Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1

Seven temperate terrestrial planets around the nearby ultracool

dwarf star TRAPPIST-1

Michaël Gillon

Amaury H. M. J. Triaud

Brice-Olivier Demory

3,4

Emmanuël Jehin

Eric

Agol

5,6

Katherine M. Deck

Susan M. Lederer

Julien de Wit

Artem Burdanov

James

G. Ingalls

Emeline Bolmont

11,12

Jeremy Leconte

Sean N. Raymond

Franck

Selsis

Martin Turbet

Khalid Barkaoui

Adam Burgasser

Matthew R. Burleigh

Sean J. Carey

Aleksander Chaushev

Chris M. Copperwheat

Laetitia Delrez

1,4

Catarina S. Fernandes

Daniel L. Holdsworth

Enrico J. Kotze

Valérie Van Grootel

Yaseen Almleaky

21,22

Zouhair Benkhaldoun

Pierre Magain

, and

Didier Queloz

4,23

Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège,

Allée du 6 Août 17, Bat. B5C, 4000 Liège, Belgium

Institute of Astronomy, Madingley Road,

Cambridge CB3 0HA, UK

University of Bern, Center for Space and Habitability, Sidlerstrasse 5,

CH-3012, Bern, Switzerland

Cavendish Laboratory, J J Thomson Avenue, Cambridge, CB3 0HE,

Astronomy Department, University of Washington, Seattle, WA, 98195, USA

NASA

Astrobiology Institute's Virtual Planetary Laboratory, Seattle, WA, 98195, USA

Department of

Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, USA

NASA Johnson Space Center, 2101 NASA Parkway, Houston, Texas, 77058, USA

Department

of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, 77

Massachusetts Avenue, Cambridge, MA 02139, USA

Spitzer Science Center, California Institute

of Technology, 1200 E California Boulevard, Mail Code 314-6, Pasadena, CA 91125, USA

NaXys, Department of Mathematics, University of Namur, 8 Rempart de la Vierge, 5000 Namur,

Belgium

Laboratoire AIM Paris-Saclay, CEA/DRF - CNRS - Univ. Paris Diderot - IRFU/SAp,

Centre de Saclay, F- 91191 Gif-sur-Yvette Cedex, France

Laboratoire d'astrophysique de

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Correspondence and requests for materials should be addressed to M.G. (michael.gillon@ulg.ac.be).

Author Contributions.

MG leads the ultracool dwarf transit survey of TRAPPIST and the photometric follow-up of TRAPPIST-1, planned and analysed most

of the observations, led their scientific exploitation, and wrote most of the manuscript. AHMJT led the observational campaign with

La Palma telescopes (LT & WHT), CMC managed the scheduling of the LT observations, and ArB performed the photometric analysis

of the resulting LT & WHT images. BOD led the TTV/dynamical simulations. EA and KMD performed independent analyses of the

transit timings. JI and SC helped optimizing the Spitzer observations. BoD, JI, and JdW performed independent analyses of the Spitzer

data. MG, EJ, LD, ArB, PM, KB, YA, and ZB performed the TRAPPIST observations and their analysis. SL obtained the DD time on

UKIRT and managed with EJ the preparation of the UKIRT observations. MT, JL, FS, EB, and SNR performed atmospheric modeling

for the planets and worked on the theoretical interpretation of their properties. VVG managed the SAAO observations performed by

CSF, MRB, DLH, AS and EJK. All co-authors assisted writing the manuscript. AHMJT prepared most of the figures in the paper.

Acknowledgments are presented online as Supplementary Information.

Author Information.

Reprints and permissions information is available at

www.nature.com/reprints

The authors declare no competing financial interests. Readers are welcome to comment on the online version of the paper.

Online Content.

Methods, along with any additional Extended Data display items and Source Data, are available in the online version of the paper;

references unique to these sections appear only in the online paper.

Europe PMC Funders Group

Author Manuscript

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. Author manuscript; available in PMC 2017 August 22.

Published in final edited form as:

Nature

. 2017 February 22; 542(7642): 456–460. doi:10.1038/nature21360.

Europe PMC Funders Author Manuscripts

Bordeaux, Univ. Bordeaux, CNRS, B18N, Allée Geoffroy Saint-Hilaire, F-33615 Pessac, France

Laboratoire de Météorologie Dynamique, Sorbonne Universités, UPMC Univ Paris 06, CNRS, 4

place Jussieu, 75005 Paris, France

Laboratoire LPHEA, Oukaimeden Observatory, Cadi Ayyad

University/FSSM, BP 2390, Marrakesh, Morocco

Center for Astrophysics and Space Science,

University of California San Diego, La Jolla, CA, 92093, USA

Leicester Institute for Space and

Earth Observation, Dept. of Physics and Astronomy, University of Leicester, Leicester LE1 7RH,

Astrophysics Research Institute, Liverpool John Moores University, Liverpool L3 5RF, UK

Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1 2HE, UK

South

African Astronomical Observatory, PO Box 9, Observatory 7935, Cape Town, South Africa

Space and Astronomy Department, Faculty of Science, King Abdulaziz University, 21589

Jeddah, Saudi Arabia

King Abdulah Centre for Crescent Observations and Astronomy

(KACCOA), Makkah Clock, Saudia Arabia

Observatoire de Genève, Université de Genève, 51

chemin des Maillettes, CH-1290 Sauverny, Switzerland

Abstract

One focus of modern astronomy is to detect temperate terrestrial exoplanets well-suited for

atmospheric characterisation. A milestone was recently achieved with the detection of three Earth-

sized planets transiting (i.e. passing in front of) a star just 8% the mass of the Sun 12 parsecs

away

. Indeed, the transiting configuration of these planets combined with the Jupiter-like size of

their host star - named TRAPPIST-1 - makes possible in-depth studies of their atmospheric

properties with current and future astronomical facilities

. Here we report the results of an

intensive photometric monitoring campaign of that star from the ground and with the Spitzer

Space Telescope. Our observations reveal that at least seven planets with sizes and masses similar

to the Earth revolve around TRAPPIST-1. The six inner planets form a near-resonant chain such

that their orbital periods (1.51, 2.42, 4.04, 6.06, 9.21, 12.35 days) are near ratios of small integers.

This architecture suggests that the planets formed farther from the star and migrated inward

The seven planets have equilibrium temperatures low enough to make possible liquid water on

their surfaces

Among the three initially reported TRAPPIST-1 planets, one of them - called

'TRAPPIST-1d' in the discovery publication

- was identified based on only two transit

signals observed at moderate signal-to-noise. We also observed its second transit signal -

blended with a transit of planet c - with the HAWK-I infrared imager on the Very Large

Telescope (Chile). Our analysis of the VLT/HAWK-I data - subsequent to the submission of

the discovery paper - resulted in a light curve of high enough precision to firmly reveal the

triple nature of the observed eclipse (Extended Data Fig. 1). This intriguing result motivated

us to intensify our photometric follow-up of the star which resumed in February and March

2016 with observations of six possible transit windows of 'TRAPPIST-1d' with the Spitzer

Space Telescope. It continued in May 2016 with the intense ground-based observations of

the star with TRAPPIST-South in Chile, its newly-commissioned Northern twin TRAPPIST-

North in Morocco, the 3.8m UKIRT telescope at Hawaii, the 4m William Herschel and the

2m Liverpool telescopes at La Palma, and the SAAO 1.0m telescope in South Africa. It

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culminated on 19 September 2016 with the start of a 20d-long nearly continuous monitoring

campaign of the star by the Spitzer Space Telescope at 4.5 μm.

The light curves obtained prior to 19 September 2016 allowed us to discard the eleven

possible periods of 'TRAPPIST-1d'

, indicating that the two observed transits originated

from different objects. Furthermore, these light curves showed several transit-like signals of

unknown origins that we could not relate to a single period (Extended Data Fig. 2 and 3).

The situation was resolved through the 20d-long photometric monitoring campaign of the

star by Spitzer. Its resulting light curve shows 34 clear transits (Fig. 1) that - when combined

with the ground-based dataset - allowed us to unambiguously identify four periodic transit

signals of periods 4.04d, 6.06d, 8.1d and 12.3d that correspond to four new transiting planets

named respectively TRAPPIST-1d, e, f, and g (Fig. 1, Extended Data Fig. 2 and 3). The

uniqueness of the solution is ensured by the sufficient numbers of unique transits observed

per planet (Table 1), by their consistent shapes for each planet (see below), and by the near-

continuous nature of the Spitzer light curve and its duration longer than the periods of the

four planets. The Spitzer photometry also shows an orphan transit-shaped signal with a

depth of ~0.35% and a duration of ~75min occurring at JD~2,457,662.55 (Fig. 1) that we

attribute to a seventh outermost planet of unknown orbital period, TRAPPIST-1h. We

combed our ground-based photometry in search of a second transit of this planet h, but no

convincing match was identified.

We analysed our extensive photometric dataset in three phases. First, we performed

individual analyses of all transit light curves with an adaptive Markov-Chain Monte Carlo

(MCMC) code

to measure their depths, durations, and timings (see Methods). We derived

a mean transit ephemeris for each planet from their measured transit timings. We

successfully checked the consistency of the durations and depths of the transits for planets b

to g. For each planet, and especially for f and g, the residuals of the fit show transit timing

variations (TTVs) with amplitudes ranging from a few tens of seconds to more than 30

minutes that indicate significant mutual interactions between the planets

(Extended

Fig. 2 and 3).

In a second phase, we performed a global MCMC analysis of the transits observed by

Spitzer to constrain the orbital and physical parameters of the seven planets. We decided to

use only the Spitzer data due to their better precision compared with most of our ground-

based data, and of the minimal amplitude of the limb-darkening at 4.5μm which strengthens

constraints possible on the transit shapes - and thus on the stellar density and, by extension,

on the physical and orbital parameters of the planets

. We assumed circular orbits for all of

the planets, based on the results of N-body dynamical simulations that predicted orbital

eccentricities < 0.1 for the six inner planets (Table 1); the orbital eccentricity of the outer

planet h cannot be constrained from a single transit. This global analysis assumed the

priori

knowledge for the star that is described in

ref. 1

(see Methods). To account for

significant planet-planet interaction, TTVs were included as free parameters for the six inner

planets. We used each planet's transit ephemeris (derived in the first phase) as a prior on the

orbital solution.

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In a third phase, we used the results obtained above to investigate the TTV signals

themselves. By performing a series of analytical and numerical N-body integrations (see

Methods), we could determine initial mass estimates for the six inner planets, along with

their orbital eccentricities. We emphasise the preliminary nature of this dynamical solution

which may not correspond to a global minimum of the parameter space, and that additional

transit observations of the system will be required to lift the existing degeneracies (see

Methods).

Table 1 shows the main planetary parameters derived from our data analysis. We find that

five planets (b, c, e, f, g) have sizes similar to the Earth, while the other two (d and h) are

intermediate between Mars (~0.5

Earth

) and Earth. The mass estimates for the six inner

planets broadly suggest rocky compositions

(Fig. 2.a). Their precisions are not high

enough to constrain the volatile contents of the planets, except for TRAPPIST-1f whose low

density favors a volatile-rich composition. The volatile content could be in the form of an ice

layer and/or of an atmosphere, something that can be verified with follow-up observations

during transit with space telescopes like Hubble

and James Webb

. We note that the ratio

of masses between the six inner planets and TRAPPIST-1 and that of the Galilean satellites

and Jupiter are both ~0.02%, maybe implying a similar formation history

The derived planets' orbital inclinations are all very close to 90°, indicating a dramatically

coplanar system seen nearly edge-on. Furthermore, the six inner planets form the longest

currently-known near-resonant chain of exoplanets, with the orbital periods ratios

, and

close to the ratios of small integers 8:5, 5:3, 3:2, 3:2, and 4:3,

respectively. This proximity to mean motion resonances of several planet pairs explains the

significant amplitudes of the measured TTVs. Similar near-resonant chains involving up to

four planets have been discovered in compact systems containing super-Earths and Neptunes

orbiting Sun-like stars

. Orbital resonances are naturally generated when multiple planets

interact within their nascent gaseous discs

. The favoured theoretical scenario for the origin

of the TRAPPIST-1 system is an accretion of the planets farther from the star followed by a

phase of disc-driven inward migration

, a process first studied in the context of the

Galilean moons around Jupiter

. The planets’ compositions should reflect their formation

zone so this scenario predicts that the planets should be volatile-rich and have lower

densities than Earth

, in good agreement with our preliminary result for TRAPPIST-1f

(Fig. 2a).

The stellar irradiation of the planets cover a range of ~4.3 to ~0.13

Earth

(=solar irradiation

at 1 au) which is very similar to the one of the inner solar system (Mercury=6.7

Earth

Ceres=0.13

Earth

,). Notably, planets c, d, and f have stellar irradiations very close to those

of Venus, Earth, and Mars, respectively (Fig. 2). However, even at these low insolations, all

seven planets are expected to be either tidally synchronized

, or trapped in a higher-order

spin-orbit resonance, the latter being rather unlikely considering the constraints on the

orbital eccentricities

(Table 1). Using a 1D cloud-free climate model accounting for the

low-temperature spectrum of the host star

, we infer that the three planets e, f, and g could

harbour water oceans on their surfaces, assuming Earth-like atmospheres. The same

inference is obtained when running a 3D climate model

assuming that the planets are

tidally synchronous. For the three inner planets (b,c,d), our 3D climate modeling results in

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runaway greenhouses. The cloud feedback that usually decreases the surface temperatures

for synchronous planets is rather inefficient for such short period objects

. Nevertheless, if

some water survived the hot early phase of the system

, the irradiation received by planets

(b,c,d) are still low enough to make possible for limited regions on their surfaces to harbour

liquid water

.While the orbital period, and therefore distance of planet h is not yet well

defined, its irradiation is probably too low to sustain surface temperatures above the melting

point of water. However, it could still harbour surface liquid water providing a large enough

internal energy - e.g. from tidal heating - or the survival of a significant fraction of its

primordial H

-rich atmosphere that could strongly slow down the loss of its internal heat

We found the long-term dynamical evolution of the system to be very dependent on the exact

orbital parameters and masses of the seven planets, which are currently too uncertain to

make possible any reliable prediction (see Methods). All our dynamical simulations predict

small but non-zero orbital eccentricities for the six inner planets (see 2-

upper limits in

Table 1). The resulting tidal heating could be strong enough to significantly impact their

energy budgets and geological activities

The TRAPPIST-1 system is a compact analog of the inner solar system (Fig. 2.b). It

represents a unique opportunity to thoroughly characterise

temperate Earth-like planets

orbiting a much cooler and smaller star than the Sun, and notably to study the impact of tidal

locking

, tidal heating

, stellar activity

and an extended pre-main-sequence phase

their atmospheric properties.

Methods

Observations and photometry

In addition to the ground-based observations described in

ref. 1

, this work was based on

1333 hrs of new observations gathered from the ground with the 60cm telescopes

TRAPPIST-South (469 hrs) and TRAPPIST-North (202 hrs), the 8m Very Large Telescope

(3 hrs), the 4.2m William Herschel telescope (26 hrs), the 4m UKIRT telescope (25 hrs), the

2m Liverpool telescope (50 hrs), and the 1m SAAO telescope (11 hrs), and from space with

Spitzer (518 hrs).

The new observations of the star gathered by the TRAPPIST-South

60cm telescope

(La Silla Observatory, Chile) occurred on the nights of 29 to 31 December 2015 and from 30

April to 11 October 2016. The observational strategy used was the same as that described in

ref. 1

for previous TRAPPIST-South observations of the star.

TRAPPIST-North

is a new 60cm robotic telescope installed in spring 2016 at

Oukaïmeden Observatory in Morocco. It is an instrumental project led by the University of

Liège, in collaboration with the Cadi Ayyad University of Marrakesh, that is, like its

southern twin TRAPPIST-South, totally dedicated to the observations of exoplanet transits

and small bodies of the solar system. TRAPPIST-North observations of TRAPPIST-1 were

performed from 1 June to 12 October 2016. Each run of observations consisted of 50s

exposures obtained with a thermoelectrically-cooled 2k×2k deep-depletion CCD camera

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(field of view of 19.8' × 19.8', image scale of 0.61"/pixel). The observations employed the

same 'I+z' filter as for most of the TRAPPIST-South observations

The new VLT/HAWK-I

(Paranal Observatory, Chile) observations that revealed a triple

transit of planets c-e-f (see main text and Extended Data Fig. 1) were performed during the

night of 10 to 11 December 2015 with the same observational strategy than described in

ref.

(NB2090 filter), except that each exposure was composed of 18 integrations of 2s.

The 4m telescope UKIRT (Mauna Kea, Hawaii) and its WFCAM infrared camera

observed the star on 24 June, 16-18-29-30 July, and 1 August 2016. Here too, the exact same

observational strategy as its previous observations of the star

was used for these new

observations (J filter, exposures of 5 integrations of 1s).

The 4.2m William Herschel Telescope (La Palma, Canary Islands) observed the star for

three nights in a row from 23 to 25 August 2016 with its optical 2k × 4k ACAM camera

that has an illuminated circular field of view of 8' diameter and an image scale of 0.25"/

pixel. The observations were performed in the Bessel I filter with exposure times between 15

and 23s.

10 runs of observation of TRAPPIST-1 were performed by the robotic 2m Liverpool

Telescope between June and October 2016. These observations were obtained through a

Sloan-z filter with the 4k × 4k IO:O CCD camera

(field of view of 10' × 10'). A 2 × 2

binning scheme resulted in an image scale of 0.30"/pixel. An exposure time of 20s was used

for all images.

The 1m telescope at the South African Astronomical Observatory (Sutherland, South Africa)

observed the star on the nights of 18-19 June, 21-22 June, and 2-3 July 2016. The

observations consisted of 55s exposures taken by the 1k × 1k SHOC CCD camera

(field

of view of 2.85' × 2.85') using a Sloan z filter and with a 4 × 4 binning, resulting in an image

scale of 0.67"/pixel.

For all ground-based data, a standard pre-reduction (bias, dark, flat-field correction) was

applied, followed by the measurements of the stellar fluxes from the calibrated images using

the DAOPHOT aperture photometry software

. In a final stage, a selection of stable

comparison stars was manually performed to obtain the most accurate differential

photometry possible for TRAPPIST-1.

The Spitzer Space Telescope observed TRAPPIST-1 with its IRAC detector

for 5.7 hrs on

21 February 2016, 6.5 hrs on 3-4-7-13-15-18 March 2016, and continuously from 19

September to 10 October 2016. All these observations were done at 4.5 μm in subarray

mode (32x32 pixel windowing of the detector) with an exposure time of 1.92s. The

observations were done without dithering and in the PCRS peak-up mode

that maximizes

the accuracy in the position of the target on the detector to minimize the so-called pixel

phase effect of IRAC InSb arrays

. All the Spitzer data were calibrated with the Spitzer

pipeline S19.2.0 and delivered as cubes of 64 subarray images. Our photometric extraction

was identical to the one described in

ref. 43

. DAOPHOT was used to measure the fluxes by

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aperture photometry and the measurements were combined per cube of 64 images. The

photometric errors were taken as the errors on the average flux measurements for each cube.

The observations used in this work are summarized in Extended Data Table 1.

Analysis of the photometry

The total photometric dataset - including the data presented in

ref. 1

- consists in 81,493

photometric measurements spread over 351 light curves. We converted each universal time

(

) of mid-exposure to the BJD

TDB

time system

. We then performed an individual model

selection for each light curve, tested a large range of models composed of a baseline model

representing the flux variations correlated to variations of external parameters (e.g. point-

spread function size or position on the chip, time, airmass) as low-order (0 to 4) polynomial

functions, eventually added to a transit model

and/or to a flare model (instantaneous flux

increase followed by an exponential decrease) if a structure consistent in shape with these

astrophysical signals was visible in the light curve (two of them were captured by Spitzer

during its 20d-monitoring campaign, see Fig. 1). The final model of each light curve was

selected by minimization of the Bayesian Information Criterion (BIC)

. For all the Spitzer

light curves, it was necessary to include a linear or quadratic function of the

- and

positions of the point-spread function (PSF) centre (as measured in the images by the fit of a

2D-gaussian profile) in the baseline model to account for the pixel phase effect

complemented for some light curves by a linear or quadratic function of the measured

widths of the PSF in the

- and/or

-directions

For each light curve presenting a transit-like structure whose existence was favoured by the

BIC, we explored the posterior probability distribution function (PDF) of its parameters

(width, depth, impact parameter, mid-transit timing) with an adaptive Markov-chain Monte

Carlo (MCMC) code

. For the transits originating from the firmly confirmed planets b and

c, we fixed the orbital period to the values presented in

ref. 1

. For the other transit-like

structures, the orbital period was also a free parameter. As in

ref. 1

, circular orbits were

assumed for the planets, and the normal distributions

(0.04, 0.08

) dex,

(2,555, 85

) K,

(0.082, 0.011

)

⊙

, and

(0.114, 0.006

)

⊙

were assumed as prior PDF for the stellar

metallicity, effective temperature, mass, and radius, respectively, on the basis of

a priori

knowledge of the stellar properties

. A quadratic limb-darkening law was assumed for

the star

with coefficients interpolated for TRAPPIST-1 from the tables of

ref. 49

. The

details of the MCMC analysis of each light curve were the same as described in

ref. 1

The resulting values for the timings of the transits were then used to identify planetary

candidates by searching for periodicities and consistency between the derived transit shape

parameters. Owing to the high-precision and nearly-continuous nature of the photometry

acquired by Spitzer on September and October 2016, this process allowed us to firmly

identify the four new planets d-e-f-g with periods of 4.1d, 6.1d, 9.2d and 12.3d (Extended

Data Fig. 2 & 3). We then measured updated values for their transit timings through new

MCMC analyses of their transit light curves for which the orbital periods were fixed to the

determined values. For the six planets b-c-d-e-f-g, we then performed a linear regression

analysis of the measured transit timings as a function of their epochs to derive a transit

ephemeris

(±

) +

P (±

)

, with

the timing of a reference transit for which

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the epoch is arbitrarily set to 0,

the orbital period, and

and

their errors as deduced

from the covariance matrix (Table 1). For all planets, the residuals of the fit showed some

significant deviation indicating TTVs, which is unsurprising given the compactness of the

system and the near-resonant chain formed by the six inner planets (see below).

For a transit-like signal observed by Spitzer at JD~2,457,662.55 (Fig. 1), the significance of

the detection (>10

) was large enough to allow us to conclude that a seventh, outermost

planet exists as well. This conclusion is not only based on the high significance of the signal

and the consistency of its shape with one expected for a planetary transit, but also on the

photometric stability of the star at 4.5 μm (outside of the frequent transits and the rare -

about 1 per week - flares) as revealed by Spitzer (Fig. 1).

In a final stage, we performed the global MCMC analysis of the 35 transits observed by

Spitzer which is described in the main text. It consisted in 2 chains of 100,000 steps whose

convergence was successfully checked using the statistical test of Gelman & Rubin

. The

parameters derived from this analysis for the star and its planets are shown in Table 1.

TTV analysis

We used the TTV method

to estimate the masses of the TRAPPIST-1 planets. The

continuous exchange of angular momentum between gravitationally interacting planets

causes them to accelerate and decelerate along their orbits, making their transit times occur

early or late compared to a Keplerian orbit

All six inner TRAPPIST-1 planets exhibit transit timing variations due to perturbations from

their closest neighbours (Extended Data Fig. 4). The TTV signal for each planet is

dominated primarily by interactions with adjacent planets, and these signals have the

potential to be particularly large because each planet is near a mean motion resonance with

its neighbours. As calculated from the current data, the TTV amplitudes range in magnitude

from 2 to more than 30 minutes However, the distances of these pairs to exact resonances

controls the amplitude and the period of the TTV signals and is not precisely pinned down

by the current dataset. Additionally, the relatively short timeframe during which transits have

been monitored prevents an efficient sampling of the TTV oscillation frequencies for the

different pairs of planets defined by

f(TTV)

, where

is the orbital period,

the

mean motion, and

and

the planet indices

We modeled TTV using both numerical (TTVFast

, Mercury

) and analytical

(TTVFaster

) integrations of a system of six gravitationally interacting, coplanar planets.

TTVFaster is based on analytic approximations of TTVs derived using perturbation theory

and includes all terms at first order in eccentricity. Furthermore, it only includes

perturbations to a planet from adjacent planets. To account for the 8:5 and 5:3 near

resonances in the system, we also included the dominant terms for these resonances which

appear at second and third order in the eccentricities. We determined these higher order

terms using the results of

ref. 54

. TTVFaster has the advantage that the model is

significantly faster to compute compared with N-body integrations. It is applicable for this

system given the low eccentricities determined via TTV analysis (determined independently

from N-body integrations and self-consistently with TTVFaster).

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Two different minimization techniques were used: Levenberg-Marquardt

and Nelder-

Mead

. For the purpose of the analyses, we used the 98 independent transit times for all six

planets and 5 free parameters per planet (mass, orbital period, transit epoch and eccentricity

vectors

cos

and

sin

with

the eccentricity and

the argument of periastron). We

elected not to include the seventh planet TRAPPIST-1h in the fit because only a single

transit has been observed and there is not yet an indication of detectable interactions with

any of the inner planets. Likewise, we did not detect any perturbation that would require the

inclusion of an additional, undetected non-transiting planet in the dynamical fit. The 6-planet

model provided a good fit to the existing data (Extended Data Fig. 4), and we found no

compelling evidence for extending the current model complexity given the existing data.

Our three independent analyses of the same set of transit timings revealed multiple, mildly

inconsistent, solutions that fit the data equally well provided non-circular orbits are allowed

in the fit. It is likely that this solution degeneracy originates from the high-dimensionality of

the parameter space combined with the limited constraints brought by the current dataset.

The best-fit solution that we found - computed with Mercury - has a chi-squared of 92 for 68

degrees of freedom, but involves non-negligible eccentricities (0.03 to 0.05) for all planets,

likely jeopardising the long-term stability of the system. In this context, we decided to

present conservative estimates of the planets' masses and upper limits for the eccentricities

without favouring one of the three independent analyses. For each parameter, we considered

as the 1-

lower/upper limits the smallest/largest values of the 1-

lower/upper limits of the

three posterior PDFs, and the average of the two computed limits as the most representative

value. The values and error bars computed for the planets' masses and the 2-

upper limits

for their orbital eccentricities are given in Table 1.

Additional precise transit timings for all seven planets will be key in constraining further the

planet masses and eccentricities and in isolating a unique, well-defined, dynamical solution.

Preliminary assesment of the long-term stability of the system

We investigated the long-term evolution of the TRAPPIST-1 system using two N-body

integration packages: Mercury

and WHFAST

. We started from the orbital solution

produced in Table 1, and integrated over 0.5 Myr. This corresponds to roughly 100 million

orbits for planet b. We repeated this procedure by sampling a number of solutions within the

intervals of confidence. Most integrations resulted in the disruption of the system on a

0.5 Myr timescale.

We then decided to employ a statistical method yielding the probability for a system to be

stable for a given period of time, based on the planets' mutual separations

. Using the

masses and semi-major axes in Table 1, we calculated the separations between all adjacent

pairs of planets in units of their mutual Hill spheres

. We found an average separation of

10.5 ± 1.9 (excluding planet h), where the uncertainty is the rms of the six mutual

separations. We computed that TRAPPIST-1 has a 25% chance of suffering an instability

over 1 Myr, and 8.1% to survive over 1 Gyr, in line with our N-body integrations.

Those results obtained by two different methods imply that the TRAPPIST-1 system could

be unstable over relatively short timescales. However, they do not take into account the

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proximity of the planets to their host star and the resulting strong tidal effects that can act to

stabilise the system. We included tidal effects in an ameliorated version of the Mercury

package

, and found that they significantly enhance the system's stability. However, the

disruption is only postponed by tides in most simulations, and further investigations are

needed in order to better understand the dynamics of the system. In general, the stability of

the system appears to be very dependent on the assumptions on the orbital parameters and

masses of the planets, and on the inclusion or exclusion of planet h and on its assumed

orbital period and mass. It is also possible that other, still undetected, planets help stabilizing

the system. The masses and exact eccentricities of the planets remain currently uncertain,

and our results make likely that only a very small number of orbital configurations lead to

stable configurations. For instance, mean-motion resonances can protect planetary systems

over long timescales

. The system clearly exists, and it is unlikely that we are observing it

just before its catastrophic disruption, so it is most probably stable over a significant

timescale. These facts and the results of our dynamical simulations indicate that, provided

enough data, the very existence of the system should bring strong constraints on its

components' properties: masses, orbital elements, tidal dissipation efficiencies, which are

dependent on the planets' compositions, mutual tidal effects of the planets, mutual

inclinations, orbit of planet h, existence of other, maybe not transiting planets, etc.

Code availability

The conversion of the UT times of the photometric measurements to the BJD

TDB

system

was performed using the online program created by J. Eastman and distributed at

http://

astroutils.astronomy.ohio-state.edu/time/utc2bjd.html

. The MCMC software used to analyse

the photometric data is a custom Fortran 90 code that can be obtained from the

corresponding author on reasonable request. The N-body integration codes TTVFast,

TTVFaster, and Mercury are freely available online at

https://github.com/kdeck/TTVFast

https://github.com/ericagol/TTVFaster

, and

https://github.com/smirik/mercury

. To realise

Fig.2a, we relied on TEPCAT, an online catalogue of transiting planets maintained by John

Southworth (

http://www.astro.keele.ac.uk/jkt/tepcat/

Data availability

The Spitzer data that support the findings of this study are available from the Spitzer

Heritage Archive database (

http://sha.ipac.caltech.edu/applications/Spitzer/SHA

). Source

data for Fig. 1 and Extended Data Fig. 1, 2, 3, and 4 are provided with the paper. The other

datasets generated during and/or analysed during the current study are available from the

corresponding author on reasonable request.

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Extended Data

Extended Data Figure 1. Light curve of a triple transit of planets c-e-f

The black points show the differential photometric measurements extracted from VLT/

HAWK-I images, with the formal 1-sigma errors shown as vertical lines. The best-fit triple

transit model is shown as a red line. Possible configurations of the planets relative to the

stellar disc are shown below the light curve for three different times (red = planet c, yellow =

planet e, green = planet f). The relative positions and sizes of the planets, as well as the

impact parameters correspond to the values given in Table 1.

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Extended Data Figure 2. Transit light curve of TRAPPIST-1d and e

The black points show the photometric measurements - binned per 0.005d = 7.2min. The

error for each bin (shown as vertical line) was computed as the 1-sigma error on the average.

These light curves are divided by their best-fit instrumental models and by the best-fit transit

models of other planets (for multiple transits). The best-fit transit models are shown as solid

lines. The light curves are period-folded on the best-fit transit ephemeris given in Table 1,

their relative shifts on the

-axis reflecting TTVs due to planet-planet interactions (see text).

The epoch of the transit and the facility used to observe it are mentionned above each light

curve.

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Extended Data Figure 3.

Transit light curves of TRAPPIST-1f and g. Same as Extended Data Fig. 2 for the planets f

and g.

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Extended Data Figure 4. Transit Timing Variations (TTVs) measured for TRAPPIST-1b-c-d-e-f-

For each planet, the best-fit TTV model computed with the N-body numerical integration

code Mercury

is shown as a red line. The 1-sigma errors of the transit timing

measurements are show as vertical lines.

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Extended Data Table 1

Summary of the observations set used in this work.

For each facility/instrument, the following parametrs are given: the effective number of observation (not accounting for calibration and overhead times),

the year(s) of observation, the number of resulting light curves, the used filter or grism, and the number of transits observed for the seven planets

TRAPPIST-1 b-c-d-e-f-g-h.

Facility/instrument

Number of hrs

Year(s)

Number of light curves

Filter/grism

Number of transits

TRAPPIST-South

677.9

2013

2015

2016

214

1+z

b: 13, c: 1, d: 3, e: 5, f: 3, g: 4

Spitzer/IRAC

476.8

2016

4.5 μm

b: 16, c: 11, d: 5, e: 2, f: 3, g: 2, h: 1

TRAPPIST-North

206.7

2016

I+z

b: 4, c: 3, e: 1

LT/IO:O

50.3

2016

b: 1, c: 1, e: 1, f: 1

UKIRT/WFCAM

34.5

2015

2016

b: 4, c: 3

WHT/ACAM

25.8

2016

b: 1, c: 1, d: 1

SAAO- lm/SHOC

10.7

2016

None

VLT/HAWK-I

6.5

2015

NB2090

b: 1, c: 1, e: 1, f: 1

HCT/HFOSC

4.8

2016

b: 1

HST/WFC3

3.9

2016

G141(1.1-1.7 μm)

b: 1, c: 1

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Acknowledgments

This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet

Propulsion Laboratory, California Institute of Technology under a contract with NASA. The material presented here

is based on work supported in part by NASA under Contract No. NNX15AI75G. TRAPPIST-South is a project

funded by the Belgian F.R.S.-FNRS under grant FRFC 2.5.594.09.F, with the participation of the Swiss FNS.

TRAPPIST-North is a project funded by the University of Liège, and performed in collaboration with Cadi Ayyad

University of Marrakesh. The research leading to these results has received funding from the European Research

Council under the FP/2007- 2013 ERC Grant Agreement n° 336480 and under the H2020 ERC Grant Agreement n°

679030, and from the ARC grant for Concerted Research Actions, financed by the Wallonia- Brussels Federation.

UKIRT is supported by NASA and operated under an agreement among the University of Hawaii, the University of

Arizona, and Lockheed Martin Advanced Technology Center; operations are enabled through the cooperation of the

East Asian Observatory. The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores

University (JMU) in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de

Canarias with financial support from the UK Science and Technology Facilities Council. This paper uses

observations made at the South African Astronomical Observatory (SAAO). MG, EJ, and VVG are F.R.S.-FNRS

Research Associates. BOD acknowledges support from the Swiss National Science Foundation in the form of a

SNSF Professorship (PP00P2_163967). EA acknowledges support from National Science Foundation (NSF) grant

AST-1615315, and NASA grants NNX13AF62G and NNH05ZDA001C. EB acknowledges that this work is part of

the F.R.S.-FNRS ExtraOrDynHa research project and acknowledges funding by the European Research Council

through ERC grant SPIRE 647383. SNR thanks the Agence Nationale pour la Recherche for support via grant

ANR-13-BS05-0003-002 (project MOJO). DHL acknowledges financial support form the STFC. The authors thank

C. Owen, C. Wolf, and the rest of the SkyMapper team for their attempts to monitor the star from Australia; for

UKIRT the director R. Green and the staff scientists W. Varricatt and T. Kerr; the ESO staff at Paranal for their

support on the HAWK-I observations; JMU and their flexibility for the LT schedule which allowed us to search

actively for the planets, and to extend our time allocation in the face of amazing results; for the WHT, C. Fariña, F.

Riddick, F. Jímenez and O. Vaduvescu for their help and kindness during observations; and for SAAO the

telescopes operations manager R. Sefako for his support.

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