CHEOPS observations of the HD 108236 planetary system: A fifth planet, improved ephemerides, and planetary radii
A. Bonfanti, L. Delrez, M.J. Hooton, T.G. Wilson, L. Fossati, Y. Alibert, S. Hoyer, A.J. Mustill, H.P. Osborn, V. Adibekyan, D. Gandolfi, S. Salmon, S.G. Sousa, A. Tuson, V. Van Grootel, J. Cabrera, V. Nascimbeni, P.F.L. Maxted, S.C.C. Barros, N. Billot, X. Bonfils, L. Borsato, C. Broeg, M.B. Davies, M. Deleuil, O.D.S. Demangeon, M. Fridlund, G. Lacedelli, M. Lendl, C. Persson, N.C. Santos, G. Scandariato, Gy.M. Szabó, A. Collier Cameron, S. Udry, W. Benz, M. Beck, D. Ehrenreich, A. Fortier, K.G. Isaak, D. Queloz, R. Alonso, J. Asquier, T. Bandy, T. Bárczy, D. Barrado, O. Barragán, W. Baumjohann, T. Beck, A. Bekkelien, M. Bergomi, M-D. Busch, A. Brandeker, V. Cessa, S. Charnoz, B. Chazelas, C. Corral Van Damme, B.-O. Demory, A. Erikson, J. Farinato, D. Futyan, A. Garcia Muñoz, M. Gillon, M. Guedel, P. Guterman, J. Hasiba, K. Heng, E. Hernandez, L. Kiss, T. Kuntzer, J. Laskar, A. Lecavelier des Etangs, C. Lovis, D. Magrin, L. Malvasio, L. Marafatto, H. Michaelis, M. Munari, G. Olofsson, H. Ottacher, R. Ottensamer, I. Pagano, E. Pallé, G. Peter, D. Piazza, G. Piotto, D. Pollacco, R. Ragazzoni, N. Rando, F. Ratti, H. Rauer, I. Ribas, M. Rieder, R. Rohlfs, F. Safa, M. Salatti, D. Ségransan, A.E. Simon, A.M.S. Smith, M. Sordet, et al. (9 additional authors not shown)
AAstronomy & Astrophysics manuscript no. TOI-1233 © ESO 2021February 5, 2021
CHEOPS observations of the HD 108236 planetary system: A fifthplanet, improved ephemerides, and planetary radii
A. Bonfanti , L. Delrez , , , M.J. Hooton , T.G. Wilson , L. Fossati , Y. Alibert , S. Hoyer , A.J. Mustill ,H.P. Osborn , , V. Adibekyan , D. Gandolfi , S. Salmon , S.G. Sousa , A. Tuson , V. Van Grootel , J. Cabrera ,V. Nascimbeni , P.F.L. Maxted , S.C.C. Barros , , N. Billot , X. Bonfils , L. Borsato , C. Broeg , M.B. Davies ,M. Deleuil , O.D.S. Demangeon , , M. Fridlund , , G. Lacedelli , , M. Lendl , C. Persson , N.C. Santos , ,G. Scandariato , Gy.M. Szabó , , A. Collier Cameron , S. Udry , W. Benz , , M. Beck , D. Ehrenreich ,A. Fortier , K.G. Isaak , D. Queloz , , R. Alonso , , J. Asquier , T. Bandy , T. Bárczy , D. Barrado ,O. Barragán , W. Baumjohann , T. Beck , A. Bekkelien , M. Bergomi , A. Brandeker , M-D. Busch , V. Cessa ,S. Charnoz , B. Chazelas , C. Corral Van Damme , B.-O. Demory , A. Erikson , J. Farinato , D. Futyan ,A. Garcia Muñoz , M. Gillon , M. Guedel , P. Guterman , , J. Hasiba , K. Heng , E. Hernandez , L. Kiss ,T. Kuntzer , J. Laskar , A. Lecavelier des Etangs , C. Lovis , D. Magrin , L. Malvasio , L. Marafatto ,H. Michaelis , M. Munari , G. Olofsson , H. Ottacher , R. Ottensamer , I. Pagano , E. Pallé , , G. Peter ,D. Piazza , G. Piotto , , D. Pollacco , R. Ragazzoni , N. Rando , F. Ratti , H. Rauer , , , I. Ribas , ,M. Rieder , R. Rohlfs , F. Safa , M. Salatti , D. Ségransan , A.E. Simon , A.M.S. Smith , M. Sordet , M. Steller ,N. Thomas , M. Tschentscher , V. Van Eylen , V. Viotto , I. Walter , N.A. Walton , F. Wildi , and D. Wolter (A ffi liations can be found after the references) ABSTRACT
Context.
The detection of a super-Earth and three mini-Neptunes transiting the bright ( V = TESS and ground-based light curves.
Aims.
We perform a first characterisation of the HD 108236 planetary system through high-precision
CHEOPS photometry and improve the transitephemerides and system parameters.
Methods.
We characterise the host star through spectroscopic analysis and derive the radius with the infrared flux method. We constrain the stellarmass and age by combining the results obtained from two sets of stellar evolutionary tracks. We analyse the available
TESS light curves and one
CHEOPS transit light curve for each known planet in the system.
Results.
We find that HD 108236 is a Sun-like star with R (cid:63) = . ± . R (cid:12) , M (cid:63) = . + . − . M (cid:12) , and an age of 6 . + . − . Gyr. We reportthe serendipitous detection of an additional planet, HD 108236 f, in one of the
CHEOPS light curves. For this planet, the combined analysisof the
TESS and
CHEOPS light curves leads to a tentative orbital period of about 29.5 days. From the light curve analysis, we obtain radii of1 . ± . . ± . . + . − . , 3 . ± . . + . − . R ⊕ for planets HD 108236 b to HD 108236 f, respectively. These valuesare in agreement with previous TESS -based estimates, but with an improved precision of about a factor of two. We perform a stability analysis ofthe system, concluding that the planetary orbits most likely have eccentricities smaller than 0.1. We also employ a planetary atmospheric evolutionframework to constrain the masses of the five planets, concluding that HD 108236 b and HD 108236 c should have an Earth-like density, while theouter planets should host a low mean molecular weight envelope.
Conclusions.
The detection of the fifth planet makes HD 108236 the third system brighter than V =
10 mag to host more than four transitingplanets. The longer time span enables us to significantly improve the orbital ephemerides such that the uncertainty on the transit times will beof the order of minutes for the years to come. A comparison of the results obtained from the
TESS and
CHEOPS light curves indicates that fora V ∼ ∼
500 ppm, one
CHEOPS transit light curve ensures the same level of photometric precision aseight
TESS transits combined, although this conclusion depends on the length and position of the gaps in the light curve.
Key words.
Planetary systems — Planets and satellites: detection — Planets and satellites: fundamental parameters — Planets and satellites:individual: HD 108236
1. Introduction
Transiting exoplanets provide the unique opportunity to thor-oughly characterise planetary systems, from atmospheres to or-bital dynamics, and transiting multi-planet systems play a specialrole. Multi-planet systems enable one, for example, to identifythe presence of orbital resonances among the detected planets ina system, giving the possibility to use transit timing variations(TTVs) to measure planetary masses and / or detect other plan- ets in the system (e.g. Miralda-Escudé 2002; Holman & Murray2005; Agol et al. 2005).There are many additional reasons why multi-planet systemsare of particular interest. The existence of multiple planets thatformed in the same disk places stronger constraints on formationmodels relative to planets in isolation, motivating the quantifi-cation of orbital spacings, correlations and di ff erences within asystem (Lissauer et al. 2011; Fabrycky et al. 2014; Winn & Fab-rycky 2015; Weiss et al. 2018), and inspiring novel approaches toclassification and statistical description (Alibert 2019; Sandford Article number, page 1 of 22 a r X i v : . [ a s t r o - ph . E P ] F e b & A proofs: manuscript no. TOI-1233 et al. 2019; Gilbert & Fabrycky 2020). The spacing of planetsrelative to mean motion resonances provides information aboutplanetary migration during formation, as well as later tidal ef-fects on orbits (Delisle et al. 2012; Izidoro et al. 2017). A sys-tem’s multiplicity is a ff ected after formation by long-term or-bital dynamics, whether driven internally or as a result of moredistant undetected planetary perturbers (Pu & Wu 2015; Mustillet al. 2017; He et al. 2020). Changes to orbits can even a ff ectthe climate of planets (Spiegel et al. 2010). Given that our ownSolar System contains multiple planets, this all helps us to un-derstand points of similarity and divergence between our systemand others.Multi-planet systems also o ff er the opportunity to study thecorrelation between the composition (bulk and / or atmospheric)of planets and their periods or equilibrium temperatures, particu-larly when both planetary masses and radii have been measured.This correlation is a powerful constraint on planet formation andcomposition models as the number of degrees of freedom onecan play with in models is reduced by the fact that all plan-ets formed in the same protoplanetary disk. However, observ-ing such a correlation requires precise transit measurements anddynamical analyses (to assess mass values via TTVs or radialvelocity follow-up), which in turn can be more easily done onceprecise ephemerides of the di ff erent planets in the system areknown.Finally, multi-planet systems are ideal laboratories for study-ing the evolution of planetary atmospheres. This process is con-trolled by the host star’s evolution (i.e. evolution of the stellarradius, mass, and high-energy radiation), by the physical char-acteristics of each planet (e.g. planetary mass, radius, and ini-tial atmospheric mass fraction and composition), and by the or-bital evolution of each planet. Within multi-planet systems, eachplanet evolved in its own way as a result of its specific planetaryand orbital characteristics, but the range of possible evolutionarypaths is limited by the fact that all planets in the system orbit thesame star. This enables one not only to constrain the evolutionhistory of the planets, but also aspects of the host star that wouldbe unattainable otherwise, such as the evolution of the stellarrotation rate (e.g. Kubyshkina et al. 2019a,b; Owen & CamposEstrada 2020).The majority of transiting multi-planet systems known todate were detected by the Kepler and K2 missions (e.g. Cough-lin et al. 2016; Mayo et al. 2018). Among these, about 60 sys-tems host four or more transiting planets, but only two havea host star brighter than V =
10 mag (Kepler-444: Campanteet al. 2015; HIP 41378: Vanderburg et al. 2016). The launchesof the TESS (Transiting Exoplanet Survey Satellite; Ricker et al.2015) and
CHEOPS (CHaracterising ExOPlanets Satellite; Benzet al. 2020) satellites have shifted the focus of the detection andcharacterisation of multi-planet systems towards brighter stars.While
TESS , similarly to
Kepler and K2 , has a wide field of view(FoV) that is optimised for the detection of a large number oftransiting planets, CHEOPS is a targeted mission, observing onesystem at a time to perform a precise characterisation.As of 19 November 2020,
TESS had discovered 82 confirmedplanets and ∼
60% of them belong to multi-planet systems. Anon-exhaustive list of the multi-planet systems discovered by
TESS includes HD 15337 (Gandolfi et al. 2019), TOI-125 (Quinnet al. 2019), HD 21749 (Dragomir et al. 2019), HR 858 (Van-derburg et al. 2019), LP 791-18 (Crossfield et al. 2019), L98-59(Kostov et al. 2019), TOI-421 (Carleo et al. 2020), HD 63433(Mann et al. 2020), and TOI-700 (Gilbert et al. 2020). Follow- From https://exoplanetarchive.ipac.caltech.edu/ ing the completion of its prime mission on 5 July 2020,
TESS was extended for a further 27 months. This will not only allowus to re-observe many of the targets already studied during theprime mission to better characterise them, but also to observeadditional stars for the first time.Daylan et al. (2020, D20 hereafter) announced the detec-tion with
TESS of four transiting planets orbiting the bright( V = ≈ R ⊕ ) suggests that this is possibly arocky super-Earth, while the larger radii of the three outer plan-ets ( ≈ R ⊕ ) indicate that they may still host alightweight gaseous envelope (Fulton et al. 2017; Owen & Wu2017; Jin & Mordasini 2018). From the TESS measurements,it follows that the inner planet lies inside the radius gap (Ful-ton et al. 2017), while the three larger outer planets are locatedaround the peak comprising planets with a gaseous envelope,hence making this system of particular interest for atmosphericevolution studies.D20 performed orbital dynamic simulations that showed thatthe system is stable, though a significant exchange of angularmomentum among the planets in the system likely occurred. Fur-thermore, on the basis of these simulations, D20 suggested thepossible presence of a fifth planet in the system with a periodof 10.9 days. However, a dedicated analysis of the
TESS lightcurve (LC) did not give definitive proof. Finally, the bright hoststar makes the HD 108236 system a primary target for plane-tary mass measurements through radial velocities (RVs) and forconstraining the atmospheric properties of multi-planet systems(D20).We report here the results obtained from
CHEOPS high-precision photometric observations of one transit of each de-tected planet composing the HD 108236 system, taken almostone year after the
TESS observations. The main goals of the ob-servations presented here were to secure the ephemerides of alldetected planets, to employ the exquisite quality of
CHEOPS photometry to provide a first refinement of the system’s mainproperties, and to confirm or disprove the presence of the puta-tive fifth planet at the approximately 10.9 days indicated by D20.This paper is organised as follows. Section 2 presents thehost star properties, and Section 3 describes the
CHEOPS and
TESS
LCs. The data analysis is presented in Section 4, and re-sults are reported in Section 5. Section 6 summarises the workand presents our conclusions.
2. Host star properties
HD 108236 is a bright Sun-like star (spectral type G3V)that is also known as HIP 60689, TOI-1233, and Gaia DR26125644402384918784. Between 13 December 2019 and 23January 2020 (UT) we acquired 13 high-resolution spectra( R =
115 000) of HD 108236 (programme ID 1102.C-0923, PI:Gandolfi) using the High Accuracy Radial velocity PlanetSearcher (HARPS, Mayor et al. 2003) spectrograph mountedat the ESO-3.6 m telescope of La Silla Observatory, Chile. Weset the exposure time to T exp = / N) per pixel of ∼
100 at 550 nm. We used the co-added HARPS spectrum – which has a consequent S / N ∼ ff ective temperature T e ff , surface gravitylog g , and metal content [Fe / H]. We obtained T e ff = ±
61 K,log g = . ± .
11, and [Fe / H] = − . ± .
04 dex, from spec-tral analysis, which made use of the ARES + MOOG tools (Sousa
Article number, page 2 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system (Sousa et al. 2007, 2015) on the com-bined HARPS spectrum. In this step, we used the list of ironlines presented in Sousa et al. (2008). The best fitting atmo-spheric parameters were obtained looking for convergence ofboth ionisation and excitation equilibria. For this step, we madeuse of a grid of Kurucz model atmospheres (Kurucz 1993) andthe radiative transfer code MOOG (Sneden 1973). We also anal-ysed the same spectra using the ’spectroscopy made easy’ (SME)code (Piskunov & Valenti 2017), which uses a di ff erent methodand a di ff erent grid of models ( atlas
12, Kurucz 2013) achiev-ing results well within 1 sigma of those obtained employingARES + MOOG.It has been suggested that individual abundances of heavy el-ements and specific elemental ratios end up controlling the struc-ture and composition of the planets (e.g. Bond et al. 2010; Thi-abaud et al. 2015; Unterborn et al. 2016; Santos et al. 2015). Inparticular, Mg / Si and Fe / Si mineralogical ratios were proposedas probes to constrain the internal structure of terrestrial plan-ets (e.g. Dorn et al. 2015). Therefore, we specifically derivedthe abundances of Mg and Si using the same tools and mod-els as for the atmospheric parameter determination, as well asusing the classical curve-of-growth analysis method assuminglocal thermodynamic equilibrium. For deriving the abundances,we closely followed the methods described in Adibekyan et al.(2012) and Adibekyan et al. (2015). The solar reference Mg andSi abundances are taken from (Asplund et al. 2009). The Mg / Siand Fe / Si abundance ratios were calculated as A / B = N A / N B = log (cid:15) ( A ) / log (cid:15) ( B ) , (1)where N A and N B represent the number of atoms of elementsA and B, respectively, scaled assuming a hydrogen content of10 atoms, while log (cid:15) ( A ) and log (cid:15) ( B ) are the respective abso-lute elemental abundances (total number of atoms) expressed inlogarithmic scale.We employed the infrared flux method (IRFM; Blackwell& Shallis 1977) to calculate the radius of the host star throughthe determination of the stellar angular diameter θ and e ff ectivetemperature using known relationships between these proper-ties, optical and infrared broadband fluxes, and synthetic pho-tometry obtained from stellar atmospheric models (Castelli &Kurucz 2003) over various standard bandpasses. The Gaia
G,G BP , and G RP , the 2MASS J, H, and K, and the WISE
W1and W2 fluxes and relative uncertainties were retrieved fromthe most recent data releases (Gaia Collaboration et al. 2018;Skrutskie et al. 2006; Wright et al. 2010, respectively). We ap-plied a Markov chain Monte Carlo (MCMC) approach, settingpriors on the stellar parameters taken from the spectroscopicanalysis detailed above. Within this framework, accounting forthe reddening E ( B − V ), we compared the observed photome-try with the synthetic one obtained from convolving stellar syn-thetic spectral energy distributions from the atlas Catalogues(Castelli & Kurucz 2003) with the throughput of the consideredphotometric bands. From this analysis, we determined the stel-lar radius and E ( B − V ) to be R IRFM ,(cid:63) = . ± . R (cid:12) and E ( B − V ) IRFM = . ± .
09, respectively. These values are inagreement with those provided in the literature (D20), but have aprecision on the stellar radius of twice that previously reported.The stellar mass M (cid:63) and age t (cid:63) were inferred from evolu-tionary models. To obtain more robust results, we considered twodi ff erent sets of tracks and isochrones: one set generated from the The latest version of the ARES code (ARES v2) can be downloadedat ∼ sousasag/ares . PARSEC v1.2S code (Marigo et al. 2017) and another with theCLES code (Code Liègeois d’Évolution Stellaire; Scuflaire et al.2008). The two models di ff er for example in terms of solar mix-ture, helium-to-metal enrichment ratio, adopted reaction rates,and opacity and overshooting treatment. The PARSEC modelsadopt the solar-scaled composition given by Ca ff au et al. (2011),while the CLES models consider that given by Asplund et al.(2009). In PARSEC, the helium content Y is assumed to increasewith Z according to a linear relation of the form Y = ∆ Y ∆ Z Z + Y p ,where ∆ Y ∆ Z = .
78 has been inferred from solar calibration and Y p = . ff erences on the treatment of overshooting can beidentified by comparing the relative descriptions in Bressan et al.(2012) for the PARSEC models and Scuflaire et al. (2008) for theCLES models.To assess the discrepancies arising from the use of the twodi ff erent stellar evolutionary models, we analysed a wide sam-ple of CHEOPS targets with the isochrone placement techniquepresented in Bonfanti et al. (2015, 2016) considering both setsof isochrones and tracks. We calculated that di ff erences in ageand mass may amount to ∼
20% and ∼ M (cid:63) and age t (cid:63) . The adopted input parameters were the T e ff , [Fe / H], and stellar radius R IRFM ,(cid:63) . Two independent analy-ses were carried out considering both PARSEC and CLES evo-lutionary models. The first analysis used the Isochrone place-ment technique and its interpolating capability applied to pre-computed PARSEC grids of isochrones and tracks to derive theset of stellar masses ( M (cid:63), ± ∆ M (cid:63), ) and ages ( t (cid:63), ± ∆ t (cid:63), ) thatbest match the input parameters. The second analysis, instead,was performed by directly fitting the input parameters to theCLES stellar models to infer M (cid:63), ± ∆ M (cid:63), and t (cid:63), ± ∆ t (cid:63), . Toaccount for model-related uncertainties, we added in quadraturean uncertainty of 20% in age and of 4% in mass to the estimatesobtained from each set of models. The values obtained from eachof the two analyses are listed in Table 1.From these values we built the corresponding Gaussian prob-ability density functions to then obtain the final estimates of bothmass and age. To avoid underestimating the final uncertainties,for each parameter we summed the two Gaussian distributionsrepresenting the outputs of the PARSEC and CLES analyses.The median of the combined distribution was assumed as ourreference final value, and its corresponding error bars were in-ferred from the 15.87 th and 84.14 th percentile of the combineddistribution, in order to provide the 1 σ (68.3%) standard con-fidence interval. At the end, we obtained M (cid:63) = . + . − . M (cid:12) Padova and Trieste Stellar Evolutionary Code http://stev.oapd.inaf.it/cgi-bin/cmd .Article number, page 3 of 22 & A proofs: manuscript no. TOI-1233
Table 1.
Stellar mass and age values computed considering the PAR-SEC and CLES models. Their weighted average consistence has beensuccessfully checked through the p -value criterion based on χ tests(see text for details). Parameter PARSEC CLES p -value M (cid:63) [ M (cid:12) ] 0 . ± .
043 0 . ± .
049 0.61 t (cid:63) [Gyr] 7 . ± . . ± . t (cid:63) = . + . − . Gyr, as final values for the stellar mass and age,respectively.Then we applied a χ -test to identify whether results comingfrom the two di ff erent methods (i.e. PARSEC vs CLES) are con-sistent (null hypothesis), so to check whether their synthesis intosingle values is indeed a signal of the robustness of the results,rather than a mathematical artefact. To this end, we computed¯ χ = (cid:88) i = ( x i − ¯ x ) σ i , (2)where x denotes the generic variable (either M (cid:63) or t (cid:63) ), σ its un-certainty, and ¯ x the median value of the parameter of interest in-ferred from the combined distribution. We expect ¯ χ to be drawnfrom a chi-square distribution f ( χ ν ) with ν = − = x depends on x and x . Testing the null hypothesis,namely verifying whether the median of the combined distribu-tion properly describes the data, means comparing the ¯ χ valueobtained from Equation (2) to a reference χ α value defined by (cid:90) + ∞ χ α f ( χ )d χ = α , (3)where α is the adopted significance level, which we set equal to0.05. If ¯ χ > χ α , then we are 100(1 − α )% =
95% confidentthat the null hypothesis is false; otherwise, the null hypothesis isconfirmed when¯ χ < χ α ⇔ p − value > α , (4)where p − value = (cid:90) + ∞ ¯ χ f ( χ )d χ . (5)These calculations (see p -values in Table 1) confirm that the twoindependent derivations of the stellar mass and age are consis-tent, implying that the median of the combined distribution canbe used to assess M (cid:63) and t (cid:63) from our two sets of measurements.Table 2 lists the final adopted stellar parameters.D20 also derived the stellar fundamental parameters, butemploying di ff erent approaches: they started either from high-resolution spectroscopy or broad-band photometry to obtain dif-ferent pairs of ( R (cid:63) , M (cid:63) ). All obtained values agree with our es-timates within 1 σ , except for the M (cid:63) value that they computedfrom the mass-radius relation of Torres et al. (2010), which isin any case ∼ σ away also from the other M (cid:63) values obtainedby D20. By combining the observed spectral energy distribu-tion and the MESA (Paxton et al. 2018) isochrones and stellartracks (MIST, Choi et al. 2016; Dotter 2016), D20 find an ageof t (cid:63), D = . ± . σ . Table 2.
Properties of HD 108236 and the methods employed to derivethem. See the text for further details.
HD 108236Alternativenames TOI-1233HIP 60689Gaia DR2 6125644402384918784Parameter Value Method V [mag] 9.24 Simbad G [mag] 9.0875 Simbad J [mag] 8.046 Simbad T e ff [K] 5660 ±
61 spectroscopylog g [cgs] 4 . ± .
11 spectroscopy[Fe / H] [dex] − . ± .
04 spectroscopy[Mg / H] [dex] − . ± .
03 spectroscopy[Si / H] [dex] − . ± .
02 spectroscopy d [pc] 64 . ± . (a) θ [mas] 0 . ± . R (cid:63) [ R (cid:12) ] 0 . ± .
008 IRFM M (cid:63) [ M (cid:12) ] 0 . + . − . isochrones t (cid:63) [Gyr] 6 . + . − . isochrones L (cid:63) [ L (cid:12) ] 0 . ± .
047 from R (cid:63) and T e ff ρ (cid:63) [g / cm ] 1 . ± .
12 from R (cid:63) and M (cid:63) Notes. ( a ) Correction from Stassun & Torres (2018) applied
3. Observations
CHEOPS (Benz et al. 2020) is an ESA small-class mission, ded-icated to observing bright stars ( V (cid:46)
12 mag) that are alreadyknown to host planets by means of ultra-high-precision photom-etry. The precision of photometric signals is limited by stellarphoton noise of 150 ppm / min for a V = CHEOPS achieves a photo-metric precision of 15.5 ppm in 6 hours of integration time for a V ∼ CHEOPS instrument is composed of an F / ff ective diameter) equippedwith a single frame-transfer back-side illuminated charge-coupled device (CCD) detector. The acquired images are defo-cused to minimise pixel-to-pixel variation e ff ects.The satellite was successfully launched from Kourou(French Guiana) into a ∼
700 km altitude solar synchronous orbiton 18 December 2019. The orbit of the spacecraft is nadir-locked(i.e. the Z -axis of the spacecraft is antiparallel to the nadir di-rection, see Figure 1) to ensure a thermally stable environmentfor the payload radiators. During its orbit, the spacecraft rotatesaround its X -axis (the line of sight), and this determines the ro-tation of the FoV. The angle of rotation around the X -axis ofthe spacecraft is called roll angle, with its zero value occurringwhen the Y -axis of the spacecraft is parallel to the X - Y planeof the J2000 Earth-centred reference frame. This plane closelyapproximates the Earth’s equatorial plane, coinciding with it on1 January 2000. CHEOPS opened its cover on 29 January 2020and, after passing the In-Orbit Commissioning (IOC) phase, rou-tine observational operations started on 18 April 2020.Three observation runs, or visits, of HD 108236 were ob-tained with
CHEOPS (Figure 2). The first visit, of 18.33 h du-ration, was obtained during the IOC phase using exposure timesof 42 s. The other two visits, with a total duration 18.63 h and17.04 h, were obtained during routine operations of the satelliteusing exposure times of 49 s. The observations were interrupted
Article number, page 4 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system
Table 3.
Log of the
CHEOPS observations of HD 108236. The last column gives the location of the target on the detector.Planets Start date Duration Valid points File key E ffi ciency Exp. time Location[UTC] [h] [ x ; y ) [px]c, e 2020-03-10T18:09:15.9 18.33 983 CH_PR300046_TG000101_V0102 55 42 (815; 281)d 2020-04-28T07:06:11.0 18.63 770 CH_PR100031_TG015401_V0102 55 49 (257; 859)b, f 2020-04-30T17:06:11.0 17.04 674 CH_PR100031_TG015702_V0102 60 49 (257; 859) Fig. 1.
Adopted reference frame of the
CHEOPS spacecraft. The X -axis coincides with the line of sight, while the Z -axis is antiparallel tothe nadir direction. The x and y axes of the CCD coincide with the − Y and Z axes of the spacecraft, respectively. Image taken from Benz et al.(2020), courtesy of Airbus Defence and Space, Spain. by Earth occultations and / or by South Atlantic Anomaly (SAA)crossings, where no data were downlinked, yielding an observ-ing e ffi ciency of 55%, 55%, and 60%, respectively, for each visit.The observing log of the CHEOPS data is presented in Table 3.We also note that the target location on the CCD has changedfrom March to April. This relocation of the target on the CCDhas been done to avoid hot pixels. The project science o ffi ce con-stantly monitors the hot pixels status on the detector and if keep-ing the pre-selected target location implies a significant loss inthe expected performances, then the location is changed.The raw data were automatically processed by the CHEOPS
Data Reduction Pipeline (DRP v12 ; Hoyer et al. 2020). The DRPcalibrates and corrects the images for instrumental and environ-mental e ff ects, and finally performs aperture photometry of thetarget (Figure 3). As described in Hoyer et al. (2020), the DRPuses the Gaia catalogue (Gaia Collaboration et al. 2018) to sim-ulate the FoV of the observations so to estimate the level of con-tamination in the photometric aperture. This is achieved by ro-tating background stars around the spacecraft X -axis and / or bythe smear trails produced by bright stars in the CCD, in orderto mimic the rotating CHEOPS
FoV. In particular, in v12 of theDRP the smear contamination is automatically removed whilethe background stars’ contamination within the aperture (notice-ably there is a 4.8 mag star ∼
342 arcsec from HD 108236) is pro-vided as a product to be used for further detrending during thedata analysis. Finally, the DRP extracts the photometry using 3fixed aperture sizes (radii of 22.5, 25 and 30 arcsec) and an extraaperture, the size of which depends on the level of contamina-
Fig. 2.
Raw LCs of the three
CHEOPS visits analysed here, as pro-cessed by the Data Reduction Pipeline v12 . The datasets are presentedfrom top to bottom in chronological order of observation. The periodi-cal light variations, especially visible in the first visit, correlate with theroll angle (see the text for further details). tion of the FoV. In this work we used the LCs obtained with the
DEFAULT aperture of 25 arcsec, which results in the smallest rootmean square (RMS) in the resulting LCs.We carefully inspected the LCs, looking for possible system-atics. It turned out that the stellar flux presents particular patternsagainst the telescope roll angle in all three datasets, as shown inFigure 4. These flux variations against roll angle are likely due toan internal reflection from a very bright nearby star (HD 108257, V = . Article number, page 5 of 22 & A proofs: manuscript no. TOI-1233
Fig. 3.
FoV of HD 108236. Top panel: Real FoV as observed by
CHEOPS . Bottom panel: FoV as inferred from the DRP simulation withthe target removed. The red cross indicates the location of the target’sPSF, while the photometric aperture is represented by the red circle. Thehorizontal (column number) and vertical (row number) axes correspondto the x and y axes of the CCD reference frame, respectively. Imagescale is 1 arcsec per pixel. The specific pattern of flux versus roll angle produced by thiscontamination depends on the location of the target on the CCD.As reported in Table 3, the ( x ; y ) coordinates of the target in thefirst visit di ff er from those in the following two visits. In addi-tion, the roll angle rotation rate is not constant with time, and itdepends on the target’s coordinates with respect to the anti-Sundirection. By observing the same target at di ff erent epochs, therotation rate of the spacecraft around the X -axis also changes,leading to variations in the rate at which the slanted bar moves.Consistently with this, the flux versus roll angle pattern shown inthe top panel of Figure 4 (mid-March observations) di ff ers fromthat shown in the middle and bottom panels, which are simi-lar (both observations were taken at the end of April). With thisin mind, we detrended the CHEOPS
LCs versus roll angle (seeSection 4).
Fig. 4.
Dependence of flux against roll angle. The three
CHEOPS datasets are presented from top to bottom in chronological order of ob-servation.
Fig. 5.
Full frame image of the first
CHEOPS visit. The white squarerepresents the location and size of the subarray window containingthe target. The bright star located on the left of the white square isHD 108257, which probably produces the internal reflection generatingthe flux vs roll angle patterns shown in Fig. 4.Article number, page 6 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system
Fig. 6.
Set of frames taken from the first
CHEOPS visit. The vertical dashed line indicates the smearing pattern, while the dashed red line indicatesanother pattern likely produced by the internal reflection of a contaminating source, which could be the nearby bright star HD 108257.
In addition to the three
CHEOPS datasets, we included the
TESS data analysed by D20. HD 108236 was observed by
TESS in sec-tors 10 (26 March 2019 - 22 April 2019) and 11 (22 April 2019- 21 May 2019). Therefore, combining the
TESS and
CHEOPS data significantly increases the baseline, enabling us to improvethe transit ephemerides and the system parameters (see Section5.2). We analysed the
TESS and
CHEOPS data separately, tocompare the performances, and together, to better constrain thesystem parameters.We used the
TESS data as processed by the Science Process-ing Operations Center (SPOC; Jenkins et al. 2016) pipeline. Inparticular, we considered the Pre-search Data Conditioned Sim-ple Aperture Photometry (PDCSAP) flux values with their un-certainties as they are corrected for instrumental variations andrepresent the best estimate of the intrinsic flux variation of thetarget.
4. Data analysis
We carried out the LC analysis using allesfitter (Gün-ther & Daylan 2020). Among its features, this framework al-lows one to model exoplanetary transits using the ellc pack-age (Maxted 2016), further considering multi-planetary systems,TTVs, and Gaussian processes (GPs; Rasmussen & Williams2005) for the treatment of correlated noise, implemented throughthe celerite package (Foreman-Mackey et al. 2017). The pa-rameters of interest are retrieved considering a Bayesian ap-proach, which may use either the emcee package (Foreman-Mackey et al. 2013) implementing a MCMC method (see e.g.Ford 2005) to sample the posterior probability distribution, orthe Nested Sampling inference algorithm (see e.g. Feroz & Hob-son 2008; Feroz et al. 2019). In our work, we used the Dy-namic Nested Sampling algorithm to have a direct estimate ofthe Bayesian evidence thanks to the dynesty package (Speagle2020).Since allesfitter is not able to account for the flux depen-dence against roll angle seen in the
CHEOPS data, we detrendedthe flux dependence versus roll angle through a Matérn-3 / CHEOPS
LCs into allesfitter . The de-trending was done using the celerite package, which givesthe GP model and its variance. The GP model was computedusing only the out-of-transit data points. Then, new enhanced error bars have been associated with the data points through er-ror propagation accounting for the observational errors and thevariance of the GP model.Throughout the analysis, we assumed Gaussian priors onthe following fitted parameters: the mean stellar density ρ (cid:63) = . ± .
12 g / cm , derived from our stellar characterisation, andthe quadratic limb darkening (LD) coe ffi cients ( q , q ), inferredfrom the atlas . In particular, we derived the u and u coe ffi cients of the quadratic LD law using the code of Es-pinoza & Jordán (2015), that performs a cubic spline interpo-lation within the models according to the same procedure fol-lowed by Claret & Bloemen (2011). After that, we converted u and u to the quadratic LD coe ffi cients q and q requiredby allesfitter following the relations of Kipping (2013),obtaining ( q , q ) = (0 . , .
27) for the
TESS bandpass, and( q , q ) = (0 . , .
32) for the
CHEOPS bandpass . A 1- σ uncer-tainty of 0.05 was attributed to all LD coe ffi cients. We verifiedthat this uncertainty value is conservatively in agreement withthe priors estimated by Maxted (2018), who discussed the appli-cation of the power-2 LD law to the LCs of transiting exoplanets.For each planet, the fitted parameters were: the ratio of plan-etary radius over stellar radius R p / R (cid:63) , the sum of stellar and plan-etary radius scaled to the orbital semi-major axis ( R p + R (cid:63) ) / a , thecosine of the orbital inclination cos i p , the transit timing T , theorbital period P , and √ e cos ω and √ e sin ω , where e is the or-bital eccentricity and ω is the argument of pericentre. The initialpriors used in our fits are listed in Table A.1.The CHEOPS
LCs, both binned and unbinned, with super-imposed best-fit transit models, are shown in Figures 7, 8, and9. In each Figure presenting
TESS or CHEOPS
LCs, the binneddata are shown by combining 12 data points, independently ofthe exposure times. In the case of the
CHEOPS
LCs, each re-binned data point corresponds to 8.4 min in the case of the firstvisit and 9.8 min in the case of the last two visits.During the inspection of the
CHEOPS dataset withfile key CH_PR100031_TG015702_V0102 (i.e. last observa-tion), besides finding the expected transit of HD 108236 b at T , b , CH ∼ http://kurucz.harvard.edu/grids.html The
CHEOPS filter profile (beyond many others, including the
TESS one) may be downloaded as ASCII file e.g. at http://svo2.cab.inta-csic.es/theory/fps/index.php?id=CHEOPS/CHEOPS.band&&mode=browse&gname=CHEOPS&gname2=CHEOPS\ .Article number, page 7 of 22 & A proofs: manuscript no. TOI-1233
Fig. 7.
Detrended
CHEOPS
LC (first visit, file keyCH_PR300046_TG000101_V0102) containing the transits ofHD 108236 c at T , c , CH ∼ T , e , CH ∼ Fig. 8.
Same as Figure 7, but for HD 108236 d (second visit, file keyCH_PR100031_TG015401_V0102). like feature (depth ∼
400 ppm) occurring ∼ T , b , CH (i.e. T , f , CH ∼ M ) is to be preferred over the other ( M ), we computed the Fig. 9.
Same as Figure 7, but for HD 108236 b and HD 108236 f(third visit, file key CH_PR100031_TG015702_V0102). The transit ofHD 108236 b is that at T , b , CH ∼ T , f , CH ∼ Bayes factor B , which is defined as (Kass & Raftery 1995): B = Z Z , (6)where Z i is the Bayesian evidence (i.e. the marginal likelihoodintegrated over the entire parameter space) referring to the i -thmodel. The value of Z is given by the Nested Sampling algo-rithm, thus B could be straightforwardly computed throughEquation (6). The higher the B , the higher the evidence against M ( i.e. M is to be preferred). Reference values of B and cor-responding levels of evidence against M are reported in Kass& Raftery (§3.2; 1995). Here we just recall that very strongevidence against the null hypothesis M (i.e. M is stronglyfavoured) occurs when ln B >
5. Results and discussion
The detected transit-like signal visible in Figure 9 at T , f , CH ∼ x ; y ) coordinates of the PSF centroid suggests the absenceof any PSF jumps, hence no new hot pixels have appeared insidethe PSF area during the observation (see Figure 10). Further-more, by analysing the raw data, the DRP team confirmed thatthis feature cannot be ascribed to telegraphic pixels (i.e. pixelsthat occasionally blink and twinkle), nor to cosmic rays or anyspacecraft instrumental metrics.Therefore, given the transit-like nature of the signal, welooked for similar features, in terms of both transit depthand duration, in the available TESS
LCs. Indeed, we spot-ted a similar signal in the second
TESS
LC (sector 11) at T , f , TE11 ∼ Article number, page 8 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system
Fig. 10.
All the represented quantities expressed as a function of timeduring the third
CHEOPS visit (i.e. the one containing the transits ofHD 108236 b and HD 108236 f). Top two panels: flux of contaminatingstars entering the photometric aperture and background light (both rela-tive to the flux of HD 108236). Third and fourth panels from top: x - and y -coordinate of the PSF centroid. The transit windows of planets b andf are highlighted in blue and red, respectively, while the out-of-transitpoints are in cyan. Bottom panel: residuals of the normalised fluxes(shifted vertically for visualisation purposes) obtained after subtract-ing the reference normalised flux computed considering the DEFAULT aperture to the normalised fluxes computed considering the other threeavailable apertures. No correlation is present between flux and aperturesize. Transit windows of planets b and f are marked by solid and dashedvertical lines, respectively.
Fig. 11.
Portion of the
TESS sector 11 LC. Data are binned on atimescale of 24 min. The red solid line shows the transit model forHD 108236 f. Neglecting the presence of HD 108236 f and performinga four-planet fit, the RMS of the binned residuals would be 154 ppm.Instead, a five-planet fit reduces the RMS of the binned residuals to 130ppm.
We applied both a four-planet and five-planet fit to these
TESS data and compared the RMS of the residuals binned on a 24min timescale within the [2458615.9, 2458616.2] BJD window,which contains the supposed transit. We obtained RMS values of130 ppm and 154 ppm for the five-planet and four-planet scenar-ios, respectively. The lowest RMS value in the five-planet caseshows how the transit model may justify the flux variability; asa term of comparison the RMS of the binned residuals over theentire sector 11 is 152 ppm.Then, we carefully inspected the
TESS sector 10 LC aswell, looking for further undetected signals compatible with ad F ∼
400 ppm. We noticed that ∼ ff ects the transit depth of HD 108236 e,d F e . From the five-planet scenario we inferred d F e = + − ppm, while the four-planet scenario yields to a deeper transitwith d F e = + − ppm, as expected.The temporal di ff erence between these two transits ofHD 108236 f in the two TESS sectors gives a candidate valuefor the orbital period, which also agrees with the transit epoch ofthe signal detected in the
CHEOPS visit. Therefore, we propose P = .
54 days as a possible candidate value.
Article number, page 9 of 22 & A proofs: manuscript no. TOI-1233
Fig. 12.
Portion of the
TESS sector 10 LC. The solid red line representsthe model of the transit of HD 108236 e considering the four-planetsscenario: a residual variability in the data points remains unexplained.Data are binned on a timescale of 24 min; the RMS of the binned resid-uals over the transit window is 168 ppm.
D20 investigated whether additional planets may be presentin the system and proposed a possible candidate with a period of10.9113 days, with T = . TESS dataset cannot give a definitive answer,we looked for possible signals of this candidate in the
CHEOPS
LCs. Propagating its ephemeris, we would expect a transit ofthis candidate planet at T = .
839 BJD, hence blendedwith the transit of HD 108236 c. We ran a further analysis of the
CHEOPS
LC, covering the transit of HD 108236 c consideringa scenario with six planets and compared the results with thefavoured scenario with five planets (null hypothesis), obtainingln B = − . ⇒ ln B = . >
5, which means that thereis a strong evidence for not rejecting the null hypothesis. On theone hand, the Bayes factor strongly disfavours the presence ofa planet at ∼ We carried out the analysis considering the
TESS and
CHEOPS datasets separately (’TESS-only’ and ’CHEOPS-only’ ap-proaches) and combined (’TESS + CHEOPS’ approach). As theCHEOPS-only approach involved the analysis of one single tran-sit per planet, we imposed a normal prior on the orbital peri-ods based on the results obtained from the TESS-only approach.For each approach, we fitted the data considering both four andfive planets. The four-planet fit considered the four planets fromHD 108236 b to HD 108236 e already detected by D20, while thefive-planet fit also included the planet HD 108236 f with an or-bital period of ∼ Fig. 13.
Same as Figure 12, but considering the five-planet fit. The topand middle panels show the transits of HD 108236 e and HD 108236 fseparately, while the bottom panel shows the results obtained with thecombined model. The RMS of the binned residuals over the transit win-dow is 137 ppm, which is lower than 168 ppm retrieved in the four-planet scenario, where HD 108236 f is absent.Article number, page 10 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system
Table 4.
Natural logarithm of the Bayes factors obtained when testingthe five-planet scenario against the four-planet scenario for each of ourthree approaches.
TESS-only CHEOPS-only TESS + CHEOPSln B TESS dataset, and one is blended witha transit of HD 108236 e.The Bayesian factors B obtained from the di ff erent ap-proaches, where we tested the five-planet scenario againstthe four-planet scenario, are reported in Table 4. The ln B Bayesian indicator (which is always greater than 5) stronglyfavours the scenario with five transiting planets.Supported by the Bayesian evidence, we consider the five-planet scenario to be the most appropriate description of thedata. Table 5 summarises the results obtained for this scenario.At first, we performed all analyses considering the orbital ec-centricity e as a free parameter, as also done by D20. Then, weanalysed the dynamical stability of our TESS + CHEOPS solu-tion (see Section 5.3 for further details), finding that the lack ofa constraint on e leads to a severely unstable system. Therefore,we repeated the TESS + CHEOPS analysis setting e (cid:46) .
1, whichis also supported by the dynamical stability analysis of D20 (seetheir Figure 16). The last column of Table 5 presents our refer-ence results, accounting for the constraint on e and consideringall available datasets. We emphasise that in Table 5 all reportedtransit depths are intended to be d F ≡ (cid:16) R p R (cid:63) (cid:17) to make them com-parable between CHEOPS and
TESS , that is to say independentof the instrumental bandpass and thus specific limb darkening.As a sanity check, we also carried out an independent jointanalysis of the
TESS and
CHEOPS
LCs with the code pyaneti (Barragán et al. 2019), which estimates the transit parametersusing a Bayesian approach. We imposed uniform priors for allfitted parameters. We sampled for the mean stellar density ρ (cid:63) and recovered the scaled semi-major axis for each planet ( a / R (cid:63) )using Kepler’s third law (Winn 2010). The joint modelling ofthe transit LCs of the five planets provides a mean stellar den-sity of ρ (cid:63) = + . − . g cm − , which agrees with the density of1.82 ± − derived from the stellar mass and radius pre-sented in Sect. 2. The transit parameter estimates are consistentwell within ∼ σ with those derived with allesfitter , sup-porting our results.We further carried out an independent analysis of the CHEOPS
IOC LC using the pycheops package (Maxted et al.,in prep), which is being developed specifically for the analysisof CHEOPS data (see Lendl et al. 2020, for more details). Fromthis additional analysis, we obtained values (see Table 6) fullycompatible with allesfitter results, namely with di ff erenceslying below 1.2 σ .We comment here in detail on the results listed in Table 5.The first column lists the results obtained by D20, which maybe directly compared to our TESS-only results, given that bothanalyses use the same dataset and employ the same analysis tool.However, D20 employed an MCMC technique implementedthrough the emcee package, considered the presence of fourtransiting planets, and adopted ρ (cid:63), D = . ± .
16 g / cm asprior. Instead, we employed the Dynamic Nested Sample tech-nique implemented through the dynesty package, consideredfive transiting planets, and imposed a sharper Gaussian prior onthe stellar density of ρ (cid:63) = . ± .
12 g / cm . Furthermore, we https://github.com/pmaxted/pycheops assumed normal Gaussian priors on the LD coe ffi cients (see Sec-tion 4), while D20 set uniform priors on the LD coe ffi cients.Despite the di ff erences, all the TESS-only results are consistentwithin ∼ σ , but our results have in general smaller uncertainties,most likely because of the tighter priors on the stellar density andLD coe ffi cients.The comparison of the results obtained considering TESS and
CHEOPS separately is important in order to assess the pho-tometric precision of
CHEOPS in comparison to that of
TESS .The relative uncertainties δ on the transit depth d F are reportedin Table 7. The values of δ are a function of the telescope ef-fective diameter, the number of observed transits, the exposuretime, and the transit depth. As a matter of fact, on the one hand, b , e , and ω are rather poorly constrained in the CHEOPS
LCsdue to the availability of single transits with frequent gaps andthis a ff ects our capability of reconstructing the transit model, es-pecially in case of shallow transits. On the other hand, CHEOPS guarantees a greater (relative to
TESS ) photometric precision forshallower transits than for deeper transit as CHEOPS observa-tions break through the
TESS photometric noise floor (whichlimits the photometric precision of
TESS for shallow transit). Inthe case of HD 108236, one
CHEOPS transit observation leadsto approximately the same level of precision in δ as eight TESS transits for d F ∼
500 ppm, which corresponds to the detectionof a mini-Neptune with R p ∼ R ⊕ around a solar-like star. Fordeeper transit signals ( ∼ CHEOPS transit ob-servation leads to a precision on the transit depth higher thanthat of two
TESS transits, roughly by a factor of 1.3. Finally,for shallower transits ( ∼
250 ppm), one
CHEOPS transit obser-vation leads to about the same precision on the transit depthobtained after about seven
TESS transit observations. However,these conclusions depend on the length and location of gaps inthe
CHEOPS
LCs.The comparison between the TESS + CHEOPS approach andthe analyses performed considering
TESS and
CHEOPS
LCsseparately is not straightforward. One may generally expect thatthe results coming from the combined analysis fall somewherein the middle of the range defined by the results of the sepa-rate analyses, but this is not always the case. The main reasonis that the CHEOPS-only analysis is not always as robust as theTESS-only analysis. In fact, in the former we consider just onetransit per planet, with the photometric signal of
CHEOPS
LCsthat is a ff ected by frequent gaps. In particular, we are missing theingress and / or egress phase of each transit partially or totally (seeTable 7). These are the most delicate phases of the transit as theybest constrain the impact parameter b and hence the orbital incli-nation i p . The loose constraint on b (due to the gaps in the LCs)and the treatment of e and ω as free parameters (despite onlyphotometric data are available) increase the degrees of freedomand hence the degeneracies within the multi-parametric transitmodel. This justifies the discrepancies among a few parametervalues, like d F and i p of HD 108236 b or i p of HD 108236 d,involving the CHEOPS-only approach.It is in the combined analysis where we can account for thenumerous transits from TESS (which give much more indicationsabout the transit shape, decreasing the degrees of freedom ofthe fitted model) and, simultaneously, on the exquisite
CHEOPS photometry (which allows the refinement of all the fitted pa-rameters as the robustness of the transit shape is guaranteed by
TESS ). In particular, Table 8 shows the relative uncertainties onplanetary radii derived from the TESS-only approach comparedwith those coming from the TESS + CHEOPS approach ( e free,so that the comparison is homogeneous). The improvement on Article number, page 11 of 22 & A proofs: manuscript no. TOI-1233 the radii precision can be quantified by factors ranging from 1.2for HD 108236 d up to 2.6 for HD 108236 f.This system will be observed again by
TESS in April 2021during one sector of observations. Considering that the presentday TESS-only results are based upon two sectors of observa-tions, the number of data points (hence of transits measurements)are expected to be enhanced by a factor of 1.5 in April 2021. Asa result, once we can account on the entire set of
TESS data, theuncertainties on planetary radii are expected to be reduced by afactor of √ . ≈ .
2. As a consequence, the predicted uncer-tainties on planetary radii coming from TESS-only data will becomparable with those presented here for planets c and d, whilethe contribution of the current
CHEOPS observations will stillguarantee a better precision on the radii of planets b, e, and f(see Table 8).As mentioned earlier, we performed the TESS + CHEOPSanalysis considering two cases, one leaving e as a free param-eter and one setting e (cid:46) . e constrained to be smaller than 0.1(last column of Table 5). These results are consistent with thoseof D20, but are more precise, especially in terms of transit depthand ephemerides. This is not surprising because, despite addingjust one transit per planet, CHEOPS has a larger aperture than
TESS and the
TESS data span ∼ CHEOPS transits increases the temporal coverage to ∼ CHEOPS observ-ing window (1 May 2021, according to the
CHEOPS
FeasibilityChecker ) and compare them with those obtained by consideringthe ephemerides given by D20. This comparison is presented inTable 9. The longer temporal baseline has led to a significantreduction of the uncertainties on the transit times, decreasing itfrom over an hour to a few minutes in all cases.For each planet, we also computed the timescale after whichthe 1 σ -uncertainty on the transit timing becomes compara-ble to the transit duration, to establish the epoch when wewould likely miss the full transit according to the present-dayephemerides. Starting from CHEOPS last observations, the ref-erence timescales for the ephemerides’ drifts vary from ∼ ∼
108 years for planet e (2013orbits). Dragomir et al. (2020) evaluated that ∼
98% of
TESS target stars re-observed by a follow-up mission nine months af-ter
TESS observations keep their ephemerides fresh (that is theuncertainty on T is lower than 30 min) for at least two years.In our case CHEOPS observations occur ∼ TESS observations, therefore our results may be comparable with theephemerides deterioration estimated by Dragomir et al. (2020).Similarly to what described before, we computed the time tobe elapsed from
CHEOPS last observations such that the er-ror on T becomes greater than 30 min, and we found thatthe ephemerides’ drifts vary from ∼ ∼
12 years (see Ta-ble 9), which is consistent with the predictions of Dragomir et al.(2020). When determining orbital solutions in multi-planet systems itis important to verify the dynamical stability of the fitted sys-tems, to ensure that the fits are physically plausible. Here, wedescribe the stability tests we performed for the fits presented inSection 5.2.To test the stability of these fits, we used the MEGNO(Mean Exponential Growth factor of Nearby Orbits) function-ality of the R ebound N -body package (Rein & Liu 2012; Rein& Tamayo 2016). MEGNO is a chaos indicator that can, inshort-duration integrations, reveal chaotic behaviour that can, onlonger timescales, lead to instability (Cincotta et al. 2003). TheMEGNO indicator Γ ∼ Γ divergeswith time for chaotic orbits. We calculated Γ for all the orbitsin the TESS + CHEOPS ( e free) posteriors summarised in Ta-ble 5. The stellar mass was taken to be 0 .
869 M (cid:12) , and the planetmasses were taken from the atmospheric evolution analysis de-scribed in Section 5.4 (see Table 10). As we lack the full three-dimensional geometry of the orbits, orbital coplanarity was en-forced. The systems were integrated with the whfast integrator(Rein & Tamayo 2015) with a stepsize of 0 . d or untilthe collision of two bodies or the ejection of a planet. We take0 . ff accounting for instability; in fact this value im-plies an already significant change in orbital elements of morethan three times the orbital separation for at least one planet.This scenario would produce such an instability that will ejectthe planet or lead to a collision, without needing to integrate thesystems until a planet is physically lost from the system at muchlarger distances of ∼ AU or until the collision takes place.We classified systems as unstable if the MEGNO Γ >
3, or if acollision or ejection occurred, and as stable otherwise.In this way, we tested the stability of 54 684 draws from theTESS + CHEOPS ( e free) posteriors. Only three had Γ <
3, allothers either having a higher MEGNO value, indicative of or-bital chaos, or losing a planet within the 10 d integration du-ration. This lack of stability can be attributed to the lack of aconstraint being placed on the orbital eccentricity in the LC fit-ting, resulting in fairly high eccentricities being assigned to theplanets (particularly the outer two).Noting this, and that D20 found that stable fits to the TESS
LCs had eccentricities (cid:46) .
1, we re-fit the LCs, this time im-posing | √ e cos ω | , | √ e sin ω | < .
3, and again tested the stabil-ity of the new orbital solutions. The restriction on eccentricitiessignificantly increased the number of stable configurations, with21 460 out of 57 323 systems drawn from the posterior having Γ <
3. These runs were then directly integrated for 10 Myr toverify their stability: 7 829 of the systems survived for this time.For these systems, the median eccentricities of planets b to f arerespectively 0 . . . . . As reported by D20, only a few RV measurements are cur-rently available for this system, thus D20 estimated the plan-etary masses employing the mass-radius probabilistic modelof Chen & Kipping (2017), obtaining 5 ±
2, 7 ±
2, 10 ±
2, and13 ± M ⊕ for planets HD 108236 b, HD 108236 c, HD 108236 d, Article number, page 12 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system and HD 108236 e, respectively. We also estimate the planetarymasses, but following a di ff erent approach, namely employingconstraints provided by the system parameters and the range ofpossible atmospheric evolutionary tracks realising the measuredplanetary radii. To this end, we use the algorithm described byKubyshkina et al. (2019a,b), but employ it in a slightly modifiedway, as described below. The framework mixes three ingredients: a model of the stellarhigh-energy flux (X-ray and extreme ultra-violet radiation; here-after XUV) evolution, a model relating planetary parameters andatmospheric mass, and a model computing atmospheric mass-loss rates. For late-type stars, the stellar XUV flux out of thesaturation regime depends on stellar mass and rotation period(see e.g. Vilhu 1984; Wright et al. 2011), the latter of which istime-dependent. To account for the di ff erent rotation histories ofthe host stars, the framework models the rotation period P rot ( τ )as a power law in age τ , normalised such that the computed rota-tion period at the present age P rot ( t (cid:63) ) is consistent with the nowmeasured rotation period. Following Kubyshkina et al. (2019a), P rot ( τ ) = P rot ( t (cid:63) ) (cid:16) τ t (cid:63) (cid:17) . τ ≥ P rot ( t (cid:63) ) (cid:16) t (cid:63) (cid:17) . (cid:16) τ (cid:17) x τ < , (7)where ages are expressed in Gyr and rotation periods in days.Equation (7) mimics the power-law relation given by Mamajek& Hillenbrand (2008) for τ ≥ x exponent in the young star regime as di ff erentrotators follow di ff erent evolutionary paths.The stellar XUV luminosity is then derived from the rota-tion period using scaling relations (Pizzolato et al. 2003; Sanz-Forcada et al. 2011; Wright et al. 2011; McDonald et al. 2019).To account for the evolution of the stellar bolometric luminos-ity, and hence the planetary equilibrium temperature ( T eq ), theframework uses the MIST grid. For estimating the planetary at-mospheric mass fraction as a function of mass, radius, and T eq ,the original framework employs models described by Stökl et al.(2015) and Johnstone et al. (2015b). The planetary mass-lossrates are extracted from a large grid that has been constructedusing the hydrodynamic model described in Kubyshkina et al.(2018). Starting at 5 Myr (the assumed age of the dispersal ofthe protoplanetary disk), the framework extracts the mass-lossrate from the grid at each time step, employing the stellar fluxand system parameters, and uses it to update the atmosphericmass fraction and planetary radius. This procedure is then re-peated until the age of the system is reached or the planetaryatmosphere is completely escaped.The standard free parameters of the framework are the x index of the power law, controlling the stellar rotation period(a proxy for the stellar XUV emission) within the first 2 Gyr,and the initial planetary radius (i.e. the initial atmospheric massfraction at the time of the dispersal of the protoplanetary disk).The free parameters are constrained by implementing the atmo-spheric evolution algorithm in a Bayesian framework, employ-ing the MCMC tool developed by Cubillos et al. (2017). In short,the framework takes the observed system parameters (essentiallystellar P rot , t (cid:63) , and M (cid:63) , besides planetary masses and orbitalsemi-major axes) with their uncertainties as input (i.e. priors).Then it computes millions of planetary evolutionary tracks vary-ing the input parameters according to the shape of the prior dis-tributions, and varying the free parameters within ranges given by the user, fitting the observed planetary radius at the age ofthe system, further accounting for their uncertainties. The resultsare posterior distributions of the free parameters, which are therotation period of the star when it was young and the initial at-mospheric mass fraction of the considered planets.Here we reversed the usual way the tool works, that is weasked the framework to provide posteriors for the planetarymasses by fixing the past rotation rate of the host star (henceits activity level) to the statistically most likely value. In partic-ular, we imposed a normal prior on stellar age, mass, and plan-etary semi-major axes, according to the values derived from thehost star characterisation and from the LC analysis. To describethe evolution of the activity of the host star, we fixed the stel-lar rotation period at an age of 150 Myr to P rot , = .
23 days.This is the median value of the rotation period distribution givenby Johnstone et al. (2015a), which we inferred considering thesubset of stars having masses in the 0.2 M (cid:12) -width interval cen-tred around our nominal stellar mass value of M (cid:63) = . M (cid:12) .Therefore, we run the framework considering as free parame-ters the present day rotational period of the star, the initial atmo-spheric mass fractions, and the planetary masses. The present-day stellar rotation period is formally unknown (no rotationalmodulation signal detected in the TESS
LCs; D20), but, havingfixed P rot at the age of 150 Myr, it is constrained by the imposedpower law on the evolution of P rot . Figure 14 shows the posterior distributions of the planetarymasses we obtained at the end of the run, while Table 10 com-pares our results to those in D20 according to the probabilisticmass-radius relation of Chen & Kipping (2017). Our results sug-gest that HD 108236 b and HD 108236 c have an Earth-like den-sity, while the three outer planets should host a low mean molec-ular weight atmosphere. In general, there is a good agreementbetween our results and those obtained by D20, except for themass of HD 108236 e, where our results indicate a significantlylighter planet, though our posterior distribution is skewed suchthat the 13 ± M ⊕ value proposed by D20 falls inside our uppererror bar. However, we agree with D20 on the overall conclusionthat this planet is a mini-Neptune.However, these results have to be taken with caution becausethey are based on models and may be a ff ected by our assump-tions. On the one hand, our results are significantly constrainedby the fact that the framework models all planets in the systemsimultaneously, trying to find the solution that best fits them all.On the other hand, one of the main assumptions of the frame-work is that the analysed planets have (or had) a hydrogen-dominated atmosphere and that the planetary orbital separationdoes not change after the dispersal of the protoplanetary disk. Al-though there is reason to believe the first assumption is adequatefor the vast majority of planets (Owen et al. 2020), the secondassumption is most likely true for tightly packed systems withorbital resonances (Kubyshkina et al. 2019b), but this is not thecase of HD 108236. Indeed, both the D20 and our stability anal-yses (Section 5.3) suggest that the planets may have exchangedorbital momentum throughout their evolution, which would havealso changed the planetary orbits, in turn a ff ecting the evolu-tion of the planetary atmospheres. From the system parameterslisted in Tables 2 and 5, and from the planetary masses obtainedthrough the atmospheric evolution calculations (Table 10), weestimated the semi-amplitude ( K ) of the RV curve expected foreach planet. The resulting values are listed in Table 10. Article number, page 13 of 22 & A proofs: manuscript no. TOI-1233
Fig. 14.
Posterior distributions for the masses M p of the planets composing the HD 108236 system. In each panel, the horizontal red line representsthe flat prior imposed on M p , implying that M p was set as a free parameter. The dashed black line marks the median of the distribution, while thegreen area shows the 68% highest posterior density credible interval.
6. Conclusions
We have presented the combined analysis of
TESS and
CHEOPS
LCs of the HD 108236 multi-planet system, along with the char-acterisation of the host star. Our spectroscopic analysis con-firmed that HD 108236 is a Sun-like star with T e ff = ±
61 Kand log g = . ± .
11, though it is slightly metal poor with ametallicity of [Fe / H] = − . ± .
04 dex. We estimated the stel-lar radius to be R (cid:63) = . ± . R (cid:12) , and determined robustvalues for stellar mass and age by employing two sets of stel-lar isochrones and tracks, obtaining M (cid:63) = . + . − . M (cid:12) and t (cid:63) = . + . − . Gyr.Four planets were identified in the
TESS
LCs of HD 108236by D20. We complemented this analysis by adding three
CHEOPS datasets, which were supposed to contain one furthertransit for each of these planets. Inspecting one of the datasets,we serendipitously discovered an unexpected transit-like featurewith a depth of ∼
400 ppm that we ascribed to a fifth planet,HD 108236 f. We derived the Bayesian evidence for a four-and five-planet model, finding that the latter was significantlyfavoured. The combined
TESS and
CHEOPS
LC analysis led usto derive a likely period for HD 108236 f of P f = .
54 days.Within the context of searching for additional planets in the sys-tem, we also investigated the presence in the
CHEOPS
LCs ofthe tentative candidate with a period of 10.9113 days suggestedby D20, but we could not find strong evidence supporting it.Within the scenario comprising five planets, the combinedanalysis of the
TESS and
CHEOPS
LCs resulted in sys-tem parameters in agreement with those of D20 for planetsHD 108236 b to HD 108236 e. However, our results are moreprecise in terms of transit depths (due to the high quality ofthe
CHEOPS photometry), planetary radii (due to the improvedmeasured transit depths and stellar radius), and ephemerides(due to the longer baseline covered by the data). We further ran adynamical stability analysis of the system, finding that stabilityis maximised when the eccentricities of all planets are smallerthan about 0.1. Comparing the results obtained from the analysisof the
TESS and
CHEOPS
LCs separately, we found that, for a V ∼ ∼
500 ppm (i.e. a ∼ R ⊕ mini-Neptune transiting a solar-likestar), one CHEOPS transit returns data with a quality compara-ble to that obtained from about eight
TESS transits.The refined ephemerides we obtained from the LC analy-sis will allow more accurate planning of follow-up observationsof this system. HD 108236 will be visible with
CHEOPS again, with an e ffi ciency higher than 50%, between March and June2021, at which point the planetary transit timings will be pre-dictable with uncertainties of just a few minutes. Instead, by em-ploying the T and P values from D20, based on just ∼ TESS observations, the uncertainties on the transit timingswould have been of the order of a couple of hours. We also eval-uated the timescales after which the uncertainties on the transittimings become greater than 30 minutes, following the criterionin Dragomir et al. (2020). We concluded that our ephemeridesremain fresh on timescales ranging between ∼ ∼
12 years (planet e) from the last
CHEOPS observations.
TESS will observe HD 108236 again during the extendedmission in April 2021 within one sector of observations. Ifcombined with the already available observations, and assum-ing
TESS will collect the exact same amount of transits foreach planet per sector, the entire
TESS dataset will help re-duce the uncertainties on the planetary radii by a factor of ∼ + CHEOPS approach for planets c and d; however, theresults presented here with the contribution of
CHEOPS datawould still guarantee a better precision on the radii of planetsb, e, and f by at least a factor of ∼ CHEOPS observa-tions will therefore lead to further improvements in the measure-ment of the planetary radii, even more so compared to what wasobtained through the
TESS extended mission data. Furthermore,future
CHEOPS data on this system will be important for look-ing for and measuring the TTVs that provide key informationregarding the system dynamics as well as a measurement of theplanetary masses, independent of what given by the RV method.We finally used the derived system parameters and a plane-tary atmospheric evolutionary framework to constrain the plane-tary masses, finding that HD 108236 b and HD 108236 c shouldhave an Earth-like density, while the outer planets are likely tohost a low mean molecular weight atmosphere. The brightnessand age of the host star make this an ideal target for measur-ing planetary masses using high-precision RV measurements.The expected semi-amplitudes of the RV variations are withinreach of instruments such as HARPS (Mayor et al. 2003) andESPRESSO (Pepe et al. 2020) spectrographs. This will enableus to check the impact of the modelling assumptions and to per-form more detailed planetary atmospheric evolution modelling,aimed at deriving the past and future evolution of the system.
Acknowledgements.
We are extremely grateful to the anonymous referee forthe very thorough comments, which definitely improved the quality of thismanuscript. CHEOPS is an ESA mission in partnership with Switzerland with
Article number, page 14 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system important contributions to the payload and the ground segment from Austria,Belgium, France, Germany, Hungary, Italy, Portugal, Spain, Sweden, and theUnited Kingdom. The Swiss participation to CHEOPS has been supported bythe Swiss Space O ffi ce (SSO) in the framework of the Prodex Programme andthe Activités Nationales Complémentaires (ANC), the Universities of Bern andGeneva as well as well as of the NCCR PlanetS and the Swiss National ScienceFoundation. Based on observations made with the ESO 3.6 m telescope at theLa Silla Observatory under program ID 1102.C-0923. M.Le acknowledgessupport from the Austrian Research Promotion Agency (FFG) under project859724 “GRAPPA”. A.De and D.Eh acknowledge support from the EuropeanResearch Council (ERC) under the European Union’s Horizon 2020 researchand innovation programme (project Four Aces; grant agreement No 724427).M.J.Ho acknowledges the support of the Swiss National Fund under grant200020_172746. B.-O.De acknowledges support from the Swiss NationalScience Foundation (PP00P2-190080). The Spanish scientific participationin CHEOPS has been supported by the Spanish Ministry of Science andInnovation and the European Regional Development Fund through grantsESP2016-80435-C2-1-R, ESP2016-80435-C2-2-R, ESP2017-87676-C5-1-R,PGC2018-098153-B-C31, PGC2018-098153-B-C33, and MDM-2017-0737Unidad de Excelencia María de Maeztu–Centro de Astrobiología (INTA-CSIC),as well as by the Generalitat de Catalunya / CERCA programme. The MOCactivities have been supported by the ESA contract No. 4000124370. Thiswork was supported by Fundação para a Ciência e a Tecnologia (FCT) throughnational funds and by Fundo Europeu de Desenvolvimento Regional (FEDER)via COMPETE2020 - Programa Operacional Competitividade e Internacional-ização through the research grants: UID / FIS / / / / / / / FIS-AST / / / FIS-AST / / / FIS-AST / / / / / CP1215 / CT0004, IF / / / CP1215 / CT0002. O.D.S.De issupported in the form of work contract (DL 57 / / CP1364 / CT0004) fundedby national funds through Fundação para a Ciência e Tecnologia (FCT). TheBelgian participation to CHEOPS has been supported by the Belgian FederalScience Policy O ffi ce (BELSPO) in the framework of the PRODEX Program,and by the University of Liège through an ARC grant for Concerted ResearchActions financed by the Wallonia-Brussels Federation. M.Gi is F.R.S.-FNRSSenior Research Associate. S.Sa has received funding from the EuropeanResearch Council (ERC) under the European Union’s Horizon 2020 researchand innovation programme (grant agreement No 833925, project STAREX).Gy.M.Sz acknowledges funding from the Hungarian National Research, De-velopment and Innovation O ffi ce (NKFIH) grant GINOP-2.3.2-15-2016-00003and K-119517. For Italy, CHEOPS actvities have been supported by theItalian Space Agency, under the programs: ASI-INAF n. 2013-016-R.0 andASI-INAF n. 2019-29-HH.0. L.Bo, G.Pi, I.Pa, G.Sc, and V.Na acknowledgethe funding support from Italian Space Agency (ASI) regulated by “AccordoASI-INAF n. 2013-016-R.0 del 9 luglio 2013 e integrazione del 9 luglio 2015”.G.La acknowledges support by CARIPARO Foundation, according to theagreement CARIPARO-Università degli Studi di Padova (Pratica n. 2018 / /
19 C). The dynamical simulations were enabled by resources providedby the Swedish National Infrastructure for Computing (SNIC) at Lunarcpartially funded by the Swedish Research Council through grant agreementno. 2016-07213. Simulations in this paper made use of the REBOUND codewhich is freely available at http://github.com/hannorein/rebound .S.Ho acknowledges CNES funding through the grant 837319. K.G.I. is theESA CHEOPS Project Scientist and is responsible for the ESA CHEOPSGuest Observers Programme. She does not participate in, or contribute to,the definition of the Guaranteed Time Programme of the CHEOPS missionthrough which observations described in this paper have been taken, nor toany aspect of target selection for the programme. X.Bo, S.Ch, D.Ga, M.Fr,and J.La acknowledge their roles as ESA-appointed CHEOPS science teammembers. A.Bo acknowledges B. Akinsanmi, G. Bruno, M. Günther, R. Luque,F.J. Pozuelos Romero, and L.M. Serrano for the very fruitful discussions. Weacknowledge T. Daylan for his help in planning the
CHEOPS observations.
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W. 2011, ApJ, 743, 48 Space Research Institute, Austrian Academy of Sciences, Schmiedl-strasse 6, A-8042 Graz, Austriae-mail: [email protected] Space sciences, Technologies and Astrophysics Research (STAR)Institute, Université de Liège, Allée du six Août 19C, 4000 Liège,Belgium Astrobiology Research Unit, Université de Liège, Allée du six Août19C, 4000 Liège, Belgium Observatoire de Genève, Université de Genève, Chemin des Mail-lettes 51, 1290 Sauverny, Switzerland Physikalisches Institut, University of Bern, Gesellsschaftstrasse 6,3012 Bern, Switzerland School of Physics and Astronomy, Physical Science Building, NorthHaugh, St Andrews, United Kingdom Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France Lund Observatory, Dept. of Astronomy and Theoreical Physics,Lund University, Box 43, 22100 Lund, Sweden NCCR / PlanetS, Centre for Space & Habitability, University of Bern,Bern, Switzerland Department of Physics and Kavli Institute for Astrophysics andSpace Research, Massachusetts Institute of Technology, Cambridge,MA 02139, USA Instituto de Astrofísica e Ciências do Espaço, Universidade doPorto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal INAF, Osservatorio Astrofisico di Torino, via Osservatorio 20,10025 Pino Torinese, Italy Astrophysics Group, Cavendish Laboratory, J.J. Thomson Avenue,Cambridge CB3 0He, United Kingdom Institute of Planetary Research, German Aerospace Center (DLR),Rutherfordstrasse 2, 12489 Berlin, Germany INAF, Osservatorio Astronomico di Padova, Vicolodell’Osservatorio 5, 35122 Padova, Italy Astrophysics Group, Keele University, Sta ff ordshire, ST5 5BG,United Kingdom Departamento de Física e Astronomia, Faculdade de Ciências, Uni-versidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France Leiden Observatory, University of Leiden, PO Box 9513, 2300 RALeiden, The Netherlands Department of Space, Earth and Environment, Chalmers Universityof Technology, Onsala Space Observatory, 43992 Onsala, Sweden Dipartimento di Fisica e Astronomia "Galileo Galilei", Universiàdegli Studi di Padova, Vicolo dell’Osservatorio 3, 35122 Padova,Italy INAF, Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123Catania, Italy ELTE Eötvös Loránd University, Gothard Astrophysical Observa-tory, 9700 Szombathely, Szent Imre h. u. 112, Hungary MTA-ELTE Exoplanet Research Group, 9700 Szombathely, SzentImre h. u. 112, Hungary Center for Space and Habitability, Gesellsschaftstrasse 6, 3012Bern, Switzerland ESTEC, European Space Agency, Keplerlaan 1, 2201 AZ Noord-wijk, The Netherlands Instituto de Astrofísica de Canarias (IAC), 38200 La Laguna, Tener-ife, Spain Departamento de Astrofísica, Universidad de La Laguna (ULL), E-38206 La Laguna, Tenerife, Spain Admatis, Miskok, Hungary Depto. de Astrofísica, Centro de Astrobiologia (CSIC-INTA), ESACcampus, 28692 Villanueva de la Cãda (Madrid), Spain Sub-department of Astrophysics, Department of Physics, Universityof Oxford, Oxford, OX1 3RH, UK Department of Astronomy, Stockholm University, AlbaNova Uni-versity Center, 10691 Stockholm, Sweden Institut de Physique du Globe de Paris (IPGP), 1 rue Jussieu, 75005Paris, France Center for Astronomy and Astrophysics, Technical UniversityBerlin, Hardenberstrasse 36, 10623 Berlin, Germany University of Vienna, Department of Astrophysics, Türkenschanzs-trasse 17, 1180 Vienna, Austria Division Technique INSU, BP 330, 83507 La Seyne cedex, France Konkoly Observatory, Research Centre for Astronomy and EarthSciences, 1121 Budapest, Konkoly Thege Miklós út 15-17, Hungary IMCEE, UMR8028 CNRS, Observatoire de Paris, PSL Univ., Sor-bonne Univ., 77 av. Denfert-Rochereau, 75014 Paris, France Institut d’astrophysique de Paris, UMR7095 CNRS, UniversitéPierre & Marie Curie, 98bis blvd. Arago, 75014 Paris, France Institute of Optical Sensor Systems, German Aerospace Center(DLR), Rutherfordstr. 2, 12489 Berlin, Germany Department of Physics, University of Warwick, Gibbet Hill Road,Coventry CV4 7AL, United Kingdom Institut für Geologische Wissenschaften, Freie Universität Berlin,12249 Berlin, Germany Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB,C / CanMagrans s / n, 08193 Bellaterra, Spain Institut d’Estudis Espacials de Catalunya (IEEC), Barcelona, Spain Italian Space Agency, Via del Politecnico, 00133 Rome, ItalyArticle number, page 16 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system Mullard Space Science Laboratory, University College London,Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK Article number, page 17 of 22 & A proofs: manuscript no. TOI-1233
Table 5.
HD 108236 system parameters obtained from analyses of the
TESS and
CHEOPS
LCs, in comparison to what was found by Daylan et al.(2020). The columns labelled as TESS-only, CHEOPS-only, and TESS + CHEOPS refer to the results obtained considering five transiting planetsin the system. All results have been obtained considering e as a free parameter, except for the last column for which e has been set to be smallerthan 0.1. The TESS + CHEOPS analysis with e < . + CHEOPS e free e free e free e free e < . TESS transits; 1
CHEOPS transitEclipse timing (a) T [BJD] 8572 . + . − . . + . − . . + . − . . + . − . . ± . P [days] 3 . + . − . . + . − . . + . − . . + . − . . + . − . Transit depth (b) d F [ppm] 268 ±
31 267 + − + − ±
17 285 ± W [h] 2 . + . − . . + . − . . + . − . . + . − . . ± . b [ R (cid:63) ] 0 . ± .
24 0 . + . − . . + . − . . ± .
12 0 . + . − . Semi-major axis a [AU] 0 . ± . . ± . . + . − . . ± . . + . − . Orbital inclination i p [ ◦ ] 87 . + . − . . + . − . . + . − . . + . − . . + . − . Eccentricity e . + . − . . + . − . . + . − . . + . − . . + . − . Arg. of pericentre ω [ ◦ ] 190 ±
140 262 + − + − + − . + − Radius R p [ R ⊕ ] 1 . ± .
098 1 . + . − . . + . − . . ± .
052 1 . ± . TESS transits; 1
CHEOPS transitEclipse timing (a) T [BJD] 8572 . + . − . . + . − . . + . − . . + . − . . + . − . Period P [days] 6 . + . − . . + . − . . + . − . . + . − . . + . − . Transit depth (b) d F [ppm] 455 + − + − + − + − + − Transit duration W [h] 2 . ± .
095 2 . + . − . . + . − . . ± .
10 2 . + . − . Impact parameter b [ R (cid:63) ] 0 . + . − . . ± .
12 0 . + . − . . + . − . . + . − . Semi-major axis a [AU] 0 . ± . . + . − . . + . − . . ± . . ± . i p [ ◦ ] 88 . + . − . . ± .
42 88 . + . − . . + . − . . + . − . Eccentricity e . + . − . . + . − . . + . − . . + . − . . + . − . Arg. of pericentre ω [ ◦ ] 210 ±
120 164 + − . ±
53 97 + − + − Radius R p [ R ⊕ ] 2 . + . − . . + . − . . + . − . . ± .
050 2 . ± . TESS transits; 1
CHEOPS transitEclipse timing (a) T [BJD] 8571 . + . − . . + . − . . + . − . . + . − . . + . − . Period P [days] 14 . + . − . . ± . . + . − . . + . − . . + . − . Transit depth (b) d F [ppm] 787 ±
53 740 + − + − ±
29 705 + − Transit duration W [h] 3 . + . − . . + . − . . + . − . . + . − . . + . − . Impact parameter b [ R (cid:63) ] 0 . + . − . . + . − . . + . − . . ± .
075 0 . + . − . Semi-major axis a [AU] 0 . ± . . + . − . . + . − . . ± . . ± . i p [ ◦ ] 89 . + . − . . + . − . . + . − . . + . − . . + . − . Eccentricity e . + . − . . + . − . . + . − . . + . − . . + . − . Arg. of pericentre ω [ ◦ ] 190 + − + − . + − + − + − Radius R p [ R ⊕ ] 2 . ± .
11 2 . + . − . . + . − . . ± .
057 2 . + . − . Planet e: 2
TESS transits; 1
CHEOPS transitEclipse timing (a) T [BJD] 8586 . + . − . . + . − . . + . − . . + . − . . + . − . Period P [days] 19 . + . − . . ± . . + . − . . + . − . . + . − . Transit depth (b) d F [ppm] 1043 + − + − + − + − + − Transit duration W [h] 4 . + . − . . + . − . . + . − . . + . − . . + . − . Impact parameter b [ R (cid:63) ] 0 . + . − . . + . − . . + . − . . ± .
10 0 . + . − . Semi-major axis a [AU] 0 . ± . . ± . . ± . . ± . . + . − . Orbital inclination i p [ ◦ ] 89 . + . − . . + . − . . + . − . . + . − . . + . − . Eccentricity e . + . − . . + . − . . + . − . . + . − . . + . − . Arg. of pericentre ω [ ◦ ] 170 + − + − + − + − + − Radius R p [ R ⊕ ] 3 . + . − . . + . − . . + . − . . + . − . . ± . TESS transits; 1
CHEOPS transitEclipse timing (a) T [BJD] 8616 . + . − . . + . − . . + . − . . + . − . Period P [days] 29 . + . − . . + . − . . + . − . . + . − . Transit depth (b) d F [ppm] 366 + − + − + − + − Transit duration W [h] 4 . + . − . . + . − . . + . − . . + . − . Impact parameter b [ R (cid:63) ] 0 . + . − . . + . − . . + . − . . ± . a [AU] 0 . ± . . ± . . ± . . + . − . Orbital inclination i p [ ◦ ] 89 . + . − . . + . − . . + . − . . ± . e . ± .
23 0 . ± .
092 0 . + . − . . + . − . Arg. of pericentre ω [ ◦ ] 167 + − ±
29 230 + − + − Radius R p [ R ⊕ ] 1 . ± .
16 1 . + . − . . + . − . . + . − . Notes. ( a ) Epoch shifted by − ( b ) d F ≡ (cid:16) R p R (cid:63) (cid:17) Article number, page 18 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system
Table 6.
Results obtained from the pycheops analysis of the
CHEOPS
IOC LC (first visit). Di ff erences are computed with respect to theCHEOPS-only results listed in Table 5. Parameter pycheops Di ff erence[ σ ]Planet cd F [ppm] 530 + − W [h] 2.88 ± b + . − . F [ppm] 1011 + − W [h] 4.02 + . − . b + . − . Article number, page 19 of 22 & A proofs: manuscript no. TOI-1233
Table 7.
Comparison of the photometric precision reached by
TESS (TE) and
CHEOPS (CH) , quantified by the relative uncertainty δ of the squaredratio between the planetary and stellar radius d F . Results are also influenced by specific LC features, such as gaps, especially if they occur duringthe ingress or egress phases. Columns labelled with gap ij express the temporal percentage of gaps occurring between the i th and the j th contact in CHEOPS
LCs.
Planet F gap gap gap Photometric error: δ [%] TE : CH [ppm] [%] [%] [%] TESS-only CHEOPS-onlyb 12:1 250 47 67 0 9.3 12c 8:1 500 0 38 100 5.8 5.4d 4:1 750 100 54 56 4.8 7.4e 2:1 1000 94 61 0 5.2 4.1f 2:1 450 16 43 100 16 4.8 Table 8.
Relative uncertainty on planetary radii σ R p R p as computed fromthe TESS-only and TESS + CHEOPS ( e free) approaches. As the TESS extended mission will re-observe HD 108236 again in April 2021 dur-ing one sector of observations, we also predict the expected σ R p R p once thenew TESS data will be combined to the present-day ones. The presentday contribution of
CHEOPS data still guarantees a better precision onthe radii of planets b, e, and f, while the predicted precision is compa-rable for planets c and d.
Planet σ R p R p [%]TESS-only TESS + CHEOPSThis work April 2021 This workb 4.8 3.9 3.3c 3.1 2.5 2.4d 2.6 2.1 2.2e 2.8 2.3 1.7f 8.7 7.1 3.3
Article number, page 20 of 22onfanti et al.: CHEOPS observations of the HD 108236 planetary system
Table 9.
Expected transit timings and their precision for the transit occurring closest to 1 May 2021, as computed considering T and P valuesgiven by Daylan et al. (2020) and obtained from our analysis (i.e. TESS + CHEOPS with prior constraint of e (cid:46) . CHEOPS observationsafter which the uncertainty on T is expected to be ∼
30 min (drift ) and comparable to the transit duration (drift W ). T values are given as T − Planet Daylan et al. (2020) Our work T [BJD] σ T [min] T [BJD] σ T [min] drift [yr] drift W [yr]b 9334.9540 132 9335.09891 7.3 6.6 34c 9335.4500 103 9335.41958 6.5 6.9 42d 9336.8165 81 9336.82421 6.1 8.0 66e 9331.0523 115 9330.98999 3.9 12.4 108f not discovered 9325.01948 9.6 4.1 29 Table 10.
Estimates of planetary masses, densities, and RV semi-amplitudes according to our atmospheric evolution modelling frame-work and system parameters. Planetary masses and density values arecompared with the predictions reported by D20, who used the proba-bilistic mass-radius relation of Chen & Kipping (2017).
Parameters This work D20HD 108236 b M p [ M ⊕ ] 4 . + . − . ± ρ p [ ρ ⊕ ] 1 . ± .
10 1 . ± . K [m s − ] 1 . ± . M p [ M ⊕ ] 8 . + . − . ± ρ p [ ρ ⊕ ] 1 . ± .
08 0 . ± . K [m s − ] 3 . ± . M p [ M ⊕ ] 7 . + . − . ± ρ p [ ρ ⊕ ] 0 . + . − . . ± . K [m s − ] 2 . ± . M p [ M ⊕ ] 8 . + . − . ± ρ p [ ρ ⊕ ] 0 . + . − . . ± . K [m s − ] 2 . ± . M p [ M ⊕ ] 3 . + . − . not discovered ρ p [ ρ ⊕ ] 0 . + . − . K [m s − ] 0 . ± . Article number, page 21 of 22 & A proofs: manuscript no. TOI-1233
Appendix A: Initial priors of the LC analyses.
Table A.1.
Initial priors used in our fits. N ( µ , σ ) denotes a Nor-mal (Gaussian) prior with mean µ and standard deviation σ , while U ( a , b ) denotes a uniform prior, whose bounds are a and b . ρ (cid:63) isexpressed in g / cm , T in BJD, P in days. All other quantities are di-mensionless. Parameter Prior ρ (cid:63) N (1 . , . q , TESS N (0 . , . q , TESS N (0 . , . q , CHEOPS N (0 . , . q , CHEOPS N (0 . , . R p R (cid:63) N (0 . , . R p + R (cid:63) a N (0 . , . i U (0 ., . T N (2458598 . , . P N (3 . , . √ e cos ω U ( − . , . √ e sin ω U ( − . , . R p R (cid:63) N (0 . , . R p + R (cid:63) a N (0 . , . i U (0 ., . T N (2458597 . , . P N (6 . , . √ e cos ω U ( − . , . √ e sin ω U ( − . , . R p R (cid:63) N (0 . , . R p + R (cid:63) a N (0 . , . i U (0 ., . T N (2458599 . , . P N (14 . , . √ e cos ω U ( − . , . √ e sin ω U ( − . , . R p R (cid:63) N (0 . , . R p + R (cid:63) a N (0 . , . i U (0 ., . T N (2458606 . , . P N (19 . , . √ e cos ω U ( − . , . √ e sin ω U ( − . , . R p R (cid:63) N (0 . , . R p + R (cid:63) a N (0 . , . i U (0 ., . T N (2458616 . , . P N (29 . , . √ e cos ω U ( − . , . √ e sin ω U ( − . , .9)