<figure><img src="image_1.png" /></figure>

Check for updates

# Transit detection of the long-period volatile-rich super-Earth $\nu^2$ Lupi d with CHEOPS

Laetitia Delrez ID 1,2,3 ✉, David Ehrenreich ID 3, Yann Alibert ID 4, Andrea Bonfanti ID 5,
Luca Borsato ID 6, Luca Fossati ID 5, Matthew J. Hooton ID 4, Sergio Hoyer ID 7, Francisco J. Pozuelos 1,2,
Sébastien Salmon 2,3, Sophia Sulis ID 7, Thomas G. Wilson ID 8, Vardan Adibekyan ID 9,10,
Vincent Bourrier ID 3, Alexis Brandeker ID 11, Sébastien Charnoz ID 12, Adrien Deline 3, Pascal Guterman 7,13,
Jonas Haldemann ID 4, Nathan Hara 3, Mahmoudreza Oshagh 14,15, Sergio G. Sousa 9,
Valérie Van Grootel 2, Roi Alonso ID 14,15, Guillem Anglada-Escudé 16,17, Tamás Bárczy 18, David Barrado ID 19,
Susana C. C. Barros 9,10, Wolfgang Baumjohann ID 5, Mathias Beck 3, Anja Bekkelien 3, Willy Benz 4,20,
Nicolas Billot 3, Xavier Bonfils 21, Christopher Broeg 4, Juan Cabrera ID 22, Andrew Collier Cameron ID 8,
Melvyn B. Davies 23, Magali Deleuil ID 7, Jean-Baptiste Delisle 3, Olivier D. S. Demangeon ID 9,10,
Brice-Olivier Demory ID 20, Anders Erikson 22, Andrea Fortier ID 4, Malcolm Fridlund ID 24,25,
David Futyan 3, Davide Gandolfi 26, Antonio Garcia Muñoz 27, Michaël Gillon 1, Manuel Guedel 28,
Kevin Heng ID 20, László Kiss 29,30,31, Jacques Laskar ID 32, Alain Lecavelier des Etangs 33, Monika Lendl 3,5,
Christophe Lovis 3, Pierre F. L. Maxted 34, Valerio Nascimbeni 6, Göran Olofsson 11, Hugh P. Osborn 35,36,
Isabella Pagano ID 37, Enric Pallé 14,15, Giampaolo Piotto ID 6,38, Don Pollacco 39, Didier Queloz ID 3,40,
Heike Rauer 22,27,41, Roberto Ragazzoni 6, Ignasi Ribas ID 16,17, Nuno C. Santos 9,10, Gaetano Scandariato 37,
Damien Ségransan 3, Attila E. Simon 4, Alexis M. S. Smith ID 22, Manfred Steller 5, Gyula M. Szabó 42,43,
Nicolas Thomas 4, Stéphane Udry ID 3 and Nicholas A. Walton ID 44

Exoplanets transiting bright nearby stars are key objects for advancing our knowledge of planetary formation and evolution. The wealth of photons from the host star gives detailed access to the atmospheric, interior and orbital properties of the planetary companions. $\nu^2$ Lupi (HD 136352) is a naked-eye (V=5.78) Sun-like star that was discovered to host three low-mass planets with orbital periods of 11.6, 27.6 and 107.6 d via radial-velocity monitoring¹. The two inner planets (b and c) were recently found to transit², prompting a photometric follow-up by the brand new Characterising Exoplanets Satellite (CHEOPS). Here, we report that the outer planet d is also transiting, and measure its radius and mass to be $2.56 \pm 0.09 R_⊕$ and $8.82 \pm 0.94 M_⊕$, respectively. With its bright Sun-like star, long period and mild irradiation (-5.7 times the irradiation of Earth), $\nu^2$ Lupi d unlocks a completely new region in the parameter space of exoplanets amenable to detailed characterization. We refine the properties of all three planets: planet b probably has a rocky mostly dry composition, while planets c and d seem to have retained small hydrogen-helium envelopes and a possibly large water fraction. This diversity of planetary compositions makes the $\nu^2$ Lupi system an excellent laboratory for testing formation and evolution models of low-mass planets.

CHEOPS³ is the new European mission dedicated to the study of known exoplanets around bright stars (V≤12). Unlike previous exoplanet detection missions, such as CoRoT⁴, Kepler⁵ and TESS⁶, CHEOPS is a follow-up mission, designed to collect ultrahigh-precision photometry of a single star at a time. For this purpose, it relies on a 30 cm effective aperture telescope, equipped with a single frame-transfer back-illuminated CCD detector providing a broad 330–1,100 nm bandpass⁷. CHEOPS was launched on 18 December 2019 into a 700-km-altitude Sun-synchronous dusk-dawn orbit and started routine science operations in April 2020. For very bright stars (V≈6), CHEOPS demonstrated that it can achieve an outstanding photometric precision of about 10 ppm per 1 h interval⁸.

$\nu^2$ Lupi is one of the first scientific targets observed by CHEOPS. This system of three low-mass planets orbiting one of the closest (14.7 pc) G-type main-sequence stars was discovered using radial velocities (RVs) obtained with the HARPS spectrograph¹. It was then observed by TESS during Sector 12 of its primary mission (21 May–18 June 2019), which revealed that the two inner planets are transiting². These 28-day-long observations did not cover any inferior conjunction of the outer planet d. However, the transiting configuration of the two inner planets increased the probability that it is also transiting, to about 20% for typical mutual inclinations of ~1°
<table><caption>**Table 1 | Properties of the ν² Lupi planetary system**</caption><thead><tr><th>Parameters</th><th>Values</th><th></th><th></th></tr></thead><tbody><tr><td><strong>Star</strong></td><td><strong>ν² Lupi</strong></td><td></td><td></td></tr><tr><td>Effective temperature, T<sub>eff</sub> (K)</td><td>5,664 ± 61</td><td></td><td></td></tr><tr><td>log surface gravity, log g<sub>*</sub> (cgs)</td><td>4.39 ± 0.11</td><td></td><td></td></tr><tr><td>Microturbulence, ξ<sub>t</sub> (km s<sup>-1</sup>)</td><td>0.85 ± 0.02</td><td></td><td></td></tr><tr><td>Metallicity, [M/H] (dex)</td><td>-0.24 ± 0.05</td><td></td><td></td></tr><tr><td>Radius, R<sub>*</sub> (R<sub>☉</sub>)</td><td>1.058 ± 0.019</td><td></td><td></td></tr><tr><td>Mass, M<sub>*</sub> (M<sub>☉</sub>)</td><td>0.87 ± 0.04</td><td></td><td></td></tr><tr><td>Density, ρ<sub>*</sub> (ρ<sub>☉</sub>)</td><td>0.734 ± 0.053</td><td></td><td></td></tr><tr><td>Age (Gyr)</td><td>12.3<sup>+1.2</sup><sub>-2.9</sub></td><td></td><td></td></tr><tr><td>Rotation period<sup>a</sup>, P<sub>rot</sub> (d)</td><td>23.8 ± 3.1</td><td></td><td></td></tr><tr><td>Luminosity, L<sub>*</sub> (L<sub>☉</sub>)</td><td>1.038 ± 0.059</td><td></td><td></td></tr><tr><td><strong>Planets</strong></td><td><strong>b</strong></td><td><strong>c</strong></td><td><strong>d</strong></td></tr><tr><td>Orbital period, P (d)</td><td>11.57797<sup>+0.00008</sup><sub>-0.00013</sub></td><td>27.59221 ± 0.00011</td><td>107.245 ± 0.050</td></tr><tr><td>Mid-transit time, T<sub>o</sub> (BJD<sub>TDB</sub> - 2,450,000)<sup>b</sup></td><td>8,944.3726<sup>+0.0015</sup><sub>-0.0017</sub></td><td>8,954.40990<sup>+0.00052</sup><sub>-0.00054</sub></td><td>9,009.7759<sup>+0.0101</sup><sub>-0.0096</sub></td></tr><tr><td>Planet-to-star radius ratio, R<sub>p</sub>/R<sub>*</sub></td><td>0.01442<sup>+0.00027</sup><sub>-0.00028</sub></td><td>0.02526<sup>+0.00047</sup><sub>-0.00044</sub></td><td>0.02219<sup>+0.00067</sup><sub>-0.00057</sub></td></tr><tr><td>Transit depth, d<sub>f</sub> (ppm)</td><td>208 ± 8</td><td>638<sup>+24</sup><sub>-22</sub></td><td>492<sup>+30</sup><sub>-25</sub></td></tr><tr><td>Transit impact parameter, b (R<sub>*</sub>)</td><td>0.52<sup>+0.04</sup><sub>-0.05</sub></td><td>0.872 ± 0.007</td><td>0.41<sup>+0.14</sup><sub>-0.21</sub></td></tr><tr><td>Transit duration, W (h)</td><td>3.935<sup>+0.093</sup><sub>-0.058</sub></td><td>3.251<sup>+0.033</sup><sub>-0.031</sub></td><td>8.87<sup>+0.56</sup><sub>-0.63</sub></td></tr><tr><td>Orbital inclination, i (°)</td><td>88.49<sup>+0.17</sup><sub>-0.15</sub></td><td>88.571<sup>+0.042</sup><sub>-0.045</sub></td><td>89.73<sup>+0.14</sup><sub>-0.09</sub></td></tr><tr><td>Orbital eccentricity<sup>c</sup>, e</td><td>0 (fixed, <0.17)</td><td>0 (fixed, <0.08)</td><td>0 (fixed, <0.25)</td></tr><tr><td>RV semi-amplitude, K (m s<sup>-1</sup>)</td><td>1.46 ± 0.12</td><td>2.61 ± 0.12</td><td>1.30 ± 0.13</td></tr><tr><td>Orbital semi-major axis, a (au)</td><td>0.0964 ± 0.0028</td><td>0.1721 ± 0.0050</td><td>0.425 ± 0.012</td></tr><tr><td>Scale parameter, a/R<sub>*</sub></td><td>19.60<sup>+0.45</sup><sub>-0.46</sub></td><td>34.97<sup>+0.80</sup><sub>-0.82</sub></td><td>86.46<sup>+1.96</sup><sub>-2.02</sub></td></tr><tr><td>Stellar irradiation, S<sub>p</sub> (S<sub>☉</sub>)</td><td>111.6<sup>+7.3</sup><sub>-6.8</sub></td><td>35.1<sup>+2.3</sup><sub>-2.1</sub></td><td>5.74<sup>+0.38</sup><sub>-0.35</sub></td></tr><tr><td>Equilibrium temperature<sup>d</sup>, T<sub>eq</sub> (K)</td><td>905 ± 14</td><td>677 ± 11</td><td>431 ± 7</td></tr><tr><td>Radius, R<sub>p</sub> (R<sub>☉</sub>)</td><td>1.664 ± 0.043</td><td>2.916<sup>+0.075</sup><sub>-0.073</sub></td><td>2.562<sup>+0.088</sup><sub>-0.079</sub></td></tr><tr><td>Mass, M<sub>p</sub> (M<sub>☉</sub>)</td><td>4.72 ± 0.42</td><td>11.24<sup>+0.65</sup><sub>-0.63</sub></td><td>8.82<sup>+0.93</sup><sub>-0.92</sub></td></tr><tr><td>Mean density, ρ<sub>p</sub> (ρ<sub>☉</sub>)</td><td>1.02<sup>+0.13</sup><sub>-0.12</sub></td><td>0.453<sup>+0.045</sup><sub>-0.041</sub></td><td>0.522<sup>+0.078</sup><sub>-0.072</sub></td></tr></tbody></table>

(ref. ²). ν² Lupi is one of only three naked-eye stars known to host several transiting planets, the other two being HD 219134 (refs. ⁹,¹⁰) and HR 858 (ref. ¹¹). The multitransiting nature of these systems, combined with the brightness of their stars, make them targets of paramount importance for comparative exoplanetology studies. The primary objective of our follow-up of ν² Lupi with CHEOPS was to refine the properties of the two inner planets, most notably their radii but also their ephemerides, since being able to predict precise transit times is essential to enable follow-up observations with heavily subscribed facilities¹².

Six observation runs (visits) were obtained with CHEOPS between 4 April and 6 July 2020 (Supplementary Table 1), targeting four transits of planet b and three of planet c (the last visit contained one transit of each planet). The data were processed with the CHEOPS data reduction pipeline¹³ (DRP, Methods) and the resulting individual light curves are shown in Supplementary Fig. 1.

During the fifth visit (8–9 June 2020), we serendipitously detected a ~500 ppm transit-like flux drop, which started during the targeted transit of planet c, and lasted for the rest of the visit (Supplementary Fig. 1, bottom left panel). We carefully checked the data for systematics and found this signal to be very robust (Methods). Furthermore, the star does not show any comparable photometric variability in either the CHEOPS or TESS data (Supplementary Fig. 4). This flux drop occurred at 1.3σ of an inferior conjunction of ν² Lupi d, as predicted by the RV orbital solution of ref. ¹, and we show in Methods that it most probably originates from a transit of this outer planet. This makes ν² Lupi d the first long-period (>100 d) planet detected to transit a naked-eye star.

To determine the system parameters, we performed a global analysis of our six CHEOPS light curves together with other available photometric and RV data. This includes first a custom TESS light curve, which we extracted from the target pixel files following

<footnote><sup>a</sup> From ref. 1. <sup>b</sup> BJD<sub>TDB</sub>, barycentric Julian date in barycentric dynamical time. <sup>c</sup> 2σ upper limits derived from our global analysis allowing all orbits to be eccentric. <sup>d</sup> T<sub>eq</sub> = T<sub>eff</sub>√R<sub>*</sub>/a [f(1 - A<sub>8</sub>)]<sup>1/4</sup>, assuming an efficient heat redistribution (f=1/4) and a null Bond albedo (A<sub>8</sub> = 0).</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1 | CHEOPS transit photometry of the v² Lupi planets.** a, Corrected and phase-folded CHEOPS transit photometry of v² Lupi b, c and d. The blue dots show the unbinned measurements, with error bars corresponding to the quadratic sum of the formal photometric errors and the fitted extra jitter term. Open circles show the light curves binned into 20 min intervals. The best-fit transit models from our global analysis are shown as orange lines. b, Corresponding residuals. In both panels, the light curves corresponding to planets c and d are shifted vertically for clarity.</figcaption></figure>

ref. ², to conduct a careful treatment of instrumental systematics (Methods and Supplementary Fig. 4). We also included 246 previously published¹,² RV measurements obtained with HARPS between May 2004 and August 2017 (Methods and Supplementary Fig. 6).

Since transit and RV data only yield the parameters of the planets relative to those of their star, we performed a detailed characterization of the host star (Methods), whose main derived parameters are given in Table 1. We carried out our global data analysis using the juliet package¹⁴, which allows the joint modelling of transits and RVs simultaneously with signals of non-planetary origin (instrumental systematics, stellar variability) to ensure a full propagation of the uncertainties on the derived system parameters. A key feature of juliet is that it uses nested sampling algorithms¹⁵ to explore the parameter space, which also allows us to perform model comparison via Bayesian evidences. We first analysed each dataset individually, to explore for each of them a large range of correlated noise models and select the best one, on the basis of Bayesian evidence (Methods). During this process, we detected in the CHEOPS light curves, besides typical instrumental noise phased with the spacecraft roll angle, some extra higher-frequency correlated noise, which we attribute to stellar granulation and oscillations. We modelled this stellar noise using a Gaussian process (GP; Methods) and studied it in detail in an independent analysis (below). We then performed several global analyses assuming circular or eccentric orbits for some or all the planets (Methods). We found the simplest model with circular orbits for the three planets to be the one with the highest Bayesian evidence and thus adopted this as our nominal solution. We also explored the data for transit timing variations (TTVs) but did not detect any (Methods). Table 1 presents the results of our global analysis, which significantly refines the system parameters (Methods). The best-fit models for the individual light curves are shown in Supplementary Figs. 1 (CHEOPS) and 4 (TESS). The

corrected light curves, phase-folded for each planet, are presented together with the best-fit transit models in Fig. 1 for CHEOPS and Supplementary Fig. 5 for TESS. Finally, the phase-folded RVs are shown in Supplementary Fig. 6, together with the best-fit RV model for each planet. To test our results, we explored the orbital stability of the system for masses and eccentricities around our derived solution and found it to be very stable (Methods).

As mentioned above, the exquisite precision of our CHEOPS photometry (~15 ppm with a 10 min binning) makes it sensitive to stellar granulation and oscillations. To characterize this stellar signal, we analysed the power spectral density (PSD) of the photometric residuals obtained after subtracting our best-fit transit and instrumental models (Methods and Supplementary Fig. 10). We measured for the stellar oscillations a frequency at maximum power $v_{max} = 2,710 \pm 77$ µHz and a flicker index $\alpha_g = 1.14 \pm 0.22$ (slope of the PSD associated with granulation) that are in agreement with the values expected from our derived stellar parameters and with the trends observed for Kepler stars¹⁶ (Supplementary Fig. 11). This asteroseismic detection is in good agreement with, and even exceeds, the expectations of ref. ¹⁷, thus spectacularly demonstrating the potential of CHEOPS for asteroseismology.

With a radius of $1.664 \pm 0.043 R_⊕$ and a stellar irradiation of $111.6^{+7.3}_{-6.8} S_⊕$, v² Lupi b lies near the inner edge of the well known radius valley¹⁸, while planets c ($2.916^{+0.075}_{-0.073} R_⊕$, $35.1^{+2.3}_{-2.1} S_⊕$) and d ($2.562^{+0.088}_{-0.079} R_⊕$, $5.74^{+0.38}_{-0.35} S_⊕$) are located on the other side (Fig. 2b). This gap in the planetary radius distribution separates predominantly rocky planets from larger volatile-rich (hydrogen, helium, water) sub-Neptunes. The v² Lupi planets seem to fit this picture well: planet b has an Earth-like bulk density of $1.02^{+0.13}_{-0.12} \rho_⊕$, while planets c and d have significantly lower densities of $0.453^{+0.045}_{-0.041} \rho_⊕$ and $0.522^{+0.078}_{-0.072} \rho_⊕$, respectively, implying that they contain water and/or gas (Fig. 2c). Several theories have been put forward to explain the radius valley, such as photoevaporation¹⁹,²⁰, core-powered mass loss²¹ or combined formation and evolution effects²². With three transiting planets spanning the valley, the v² Lupi system provides a valuable opportunity to test these scenarios.

To go one step further, we performed a detailed Bayesian analysis (Methods) to derive the joint posterior distribution of the present-day internal structures of the three planets²³,²⁴ (Fig. 3 and Supplementary Figs. 12–14), assuming four layers (iron–sulfur core, silicate mantle, water layer, gas envelope). The innermost planet is found to be mostly dry (water mass equal to $0.57^{+0.60}_{-0.49} M_⊕$, that is $12.6^{+14.7}_{-11.0}$ wt%) and gas poor (gas mass less than $10^{-5} M_⊕$), whereas the two outer planets have a similarly massive water layer ($2.81^{+2.52}_{-2.52} M_⊕$, that is $25.01^{+22.2}_{-22.4}$ wt%, for planet c; $2.31^{+2.09}_{-2.13} M_⊕$, that is $26.8^{+21.2}_{-23.7}$ wt%, for planet d) and a small but non-negligible amount of gas ($0.13^{+0.103}_{-0.078} M_⊕$, that is $1.2^{+0.91}_{-0.70}$ wt%, for planet c; $0.058^{+0.069}_{-0.050} M_⊕$, that is $0.66^{+0.79}_{-0.58}$ wt%, for planet d). The dichotomy between the derived amounts of water is consistent with a formation by migration, where the innermost planet would start its formation inside the ice line (located a few AU from the star for typical protoplanetary disks) whereas the two outer planets would have spent at least part of their formation time outside the ice line, and therefore accreting icy bodies.

With regard to the derived amounts of gas, planetary atmospheric evolution calculations²⁵,²⁶ indicate that the innermost planet b was subject to substantial atmospheric loss, while planets c and d did not suffer strong evaporation (Methods and Supplementary Fig. 15). The two outer planets are indeed sufficiently massive and far away from the host star to be only slightly affected by mass loss throughout their evolution. Therefore, the current low gas content returned by our internal structure modelling for these two planets is probably of primordial origin. In the standard core-accretion model, planets start to accrete substantial amounts of gas when they reach the critical mass, which is of the order of ~10 $M_⊕$ but also depends strongly on different parameters, in particular the accretion rate of solids
<figure><img src="image_3.png" /></figure>

**Fig. 2** | The $v^2$ Lupi planets in the context of other known transiting exoplanets. Data on known exoplanets were taken from the NASA Exoplanet Archive (https://exoplanetarchive.ipac.caltech.edu/) on 18 February 2021. We only considered planets with radius uncertainties less than 20% here. **a**, V magnitude versus orbital period. **b**, Planetary radius versus stellar irradiation for planets with radii below $4 R_⊕$. The background colours describe the density of data points, from yellow for empty regions of the diagram to violet for densely populated ones. **c**, Mass-radius diagram for the planets in this sample that also have mass uncertainties less than 20%. Error bars represent $1\sigma$ confidence intervals. The dashed lines show theoretical mass-radius curves for some idealized compositions$^{147}$. **d**, For the same subset of planets, the TSM of ref. 29 is shown as a function of equilibrium temperature (computed assuming an efficient heat redistribution and a null Bond albedo). The size of the symbols is proportional to the host star effective temperature.

<figure><img src="image_4.png" /></figure>

(higher accretion rates translating into larger critical masses)$^{27}$. The structure of the two outer planets, as observed today, being probably primordial, these two objects provide a very important anchor for planet formation models, as this indicates that neither of them reached the critical mass during their formation. These two planets, by giving access to both the core mass and gas-to-core ratio for two objects in the same system, will provide strong constraints on the understanding of the formation of subcritical planets. Since the presence of large gas envelopes hinders habitability$^{28}$, the $v^2$ Lupi system, with its two subcritical outer planets, also provides an interesting case study for numerical models targeting the emergence of habitable worlds.

A thorough characterization of the system will require atmospheric measurements with, for example, the upcoming James Webb Space Telescope (JWST) or future ground-based extremely large telescopes. On the basis of the transmission spectroscopy metric (TSM) of ref. 29, the three planets are attractive targets, with TSM values of 125, 214 and 117 for planets b, c and d, respectively

(Methods and Fig. 2d). In particular, $v^2$ Lupi d is the best target found so far around a Sun-like star for atmospheric studies in the low-temperature regime (<500 K). It is also a potentially promising object to search for moons or rings (Methods). Our transit detection of this exciting planet with CHEOPS thus further increases the importance of $v^2$ Lupi as a cornerstone system for comparative exoplanetology studies of small worlds.

## Methods

**CHEOPS observations and data reduction.** Six observation runs (visits) were obtained with CHEOPS between 4 April and 6 July 2020. The log of these observations is presented in Supplementary Table 1. Each visit lasted between 11 and 12.8 h, so as to cover transits of planets b and c (duration of ~3.9 and ~3.2 h, respectively) together with a substantial out-of-transit baseline. Due to CHEOPS's low Earth orbit (altitude ~700 km), the data show some gaps corresponding to Earth occultations or passages through the South Atlantic Anomaly, resulting in observing efficiencies between 49 and 60%. Due to the target's brightness ($V=5.78$), we used a short exposure time of 1.7 s and co-added on board 26 exposures, yielding a cadence of 44.2 s. For a detailed description of CHEOPS' instrumentation, technicalities of its observations, and on-board processing, see ref. 3.
<figure><img src="image_5.png" /><figcaption>**Fig. 3** | Internal structures of the v² Lupi planets. Present-day internal structures returned by our Bayesian analysis<sup>23,24</sup> (Methods), assuming four layers (iron-sulfur core, silicate mantle, water layer, and H-He envelope). For each planet, a ternary diagram shows the mass fractions of the iron core, silicate mantle and water layer. The yellow (respectively, dark violet) colours represent zones of highest (respectively, lowest) posterior probability distribution, and the grey area (lower left part) represents the zone that is excluded by the assumed prior (water mass fraction smaller than 50% so that it cannot be larger than the icy fraction inside planetary solid building blocks; see Methods and references therein). Next to each ternary diagram, we also show an illustration representing the radius fractions of the core + mantle (dark grey), water layer (blue) and gas envelope (magenta), corresponding to the medians of the posterior distributions.</figcaption></figure>

The data were automatically processed with the CHEOPS DRP¹³ (version 12), a detailed description of which can be found in ref. ¹³. In short, the DRP calibrates the raw images (event flagging, bias and gain corrections, linearization, dark current and flat-field corrections), corrects them for environmental effects (smearing trails, depointing, background and stray light) and performs aperture photometry to extract target fluxes for various apertures. For all the visits, we found a minimal light curve root mean squared (r.m.s.) with the default aperture of 25 pixels. The resulting light curves are shown in Supplementary Fig. 1 (upper panels for each visit). Owing to the extended and irregular shape of the CHEOPS point spread function¹ and the fact that the field rotates around the target along the spacecraft's orbit, nearby background stars can introduce a time-variable flux contamination in the photometric aperture, in phase with the spacecraft roll angle. The DRP also estimates this contamination by using the Gaia DR2 catalogue³⁰ to simulate CHEOPS images of the field of view. For our v² Lupi observations, this contamination was very small, varying between 0.025 and 0.030% of the target's flux.

In the light curve of the fifth visit (8–9 June 2020), we serendipitously detected a ~500 ppm transit-like flux drop, which started during the targeted transit of planet c, and lasted for the rest of the visit (Supplementary Fig. 1, bottom left panel). We carefully checked the data for systematics and found this signal to be very robust. As shown in Supplementary Fig. 2, it does not show any correlation with the size of the photometric aperture, or with any instrumental or environmental parameter (background, position of the target's point spread function centroid on the CCD, various voltages and temperatures, dark current and so on). Neither can the signal be ascribed to cosmic rays or telegraphic pixels (noisy unstable pixels whose state randomly flips between a normal behaviour and an arbitrary high response). Having ruled out any systematics as the origin of this signal, we then turned towards another possible culprit, v² Lupi d. This planet is the third one detected in HARPS RVs by ref. ¹, which reported an orbital period of ~107.6 d and a minimum mass ($M_p \sin i$) of ~8.6 $M_⊕$. Ref. ² did not find any evidence for a transit of planet d in the TESS data but also noted that this was totally expected, since the 28-d-long observations actually did not cover any inferior conjunction of the planet, as predicted from the RVs. On the basis of the orbital solution of ref. ¹, the inferior conjunction that is the nearest in time to the fifth CHEOPS visit was predicted to be 2,459,023.21 ± 10.33 BJD. The transit-like signal that we detected started around 2,459,009.59 BJD, thus at 1.3σ. We demonstrate below (Origin of the CHEOPS single transit event) that it most probably originates from a transit of v² Lupi d.

**TESS observations and data reduction.** v² Lupi was observed by TESS⁶ during Sector 12 of its primary mission, from 21 May until 18 June 2019. During these 28 days, TESS saved and downlinked images of v² Lupi every 2 min, resulting in a total of 20,119 photometric measurements. Ref. ² recently reported the detection of two transits of planet b and one of planet c in these data. As mentioned above, these observations did not cover any transit of planet d.

Following an approach similar to that used by ref. ², we extracted our own custom light curve from the TESS pixel files, to conduct a careful treatment of spacecraft systematics. Using the lightkurve Python package³¹, we retrieved the calibrated 2 min target pixel image files from the Mikulski Archive for Space Telescopes (https://archive.stsci.edu) using the default-quality bitmask. We extracted light curves for 20 different apertures centred on the target, which were then background corrected by subtracting the sky contribution determined using a custom background mask (Supplementary Fig. 3). We chose the photometric aperture minimizing the 1 h combined differential photometric precision metric³², in this case a circular aperture with a radius of 4.6 pixels. We corrected the extracted fluxes for the contamination from other faint sources in the aperture, on the basis of their magnitudes from the TESS Input Catalog³³. We note that, despite the large pixel scale of TESS (21 arcsec per pixel), v² Lupi is so much brighter than other nearby stars that the contamination ($flux_{contaminants}/flux_{target}$) is only 0.95% in this case.

As can be seen in the upper panel of Supplementary Fig. 4, the resulting light curve suffers from instrumental systematics, mostly related to the pointing jitter of the spacecraft. To correct for these systematics, we retrieved the engineering quaternion measurements for camera 1 (which observed v² Lupi), which are 2-s-cadence vector time series that describe the spacecraft attitude on the basis of observations of a set of guide stars (https://archive.stsci.edu/missions/tess/engineering/). For each of the three vector components, we computed the means and s.d.s of the measurements within each 2 min science image. We also retrieved the various cotrending basis vectors (CBVs, https://archive.stsci.edu/tess/bulk_downloads/bulk_downloads_cbv.html) computed by the preresearch data conditioning module³⁴,³⁵ of the TESS Science Processing Operations Center pipeline³⁶. We then decorrelated our light curve against the quaternion and CBV time series using Bayesian linear regression, while masking the in-transit points in the fit. We tested many different combinations of regressors and kept the one minimizing the Bayesian information criterion³⁷, which notably comprised the first and second-order quaternion time series as well as the high-frequency (band 3) CBVs. At the end of the process, 1,000 samples were drawn from the
posterior distribution of the regression coefficients to estimate the uncertainty of the model, which was then added quadratically to the error bars of the corrected data points. The resulting decorrelated light curve is shown in the second panel of Supplementary Fig. 4. The 1h combined differential photometric precision improved from 62 to 37 ppm h⁻¹, which is comparable with the precision achieved by ref. ¹¹ for HR 858, a similarly bright star. We used this decorrelated light curve in our subsequent global analysis.

**Archival RVs.** In our global analysis, we also included 246 previously published¹,² RV measurements that were obtained between 27 May 2004 and 4 August 2017 with the HARPS spectrograph on the ESO 3.6 m telescope (La Silla, Chile). Among these, the last six measurements were acquired after an instrument upgrade and we thus treated them as an independent dataset in our analysis. These RV data are shown in the upper panel of Supplementary Fig. 6. For details of the instrument, observations and data reduction, see refs. ¹,² and references therein.

Ref. ² also published 169 RV measurements obtained with the UCLES spectrograph on the 3.9 m Anglo-Australian Telescope (Siding Spring, Australia), as well as 43 RV measurements obtained with the HIRES spectrograph on the 10 m Keck I telescope (Mauna Kea, HI, USA). However, these data have significantly larger uncertainties than the HARPS data (mean measurement uncertainties of 1.27 and 1.17 m s⁻¹ for UCLES and HIRES versus 0.42 m s⁻¹ for HARPS) and show a significantly larger scatter (5.7 and 4.5 m s⁻¹ for UCLES and HIRES versus 2.7 m s⁻¹ for HARPS—Fig. 1 of ref. ²). After some preliminary analyses of the RV data (see below), it appeared that including the UCLES and HIRES data did not improve the fit, which is mostly dominated by the precise HARPS data. Thus, we only included the HARPS data in our final global analysis.

**Host star properties.** The main stellar parameters are presented in the upper part of Table 1. The spectroscopic parameters ($T_{\text{eff}}$, log g, $\dot{\epsilon}_i$, and [Fe/H]) were taken from ref. ³⁸. These parameters were derived with the same methodology as used in ARES+MOOG, which was recently described in detail in refs. ³⁹,⁴⁰. The uncertainties were updated following the discussion in ref. ⁴¹ about precision versus accuracy errors. In summary, the method starts with the measurement of equivalent widths of iron lines using the ARES code⁶²,⁶³. Then a minimization process is applied to find the ionization and excitation equilibrium and converge to the best set of spectroscopic parameters. This process makes use of a grid of Kurucz model atmospheres⁴⁴ and the radiative transfer code MOOG⁴⁵.

Stellar atmospheric abundances of several refractory elements are given in Supplementary Table 2. They were computed using the same tools and models of atmospheres as for the determination of the stellar atmospheric parameters (see above). In our analysis, we followed the classical curve-of-growth method under assumption of local thermodynamic equilibrium⁶⁶,⁴⁷. Our results show that the star is enhanced in α-elements (Mg, Si, Ti and Ca) relative to iron.

Using the stellar parameters derived above and Gaia, 2MASS and WISE broadband photometry, we determined the radius of $v^2$ Lupi via the infrared flux method⁸⁸, which, via the comparison of observed fluxes with synthetic photometry of atmospheric models, allows for the calculation of stellar effective temperature and angular diameter, and thus stellar radius when combined with the parallax. Following the retrieval of Gaia G, $G_{BP}$ and $G_{RP}$, 2MASS J, H and K and WISE W1 and W2 fluxes and relative uncertainties³⁰,⁴⁹,⁵⁰, we employed a Markov chain Monte Carlo (MCMC) approach to compare the observed photometry with synthetic values derived by convolving stellar atmospheric models⁵¹ with the throughput of the broadband bandpasses, taking the stellar parameters determined above as normal priors on the synthetic spectral energy distributions used. Via this method, we derived $R_*$ = 1.058 ± 0.019 $R_⊙$ which is in agreement ($1.8\sigma$) with the value reported in previous work² (1.012 ± 0.018 $R_⊙$), with differences potentially arising from differing methods used to derive $R_*$ or the careful treatment of stellar metallicity conducted in our study.

We derived the stellar age and mass from stellar models calibrated to reproduce the aforementioned infrared flux method radius, metallicity accounting for alpha enrichment, and effective temperature. Two sets of stellar parameters were computed with different stellar evolution codes, respectively using the CLES code⁵² and the PARSEC stellar tracks and isochrones⁵³. In the first case, with CLES, the optimal stellar parameters were determined following a Levenberg-Marquardt local minimization scheme. The CLES stellar models adopt the solar chemical mixture⁴⁴, OPAL opacities⁵⁵, the FreeEOS equation of state⁵⁶ and nuclear reactions from ref. ⁵⁷. In the second case, with PARSEC, output parameters were inferred using the isochrone placement interpolation scheme⁵⁸,⁵⁹. The PARSEC models adopt the solar-scaled composition given by ref. ⁶⁰, nuclear reaction rates considering the JINA REACLIB database⁶¹, OP⁶² and ÆSOPUS⁶³ opacities and the FreeEOS equation of state⁵⁶. For each method, we assumed that the stellar mass and age probability distribution functions follow Gaussians whose medians and s.d.s correspond to the values and errors returned by the fit. We then combined the results of the two approaches by merging the respective Gaussian distributions. The medians and s.d.s of the resulting combined distributions were adopted as the final stellar mass and age, and their associated errors. We find a stellar mass of 0.87 ± 0.04 $M_⊙$ and an old age of $12.3_{-2.9}^{+1.2}$ Gyr, consistent with the star's thick-disk kinematics⁶⁴ and low iron abundance ($-0.34 \pm 0.04$ dex).

**Global data analysis and derivation of the system parameters.** To determine the system parameters, we performed a combined analysis of the CHEOPS and TESS transit photometry, together with the HARPS RV data. For this purpose, we used the publicly available juliet library¹⁴ (https://github.com/nespinoza/juliet), which is built over batman⁶⁶ for the modelling of transits and radel⁶⁶ for RVs. A key feature of juliet is that it uses nested sampling algorithms (in this work dynasty¹⁵) to explore the parameter space, which also allows us to perform model comparison via Bayesian evidences. For this analysis, we assumed that the CHEOPS single transit event was caused by $v^2$ Lupi d (Origin of the CHEOPS single transit event).

juliet is very versatile and allows for a variety of parametrizations. In our analysis, we used the following model parameters.

* For each planet, *P* and *T*₀.

* For each planet, the parameters *r*₁ and *r*₂ as introduced by ref. ⁶⁷. This parametrization allows to efficiently explore the physically plausible zone in the (*b*,*p*) plane, where *p* is the planet-to-star radius ratio ($R_p/R_*$) (see ref. ⁶⁷ for details).

* $\rho_*$, which, together with the *P* of each planet, defines through Kepler's third law a value for $a/R_*$ of each planet. This parametrization offers the advantage of defining a single common value of the stellar density for the system rather than fitting for the scaled semi-major axis of each planet, thus reducing the number of fitted parameters. We placed a normal prior ($N(1,035,76^2)$ kg m⁻³) on the stellar density based on the stellar mass ($M_*=0.87 \pm 0.04 M_⊙$) and radius ($R_*=1.058 \pm 0.019 R_⊙$) that we previously derived.

* For each bandpass (CHEOPS and TESS), two transformed limb-darkening coefficients ($q_1, q_2$), referring to the formalism introduced by ref. ⁶⁸. This parametrization allows an efficient uninformative sampling from the physically plausible ($u_1, u_2$) parameter space, where $u_1$ and $u_2$ are the quadratic limb-darkening coefficients.

* For each planet, $\sqrt{e} \sin \omega$ and $\sqrt{e} \cos \omega$, where $\omega$ is the argument of periastron, as well as $K$.

* Together, these model parameters describe the planetary signals present in the photometric and RV data. To these should be added some 'nuisance' parameters describing the instrumental or astrophysical noise. Juliet does indeed allow us to model the planetary signals simultaneously with some possibly underlying correlated noise, ensuring this way a full propagation of the uncertainties on the derived system parameters. This is done using either linear models (against any relevant external parameter) or GPs (celerite⁶, george²⁰).

We first performed individual analyses of each of our light curves, to select for each of them the best correlated noise model, based on Bayesian evidence. We explored a large range of models for the CHEOPS light curves, consisting of first- to fourth-order polynomials in the recorded external parameters (most importantly time, background level, position of the point spread function centroid, spacecraft roll angle), as well as GPs against time, roll angle or a combination of the two. In this process, we only selected a more complicated model over a simpler one if the difference in its Bayesian log evidence ($\Delta \ln Z$) was greater than two¹⁴.¹⁵. We found that linear functions of $\sin(n\phi)$ and $\cos(n\phi)$, where $n=1,2,3$ (depending on the visit, Supplementary Table 3) and $\phi$ is the spacecraft roll angle¹, are favoured for all visits and account for most of the instrumental noise (shown in turquoise in the top panels of Supplementary Fig. 1). On top of this, we noticed in the photometric residuals some higher-frequency correlated noise, which we attribute to stellar granulation and oscillations (see below for a detailed study of the power spectrum of the residuals and characterization of the stellar noise). If not properly accounted for, such stellar noise can introduce biases in the inferred transit parameters¹⁶,⁷². In our analysis, we modelled the stellar noise using a GP with a stochastically driven damped simple harmonic oscillator kernel¹⁸, with a quality factor of $1/\sqrt{2}$. In this particular case, the simple harmonic oscillator kernel indeed has a similar PSD to stellar granulation⁷³,⁷⁴, to a first approximation. Since this stellar variability is seen in all the CHEOPS light curves, a single common simple harmonic oscillator GP was fitted across the six CHEOPS visits in our combined analysis (shown in green in the upper panels of Supplementary Fig. 1). The TESS light curve is not sensitive to such a short-timescale low-amplitude stellar signal; however, it shows some residual systematics, which we modelled using a Matèrn GP (shown in orange in the second panel of Supplementary Fig. 4), as favoured by the Bayesian evidence. As for the RVs, we simply modelled them using a sum of three Keplerians (to account for the three planets), with a different zero point for each dataset (before and after upgrade). No correlated noise model was necessary in this case. Finally, we also fitted for each of our photometric and RV datasets an extra jitter term, which was added quadratically to the error bars of the data points, to account for any underestimation of the uncertainties or any excess noise not captured by our modelling.

Altogether, this yields a total of 70 free model parameters, of which 26 describe the planetary signals and the other 44 are nuisance parameters. These parameters are listed together with their priors in Supplementary Table 3. To aid convergence, we placed normal priors on the nuisance parameters, based on the posterior distributions returned by our individual analyses. This approach allowed us to properly account for the covariances between the physical and nuisance parameters, while propagating the prior information we had on the nuisance parameters from our individual analyses. All the physical parameters were sampled
from wide uniform priors, except the stellar density, for which we used the normal prior mentioned previously.

We performed several global analyses: one assuming circular orbits (e set to zero) for all three planets (hereafter the 'reference model'), one allowing the orbits of all three planets to be eccentric (hereafter the 'eccentric model') and three more analyses allowing the orbit of one planet to be eccentric while assuming circular orbits for the other two. A comparison between the Bayesian evidences of these models is provided in Supplementary Table 4. The reference model is the one with the highest Bayesian evidence. The eccentric model is marginally disfavoured compared with the reference model (ΔlnZ = -3.6). The models allowing the orbit of only one of the planets to be eccentric are statistically indistinguishable from the reference model (ΔlnZ between -0.9 and -1.7). However, given that the reference model is the simplest model and it has the highest Bayesian evidence, it appears to be the best model given the data at hand. We thus adopted it as our nominal solution.

The posterior distributions of the main fitted parameters of our global analysis are shown in Supplementary Fig. 7, while Table 1 presents our results for the most relevant physical parameters of the system. The best-fit models for the individual light curves are shown in Supplementary Figs. 1 (CHEOPS) and 4 (TESS). The unbinned CHEOPS light curves, which have a cadence of 44.2s, have a residual r.m.s. between 47 and 53 ppm. When binning into 10 min and 1 h intervals, we reach r.m.s. values between 14 and 17 ppm and between 5 and 7 ppm, respectively. For comparison, the residual r.m.s. of the unbinned (2-min-cadence) TESS light curve is 149 ppm. This r.m.s. decreases to 80 and 30 ppm when binning into 10 min and 1 h intervals, respectively. The corrected light curves, phase-folded for each planet, are shown in Fig. 1 (CHEOPS) and Supplementary Fig. 5 (TESS) together with the best-fit transit models. The phase-folded RVs are shown in Supplementary Fig. 6, together with the best-fit RV model for each planet.

**Refinement of the system parameters.** To assess the improvement brought by our CHEOPS data for planets b and c compared with the previous TESS measurements², we also analysed both datasets individually, in a homogeneous way, using the same methods and priors as above. For this exercise, we assumed eccentric orbits for the planets to allow a direct comparison with the results of ref. ². We first made a combined analysis of the TESS light curve and the RVs. The results of this analysis are compared with those of ref. ² in Supplementary Table 5 (second and third columns) for some key parameters. Our results are consistent, but our uncertainties are significantly larger, for example by factors of ~1.7 and ~2.1 for the planet-to-star radii ratios of planet b and c, respectively. These larger uncertainties are probably related to our modelling of the residual systematics with a GP that is fitted simultaneously with the transits, while ref. ² performed a full detrending of the TESS light curve before the transit fitting. We consider our approach to be more robust, as it accounts for the possible covariances between the nuisance and transit parameters, thus ensuring a proper propagation of the uncertainties on the derived transit parameters.

We then performed a combined analysis of our six CHEOPS visits together with the RVs. The results are reported in the fourth column of Supplementary Table 5. They are in good agreement with those of our TESS data analysis and also provide tighter constraints on the transit parameters. The planet-to-star radius ratios are measured with relative precisions of 2.8% and 2.1% for planets b and c, respectively, a factor of ~2 more precise than the measurements returned by our analysis of the TESS data. This significant refinement stems from both the higher photometric precision of CHEOPS and the larger number of transits observed (four transits of planet b observed with CHEOPS versus two with TESS; three transits of planet c observed with CHEOPS versus only one with TESS).

Of course, the best constraints are obtained when combining all the data (TESS + CHEOPS + RVs) together (last column of Supplementary Table 5). Thanks to the longer temporal baseline, the transit ephemerides are significantly refined, thus enabling efficient follow-up observations. The mid-transit times of planets b and c in May 2021 (middle of the next observing window) now have uncertainties of only 10.1 and 2.6 min, respectively. This is a major improvement when compared with the previous respective uncertainties of 88 and 106 min obtained when using the ephemerides of ref. ¹. The other transit parameters (for example planet-to-star radii ratios and impact parameters) are only slightly refined when comparing with the results of our CHEOPS data analysis, which demonstrates that they are mostly constrained by CHEOPS. The planetary radii derived from our global analysis are slightly larger than those reported in ref. ¹. This is due to the combined effect of both our slightly larger planet-to-star radii ratios and stellar radius (Host star properties). We note however that the planetary radii are still consistent within the uncertainties.

**Transit timing variations.** The identification of mean-motion resonance (MMR) configurations or the detection of significant TTVs in multiplanet systems can yield valuable information about their formation and evolution⁷. In particular, the TTV signal is enhanced when the planets are in, or close to, an MMR⁷⁻⁸, and the lower the order of the MMR the stronger the TTV amplitude. Looking at the period commensurability, that is the ratio of the periods of planet pairs in the system, is the first step to identify a possible MMR. In the $v^2$ Lupi system, both pairs of planets b–c and c–d show a period commensurability close to a third-order MMR, that is a 5:2 MMR for the b–c pair and a 4:1 MMR for the c–d pair.

The common method to identify TTVs is to plot the so-called O–C (observed–calculated) diagram, where O are the observed (measured) transit times and C are transit times computed from a linear ephemeris. To compute the expected TTV signals, we simulated the system with a *N*-body integrator. We used the parameters in Table 1 to integrate the orbits of the three planets for 3.5 yr (that is, the nominal duration of the CHEOPS mission) with the TRADES⁸¹⁻⁸³ program, which allows us to compute the simulated transit times for each planet. We then extracted the semi-amplitude of the O–C diagram of each planet, assuming the simulated transit times as O and subtracting the transit times C calculated from the linear ephemeris based on P and $T_0$ in Table 1. We found that the expected TTV semi-amplitudes are rather small: about 20 s for planets b and d, and about 40 s for planet c.

To explore our current dataset for possible TTVs, we ran another global analysis with juliet, additionally including a free TTV offset parameter for every transit of planet b (six transits) and planet c (four transits), while keeping their P and $T_0$ fixed to the values given in Table 1. For the TTV offsets, we assumed uniform priors between -15 and +15 min. We assumed the same priors as previously (Supplementary Table 3) for the other physical and nuisance parameters, as well as circular orbits. This analysis returned uncertainties on the individual transit times of ~4–5 min for planet b and ~1–2 min for planet c, which did not allow us to detect any significant TTVs.

**Origin of the CHEOPS single transit event.** In all of the above, we assumed that the single transit event caught by CHEOPS was caused by $v^2$ Lupi d. However, one might ask whether this transit may instead be caused by an additional as yet unknown planet in the system.

The single transit event that we detected in the fifth CHEOPS visit is partial (that is, the observations did not cover the end of the transit), hence its duration is not well constrained. Additionally, the observations also did not cover the ingress, which occurred during an Earth occultation. Because of this, the impact parameter and orbital period are very poorly constrained. Some more constraints on the orbital period may arise from the other photometric observations, especially the 28-d-long TESS observations. A ~9-h-long transit with a ~500 ppm depth would have been very clearly detected in these data (see for example how the transit of $v^2$ Lupi c, which has a similar depth, appears clearly in Supplementary Fig. 4), meaning that they can be used to exclude some orbital periods. To assess the constraints brought by the photometry on the orbital period of the transiting object, we performed a combined fit of all the CHEOPS and TESS data with juliet. We assumed the same normal priors as used previously for the stellar density and nuisance parameters and wide uniform priors for the planet parameters (Supplementary Table 3). For the third transiting planet corresponding to the CHEOPS single transit event, we assumed a uniform prior between 30 and 1,000 d for the orbital period, and a uniform prior between 2,459,009.6 and 2,459,010.0 BJD for the mid-transit time. The posterior distributions of the fitted parameters for the third planet are shown in Supplementary Fig. 8. A wide range of orbital periods are compatible with the photometry, with a $3\sigma$ upper limit of 624 d. The few blank vertical stripes seen in the corner plot for some orbital periods (for example around 185 d and 370 d) correspond to periods that can be excluded on the basis of the TESS data.

To assess the possibility of a fourth unknown planet in the system, we also searched for some additional signals in the HARPS RVs. We computed the $\ell'_1$ periodogram³, which searches for several periodic signals simultaneously and thus is less prone to show spurious peaks due to aliasing than a regular periodogram. The $\ell'_1$ periodogram (Supplementary Fig. 9, top) shows two possible peaks around 123 and 485 d, but with high false-alarm probabilities of 14.5% and 9.6%, respectively. We note that the signal at 123 d has already been discussed in ref. ¹, which came to the conclusion that it was more probably an artefact induced by noise in the data or interaction with the window function (period ~1/3 of a year) rather than an additional planet in the system. To assess the possibility of one of these two candidates being at the origin of the CHEOPS single transit event, we fitted a fourth planet to the HARPS RVs and checked if the posterior distributions obtained for P and $T_0$ were compatible with the photometry, that is, what percentage of the posterior samples could produce a transit in the fifth CHEOPS visit but no transit in the TESS data. For the 123 d signal, we found that the derived P (122.26$^{+0.87}_{-0.83}$ d) and $T_0$ (2,455,509.75 ± 4.32 BJD) posterior distributions are completely incompatible with the photometry: all the posterior samples that are compatible with a transit during the fifth CHEOPS visit would have also produced a transit in the TESS data. Furthermore, a dynamical stability analysis reveals that a fourth planet with a period of 123 d would make the system unstable (Orbital stability). This candidate signal at 123 d can thus be discarded. For the 485 d signal, we find that 0.02% of the derived P (481.72$^{+17.35}_{-14.88}$ d) and $T_0$ (2,455,727.22$^{+20.63}_{-18.89}$ BJD) posterior samples are compatible with the photometry. By way of comparison, this is 20 times less than the corresponding percentage of 0.4% obtained for $v^2$ Lupi d.

As a complementary check, we performed two more global analyses of all the data (CHEOPS, TESS, HARPS) assuming a fourth planet with a period of 485 d (planet e). For one of these analyses, we assumed that planet e is responsible for the CHEOPS single transit event ('4 planets-e transiting' model) and that planet d was thus not detected in transit in the photometry. For the second one, we assumed the opposite, that is that planet d is responsible for the CHEOPS single transit event and that planet e is not detected in the photometry ('4 planets-d
transiting' model). A comparison between the Bayesian evidences of these two
models and our reference model (for which we assumed three planets with planet
d responsible for the single transit, see above) is provided in Supplementary Table
4. The 4 planets—e transiting model is marginally disfavoured compared with the
4 planets—d transiting model, with a Δln Z = -3.1, that is posterior odds of ~1:22
assuming equiprobable models. However, these two models are not equiprobable,
planet d having also a ~2.8 times higher geometric transit probability than planet
e. This results in posterior odds of ~1:62 in favour of the 4 planets—d transiting
model. This model is statistically indistinguishable from our '3 planets—d
transiting' reference model (Δln Z = 0.6), which reflects the low significance of the
485 d signal in the RV data. Our simpler reference model is thus the best model
given the data at hand.

Finally, we also assessed the possibility that the CHEOPS single transit is
caused by a fourth planet that is completely undetected in the HARPS RVs. A
detailed computation of RV detection limits, via injection and recovery tests, is
beyond the scope of this paper. To estimate the detection limits of the HARPS
dataset, we instead used the results of the RV fitting challenge reported in ref. ⁸⁵.
This showed that signals with $K \ge 7.5 \text{ RV}_{\text{rms}}/\sqrt{N_{\text{obs}}}$, with $N_{\text{obs}}$ the number of data
points and $RV_{\text{rms}}$ their r.m.s., are typically confidently detected in RV time series.
For our HARPS dataset, we have $N_{\text{obs}} = 246$ and $RV_{\text{rms}} = 1.37 \text{ m s}^{-1}$ after removing
the signals of the three known planets, yielding a detection threshold $K = 0.66 \text{ m s}^{-1}$.
From this value, we can derive a minimum planetary mass that should be detected
for a given orbital period. Supplementary Fig. 9 (bottom) shows this minimum
planetary mass as a function of orbital period for periods up to 624 d (3σ upper
limit from our analysis of the photometry, see above). Since we know that the
radius of the transiting object is ~2.6 $R_{\oplus}$ on the basis of its transit depth, we can
estimate its mass using for example the empirical mass-radius relationship of
ref. ⁸⁶: $M_p = 1.436 R_p^{1.70}$, thus ~7.3 $M_{\oplus}$ in this case. As shown in Supplementary
Fig. 9 (bottom), planets in this mass range with periods up to ~480 d should be
confidently detected in the HARPS data according to this criterion. Planets in
this mass range with longer periods up to ~624 d should produce low-significance
peaks in the RV periodogram. This is for example the case for the 485 d candidate
discussed above, which has $K \approx 0.5 \text{ m s}^{-1}$, thus lower than our approximate
detection threshold, but still produces a low-significance peak in the periodogram.

On the basis of all these elements, we conclude that the CHEOPS single
transit event was most probably caused by $v^2$ Lupi d, rather than by an additional
unknown planet in the system.

**Orbital stability.** In this section, we sought to test the results of our global fit by
exploring the stability of the system. To achieve this, we made use of the mean
exponential growth factor of nearby orbits (MEGNO), $Y(t)$ (refs. ⁸⁷⁻⁸⁹). MEGNO
is a chaos index that has been extensively used within dynamical astronomy, in
particular for extrasolar planetary systems⁹⁰⁻⁹². Its time-averaged mean value,
$\langle Y(t) \rangle$, amplifies any stochastic behaviour, allowing the detection of hyperbolic
regions during the integration time. Therefore, $\langle Y(t) \rangle$ allows us to distinguish
between chaotic and quasiperiodic trajectories: if $\langle Y(t) \rangle \to \infty$ for $t \to \infty$ the system
is chaotic; while if $\langle Y(t) \rangle \to 2$ for $t \to \infty$ the motion is quasiperiodic. We used the
MEGNO implementation within the N-body integrator REBOUND⁹³, which
makes use of the Wisdom-Holman WHFast code⁹⁴.

We explored the masses and eccentricities of the planets, two parameters that
have the most marked effect on the orbital dynamics, by building stability maps of
adjacent planets. The map building entailed exploring the parameter space of $M_b$–
$M_c$ and $e_b–e_c$ for the inner planets b and c, and $M_c–M_d$ and $e_c–e_d$ for planets c and d.
Hence, we studied planetary masses ranging from 1 to 10 $M_{\oplus}$ for planet b and 5 to
15 $M_{\oplus}$ for planets c and d, and eccentricities in the range of 0.0–0.6 for all planets.
In our sets of simulations, we took 10 values from each range, meaning that the
size of each stability map was 10 × 10 pixels. Moreover, for each scenario, we set 20
different random initial conditions by varying the argument of pericentre in the
range of its nominal value ±1σ (on the basis of our global eccentric analysis), and
the longitude of ascending node and mean anomaly in the range 0–360°. We then
averaged these 20 initial conditions to obtain the averaged value of $\langle Y(t) \rangle$ of each
pixel of the stability maps. Hence, for each stability map, we ran 2,000 simulations.
The integration time was set to 10⁶ times the orbital period of the outermost planet
d. The time step was set to 5% of the orbital period of the innermost planet b. Note
that we explored the nominal values of the planetary masses and eccentricities
presented in Table 1 up to well beyond their 5σ ranges. This strategy allowed us to
better understand the full architecture of the system, as well as its limitations. We
found that the system is fully stable over the whole range of masses explored, with a
$\Delta\langle Y(t) \rangle = 2.0 – \langle Y(t) \rangle < 10^{-3}$. With regard to the eccentricities, we obtained that
the planets may tolerate eccentricities up to 0.3, 0.3 and 0.4 for planets b, c and
d, respectively. These masses and eccentricities are all well above their nominal
values, which highlights the goodness of the solution from our global analysis.

As mentioned in the previous section, the RV periodogram shows two possible
signals at 123 and 485 d. A fourth planet with an orbital period of 485 d would
not affect the stability of the system, but a planet with a period of 123 d could
make the system unstable. To test the stability of the system in such a four-planet
configuration, we included a planet with an orbital period of 123 d, and then built
stability maps exploring the parameter space $e_{1234}–M_{1234}$ (with $e_{1234}$ and $M_{1234}$ the
eccentricity and mass of the planet at 123 d, respectively). These stability maps

were built following the same procedure as presented above, but we increased the
number of pixels to 15×15. We then explored eccentricities in the range of 0.0–0.6
and masses ranging from 1 to 15 $M_{\oplus}$. We ran two suites of simulations: (1) planets
b, c and d were given circular orbits, and (2) they were given eccentric orbits using
the eccentricities derived from our global eccentric analysis. For each pixel (or
equivalently, each combination of $e_{1234}–M_{1234}$), we ran 20 different initial conditions
by randomly varying the orbital angles, and then averaged the results. That is, each
stability map contained 4,500 scenarios. We found that such a four-planet system
would be fully unstable for times shorter than 10⁶ orbits of the outermost planet.
On the basis of these results, a fourth planet at 123 d can thus be discarded.

**Tidal interactions.** The planets are close enough to their host star to experience
notable tidal interactions. To investigate this aspect, we quantified the influence
of tides by means of the constant-time-lag model, in which a planet is considered
as a weakly viscous fluid that is deformed due to gravitational effects⁹⁵⁻⁹⁷. In
this context, the tidal dissipation of a given planet is defined by the product
of the potential Love number of degree 2 and the constant time lag, $k_2 \Delta \tau$. For
terrestrial exoplanets, a range of possibilities centred on Earth's dissipation factor⁹⁸
$k_2 \Delta \tau_{\text{fb}} = 213$ s, that is (0.1–10)$k_2 \Delta \tau_{\text{fb}}$, is generally adopted, so as to explore a
range of possible tidal behaviours⁹⁹,¹⁰⁰. This assumption is valid for the innermost
planet in the system, $v^2$ Lupi b, which has an Earth-like mean density (Table 1).
This is not the case for $v^2$ Lupi c and d, whose lower densities suggest that they
are probably volatile rich and have small gaseous envelopes (Internal planetary
structures). Hence, we assumed a tidal dissipation factor similar to Jupiter's
value¹⁰¹, $k_2 \Delta \tau \approx 2.5 \times 10^{-2}$ s, and explored a range of 1–100 times this value¹⁰². We
then performed a suite of simulations with the N-body code Posidonius¹⁰³, which
includes the effects of tides, rotational flattening and general relativity, using the
same prescriptions as given in ref. ¹⁰⁴.

We found that the innermost planet b evolved rapidly into a pseudorotational
state: that is, into a tidally locked configuration where its orbital and rotational
periods became synchronized, and its obliquity close to zero, so that its orbital
axis became aligned with the spin axis of the star. This state was reached within
a short timescale, at a maximum $10^4–10^6$ yr. This process is slower for the two
outermost planets, which should reach pseudorotational states after $10^8–10^{10}$ yr
for planet c and $10^{11}–10^{13}$ yr for planet d. Concerning the circularization of the
orbits, we found that this should be reached after $10^7–10^9$ yr for planet b and after
$10^{11}–10^{13}$ yr for planet c. For planet d, the circularization time exceeds $10^{14}$ yr.
Dynamical tidal processes thus do not seem to be very efficient in this system.
Considering that the estimated age of the system is $12.3 \times 10^{-2}$ Gyr (Table 1), we
conclude that circularization may be complete for planet b, but still ongoing for
planets c and d. However, while eccentric orbits may not be fully discarded from
our global analysis, we found the model with circular orbits for all three planets
to be marginally favoured. If this is the case, this would mean that planets c and
d dissipated more energy than was explored in this study, hinting that other
processes such as tidal inertial waves in the convective region of the planets might
be affecting the system¹⁰⁵. In this case, enhancement of the tidal dissipation rates
would imply a more rapid synchronization of the planets' spins with their orbits,
and faster circularization of their orbits.

**Characterization of the stellar signal seen in CHEOPS photometry.** To precisely
characterize the stellar noise detected in the CHEOPS light curves, we removed the
best-fit transit and instrumental noise models from the data and analysed the PSD
of the resulting residuals (Supplementary Fig. 10, grey curve). We clearly observe
the bump of the stellar acoustic modes at high frequency, and the characteristic
increase of the PSD towards the lower frequencies associated with the signature of
stellar granulation⁷³.

To characterize this stellar signal, we first performed a GP regression in
the time domain based on the model described in ref. ¹⁰⁶ (dashed lines in
Supplementary Fig. 10). This GP model consists of a sum of three kernels chosen
such that their respective PSDs correspond to a Gaussian-like envelope to
describe the oscillation bump, a Harvey-like function to describe the granulation
component and a stochastic term to describe the high-frequency (photon) noise.
Using an MCMC approach¹⁰⁷ to derive the parameters of this model, we inferred
a characteristic amplitude and frequency for the granulation of 49 ± 2 ppm and
1,026+85/80 µHz, respectively, and a $v_{\text{max}}$ of 2,710 ± 77 µHz. The latter is in agreement
(1.8σ) with the $v_{\text{max}}$ of 2,414+141/-133 µHz expected from the stellar parameters given in
Table 1.

Considering that there is still some debate as to which model best describes the
granulation signature (see for example refs. ⁷⁴,¹⁰⁸ and references therein), we tested
another model based on simple power laws¹⁶,¹⁰⁹. Making the approximation that
the power background follows frequency power functions, this model is defined
as $\log P(\nu) = \alpha_g \log(\nu) + \beta$, with $\nu$ the frequency, $\alpha_g$ the flicker index measured
between two cutoff frequencies $\nu \in [f_c, f_g]$ and $\beta$ a constant. Using again an MCMC
approach¹¹⁰ to derive the parameters of this power-law model, we inferred
$\alpha_g = 1.14 \pm 0.22$ between $f_c = 1,964 \pm 36$ µHz and $f_g = 830 \pm 130$ µHz (red dotted line
in Supplementary Fig. 10). Based on Kepler observations, it has been shown that
this flicker index and the corresponding cutoff frequencies are strongly correlated
with the stellar fundamental parameters¹⁶, particularly with the stellar mass, radius
and surface gravity (Supplementary Fig. 11). Comparing the flicker index we
inferred for $v^2$ Lupi (red dot with error bars) with results obtained previously for Kepler stars (grey and black dots), we observe that it follows the expected trends well. Moreover, this first CHEOPS measurement opens the way to studies of granulation signatures on bright stars that were not covered by Kepler.

**Internal planetary structures.** We performed a Bayesian analysis to infer the possible interior structures of the three transiting planets$^{23,24}$. We assumed the planet to be made of four different layers: a central core made of iron and sulfur, a silicate mantle (containing Si, Mg and Fe), a water layer and a gas layer made of pure H and He. Compared with previous similar models$^{23,24}$, the physical models used here have been improved$^{11}$, namely with a new equation of state for the water layer$^{12}$, and the equation of state for the iron core$^{13}$ (which can also contain some sulfur). The equation of state for the silicate mantle$^{14}$ depends on the mole fractions of Si, Mg and Fe, and the gas envelope model$^{15}$ gives the thickness of the gas envelope as a function of age, planetary mass and so on. In this analysis, we did not include the compression effect of the gas envelope on the innermost layers of the planet (core, mantle and water layer). The validity of this hypothesis can be checked a posteriori, as the mass of gas is small for the three planets (see below).

The transit and RV data provide measurements of the planetary radii and masses relative to those of the star. This introduced some correlation between the absolute planetary radii and masses, which we take into account by fitting with our model the planetary system as a whole, and not each planet individually. For this, we assume that the planetary Si/Mg/Fe molar ratio for all planets is equal to the stellar one, and we fit directly the transit depths and RV semi-amplitudes of the three planets at once. The data used by the model are therefore the stellar mass, radius, effective temperature and age, as well as the chemical abundances of Fe, Mg and Si and the planetary RV semi-amplitudes, transit depths and orbital periods. The prior distribution of the mass fractions of core, mantle and water layer, which add up to unity, is assumed to be uniform on the simplex (the surface defined by the sum of the three mass fractions equal to unity). In addition, it is likely that the maximum water mass fraction of planets cannot be larger than the icy fraction inside planetary solid building blocks (whatever their nature—planetsimals or pebbles). We therefore assume that the mass fraction of water is less than 50% (refs. $^{116,117}$). The prior of the gas mass is assumed to be uniform in log. The posterior distributions of the relevant internal structure parameters are shown in Supplementary Figs. 12–14 for the three planets.

Under the assumed priors, the gas mass in the three planets shows strong variations between planet b, which can be seen as a bare core, planet c, with a gas mass (5% and 95% quantiles) of $0.13_{-0.078}^{+0.103} M_{\oplus}$ ($1.2_{-0.70}^{+0.91} \text{ wt%}$), and planet d, having a somewhat smaller gas mass of $0.058_{-0.050}^{+0.069} M_{\oplus}$ ($0.66_{-0.58}^{+0.79} \text{ wt%}$). Since we have derived the joint posterior probability of the three planetary internal structure parameters, we can easily estimate the probability that planet d has less gas than planet c, and we found this probability to be ~90%. The water mass is found to be $0.57_{-0.49}^{+0.60} M_{\oplus}$ ($12.6_{-11.0}^{+14.7} \text{ wt%}$) for the innermost planet b, $2.81_{-2.52}^{+2.52} M_{\oplus}$ ($25.01_{-22.4}^{+22.2} \text{ wt%}$) for planet c and $2.31_{-2.13}^{+2.09} M_{\oplus}$ ($26.8_{-23.7}^{+21.2} \text{ wt%}$) for planet d. Finally, the radii of the high-Z parts (iron core, mantle and water layer) are similar for the two outer planets: $2.14_{-0.20}^{+0.17} R_{\oplus}$ for planet c and $2.04_{-0.21}^{+0.19} R_{\oplus}$ for planet d.

**Atmospheric evolution.** We constrained the initial atmospheric mass fraction of the three planets composing the $v^2$ Lupi system and the evolution of the rotation rate of the host star employing a slightly modified version of the tool presented by refs. $^{25,26}$. The algorithm models the evolution of planetary atmospheres accounting for atmospheric mass loss combining a model of the stellar high-energy (X-ray plus extreme ultraviolet, XUV) flux evolution, a model relating planetary parameters and atmospheric mass and a model computing planetary atmospheric escape.

The XUV flux of late-type stars (later than F5) out of the saturation regime depends on stellar mass and, more importantly, on rotation period$^{118}$, which increases with time, but the evolution of the stellar rotation rate, and thus of the XUV emission, does not follow a unique path$^{19}$. To account for the different rotation histories, the framework models the rotation period as a power law in age$^{120}$ normalized such that the computed rotation period at the present age is consistent with the current estimate$^{25}$ of $23.8 \pm 3.1$ d (ref. 1). The stellar XUV luminosity is then derived from the rotation period using scaling relations$^{118,121,122}$, while the evolution of the stellar bolometric luminosity, which drives the evolution of the equilibrium temperature of the planets, is obtained by interpolating a grid of stellar structure models$^{123,124}$.

To estimate the planetary atmospheric mass fraction as a function of mass, radius and equilibrium temperature, we generated a grid of interior structure models as used in the previous section, and performed an average over the ‘hidden’ parameters (stellar age, core radius and so on). Finally, the tool extracts the planetary mass-loss rates as a function of the system parameters by interpolating over a large grid of hydrodynamic upper-atmosphere models$^{125}$. This approach has the advantage over the other commonly used analytical estimates, to appropriately and simultaneously account for both XUV-driven and core-powered mass loss$^{125,126}$. The key assumptions of the framework are that the planetary orbits do not change with time following the dispersal of the protoplanetary disk and that the planetary atmospheres are hydrogen dominated.

For each planet, the planetary atmospheric evolution calculations begin at an age of 5 Myr, which is the assumed age of the dispersal of the protoplanetary

disk. At each time step, the framework then extracts the mass-loss rate from the grid employing the stellar flux and system parameters, and uses it to update the atmospheric mass fraction. This procedure is then repeated until the age of the system is reached or the planetary atmosphere has completely escaped. The free parameters of the algorithm are the initial atmospheric mass fraction at the time of the dispersal of the protoplanetary disk, and the index of the power law controlling the stellar rotation period (a proxy for the stellar XUV emission) within the first 2 Gyr. Afterwards, the relation between rotation period and age is modelled through a power law$^{120}$, assuming the exponent 0.566.

The free parameters are constrained by implementing the atmospheric evolution algorithm in a Bayesian framework employing an MCMC tool$^{110}$. The framework uses the system parameters with their uncertainties as inputs (that is priors). It then computes millions of forward planetary evolutionary tracks, varying the input parameters according to the shape of the prior distributions, and varying the free parameters within predefined ranges, fitting the current planetary atmospheric mass fractions obtained as described in the previous section. The fit is done for the three planets simultaneously. The results are posterior distributions of the free parameters, which are the rotation period of the star when it was young and the planetary initial atmospheric mass fractions. The modifications to the original tool are fitting for the planetary atmospheric mass fractions, instead of the planetary radii, and employing the stellar rotation period as a step parameter for the MCMC algorithm, instead of the index of the power law controlling the stellar rotation period within the first 2 Gyr. The former modification enables the code to be more accurate by avoiding continuously converting the atmospheric mass fraction into planetary radius, given the other system parameters. The latter modification avoids biasing the MCMC calculations towards faster-rotating stars.

Supplementary Figure 15 shows the resulting posterior probability distribution functions for the rotation period of the host star at the age of 150 Myr and for the initial atmospheric mass fraction of each of the three planets. In this figure, the stellar rotation period at an age of 150 Myr is also compared with the distribution obtained from stars with masses between 0.75 and $1 M_{\odot}$ that are members of open clusters of comparable age$^{127}$. Our result suggests that $v^2$ Lupi evolved as a medium rotator, with a most probable rotation period at an age of 150 Myr ranging between 1 and 10 d and peaking at about 7 d, in agreement with the rotation period observed for most of the stars that are members of open clusters of similar age.

The posterior distribution obtained for the initial atmospheric mass fraction of $v^2$ Lupi b is flat, evidencing that the planet has completely lost its primary hydrogen-dominated atmosphere at some unknown point in time during the evolution. Therefore, the framework is unable to identify how much atmosphere there was when the planet stopped accreting. For both $v^2$ Lupi c and $v^2$ Lupi d, the posterior distribution of the initial atmospheric mass fraction presents one strong, rather narrow peak close to the one that is obtained for the current atmospheric mass fraction through the interior structure modelling (see previous section). These results suggest that both planets experienced little atmospheric evolution through mass loss. This indicates that both planets accreted only a small atmosphere and that their current low gas content is thus probably of primordial origin. On the basis of the evolution simulations, we estimate the current mass-loss rates of $v^2$ Lupi c and $v^2$ Lupi d to be of the order of $3.2 \times 10^8$ and $1.8 \times 10^7$ g s$^{-1}$, respectively.

**Potential of the system for atmospheric characterization.** To assess quantitatively the potential of the system for atmospheric characterization, we used the TSM of ref. $^{29}$. This metric is proportional to the expected transmission spectroscopy signal-to-noise ratio and is defined as

$$ \text{TSM} = \text{scale factor} \times \frac{R_{\oplus}^3 T_{\text{eq}}}{M_{\odot} R_{\star}^2} \times 10^{-m_j/5} $$

where $m_j$ is the apparent magnitude of the planet in the J band. The scale factor depends on the radius of the planet and allows a one-to-one scaling between the TSM values and the signal-to-noise ratios estimated in ref. $^{128}$ assuming 10 h of observations with the Near InfraRed Imager and Slitless Spectrograph (NIRISS) aboard the JWST. Using the system parameters derived from our global analysis (Table 1), we obtained TSM values of 125, 214 and 117, for $v^2$ Lupi b, c and d, respectively. To provide context, Fig. 2d compares these TSM values with those of the currently known population of small ($R_p < 4 R_{\oplus}$) transiting exoplanets as a function of their $T_{\text{eq}}$. The size of the symbols is proportional to the host star effective temperature. To identify the top atmospheric characterization targets among the exoplanet population, ref. $^{29}$ recommends a threshold of 92 for planets with $1.5 R_{\oplus} < R_p < 2.75 R_{\oplus}$, such as $v^2$ Lupi b and d, and a threshold of 84 for planets with $2.75 R_{\oplus} < R_p < 4 R_{\oplus}$, such as $v^2$ Lupi c. All three $v^2$ Lupi planets are above these suggested thresholds, thus opening up promising perspectives for comparative atmospheric studies. We note that the TSM is only intended as a general metric for the ranking of transmission spectroscopy targets and that atmospheric observations of the $v^2$ Lupi planets may turn out to be challenging in practice. With a K-band magnitude of 4.16, $v^2$ Lupi c is close to the JWST saturation limit for spectroscopy of $K \approx 4$ (ref. $^{129}$). Still, higher-efficiency readout modes for observations of bright stars are currently being investigated$^{130}$. In particular, a new
mode¹³¹ was proposed for the Near InfraRed Camera (NIRCam) that would allow us to measure spectra of targets up to $K \approx 1-2$ between 1 and 2 µm.

With its rocky and mostly dry composition, $v^2$ Lupi b might not be an ideal target for atmospheric characterization. Still, its high temperature (~900 K) opens the interesting possibility that its surface is molten and sustains a secondary atmosphere in equilibrium with the underlying magma¹³². High-resolution ultraviolet spectroscopy with the Hubble Space Telescope could be used to detect the strong electronic transitions from metal effluents in this envelope.

In contrast, the nature of $v^2$ Lupi c makes it a particularly promising target. Among the three planets, this is the one with the lowest bulk density. Measuring the hydrogen and helium content of its gas envelope, and its mass loss, would bring useful constraints to simulations of the planet evolution. High-resolution ground-based spectroscopy in the near infrared will allow measurement of the absorption lines from metastable helium in the upper atmosphere¹³³,¹³⁴. Interestingly, $v^2$ Lupi c is in similar irradiation conditions to GJ 3470 b (Fig. 2), a warm Neptune that was found to be markedly evaporating¹³⁵ (at a rate of about $10^{10} g \text{ s}^{-1}$) and whose atmosphere has already been intensively studied using both space-¹³⁵,¹³⁶ and ground-based¹³⁷ facilities. While the smaller present-day size of $v^2$ Lupi c probably makes it less efficient at capturing the stellar energy and evaporate, its lower density could favour the formation of a large exosphere of neutral hydrogen, sustained by the photodissociation of water from its massive reservoir¹³⁸. At only 14.7 pc, the Lyman α line of a G-type star such as $v^2$ Lupi will show reduced absorption by the interstellar medium and could readily be used to search for the absorption signature of this exosphere with the Hubble Space Telescope¹³⁹.

At lower temperatures ($T_{eq} < 500$ K), the only target more favourable than $v^2$ Lupi d according to the TSM is L 98-59 d, a low-density super-Earth transiting an M-dwarf star¹⁴⁰. Despite a somewhat small gas envelope, the long-period and bright host star of $v^2$ Lupi d makes it a unique target to probe a low-temperature atmosphere around a Sun-like star. Water absorption bands could be searched for in the near future with the JWST, or with future ground-based extremely large telescopes using the cross-correlation technique¹⁴¹,¹⁴². Meanwhile, searching for the signature of helium in the near infrared (using for example the upcoming NIRPS spectrograph in the Southern Hemisphere) would allow disentanglement between a water-dominated and an H-He envelope. We note, however, that the long and rare transits of $v^2$ Lupi d will be an important limitation for the study of this planet from the ground.

**Prospects for moons or rings around $v^2$ Lupi d.** The possibility for a planet to have rings depends primarily on the size of its Roche radius $R_r = 2.456 R_p (\rho_g / \rho_e)^{1/3}$, where $\rho_g$ is the ring material density. Since planet d has an equilibrium temperature above 400 K, hypothetical rings should be water free and presumably silicate rich, with $\rho_e \approx 3 \text{ g cm}^{-3}$. With the parameters in Table 1, we obtain $R_r = 2.4 R_p$, which leaves open the possibility for planet d to have enough space for rings in its Roche zone. Either the rings could be faint and dusty (with optical depth $\ll 1$, like those of Jupiter), in which case their presence would not affect the measurement of the planet's radius, or they could be dense and opaque (with optical depth $> 1$), which would then lead to an overestimate of the planet's radius. Rings can be detected in transit mostly during the ingress and egress phases, which were unfortunately not covered in the CHEOPS dataset presented here. If the planet is tidally locked, the rings may be torqued toward the planet's orbital plane beyond about 1 $R_p$, making their detection in transit difficult as they would then be seen edge on¹⁴³,¹⁴⁴. However, our tidal evolution simulations (see above) suggest that $v^2$ Lupi d may not be tidally locked yet. In our Solar System, whereas the terrestrial planets could theoretically have rings (following the same arguments as above), they do not. The absence of rings around terrestrial planets is still not understood but could be attributed to the Poynting-Robertson effect, by which micrometre-sized grains spiral down to the planet¹⁴⁵ by interacting with the star light. In that case, the relative proximity of planet d to its host star might prevent the long-term survival of dusty rings. Other putative removal processes are plasma drag, or meteoritic or ion sputtering¹⁴⁶, using the dissipation Q and $k_\phi$ Love number of the planet, shows that over 12 Gyr (the estimated age of the system, Table 1) a 3,000 kg m⁻³ satellite with a 1,000 km radius may survive if it orbits at >10 $R_p$ and the planet's Q > 100. A larger satellite with a 3,000 km radius may survive only if it orbits at >30 $R_p$. On the other hand, satellites smaller than 100 km may survive even as close as a few $R_p$ if Q > 1. However, Q is a poorly constrained quantity. It may be in the range of 1-10 for terrestrial planets and >1,000 for gas-giant planets. For a low-density super-Earth such as $v^2$ Lupi d, Q is unknown, but presumably between the terrestrial and gas-giant values. On the basis of the exquisite photometric

Satellites orbiting a planet are subject to rapid tidal evolution, leading to their radial migration due to the exchange of angular momentum with the host planet. The region inside which satellites may be gravitationally bound to a planet is a fraction of the Hill radius ($R_h = a(M_p/3M_\infty)^{1/3}$). For $v^2$ Lupi d, we obtain $R_h = 84 R_p$. Depending on whether the planet is tidally locked or not, its synchronous radius may be as great as 125 $R_p$, implying that everywhere inside the planet's Hill sphere any satellite should migrate toward the planet, at a increasing rate as the satellite becomes closer to the planet. A simple analysis of tidal evolution with averaged $da/dt$ equations¹⁴⁶ using the dissipation Q and $k_\phi$ Love number of the planet, shows that over 12 Gyr (the estimated age of the system, Table 1) a 3,000 kg m⁻³ satellite with a 1,000 km radius may survive if it orbits at >10 $R_p$ and the planet's Q > 100. A larger satellite with a 3,000 km radius may survive only if it orbits at >30 $R_p$. On the other hand, satellites smaller than 100 km may survive even as close as a few $R_p$ if Q > 1. However, Q is a poorly constrained quantity. It may be in the range of 1-10 for terrestrial planets and >1,000 for gas-giant planets. For a low-density super-Earth such as $v^2$ Lupi d, Q is unknown, but presumably between the terrestrial and gas-giant values. On the basis of the exquisite photometric

precision of the current dataset, observing the transit of the whole planet's Hill sphere with CHEOPS could allow the detection of satellites down to the Mars-size regime.

## Data availability

The CHEOPS light curves used in this work will be made available for download at the CDS (Centre de Données astronomiques de Strasbourg). We will provide both the raw and detrended light curves. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

## Code availability

The CHEOPS DRP is built over several public Python libraries, such as Astropy¹⁴⁸,¹⁴⁹, NumPy¹⁵⁰ and SciPy¹⁵¹. The TESS light curve was extracted using the lightkurve¹⁵³ open-source Python package. The data analysis was performed using the juliet Python library, which is also publicly available. The figures were produced using the Matplotlib¹⁵² and corner¹⁵³ open-source Python modules. The codes used in this work are available upon reasonable request from the corresponding author.

Received: 13 October 2020; Accepted: 29 April 2021;
Published online: 28 June 2021

## References

1. Udry, S. et al. The HARPS search for southern extra-solar planets. *XLIV. Eight HARPS multiplanet systems hosting 20 super-Earth and Neptune-mass companions*. *Astron. Astrophys.* **622**, A37 (2019).

2. Kane, S. R. et al. Transits of known planets orbiting a naked-eye star. *Astron. J.* **160**, 129 (2020).

3. Benz, W. et al. The CHEOPS mission. *Exp. Astron.* **51**, 109–151 (2021).

4. Baglin, A. et al. Scientific objectives for a minisat: CoRoT. In *Proc. 'The CoRoT Mission Pre-Launch Status—Stellar Seismology and Planet Finding' (eds Fridlund, M. et al.) 33–37 (ESA, 2006)*.

5. Borucki, W. J. et al. Kepler planet-detection mission: introduction and first results. *Science* **327**, 977–980 (2010).

6. Ricker, G. R. et al. Transiting Exoplanet Survey Satellite (TESS). *J. Astron. Telesc. Instrum. Syst.* **1**, 014003 (2015).

7. Deline, A. et al. Expected performances of the Characterising Exoplanet Satellite (CHEOPS). I. Photometric performances from ground-based calibration. *Astron. Astrophys.* **635**, A22 (2020).

8. Lendl, M. et al. The hot dayside and asymmetric transit of WASP-189 b seen by CHEOPS. *Astron. Astrophys.* **643**, A94 (2020).

9. Motalebli, F. et al. The HARPS-N Rocky Planet Search. I. HD 219134 b: a transiting rocky planet in a multiplanet system at 6.5 pc from the Sun. *Astron. Astrophys.* **584**, A72 (2015).

10. Gillon, M. et al. Two massive rocky planets transiting a K-dwarf 6.5 parsecs away. *Nat. Astron.* **1**, 0056 (2017).

11. Vanderburg, A. et al. TESS spots a compact system of super-Earths around the naked-eye star HR 858. *Astrophys. J. Lett.* **881**, L19 (2019).

12. Dragomir, D. et al. Securing the legacy of TESS through the care and maintenance of TESS planet ephemerides. *Astron. J.* **159**, 219 (2020).

13. Hoyer, S. et al. Expected performances of the Characterising Exoplanet Satellite (CHEOPS). III. Data reduction pipeline: architecture and simulated performances. *Astron. Astrophys.* **635**, A24 (2020).

14. Espinoza, N., Kossakowski, D. & Brahm, R. juliet: a versatile modelling tool for transiting and non-transiting exoplanetary systems. *Mon. Not. R. Astron. Soc.* **490**, 2262–2283 (2019).

15. Speagle, J. S. DYNESTY: a dynamic nested sampling package for estimating Bayesian posteriores and evidences. *Mon. Not. R. Astron. Soc.* **493**, 3132–3158 (2020).

16. Sulis, S. et al. Mitigating flicker noise in high-precision photometry. I. Characterization of the noise structure, impact on the inferred transit parameters, and predictions for CHEOPS observations. *Astron. Astrophys.* **636**, A70 (2020).

17. Moya, A. et al. Asteroseismic potential of CHEOPS. *Astron. Astrophys.* **620**, A203 (2018).

18. Fulton, B. J. et al. The California-Kepler Survey. III. A gap in the radius distribution of small planets. *Astron. J.* **154**, 109 (2017).

19. Owen, J. E. & Wu, Y. The evaporation valley in the Kepler planets. *Astrophys. J.* **847**, 29 (2017).

20. Van Eylen, V. et al. An asteroseismic view of the radius valley: stripped cores, not born rocky. *Mon. Not. R. Astron. Soc.* **479**, 4786–4795 (2018).

21. Ginzburg, S., Schlichting, H. E. & Sari, R. Core-powered mass-loss and the radius distribution of small exoplanets. *Mon. Not. R. Astron. Soc.* **476**, 759–765 (2018).

22. Venturini, J., Guilera, O. M., Haldemann, J., Ronco, M. P. & Mordasini, C. The nature of the radius valley. Hints from formation and evolution models. *Astron. Astrophys.* **643**, L1 (2020).
23. Dorn, C. et al. Can we constrain the interior structure of rocky exoplanets from mass and radius measurements? *Astron. Astrophys.* **577**, A83 (2015).

24. Dorn, C. et al. A generalized Bayesian inference method for constraining the interiors of super Earths and sub-Neptunes. *Astron. Astrophys.* **597**, A37 (2017).

25. Kubyshkina, D. et al. Close-in sub-Neptunes reveal the past rotation history of their host stars: atmospheric evolution of planets in the HD 3167 and K2-32 planetary systems. *Astrophys. J.* **879**, 26 (2019).

26. Kubyshkina, D. et al. The Kepler-11 system: evolution of the stellar high-energy emission and initial planetary atmospheric mass fractions. *Astron. Astrophys.* **632**, A65 (2019).

27. Papaloizou, J. C. B. & Terquem, C. Critical protoplanetary core masses in protoplanetary disks and the formation of short-period giant planets. *Astrophys. J.* **521**, 823–838 (1999).

28. Alibert, Y. On the radius of habitable planets. *Astron. Astrophys.* **561**, A41 (2014).

29. Kempton, E. M. R. et al. A framework for prioritizing the TESS planetary candidates most amenable to atmospheric characterization. *Publ. Astron. Soc. Pac.* **130**, 114401 (2018).

30. Gaia Collaboration et al. Gaia Data Release 2. Summary of the contents and survey properties. *Astron. Astrophys.* **616**, A1 (2018).

31. Lightkurve Collaboration et al. Lightkurve: Kepler and TESS time series analysis in Python. *Astrophysics Source Code Library* ascl:1812.013 (2018).

32. Christiansen, J. L. et al. The derivation, properties, and value of Kepler's combined differential photometric precision. *Publ. Astron. Soc. Pac.* **124**, 1279–1287 (2012).

33. Stassun, K. G. et al. The revised TESS Input Catalog and Candidate Target List. *Astron. J.* **158**, 138 (2019).

34. Smith, J. C. et al. Kepler presearch data conditioning II—a Bayesian approach to systematic error correction. *Publ. Astron. Soc. Pac.* **124**, 1000 (2012).

35. Stumpe, M. C. et al. Multiscale systematic error correction via wavelet-based bandsplitting in Kepler data. *Publ. Astron. Soc. Pac.* **126**, 100 (2014).

36. Jenkins, J. M. et al. The TESS Science Processing Operations Center. *Proc. SPIE* **9913**, 99133E (2016).

37. Schwarz, G. Estimating the dimension of a model. *Ann. Stat.* **6**, 461–464 (1978).

38. Sousa, S. G. et al. Spectroscopic parameters for 451 stars in the HARPS GTO planet search program. Stellar [Fe/H] and the frequency of exo-Neptunes. *Astron. Astrophys.* **487**, 373–381 (2008).

39. Sousa, S. G. in *Determination of Atmospheric Parameters of B-, A-, F- and G-Type Stars*. *GeoPlanet: Earth and Planetary Sciences* (eds Niemczura, E. et al.) 297–310 (Springer, 2014).

40. Santos, N. C. et al. SWEET-Cat: a catalogue of parameters for Stars With ExoplanETS. I. New atmospheric parameters and masses for 48 stars with planets. *Astron. Astrophys.* **556**, A150 (2013).

41. Sousa, S. G. Spectroscopic characterization of a sample of metal-poor solar-type stars from the HARPS planet search program. Precise spectroscopic parameters and mass estimation. *Astron. Astrophys.* **526**, A99 (2011).

42. Sousa, S. G., Santos, N. C., Israelian, G., Mayor, M. & Monteiro, M. J. P. F. G. A new code for automatic determination of equivalent widths: Automatic Routine for line Equivalent widths in stellar Spectra (ARES). *Astron. Astrophys.* **469**, 783–791 (2007).

43. Sousa, S. G., Santos, N. C., Adibekyan, V., Delgado-Mena, E. & Israelian, G. ARES v2: new features and improved performance. *Astron. Astrophys.* **577**, A67 (2015).

44. Kurucz, R. L. SYNTHE Spectrum Synthesis Programs and Line Data (Smithsonian Astrophysical Observatory, 1993).

45. Sneden, C. A. *Carbon and Nitrogen Abundances in Metal-Poor Stars*. PhD thesis, Univ. of Texas at Austin (1973).

46. Adibekyan, V. Z. et al. Chemical abundances of 1111 FGK stars from the HARPS GTO planet search program. Galactic stellar populations and planets. *Astron. Astrophys.* **545**, A32 (2012).

47. Adibekyan, V. et al. Identifying the best iron-peak and α-capture elements for chemical tagging: the impact of the number of lines on measured scatter. *Astron. Astrophys.* **583**, A94 (2015).

48. Blackwell, D. E. & Shallis, M. J. Stellar angular diameters from infrared photometry. Application to Arcturus and other stars; with effective temperatures. *Mon. Not. R. Astron. Soc.* **180**, 177–191 (1977).

49. Skrutskie, M. F. et al. The Two Micron All Sky Survey (2MASS). *Astron. J.* **131**, 1163–1183 (2006).

50. Wright, E. L. et al. The Wide-field Infrared Survey Explorer (WISE): mission description and initial on-orbit performance. *Astron. J.* **140**, 1868–1881 (2010).

51. Castelli, F. & Kurucz, R. L. New grids of ATLAS9 model atmospheres. In *Modelling of Stellar Atmospheres, Poster Contributions. Proc 210th Symposium of the International Astronomical Union held at Uppsala University, Uppsala, Sweden, 17-21 June, 2002* (eds Piskunov, N. et al.) A20 (Astronomical Society of the Pacific, 2003).

52. Scuflaire, R. et al. CLÉS, Code Liégeois d'Évolution Stellaire. *Astrophys. Space Sci.* **316**, 83–91 (2008).

53. Marigo, P. et al. A new generation of PARSEC-COLIBRI stellar isochrones including the TP-AGB phase. *Astrophys. J.* **835**, 77 (2017).

54. Asplund, M., Grevesse, N., Sauval, A. J. & Scott, P. The chemical composition of the sun. *Annu. Rev. Astron. Astrophys.* **47**, 481–522 (2009).

55. Iglesias, C. A. & Rogers, F. J. Updated OPAL opacities. *Astrophys. J.* **464**, 943 (1996).

56. Irwin, A. W. FreeEOS: equation of state for stellar interiors calculations. *Astrophysics Source Code Library* ascl:1211.002 (2012).

57. Adelberger, E. G. et al. Solar fusion cross sections. II. The *pp* chain and CNO cycles. *Rev. Mod. Phys.* **83**, 195–246 (2011).

58. Bonfanti, A., Ortolani, S., Piotto, G. & Nascimbeni, V. Revising the ages of planet-hosting stars. *Astron. Astrophys.* **575**, A18 (2015).

59. Bonfanti, A., Ortolani, S. & Nascimbeni, V. Age consistency between exoplanet hosts and field stars. *Astron. Astrophys.* **585**, A5 (2016).

60. Caffau, E., Ludwig, H.-G., Steffen, M., Freytag, B. & Bonifacio, P. Solar chemical abundances determined with a CO5BOLD 3D model atmosphere. *Sol. Phys.* **268**, 255–269 (2011).

61. Cyburt, R. H. et al. The JINA REACLIB database: its recent updates and impact on type-I X-ray bursts. *Astrophys. J. Suppl.* **189**, 240–252 (2010).

62. Seaton, M. J. Opacity Project data on CD for mean opacities and radiative accelerations. *Mon. Not. R. Astron. Soc.* **362**, L1–L3 (2005).

63. Marigo, P. & Aringer, B. Low-temperature gas opacity. ÆSOPUS: a versatile and quick computational tool. *Astron. Astrophys.* **508**, 1539–1569 (2009).

64. Ecvilloux, A., Israelian, G., Pont, F., Santos, N. C. & Mayor, M. Kinematics of planet-host stars and their relation to dynamical streams in the solar neighbourhood. *Astron. Astrophys.* **461**, 171–182 (2007).

65. Kreidberg, L. batman: Basic Transit Model cCalculationN in Python. *Publ. Astron. Soc. Pac.* **127**, 1161 (2015).

66. Fulton, B. J., Petigura, E. A., Blunt, S. & Sinukoff, E. RadVel: The Radial Velocity Modeling Toolkit. *Publ. Astron. Soc. Pac.* **130**, 044504 (2018).

67. Espinoza, N. Efficient joint sampling of impact parameters and transit depths in transiting exoplanet light curves. *Res. Not. Am. Astron. Soc.* **2**, 209 (2018).

68. Kipping, D. M. Efficient, uninformative sampling of limb darkening coefficients for two-parameter laws. *Mon. Not. R. Astron. Soc.* **435**, 2152–2160 (2013).

69. Foreman-Mackey, D., Agol, E., Angus, R. & Ambikasaran, S. Fast and scalable Gaussian process modeling with applications to astronomical time series. *Astron. J.* **154**, 220 (2017).

70. 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 (2015).

71. Trotta, R. Bayes in the sky: Bayesian inference and model selection in cosmology. *Contemp. Phys.* **49**, 71–104 (2008).

72. Barros, S. C. C. et al. Improving transit characterisation with Gaussian process modelling of stellar variability. *Astron. Astrophys.* **634**, A75 (2020).

73. Harvey, J. High-resolution helioseismology. In *Future Missions in Solar, Heliospheric & Space Plasma Physics. Proc. ESA Workshop held in Garmisch-Partenkirchen, Germany, April 30-May 3, 1985* (eds Rolfe, E. & Battrick, B.) 199 (ESA, 1985).

74. Kallinger, T. et al. The connection between stellar granulation and oscillation as seen by the Kepler mission. *Astron. Astrophys.* **570**, A41 (2014).

75. Lissauer, J. J. et al. Architecture and dynamics of Kepler's candidate multiple transiting planet systems. *Astrophys. J. Suppl.* **197**, 8 (2011).

76. Miralda-Escudé, J. Orbital perturbations of transiting planets: a possible method to measure stellar quadrupoles and to detect Earth-mass planets. *Astrophys. J.* **564**, 1019–1023 (2002).

77. Agol, E., Steffen, J., Sari, R. & Clarkson, W. On detecting terrestrial planets with timing of giant planet transits. *Mon. Not. R. Astron. Soc.* **359**, 567–579 (2005).

78. Holman, M. J. & Murray, N. W. The use of transit timing to detect terrestrial-mass extrasolar planets. *Science* **307**, 1288–1291 (2005).

79. 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).

80. Winn, J. N. & Fabrycky, D. C. The occurrence and architecture of exoplanetary systems. *Annu. Rev. Astron. Astrophys.* **53**, 409–447 (2015).

81. Borsato, L. et al. TRADES: a new software to derive orbital parameters from observed transit times and radial velocities. Revisiting Kepler-11 and Kepler-9. *Astron. Astrophys.* **571**, A38 (2014).

82. Malavolta, L. et al. The Kepler-19 system: a thick-envelope super-Earth with two Neptune-mass companions characterized using radial velocities and transit timing variations. *Astron. J.* **153**, 224 (2017).

83. Borsato, L. et al. HARPS-N radial velocities confirm the low densities of the Kepler-9 planets. *Mon. Not. R. Astron. Soc.* **484**, 3233–3243 (2019).
84. Hara, N. C., Boué, G., Laskar, J. & Correia, A. C. M. Radial velocity data analysis with compressed sensing techniques. *Mon. Not. R. Astron. Soc.* **464**, 1220–1246 (2017).

85. Dumusque, X. et al. Radial-velocity fitting challenge. II. First results of the analysis of the data set. *Astron. Astrophys.* **598**, A133 (2017).

86. Chen, J. & Kipping, D. Probabilistic forecasting of the masses and radii of other worlds. *Astrophys. J.* **834**, 17 (2017).

87. Cincotta, P. & Simó, C. Conditional entropy. *Celest. Mech. Dyn. Astron.* **73**, 195–209 (1999).

88. Cincotta, P. M. & Simó, C. Simple tools to study global dynamics in non-axisymmetric galactic potentials—I. *Astron. Astrophys. Suppl. Ser.* **147**, 205–228 (2000).

89. Cincotta, P. M., Giordano, C. M. & Simó, C. Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits. *Physica D* **182**, 151–178 (2003).

90. Hinse, T. C., Christou, A. A., Alvarellos, J. L. A. & Goździewski, K. Application of the MEGNO technique to the dynamics of Jovian irregular satellites. *Mon. Not. R. Astron. Soc.* **404**, 837–857 (2010).

91. Jenkins, J. S. et al. GJ 357: a low-mass planetary system uncovered by precision radial velocities and dynamical simulations. *Mon. Not. R. Astron. Soc.* **490**, 5585–5595 (2019).

92. Pozuelos, F. J. et al. GJ 273: on the formation, dynamical evolution, and habitability of a planetary system hosted by an M dwarf at 3.75 parsec. *Astron. Astrophys.* **641**, A23 (2020).

93. Rein, H. & Liu, S.-F. REBOUND: an open-source multi-purpose N-body code for collisional dynamics. *Astron. Astrophys.* **537**, A128 (2012).

94. Rein, H. & Tamayo, D. WHFAST: a fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long-term gravitational simulations. *Mon. Not. R. Astron. Soc.* **452**, 376–388 (2015).

95. Mignard, F. The evolution of the lunar orbit revisited. I. *Moon Planets* **20**, 301–315 (1979).

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

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

98. Demory, B. O. et al. A super-Earth and a sub-Neptune orbiting the bright, quiet M3 dwarf TOI-1266. *Astron. Astrophys.* **642**, A49 (2020).

99. Bolmont, E. et al. Impact of tides on the transit-timing fits to the TRAPPIST-1 system. *Astron. Astrophys.* **635**, A117 (2020).

100. 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).

101. Nielsen, L. D. et al. Mass determinations of the three mini-Neptunes transiting TOI-125. *Mon. Not. R. Astron. Soc.* **492**, 5399–5412 (2020).

102. Blanco-Cuaresma, S. & Bolmont, E. Studying tidal effects in planetary systems with Posidonium. A N-body simulator written in Rust. In *EWASS Special Session 4 (2017): Star-Planet Interactions (EWASS-SS4-2017)* (eds Bolmont, E. & Blanco-Cuaresma, S.) https://doi.org/10.5281/zenodo.1095095 (2017).

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

104. Ogilvie, G. I. & Lin, D. N. C. Tidal dissipation in rotating giant planets. *Astrophys. J.* **610**, 477–509 (2004).

105. Pereira, F. et al. Gaussian process modelling of granulation and oscillations in red giant stars. *Mon. Not. R. Astron. Soc.* **489**, 5764–5774 (2019).

106. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: the MCMC Hammer. *Publ. Astron. Soc. Pac.* **125**, 306 (2013).

107. Mathur, S. et al. Granulation in red giants: observations by the Kepler mission and three-dimensional convection simulations. *Astrophys. J.* **741**, 119 (2011).

108. Pallé, P. L. et al. The Sun as a star: background, intensity and velocity, power spectra and convection. In *Stellar Structure: Theory and Test of Connective Energy Transport* (eds Kimenez, A. et al.) 297 (Astronomical Society of the Pacific, 1999).

109. Cubillos, P. et al. On correlated-noise analyses applied to exoplanet light curves. *Astron. J.* **153**, 3 (2017).

110. Mortier, A. et al. K2-111: an old system with two planets in near-resonance. *Mon. Not. R. Astron. Soc.* **499**, 5004–5021 (2020).

111. Haldemann, J., Alibert, Y., Mordasini, C. & Benz, W. AQUA: a collection of H₂O equations of state for planetary models. *Astron. Astrophys.* **643**, A105 (2020).

112. Hakim, K. et al. A new ab initio equation of state of hcp-Fe and its implication on the interior structure and mass-radius relations of rocky super-Earths. *Icarus* **313**, 61–78 (2018).

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

115. Lopez, E. D. & Fortney, J. J. Understanding the mass-radius relation for sub-Neptunes: radius as a proxy for composition. *Astrophys. J.* **792**, 1 (2014).

116. Thiabaud, A. et al. From stellar nebula to planets: the refractory components. *Astron. Astrophys.* **562**, A27 (2014).

117. Marboeuf, U., Thiabaud, A., Alibert, Y., Cabral, N. & Benz, W. From planetesimals to planets: volatile molecules. *Astron. Astrophys.* **570**, A36 (2014).

118. Wright, N. J., Drake, J. J., Mamajek, E. E. & Henry, G. W. The stellar-activity-rotation relationship and the evolution of stellar dynamos. *Astrophys. J.* **743**, 48 (2011).

119. Tu, L., Johnstone, C. P., Güdel, M. & Lammer, H. The extreme ultraviolet and X-ray Sun in time: high-energy evolutionary tracks of a solar-like star. *Astron. Astrophys.* **577**, L3 (2015).

120. Mamajek, E. E. & Hillenbrand, L. A. Improved age estimation for solar-type dwarfs using activity-rotation diagnostics. *Astrophys. J.* **687**, 1264–1293 (2008).

121. Pizzolato, N., Maggio, A., Micela, G., Sciortino, S. & Ventura, P. The stellar activity-rotation relationship revisited: dependence of saturated and non-saturated X-ray emission regimes on stellar mass for late-type dwarfs. *Astron. Astrophys.* **397**, 147–157 (2003).

122. Sanz-Forcada, J. et al. Estimation of the XUV radiation onto close planets and their evaporation. *Astron. Astrophys.* **532**, A6 (2011).

123. Choi, J. et al. Mesa Isochrones and Stellar Tracks (MIST). I. Solar-scaled models. *Astrophys. J.* **823**, 102 (2016).

124. Dotter, A. Mesa Isochrones and Stellar Tracks (MIST) 0: methods for the construction of stellar isochrones. *Astrophys. J. Suppl.* **222**, 8 (2016).

125. Kubyshkina, D. et al. Grid of upper atmosphere models for 1–40 M<sub>⊕</sub> planets: application to CoRoT-7 b and HD 219134 b,c. *Astron. Astrophys.* **619**, A151 (2018).

126. Kubyshkina, D. et al. Overcoming the limitations of the energy-limited approximation for planet atmospheric escape. *Astrophys. J. Lett.* **866**, L18 (2018).

127. Johnstone, C. P., Güdel, M., Brott, I. & Lüftinger, T. Stellar winds on the main-sequence. II. The evolution of rotation and winds. *Astron. Astrophys.* **577**, A28 (2015).

128. Louie, D. R. et al. Simulated JWST/NIRISS transit spectroscopy of anticipated TESS planets compared to select discoveries from space-based and ground-based surveys. *Publ. Astron. Soc. Pac.* **130**, 044401 (2018).

129. Beichman, C. et al. Observations of transiting exoplanets with the James Webb Space Telescope (JWST). *Publ. Astron. Soc. Pac.* **126**, 1134 (2014).

130. Batalha, N. E., Lewis, N. K., Line, M. R., Valenti, J. & Stevenson, K. Strategies for constraining the atmospheres of temperate terrestrial planets with JWST. *Astrophys. J. Lett.* **856**, L34 (2018).

131. Schlawin, E. et al. Two NIRCam channels are better than one: how JWST can do more science with NIRCam's short-wavelength dispersed Hartmann sensor. *Publ. Astron. Soc. Pac.* **129**, 015001 (2017).

132. Ito, Y. et al. Theoretical emission spectra of atmospheres of hot rocky super-Earths. *Astrophys. J.* **801**, 144 (2015).

133. Allart, R. et al. Spectrally resolved helium absorption from the extended atmosphere of a warm Neptune-mass exoplanet. *Science* **362**, 1384–1387 (2018).

134. Nortmann, L. et al. Ground-based detection of an extended helium atmosphere in the Saturn-mass exoplanet WASP-69b. *Science* **362**, 1388–1391 (2018).

135. Bourrier, V. et al. Hubble PanCET: an extended upper atmosphere of neutral hydrogen around the warm Neptune GJ 3470b. *Astron. Astrophys.* **620**, A147 (2018).

136. Benneke, B. et al. A sub-Neptune exoplanet with a low-metallicity methane-depleted atmosphere and Mie-scattering clouds. *Nat. Astron.* **3**, 813–821 (2019).

137. Palle, E. et al. A He I upper atmosphere around the warm Neptune GJ 3470 b. *Astron. Astrophys.* **638**, A61 (2020).

138. Jura, M. An observational signature of evolved oceans on extrasolar terrestrial planets. *Astrophys. J. Lett.* **605**, L65–L68 (2004).

139. Ehrenreich, D. et al. A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b. *Nature* **522**, 459–461 (2015).

140. Cloutier, R. et al. Characterization of the L 98-59 multi-planetary system with HARPS. Mass characterization of a hot super-Earth, a sub-Neptune, and a mass upper limit on the third planet. *Astron. Astrophys.* **629**, A111 (2019).

141. Snellen, I. A. G., de Kok, R. J., de Mooij, E. J. W. & Albrecht, S. The orbital motion, absolute mass and high-altitude winds of exoplanet HD209458b. *Nature* **465**, 1049–1051 (2010).

142. Allart, R. et al. Search for water vapor in the high-resolution transmission spectrum of HD 189733b in the visible. *Astron. Astrophys.* **606**, A144 (2017).

143. Tremaine, S., Touma, J. & Namouni, F. Satellite dynamics on the Laplace surface. *Astron. J.* **137**, 3706–3717 (2009).

144. Charnoz, S., Canup, R. M., Crida, A. & Dones, L. in *Planetary Ring Systems* (eds Tiscareno, M. S. & Murray, C. D.) 517–538 (Cambridge Univ. Press, 2018).
145. Burns, J. A., Hamilton, D. P. & Showalter, M. R. in *Interplanetary Dust* (eds Grün E. et al.) 641–725 (Springer, 2001).

146. Goldreich, P. & Soter, S. Q in the Solar System. *Icarus* 5, 375–389 (1966).

147. Zeng, L. et al. Growth model interpretation of planet size distribution. *Proc. Natl Acad. Sci. USA* **116**, 9723–9728 (2019).

148. Astropy Collaboration et al. Astropy: a community Python package for astronomy. *Astron. Astrophys.* **558**, A33 (2013).

149. Astropy Collaboration et al. The Astropy Project: building an open-science project and status of the v2.0 core package. *Astron. J.* **156**, 123 (2018).

150. Harris, C. R. et al. Array programming with NumPy. *Nature* **585**, 357–362 (2020).

151. Virtanen, P. et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. *Nat. Methods* **17**, 261–272 (2020).

152. Hunter, J. D. Matplotlib: a 2D graphics environment. *Comput. Sci. Eng.* **9**, 90–95 (2007).

153. Foreman-Mackey, D. corner.py: scatterplot matrices in Python. *J. Open Source Softw.* **1**, 24 (2016).

## Acknowledgements

CHEOPS is a European Space Agency (ESA) mission in partnership with Switzerland with important contributions to the payload and the ground segment from Austria, Belgium, France, Germany, Hungary, Italy, Portugal, Spain, Sweden and the United Kingdom. The Swiss participation in CHEOPS has been supported by the Swiss Space Office in the framework of PRODEX and the Activités Nationales Complémentaires and the Universities of Bern and Geneva as well as the NCCR PlanetS and the Swiss National Science Foundation. The MOC activities have been supported by ESA contract 4000124370. S.C. acknowledges financial support by LabEx UnivEarthS (ANR-10-LABX-0023 and ANR-18-IDEX-0001). This work was supported by FCT (Fundação para a Ciência e a Tecnologia) through national funds and by FEDER (Fundo Europeu de Desenvolvimento Regional) through COMPETE2020—Programa Operacional Competitividade e Internacionalização with these grants: UID/FIS/04434/2019; UIDB/04434/2020; UIDP/04434/2020; PTDC/FIS-AST/32113/2017 and POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/2017 and POCI-01-0145-FEDER-028953; PTDC/FIS-AST/28987/2017 and POCI-01-0145-FEDER-028987. S.C.C.B., S.G.S. and V.A. acknowledge support from FCT through contracts IF/01312/2014/CP1215/CT0004, CEECIND/00826/2018, POPH/FSE (EC) and IF/0650/2015/CP1273/CT0001. O.D.S.D. is supported in the form of a work contract (DL 57/2016/CP1364/CT0004) with national funds through FCT. M.J.H. acknowledges the support of the Swiss National Fund under grant 200020_172746. A.D. and D.E. acknowledge support from the European Research Council under the European Union's Horizon 2020 research and innovation programme (project Four Aces; grant agreement 724427). S.H. acknowledges CNES funding through grant 837319. The Spanish scientific participation in CHEOPS has been supported by the Spanish Ministry of Science and Innovation and the European Regional Development Fund through grants ESP2016-80435-C2-1-R, ESP2016-80435-C2-2-R, ESP2017-87676-C5-1-R, PGC2018-098153-B-C31, PGC2018-098153-B-C33 and MDM-2017-0737 Unidad de Excelencia María de Maestu-Centro de Astrobiología (INTA-CSIC), as well as by the Generalitat de Catalunya/CERCA programme. The Belgian participation in CHEOPS has been supported by the Belgian Federal Science Policy Office in the framework of the PRODEX Programme of the ESA under contract PEA 4000131343, and by the University of Liège through an ARC grant for Concerted Research

Actions financed by the Wallonia-Brussels Federation. L.D. is an FRS-FNRS Postdoctoral Researcher. M. Gillon is an FRS-FNRS Senior Research Associate. V.V.G. is an FRS-FNRS Research Associate. M.L. acknowledges support from the Austrian Research Promotion Agency (FFG) under project 859724 'GRAPPA' B.-O.D. acknowledges support from the Swiss National Science Foundation (PP00P2-190080). S. Salmon has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (grant agreement 833925, project STAREX). G.M.S. acknowledges funding from the Hungarian National Research, Development and Innovation Office (NKFIH) grant GINOP-2.3.2-15-2016-00003 and K-119517. For Italy, CHEOPS activities have been supported by the Italian Space Agency, under the programmes ASI-NAF 2013-016-R.O and ASI-NAF 2019-29-HH.O. L.B., G.P., I.P., G.S. and V.N. acknowledge funding support from the Italian Space Agency (ASI) regulated by 'Accordo ASI-NAF 2013-016-R.O del 9 luglio 2013 e integrazione del 9 luglio 2015'. A.C.C. and T.G.W. acknowledge support from STFC consolidated grant ST/M001296/1. D.G., X.B., S.C., M.F. and J.L. acknowledge their roles as ESA-appointed CHEOPS science team members. We thank S. R. Kane for sharing some RV data before their publication and L. D. Nielsen for helping to plan the CHEOPS observations on the basis of her analysis of the TESS data. We also thank M. Cretignier for his independent analysis of the HARPS RV data.

## Author contributions

L.D. led the data analysis, with support from L.B., M.J.H., S.H., A. Brandeker, A.D., P.G., N.H., M.O. and T.G.W. L.D. also coordinated the interpretation of the results and writing of the manuscript. D.E. designed and coordinated, with support from A.D., the CHEOPS Early Science programme, within which these observations took place. Y.A. led the analysis of the internal structures, with support from J.H., A. Bonfanti and L.F. performed the atmospheric evolution simulations. L.B. carried out the TTV simulations. F.J.P studied the orbital stability and tidal interactions. S. Salmon, V.A., A. Bonfanti, S.G.S., V.V.G. and T.G.W. performed the stellar characterization. S. Sulis analysed the stellar granulation and oscillations. V.B. assessed the potential of the system for atmospheric characterization. S.C. evaluated the possibility of $v^2$ Lupi d having moons or rings. The other authors provided key contributions to the development of the CHEOPS mission. All authors read and commented on the manuscript, and helped with its revision.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41550-021-01381-5.

**Correspondence and requests for materials** should be addressed to L.D.

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

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

**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© The Author(s), under exclusive licence to Springer Nature Limited 2021

<footnote n="1">¹Astrobiology Research Unit, Université de Liège, Liège, Belgium. ²Space Sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Liège, Belgium. ³Observatoire de Genève, Université de Genève, Versoix, Switzerland. ⁴Physikalisches Institut, University of Bern, Bern, Switzerland.</footnote>

<footnote n="5">⁵Space Research Institute, Austrian Academy of Sciences, Graz, Austria. ⁶INAF, Osservatorio Astronomico di Padova, Padova, Italy. ⁷Aix Marseille University, CNRS, CNES, LAM, Marseille, France. ⁸Centre for Exoplanet Science, SUPA School of Physics and Astronomy, University of St Andrews, St Andrews, UK. ⁹Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Porto, Portugal. ¹⁰Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Porto, Portugal. ¹¹Department of Astronomy, Stockholm University, AlbaNova University Center, Stockholm, Sweden. ¹²Institut de Physique du Globe de Paris (IPGP), Paris, France. ¹³Division Technique, INSU, La Seyne, France. ¹⁴Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain. ¹⁵Departamento de Astrofísica, Universidad de La Laguna, La Laguna, Tenerife, Spain. ¹⁶Instituto de Ciências de l'Espai (ICE, CSIC), Bellaterra, Spain. ¹⁷Institut d'Estudis Espacials de Catalunya (IEEC), Barcelona, Spain. ¹⁸Admatis, Miskok, Hungary. ¹⁹Departamento de Astrofísica, Centro de Astrobiologia (CSIC-INTA), Villanueva de la Cañada, Madrid, Spain. ²⁰Center for Space and Habitability, Bern, Switzerland. ²¹Université Grenoble Alpes, CNRS, IPAG, Grenoble, France. ²²Institute of Planetary Research, German Aerospace Center (DLR), Berlin, Germany. ²³Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Lund, Sweden. ²⁴Leiden Observatory, University of Leiden, Leiden, The Netherlands.</footnote>

<footnote n="25">²⁵Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, Onsala, Sweden. ²⁶INAF, Osservatorio Astrofísico di Torino, Pino Torinese, Italy. ²⁷Center for Astronomy and Astrophysics, Technical University Berlin, Berlin, Germany. ²⁸Department of Astrophysics, University of Vienna, Vienna, Austria. ²⁹Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Budapest, Hungary.</footnote>

<footnote n="30">³⁰Institute of Physics, ELTE Eötvös Loránd University, Budapest, Hungary. ³¹Sydney Institute for Astronomy, School of Physics A29, University of Sydney, Sydney, New South Wales, Australia. ³²IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL University, Sorbonne University, Paris, France. ³³Institut d'astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, Paris, France. ³⁴Astrophysics Group, Keele University, Keele, UK. ³⁵NCCR/PlanetS, Centre for Space & Habitability, University of Bern, Bern, Switzerland. ³⁶Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA. ³⁷INAF, Osservatorio Astrofísico de Catania, Catania, Italy. ³⁸Dipartimento di Fisica e Astronomia 'Galileo Galilei', Università degli Studi di Padova, Padova, Italy. ³⁹Department of Physics, University of Warwick, Coventry, UK.</footnote>

<footnote n="40">⁴⁰Astrophysics Group, Cavendish Laboratory, University of Cambridge, Cambridge, UK. ⁴¹Institut für Geophysische Wissenschaften, Freie Universität Berlin, Berlin, Germany. ⁴²Gothard Astrophysical Observatory, ELTE Eötvös Loránd University, Szombathely, Hungary. ⁴³MTA-ELTE Exoplanet Research Group, Szombathely, Hungary. ⁴⁴Institute of Astronomy, University of Cambridge, Cambridge, UK. ⁴⁵e-mail: ldelrez@uliege.be</footnote>