429 M (middle panel; resonance barely maintained), and 0.0645 M (right panel; resonance disrupted).

Extended Data Fig. 3 Disruption of the resonances in the outer parts of the Trappist-1 system.

In this simulation, the fiducial system of planets interacted with 1000 planetesimals containing a total of 0.0967 M. The top panel shows the increase in the semimajor axis of the orbits of planets f, g and h. The other panels show the angles associated with mean-motion and Laplace resonances between the planets.

Extended Data Fig. 4 Effect of the semimajor axis distribution of rogue planetesimals.

The top left panel shows our the subset of our fiducial batch of simulations with 1000 rogue planetesimals with a total mass in rogue planetesimals between 0.01 and 1 Earth mass. The top right and bottom left panels show the sets of simulations with arogue = 0.2 − 0.3 au and arogue = 0.7 − 1 au, and the same periastron distribution as in the fiducial set (with orbits initially crossing those of only the outer planets). The bottom right panel shows a set of simulations in which the rogue planetesimals were on extremely eccentric orbits, with semimajor axes arogue = 0.7 − 1 au and periastron distance qrogue randomly chosen to sample a logarithmic distribution in the range 0.005 − 0.06 au. As in Fig. 1 in the main text, blue filled circles indicate systems that remained in resonant chains, red diamonds those that remained stable for 10 Myr but lost their resonant structure, and black empty circles those that underwent dynamical instabilities.

Extended Data Fig. 5 Effect of the assumed configuration of the Trappist-1 system.

The left-hand panels show the outcomes of simulations containing a single rogue planet, for four different ‘best-fit’ configurations of the Trappist-1 system that are consistent with current observations3. Likewise, the right-hand panels show the outcomes of simulations containing 1000 rogue planetesimals. As in Fig. 1 in the main text, systems that were stable for 10 Myr but in which resonances were broken (red diamonds) are shifted downward slightly for clarity. The top panels (‘Set 1’) represent our fiducial simulations (note that we have only used the subset of fiducial simulations with 1000 rogue planetesimals that fall in the identical mass range as the simulations for the other sets).

Extended Data Fig. 6 Effect of star-planet tidal interactions on the outer planets in the Trappist-1 system.

Left panel: Evolution of the stellar radius with time (given as t − tinit, where tinit = 3 Myr). Right panel: map showing the values of \({{\mathrm{log}}}\,{{\Delta }}| a|\) as a function of the stellar dissipation and time. The stellar dissipation is given with respect to a fiducial value corresponding to a fully convective star or brown dwarf.

Extended Data Fig. 7

Distribution of impact speeds of planetesimals in simulations in which the planets remained in resonance on each of the Trappist-1 planets.

Extended Data Table 1 Upper limits on the total mass in planetesimals that could have collided with each of the Trappist-1 planets (assuming perfect mergers), for four sets of initial orbital distributions for the rogue planetesimals. The first three columns share the same periastron distribution, with starting semimajor axes of 0.07-0.1 au (our fiducial set), 0.2-0.3 au, and 0.7-1 au. The fourth column is from the set in which rogue planetesimals have starting semimajor axes of 0.7-1 au and super-eccentric orbits, with starting periastron distances of 0.005 − 0.063 au. For each set we used the maximum total initial planetesimal mass that preserved the resonant structure of the system: 0.05 M for arogue = 0.07 − 0.1 au and arogue = 0.2 − 0.3 au, 0.1 M for arogue = 0.7 − 1 au with the standard periastron distribution, and 0.018 M for arogue = 0.7 − 1 au with super-eccentric orbits (see Extended Data Fig. 4.)
Extended Data Table 2 Starting orbital configuration of the Trappist-1 system that were used in our fiducial simulations. These are referred to as ’set 1’ in the Methods. The planets’ orbits have zero inclinations, but in our simulations rogue planets and planetesimals were given non-zero inclinations to ensure that the systems were not 2D. The system’s exact configuration was drawn from the best-fit posteriors of Agol et al.3

Supplementary information

Supplementary Information

Supplementary Tables 1–5.

Source data

Source Data Fig. 1

Source data for simulations with both one rogue planet and 1,000 rogue planetesimals.

Source Data Fig. 2

Source data for cosmochemically inferred growth curves and simulated TRAPPIST-1 analogue planets.

Source Data Fig. 3

Source data for water content models (with error bars), late water accretion limits and habitable-zone evolution.

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Raymond, S.N., Izidoro, A., Bolmont, E. et al. An upper limit on late accretion and water delivery in the TRAPPIST-1 exoplanet system. Nat Astron 6, 80–88 (2022). https://doi.org/10.1038/s41550-021-01518-6

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