B.-O.De. acknowledges support from the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number MB22.00046.
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (project Four Aces grant agreement No 724427). It has also been carried out in the frame of the National Centre for Competence in Research PlanetS supported by the Swiss National Science Foundation (SNSF). D.Eh. acknowledges financial support from the Swiss National Science Foundation for project 200021_200726.
E.E-Bo. acknowledges financial support from the European Union and the State Agency of Investigation of the Spanish Ministry of Science and Innovation (MICINN) under the grant PRE2020-093107 of the Pre-Doc Program for the Training of Doctors (FPI-SO) through FSE funds.
M.Fr. gratefully acknowledges the support of the Swedish National Space Agency (DNR 65/19, 174/18).
J.G-M. acknowledges support by the National Science Foundation through a Graduate Research Fellowship under grant No. DGE1745303 and by the Ford Foundation through a Ford Foundation Predoctoral Fellowship, administered by the National Academies of Sciences, Engineering, and Medicine.
The contributions at the University of Warwick by S.Gi. have been supported by STFC through consolidated grants ST/L000733/1 and ST/P000495/1.
M.Gi. is F.R.S.-FNRS Research Director.
Y.G.M.Ch. acknowledges support from UNAM PAPIIT-IG101321.
E.Go. acknowledge the support by the Thueringer Ministerium füër Wirtschaft, Wissenschaft und Digitale Gesellschaft.
M.N.Gu. is the ESA CHEOPS Project Scientist and Mission Representative, and as such also responsible for the Guest Observers (GO) Programme. M.N.Gu. does not relay proprietary information between the GO and Guaranteed Time Observation (GTO) Programmes, and does not decide on the definition and target selection of the GTO Programme.
A.P.Ha. acknowledges support by DFG grant HA 3279/12-1 within the DFG Schwerpunkt SPP 1992.
Ch.He. acknowledges support from the European Union H2020-MSCA-ITN-2019 under Grant Agreement no. 860470 (CHAMELEON).
S.Ho. gratefully acknowledges CNES funding through the grant 837319.
This work is partly supported by JST CREST Grant Number JPMJCR1761.
K.G.Is. is the ESA CHEOPS Project Scientist and is responsible for the ESA CHEOPS Guest Observers Programme. She does not participate in, or contribute to, the definition of the Guaranteed Time Programme of the CHEOPS mission through which observations described in this paper have been taken, nor to any aspect of target selection for the programme.
J.Ko. gratefully acknowledges the support of the Swedish National Space Agency (SNSA, DNR 2020-00104) and of the Swedish Research Council (VR: Etableringsbidrag 2017-04945).
K.W.F.La. was supported by Deutsche Forschungsgemeinschaft grants RA714/14-1 within the DFG Schwerpunkt SPP 1992, Exploring the Diversity of Extrasolar Planets.
This work was granted access to the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX-29-01) of the programme Investissements d'Avenir supervised by the Agence Nationale pour la Recherche.
A.L-E. acknowledges support from the CNES (Centre national d’études spatiales, France).
This work is partly supported by Astrobiology Center SATELLITE Research project AB022006.
This work is partly supported by JSPS KAKENHI Grant Number JP18H05439 and JST CREST Grant Number JPMJCR1761.
H.L.M.Os. acknowledges funding support by STFC through a PhD studentship.
H.Pa. acknowledges the support by the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC2021-031798-I.
This work was also partially supported by a grant from the Simons Foundation (PI Queloz, grant number 327127).
S.N.Qu. acknowledges support from the TESS mission via subaward s3449 from MIT. S.N.Qu. acknowledges support from the TESS GI Program under award 80NSSC21K1056 (G03268).
L.Sa. acknowledges support from UNAM PAPIIT project IN110122.
N.C.Sa. acknowledges funding by the European Union (ERC, FIERCE, 101052347). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
N.Sc. acknowledges support from the Swiss National Science Foundation (PP00P2-163967 and PP00P2-190080) and NASA under award number 80GSFC21M0002.
S.G.So. acknowledge support from FCT through FCT contract nr. CEECIND/00826/2018 and POPH/FSE (EC).
Gy.M.Sz. acknowledges the support of the Hungarian National Research, Development and Innovation Office (NKFIH) grant K-125015, a PRODEX Experiment Agreement No. 4000137122, the Lendület LP2018-7/2021 grant of the Hungarian Academy of Science and the support of the city of Szombathely.
A.Tu. acknowledges funding support from the STFC via a PhD studentship.
V.V.Ey. acknowledges support by STFC through the consolidated grant ST/W001136/1.
V.V.Gr. is an F.R.S-FNRS Research Associate.
J.Ve. acknowledges support from the Swiss National Science Foundation (SNSF) under grant PZ00P2_208945.
N.A.Wa. acknowledges UKSA grant ST/R004838/1.
N.Wa. is partly supported by JSPS KAKENHI Grant Number JP21K20376.

Author information

Authors and Affiliations

Author Contributions
R.Lu, H.P.Os, A.Le., E.Pa., A.Bo., O.Ba., and T.G.Wi. conceived the project and contributed notably to the writing of this manuscript. R.Lu. and H.P.Os. led the analysis of the photometric data. A.Le. led the dynamical analysis of the system and developed the method with J.-B.De. to predict the orbits of the planets based on their resonant state within the chain. R.Lu., A.Bo. and O.Ba. led the analysis of the radial velocity data and the stellar activity mitigation. T.G.Wi. led the stellar characterization with the help of V.Ad., S.G.So., A.Bo., V.V.Gr., S.Sa., and W.D.Co.

Y.Al. and J.A.Eg. led the analysis of the internal structures, while L.Fo. and A.Bo. performed the atmospheric evolution simulations.

D.Ra., J.D.Tw., and J.M.Je. improved the TESS data reduction to recover the missing cadences affected by reflected light and high background.

R.Lu., E.Pa., and G.No. planned and obtained the time for the observations with CARMENES and HARPS-N. CARMENES observations were made possible by M.La., J.C.Mo., P.J.Am., A.Qu., and I.Ri. HARPS-N observations were made possible by I.Ca., J.O-M., F.Mu., H.J.De., J.Ko., D.Ga., J.H.Li., W.D.Co., E.W.Gu., V.V.Ey., H.L.M.Os., S.Re., E.Go., F.Da., and K.W.F.La.

High-resolution imaging observations from Palomar and Gemini North were made possible by A.W.Bo., D.R.Ci, I.J.M.Cr., S.B.Ho., E.Ma., and J.E.Sc.

Ground-based photometric observations to catch the transit of planet f were made possible by the MuSCAT2 (R.Lu., E.Pa., N.Na., J.H.Li., K.Ik., E.E-B., J.O-M., N.Wa., F.Mu., G.No., A.Fu., H.Pa., M.Mo., T.Ka., J.P.Le., and T.Ko.), LCO (T.G.Wi., R.Lu., H.P.Os., E.Pa., A.Le., A.Tu., M.J.Ho., Y.Al., and D.Ga.), NGTS (H.P.Os., S.Gi., D.Ba., D.R.An., M.Mo., A.M.S.Sm., E.M.Br., and S.Ud.), Tierras (J.G-M. and D.Ch.), SAINT-EX (N.Sc., Y.G-M-C., L.Sa., S.C-G., and B.-O.De.), and MuSCAT3 (N.Na., J.H.Li., K.Ik., N.Wa., A.Fu., M.Mo., T.Ka., J.P.Le., and T.Ko.) instruments.

The remaining authors provided key contributions to the development of the TESS and CHEOPS mission. All authors read and commented on the manuscript, and helped with its revision.

Corresponding author Correspondence to Rafael Luque (rluque@uchicago.edu).

Competing interests The authors declare no competing interests.

Extended Data Figures and Tables

Transit duration versus transit depth for all unassigned transits in TESS data. TESS Sector 23 and Sector 49 are shown as different colors. The numbers above each transit denote the mid-transit time in TJD. Contours represent percentile levels, the innermost one corresponding to the 50th percentile and the outermost to the 99th percentile by increments of 10%. The transit of planet f in PLD photometry is marked with $^{*}$ to indicate that its properties are heavily affected by pre-transit systematic noise.

Generalized three-body Laplace angles for known systems in resonant chains. Included are the Galilean satellites, Kepler-60 [12, 115], Kepler-80 [159], K2-138 [112], Kepler-223 [110], TRAPPIST-1 [13], and TOI-178 [10]. Measurements belonging to the same system are marked with the same color. The line marks the observed distance to the theorized equilibrium (marked with a circle). The distances are estimated at 0th order in eccentricity [110, 111]. For most systems, a single estimation of the generalized Laplace angle is made, while [110] made an estimation for each Kepler quarter.

Observed distance from the equilibrium for all the simulated scenarios in which planets f and g continue the resonant chain. The y-axis is converted to the mean peak-to-peak amplitude from the generalized three-body Laplace angle using the following expression: mean($\mathcal{{A}}(\Psi_{i}))=C/4$. Case A2 remains the one that has the potential to be the closest to an equilibrium.

Results from the ground-based campaign to detect HD 110067 f. a, $\Delta$WAIC for each of the constrained period bins when compared to a transit-free model. b,c, Best-fit decorrelated photometry with (b) and without (c) a transit model. Each light curve from each telescope has been offset for clarity. Error bars represent 1$\sigma$ uncertainties.

Results from the two radial velocity analyses to measure the mass of each of the planets in the HD 110067 system. Each histogram represents the posterior density function (pdf) of the radial velocity semi-amplitudes as inferred from Method I (red) and Method II (blue). The area underneath each histogram is normalized to unity.

Gas mass fraction of the HD 110067 planets as a function of their equilibrium temperature. We infer two values per planet by assuming the different planetary masses from our Method I (red) and Method II (blue) radial velocity analyses. The boxes, orange lines, green triangles, and red stars represent respectively the 25% and 75% percentiles, medians, means, and modes of the posterior distributions. The opacity of the vertical lines is proportional to the posterior distribution.

CHEOPS observing log. Filler observations aim to catch transits serendipitously in between time-critical observations with higher priority. Boldface notes indicate that a transit event was detected in the data.

Start (TJD)     Length [hr]     Archive filekey     Av. eff. (%)     RMS (ppm)     Notes

$ 2681.3341 $     $ 9.93 $     PR110048_TG025701_V0200     $ 79 $     $ 202 $     e, 35.4d alias

$ 2683.1380 $     $ 10.36 $     PR110048_TG025801_V0200     $ 68 $     $ 212 $     e, 37.3d alias

$ 2685.2296 $     $ 10.4 $     PR110048_TG025901_V0200     $ 68 $     $ 196 $     e, 39.3d alias

$ 2690.0127 $     $ 9.88 $     PR110048_TG026601_V0200     $ 71 $     $ 183 $     d, 21.8d alias

$ 2692.9367 $     $ 4.84 $     PR100031_TG052101_V0200     $ 75 $     $ 187 $     filler

$ 2693.3133 $     $ 5.27 $     PR100031_TG052102_V0200     $ 60 $     $ 217 $     filler

$ 2694.6805 $     $ 8.21 $     PR100031_TG052001_V0200     $ 73 $     $ 212 $     Planet b

$ 2702.5843 $     $ 9.26 $     PR110048_TG026701_V0200     $ 72 $     $ 220 $     d, 22.65d alias

$ 2703.0623 $     $ 10.36 $     PR110048_TG026101_V0200     $ 61 $     $ 217 $     d, 18.86d alias

$ 2704.0525 $     $ 9.34 $     PR110048_TG026801_V0200     $ 62 $     $ 213 $     d, 23.38d alias

$ 2704.7545 $     $ 3.2 $     PR110031_TG052201_V0200     $ 71 $     $ 251 $     filler

$ 2706.1956 $     $ 9.38 $     PR110048_TG026401_V0200     $ 57 $     $ 256 $     d, 19.93d alias

$ 2707.9583 $     $ 9.44 $     PR110048_TG028101_V0200     $ 66 $     $ 275 $     Planet d, 20.5d alias

$ 2712.8885 $     $ 8.37 $     PR100031_TG052002_V0200     $ 61 $     $ 240 $     Planet b

$ 2713.9877 $     $ 8.76 $     PR110048_TG028001_V0200     $ 60 $     $ 247 $     d, 22.5d alias

$ 2714.4689 $     $ 4.19 $     PR100031_TG052103_V0200     $ 60 $     $ 258 $     filler

$ 2714.7439 $     $ 10.08 $     PR110048_TG028501_V0200     $ 61 $     $ 249 $     d, 24.4d alias

$ 2715.1871 $     $ 3.06 $     PR100031_TG052202_V0200     $ 52 $     $ 222 $     filler

$ 2717.2854 $     $ 9.86 $     PR110048_TG028401_V0200     $ 56 $     $ 243 $     g, $2 \times P_e$

Ground-based photometric campaign observing log.

Facility     Filter     Start (TJD)     End (TJD)     Notes

MuSCAT-2        $g$,$r$,$i$,$z_s$       2723.4534     2723.5991     Interrupted at 2723.488 for 54 min

LCO             $z_p$          2723.4797     2723.5756     No in-transit data at expected ingress

NGTS            custom         2723.4684     2723.6904     From 9 telescopes, 2 started late

Tierras         custom        2723.6260     2723.8681     Affected by cirrus

SAINT-EX        zcut          2723.6446     2723.8826     Affected by cirrus

MuSCAT-3        $g$,$r$,$i$,$z_s$       2723.7479     2723.9177     Interrupted at 2723.795 for 8 min

Transit     –       2723.5869     2723.7987     Expected in/egress for reference

Stellar parameters of HD 110067. Error bars represent 1$\sigma$ uncertainties.

Parameter                                   Value                     Reference

3cName and identifiers

Name                                HD 110067                         [160]

TIC                                 347332255                         [27]

TOI                                 1835                              [36]

3cCoordinates and spectral type

$\alpha$                                    12:39:21.503           [161]

$\delta$                                    +20:01:40.03           [161]

Epoch                                       2000.0                 [161]

Spectral type                               K0.0 V                [162]

$B$ [mag]                                   $9.203\pm0.03$            [162]

$V$ [mag]                                   $8.419\pm0.002$           [162]

$G$ [mag]                                   $8.17208\pm0.00028$       [161]

$J$ [mag]                                   $6.952\pm0.023$           [163]

$H$ [mag]                                   $6.561\pm0.017$           [163]

$K_s$ [mag]                                 $6.492\pm0.018$           [163]

3cParallax and kinematics

$\pi$ [mas]                                 $31.037\pm0.022$         [161]

$d$ [pc]                                    $32.220\pm0.023$         [161]

$\mu_{\alpha}\cos\delta$ [$\mathrm{mas\,yr^{-1}}$]      $-81.96 \pm 0.08$         [161]

$\mu_{\delta}$ [$\mathrm{mas\,yr^{-1}}$]                $-104.59 \pm 0.04$        [161]

$U$ [$\mathrm{km\,s^{-1}}]$                  +7.50$\pm$0.01           This work

$V$ [$\mathrm{km\,s^{-1}}]$                 -13.56$\pm$0.03           This work

$W$ [$\mathrm{km\,s^{-1}}]$                 -4.06$\pm$0.20            This work

3cPhotospheric parameters

$T_{\mathrm{eff}}$ [K]                          $5266 \pm 64$             This work

$\log g$                                        $4.54 \pm 0.03$           This work

[Fe/H]                                        $-0.20 \pm 0.04$          This work

[Mg/H]                                        $-0.21 \pm 0.06$          This work

[Si/H]                                        $-0.19 \pm 0.03$          This work

$v \sin i_\star$ [$\mathrm{km\,s^{-1}}$]        $2.5 \pm 1.0$             This work

3cPhysical parameters

$M$ [$M_{\odot}$]                           $0.798\pm0.042$           This work

$R$ [$R_{\odot}$]                           $0.788 \pm 0.008$         This work

Age [Gyr]                                   $8.1 \pm 4.0$             This work

Distance of the estimated generalized three-body Laplace angle $\Psi_{e=0}$ to the closest equilibrium for all period ratios that are not excluded by available observations. Case A assumes that the mono-transit at 2641.5778 TJD belongs to the 5th planet, and 2656.0944 TJD belongs to the 6th planet. Case B assumes the opposite. The flag column $^*=1$ indicates that the position of the equilibria varies with the masses of the planets, in which case the equilibrium is recomputed using [164], with masses computed using a mass-radius relation for sub-Neptunes [26]. For $^*=0$, the equilibrium is 180 degrees.

Case     $P_f/P_e$     $P_g/P_f$     $P_f$     $P_g$      $\Delta \Psi_{bcd}$     $\Delta \Psi_{cde}$     $\Delta \Psi_{def}$     $\Delta \Psi_{efg}$     $^*$

(days)     (days)      (deg)     (deg)     (deg)     (deg)

A0   $4/3$   $2/1$   $41.0575$   $82.1150$   $44.17$   $18.55$   $7.67$   $95.50$   $1$

A1   $4/3$   $3/2$   $41.0575$   $61.5862$   $44.17$   $36.13$   $88.05$   $79.21$   $1$

A2   $4/3$   $4/3$   $41.0575$   $54.7433$   $44.17$   $18.06$   $4.89$   $9.81$   $1$

A3   $4/3$   $6/5$   $41.0575$   $49.2690$   $44.17$   $37.57$   $80.14$   $95.33$   $1$

B0   $2/1$   $2/1$   $61.5862$   $123.172$   $44.17$   $10.00$   $43.60$   $21.79$   $0$

B1   $2/1$   $3/2$   $61.5862$   $92.3793$   $44.17$   $10.00$   $43.60$   $106.64$   $0$

B2   $2/1$   $4/3$   $61.5862$   $82.1150$   $44.17$   $10.00$   $43.60$   $168.50$   $0$

B3   $2/1$   $6/5$   $61.5862$   $73.9035$   $44.17$   $10.00$   $43.60$   $1.21$   $0$

B4   $3/2$   $2/1$   $46.1897$   $92.3793$   $44.17$   $10.00$   $73.33$   $167.00$   $0$

B5   $3/2$   $6/5$   $46.1897$   $55.4276$   $44.17$   $10.00$   $73.33$   $100.43$   $0$

B6   $4/3$   $2/1$   $41.0575$   $82.1150$   $44.17$   $38.56$   $136.29$   $72.06$   $1$

B7   $4/3$   $4/3$   $41.0575$   $54.7433$   $44.17$   $38.07$   $133.51$   $177.37$   $1$

B8   $5/4$   $5/4$   $38.4914$   $48.1142$   $44.17$   $10.00$   $52.81$   $110.80$   $0$

Supplementary Information
Supplementary Information is available for this paper.

Rights and permissions Reprints and permissions information is available at www.nature.com/reprints.