A seven-planet resonant chain in TRAPPIST-1


The TRAPPIST-1 system is the first transiting planet system found orbiting an ultracool dwarf star1. At least seven planets similar in radius to Earth were previously found to transit this host star2. Subsequently, TRAPPIST-1 was observed as part of the K2 mission and, with these new data, we report the measurement of an 18.77 day orbital period for the outermost transiting planet, TRAPPIST-1 h, which was previously unconstrained. This value matches our theoretical expectations based on Laplace relations3 and places TRAPPIST-1 h as the seventh member of a complex chain, with three-body resonances linking every member. We find that TRAPPIST-1 h has a radius of 0.752 R and an equilibrium temperature of 173 K. We have also measured the rotational period of the star to be 3.3 days and detected a number of flares consistent with a low-activity, middle-aged, late M dwarf.

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Figure 1: Long cadence K2 light curve of TRAPPIST-1 detrended with EVEREST.
Figure 2: Entire systematics-corrected K2 dataset with low-frequency trends removed.


  1. 1

    Gillon, M. et al. Temperate Earth-sized planets transiting a nearby ultracool dwarf star. Nature 533, 221–224 (2016).

    ADS  Article  Google Scholar 

  2. 2

    Gillon, M. et al. Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1. Nature 542, 456–460 (2017).

    ADS  Article  Google Scholar 

  3. 3

    Quillen, A. C. Three-body resonance overlap in closely spaced multiple-planet systems. Mon. Not. R. Astron. Soc. 418, 1043–1054 (2011).

    ADS  Article  Google Scholar 

  4. 4

    Howell, S. B. et al. The K2 mission: characterization and early results. Publ. Astronom. Soc. Pacif. 126, 398–408 (2014).

    ADS  Article  Google Scholar 

  5. 5

    Quintana, E. V. et al. Pixel-level calibration in the Kepler Science Operations Center pipeline. Proc. SPIE 7740, 77401X (2010).

    Article  Google Scholar 

  6. 6

    Demory, B.-O., Queloz, D., Alibert, Y., Gillen, E. & Gillon, M. Probing TRAPPIST-1-like systems with K2. Astrophys. J. Lett. 825, L25 (2016).

    ADS  Article  Google Scholar 

  7. 7

    Luger, R . et al. EVEREST: pixel level decorrelation of K2 light curves. Astron. J. 152, 100 (2016).

    ADS  Article  Google Scholar 

  8. 8

    Luger, R ., Kruse, E ., Foreman-Mackey, D ., Agol, E & Saunders, N. An update to the EVEREST K2 pipeline: short cadence, saturated stars, and Kepler-like photometry down to Kp = 15. Preprint at https://arxiv.org/abs/1702.05488 (2017).

  9. 9

    Peale, S. J. A primordial origin of the Laplace relation among the Galilean satellites. Science 298, 593–597 (2002).

    ADS  Article  Google Scholar 

  10. 10

    Rivera, E. J. et al. The Lick–Carnegie exoplanet survey: a Uranus-mass fourth planet for GJ 876 in an extrasolar Laplace configuration. Astrophys. J. 719, 890–899 (2010).

    ADS  Article  Google Scholar 

  11. 11

    Mills, S. M. et al. A resonant chain of four transiting, sub-Neptune planets. Nature 533, 509–512 (2016).

    ADS  Article  Google Scholar 

  12. 12

    MacDonald, M. G. et al. A dynamical analysis of the Kepler-80 system of five transiting planets. Astron. J. 152, 105 (2016).

    ADS  Article  Google Scholar 

  13. 13

    Baruteau, C . et al. in Protostars and Planets VI 4th edn (eds Beuther, H. et al. ) 667–689 (Univ. Arizona Press, 2014).

    Google Scholar 

  14. 14

    Raymond, S. N., Barnes, R. & Mandell, A. M. Observable consequences of planet formation models in systems with close-in terrestrial planets. Mon. Not. R. Astron. Soc. 384, 663–674 (2008).

    ADS  Article  Google Scholar 

  15. 15

    Masset, F. S., Morbidelli, A., Crida, A. & Ferreira, J. Disk surface density transitions as protoplanet traps. Astrophys. J. 642, 478–487 (2006).

    ADS  Article  Google Scholar 

  16. 16

    Terquem, C. & Papaloizou, J. C. B. Migration and the formation of systems of hot super-Earths and Neptunes. Astrophys. J. 654, 1110–1120 (2007).

    ADS  Article  Google Scholar 

  17. 17

    Ogihara, M. & Ida, S. N-Body simulations of planetary accretion around M dwarf stars. Astrophys. J. 699, 824–838 (2009).

    ADS  Article  Google Scholar 

  18. 18

    Cossou, C., Raymond, S. N., Hersant, F. & Pierens, A. Hot super-Earths and giant planet cores from different migration histories. Astron. Astrophys. 569, A56 (2014).

    ADS  Article  Google Scholar 

  19. 19

    Fabrycky, D. C. et al. Architecture of Kepler’s multi-transiting systems. II. New investigations with twice as many candidates. Astrophys. J. 790, 146 (2014).

    ADS  Article  Google Scholar 

  20. 20

    Izidoro, A . et al. Breaking the chains: hot super-Earth systems from migration and disruption of compact resonant chains. Preprint at https://arxiv.org/abs/1703.03634 (2017).

  21. 21

    Goz’dziewski, K., Migaszewski, C., Panichi, F & Szuszkiewicz, E. The Laplace resonance in the Kepler-60 planetary system. Mon. Not. R. Astron. Soc. 455, L104–L108 (2016).

    ADS  Article  Google Scholar 

  22. 22

    Pascucci, I. et al. A steeper than linear disk mass–stellar mass scaling relation. Astrophys. J. 831, 125 (2016).

    ADS  Article  Google Scholar 

  23. 23

    Matsumoto, Y., Nagasawa, M. & Ida, S. The orbital stability of planets trapped in the first-order mean-motion resonances. Icarus 221, 624–631 (2012).

    ADS  Article  Google Scholar 

  24. 24

    Ferraz-Mello, S., Rodrguez, A. & Hussmann, H. Tidal friction in close-in satellites and exoplanets: the Darwin theory re-visited. Celest. Mech. Dynam. Astron. 101, 171–201 (2008).

    ADS  MathSciNet  Article  Google Scholar 

  25. 25

    Reid, N & Hawley, S. New Light on Dark Stars: Red Dwarfs, Low-Mass Stars, Brown Dwarfs (Springer, 2013).

    Google Scholar 

  26. 26

    Newton, E. R. et al. The rotation and galactic kinematics of mid M dwarfs in the solar neighborhood. Astrophys. J. 821, 93 (2016).

    ADS  Article  Google Scholar 

  27. 27

    Aumer, M. & Binney, J. J. Kinematics and history of the solar neighbourhood revisited. Mon. Not. R. Astron. Soc. 397, 1286–1301 (2009).

    ADS  Article  Google Scholar 

  28. 28

    Burgasser, A. J. et al. The Brown Dwarf Kinematics Project (BDKP). IV. Radial velocities of 85 late-M and L dwarfs with MagE. Astrophys. J. Suppl. 220, 18 (2015).

    ADS  Article  Google Scholar 

  29. 29

    Hilton, E. J ., Hawley, S. L ., Kowalski, A. F & Holtzman, J. The galactic M dwarf flare rate. Astron. Soc. Pacif. Conf. Ser. 448, 197 (2011).

    ADS  Google Scholar 

  30. 30

    Deming, D. et al. Spitzer secondary eclipses of the dense, modestly-irradiated, giant exoplanet HAT-P-20b using pixel-level decorrelation. Astrophys. J. 805, 132 (2015).

    ADS  Article  Google Scholar 

  31. 31

    Howell, S. B. et al. Speckle imaging excludes low-mass companions orbiting the exoplanet host star TRAPPIST-1. Astrophys. J. Lett. 829, L2 (2016).

    ADS  Article  Google Scholar 

  32. 32

    Christiansen, J. L. et al. The derivation, properties, and value of Kepler’s combined differential photometric precision. Publ. Astronom. Soc. Pacif. 124, 1279–1287 (2012).

    ADS  Article  Google Scholar 

  33. 33

    Aigrain, S., Hodgkin, S. T., Irwin, M. J., Lewis, J. R. & Roberts, S. J. Precise time series photometry for the Kepler-2.0 mission. Mon. Not. R. Astron. Soc. 447, 2880–2893 (2015).

    ADS  Article  Google Scholar 

  34. 34

    Aigrain, S., Parviainen, H. & Pope, B. J. S. K2SC: flexible systematics correction and detrending of K2 light curves using Gaussian process regression. Mon. Not. R. Astron. Soc. 459, 2408–2419 (2016).

    ADS  Google Scholar 

  35. 35

    Ambikasaran, S., Foreman-Mackey, D., Greengard, L., Hogg, D. W. & O’Neil, M. Fast direct methods for Gaussian processes. IEEE Trans. Pattern. Anal. Machine Intell. 38, 252–265 (2016).

    ADS  Article  Google Scholar 

  36. 36

    Storn, R. & Price, K. Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997).

    MathSciNet  Article  Google Scholar 

  37. 37

    Mandel, K. & Agol, E. Analytic light curves for planetary transit searches. Astrophys. J. Lett. 580, L171–L175 (2002).

    ADS  Article  Google Scholar 

  38. 38

    Davenport, J. R. A. et al. Kepler flares. II. The temporal morphology of white-light flares on GJ 1243. Astrophys. J. 797, 122 (2014).

    ADS  Article  Google Scholar 

  39. 39

    Kovács, G., Zucker, S. & Mazeh, T. A box-fitting algorithm in the search for periodic transits. Astron. Astrophys. 391, 369 (2002).

    ADS  Article  Google Scholar 

  40. 40

    Gillon, M. et al. The TRAPPIST survey of southern transiting planets. I. Thirty eclipses of the ultra-short period planet WASP-43 b. Astron. Astrophys. 542, A4 (2012).

    ADS  Article  Google Scholar 

  41. 41

    Claret, A. & Bloemen, S. Gravity and limb-darkening coefficients for the Kepler, CoRoT, Spitzer, uvby, UBVRIJHK, and Sloan photometric systems. Astron. Astrophys. 529, 75 (2011).

    ADS  Article  Google Scholar 

  42. 42

    Foreman-Mackey, D. et al. A systematic search for transiting planets in the K2 data. Astrophys. J. 806, 215 (2015).

    ADS  Article  Google Scholar 

  43. 43

    Eggleton, P. P., Kiseleva, L. G. & Hut, P. The equilibrium tide model for tidal friction. Astrophys. J. 499, 853–870 (1998).

    ADS  Article  Google Scholar 

  44. 44

    Leconte, J., Chabrier, G., Baraffe, I. & Levrard, B. Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity. Astron. Astrophys. 516, A64 (2010).

    ADS  Article  Google Scholar 

  45. 45

    Bolmont, E., Raymond, S. N., Leconte, J., Hersant, F. & Correia, A. C. M. Mercury-T: a new code to study tidally evolving multi-planet systems. Applications to Kepler-62. Astron. Astrophys. 583, A116 (2015).

    ADS  Article  Google Scholar 

  46. 46

    Leconte, J., Wu, H., Menou, K. & Murray, N. Asynchronous rotation of Earth-mass planets in the habitable zone of lower-mass stars. Science 347, 632–635 (2015).

    ADS  Article  Google Scholar 

  47. 47

    Neron de Surgy, O. & Laskar, J. On the long term evolution of the spin of the Earth. Astron. Astrophys. 318, 975–989 (1997).

    ADS  Google Scholar 

  48. 48

    Bolmont, E. et al. Tidal dissipation and eccentricity pumping: implications for the depth of the secondary eclipse of 55 Cancri e. Astron. Astrophys. 556, A17 (2013).

    Article  Google Scholar 

  49. 49

    Spencer, J. R., Jessup, K. L., McGrath, M. A., Ballester, G. E. & Yelle, R. Discovery of gaseous S2 in Io’s Pele plume. Science 288, 1208–1210 (2000).

    ADS  Article  Google Scholar 

  50. 50

    Davies, J. H. & Davies, D. R. Earth’s surface heat flux. Solid Earth 1, 5–24 (2010).

    ADS  Article  Google Scholar 

  51. 51

    Turbet, M. et al. The habitability of Proxima Centauri b. II. Possible climates and observability. Astron. Astrophys. 596, A112 (2016).

    Article  Google Scholar 

  52. 52

    Kopparapu, R. K. et al. Habitable zones around main-sequence stars: new estimates. Astrophys. J. 765, 131 (2013).

    ADS  Article  Google Scholar 

  53. 53

    Sotin, C., Grasset, O. & Mocquet, A. Mass radius curve for extrasolar Earth-like planets and ocean planets. Icarus 191, 337–351 (2007).

    ADS  Article  Google Scholar 

  54. 54

    Luger, R. et al. Habitable evaporated cores: transforming mini-Neptunes into super-Earths in the habitable zones of M dwarfs. Astrobiology 15, 57–88 (2015).

    ADS  Article  Google Scholar 

  55. 55

    Luger, R. & Barnes, R. Extreme water loss and abiotic O2 buildup on planets throughout the habitable zones of M dwarfs. Astrobiology 15, 119–143 (2015).

    ADS  Article  Google Scholar 

  56. 56

    Stevenson, D. J. Life-sustaining planets in interstellar space? Nature 400, 32 (1999).

    ADS  Article  Google Scholar 

  57. 57

    Pierrehumbert, R. & Gaidos, E. Hydrogen greenhouse planets beyond the habitable zone. Astrophys. J. 734, L13 (2011).

    ADS  Article  Google Scholar 

  58. 58

    Wordsworth, R. & Pierrehumbert, R. Hydrogen–nitrogen greenhouse warming in Earth’s early atmosphere. Science 339, 64–67 (2013).

    ADS  Article  Google Scholar 

  59. 59

    Ramirez, R. M. & Kaltenegger, L. A volcanic hydrogen habitable zone. Astrophys. J. Lett. 837, L4 (2017).

    ADS  Article  Google Scholar 

  60. 60

    Wordsworth, R . et al. Transient reducing greenhouse warming on early Mars. Geophys. Res. Lett. 44, 665–671 (2017).

    ADS  Article  Google Scholar 

  61. 61

    Kurtz, D. W. An algorithm for significantly reducing the time necessary to compute a discrete Fourier transform periodogram of unequally spaced data. Mon. Not. R. Astron. Soc. 213, 773 (1985).

    ADS  MathSciNet  Article  Google Scholar 

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This paper includes data collected by the K2 mission. Funding for the K2 mission is provided by the NASA (National Space and Aeronautical Administration) Science Mission directorate. This research has made use of NASA’s Astrophysics Data System, the SIMBAD database and VizieR catalogue access tool operated at Centre de Données astronomiques de Strasbourg, Strasbourg, France. The data presented in this paper were obtained from the Mikulski Archive for Space Telescopes. R.L. and E.A. acknowledge support from NASA grant NNX14AK26G and from the NASA Astrobiology Institute’s Virtual Planetary Laboratory Lead Team, funded through the NASA Astrobiology Institute under solicitation NNH12ZDA002C and Cooperative Agreement Number NNA13AA93A. E.A. acknowledges support from NASA grant NNX13AF62G and National Science Foundation grant AST-1615315. E.K. acknowledges support from a National Science Foundation Graduate Student Research Fellowship. B.-O.D. acknowledges support from the Swiss National Science Foundation in the form of a Swiss National Science Foundation Professorship (PP00P2-163967). E.B. acknowledges funding by the European Research Council through ERC grant SPIRE 647383. D.L.H. acknowledges financial support from the UK Science and Technology Facilities Council. M.S. and K.H. acknowledge support from the Swiss National Science Foundation. A.B. acknowledges funding support from the National Science Foundation under award no. AST-1517177 and NASA under grant no. NNX15AI75G. J.L. acknowledges funding from the European Research Council under the European Unions Horizon 2020 research and innovation programme (grant agreement no. 679030/WHIPLASH). M.G., E.J. and V.V.G. are Fonds National de la Recherche Scientifique (F.R.S.-FNRS) Research Associates. S.N.R. thanks the Agence Nationale pour la Recherche for support via grant ANR-13-BS05-0003-002 (grant MOJO). The research leading to these results has received funding from the European Research Council under the FP/2007-2013 European Research Council Grant Agreement no. 336480 and from the Actions de Recherche Concertée (ARC) grant for Concerted Research Actions, financed by the Wallonia–Brussels Federation. S.B.H. wrote science cases to the K2 project office to include TRAPPIST-1 in the campaign 12 field and to make the raw data public upon downlink. D.F.M. is a Sagan Fellow.

Author information




R.L. and M.S. led the detrending efforts with EVEREST and the Gaissian process-based pipeline, with inputs from E.A., J.G.I, E.K. and D.F.M. R.L. performed the preliminary manual search for transits of TRAPPIST-1 h and the Δχ2 search, with input from E.A, E.K. and D.F.M. S.L.G. took care of the K2 data handling. B.-O.D. led the collaboration, wrote the K2 proposal and performed an independent transit search and Markov Chain Monte Carlo analysis of the K2 dataset. E.A. and D.F. led the dynamics and architecture of the system with inputs from S.N.R. and B.-O.D. E.B. took care of the tidal simulations. C.S.F, V.V.G., A.B., D.L.H. and B.M.M. conducted the work on stellar properties and variability and determined the stellar rotation period. S.N.R. led the formation and migration section. F.S., J.L. and M.T. worked on the atmospheric nature of TRAPPIST-1 h. G.B. and T.B. helped with the handling of the uncalibrated K2 fits files. Figures were prepared by R.L., A.H.M.J.T., J.G.I., E.B and E.K. M.G., E.J., A.H.M.J.T., L.D., J.d.W, S.L., Y.A., Z.B., P.M., K.H. and D.Q. contributed to the discovery and characterization of the TRAPPIST-1 system. All authors participated in the writing and commented on the paper.

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Correspondence to Rodrigo Luger.

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Luger, R., Sestovic, M., Kruse, E. et al. A seven-planet resonant chain in TRAPPIST-1. Nat Astron 1, 0129 (2017). https://doi.org/10.1038/s41550-017-0129

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