# Geometric albedo of WASP-12 b and WASP-76 b in the CHEOPS and TESS bandpasses (Corrigendum)

P. Cubillos, O. Demangeon, B. Akinsanmi, Y. Alibert, R. Alonso, J. Asquier, D. Barrado Navascues, S. Barros, W. Baumjohann, M. Beck, et al.

► To cite this version:

P. Cubillos, O. Demangeon, B. Akinsanmi, Y. Alibert, R. Alonso, et al. Geometric albedo of WASP-12 b and WASP-76 b in the CHEOPS and TESS bandpasses (Corrigendum). Astronomy & Astrophysics - A&A, 2025, 700, pp.C1. 10.1051/0004-6361/202556327e. hal-05345813

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

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# Geometric albedo of WASP-12 b and WASP-76 b in the CHEOPS and TESS bandpasses
(Corrigendum)

P. E. Cubillos<sup>28,45,*</sup>, O. D. S. Demangeon<sup>39,* ID</sup>, B. Akinsanmi<sup>43,*</sup>, Y. Alibert<sup>7,49</sup>, R. Alonso<sup>11,38 ID</sup>, J. Asquier<sup>23,24</sup>, D. Barrado Navascues<sup>17 ID</sup>, S. C. C. Barros<sup>12,39 ID</sup>, W. Baumjohann<sup>45 ID</sup>, M. Beck<sup>43 ID</sup>, T. Beck<sup>49</sup>, A. Bekkelien<sup>43 ID</sup>, W. Benz<sup>7,49</sup>, N. Billot<sup>43 ID</sup>, F. Biondi<sup>29,42</sup>, A. Bonfanti<sup>45 ID</sup>, X. Bonfils<sup>47</sup>, L. Borsato<sup>29 ID</sup>, G. Boué<sup>26</sup>, A. Brandeker<sup>13 ID</sup>, C. Broeg<sup>7,49</sup>, G. Bruno<sup>27</sup>, M. Buder<sup>36 ID</sup>, T. Bárczy<sup>1 ID</sup>, L. Carone<sup>45</sup>, S. Charnoz<sup>48</sup>, A. Collier Cameron<sup>9</sup>, A. C. M. Correia<sup>5</sup>, Sz. Csizmadia<sup>37 ID</sup>, M. B. Davies<sup>10</sup>, M. Deleuil<sup>2</sup>, A. Deline<sup>43</sup>, L. Delrez<sup>3,46</sup>, B.-O. Demory<sup>7,49 ID</sup>, D. Ehrenreich<sup>8,43</sup>, A. Erikson<sup>37</sup>, J. Farinato<sup>29</sup>, H.-G. Florén<sup>13</sup>, A. Fortier<sup>7,49</sup>, L. Fossati<sup>45 ID</sup>, M. Fridlund<sup>16,41</sup>, D. Gandolfi<sup>19</sup>, M. Gillon<sup>3</sup>, M. Güdel<sup>14 ID</sup>, M. N. Günther<sup>23,24 ID</sup>, A. Heitzmann<sup>43 ID</sup>, Ch. Helling<sup>34,45</sup>, M. J. Hooton<sup>6</sup>, S. Hoyer<sup>2 ID</sup>, K. G. Isaak<sup>23,24</sup>, L. L. Kiss<sup>21,40 ID</sup>, K. W. F. Lam<sup>37</sup>, J. Laskar<sup>26</sup>, A. Lecavelier des Etangs<sup>30</sup>, M. Lendl<sup>43 ID</sup>, D. Magrin<sup>29 ID</sup>, P. F. L. Maxted<sup>4</sup>, M. Mecina<sup>14 ID</sup>, C. Mordasini<sup>7,49 ID</sup>, V. Nascimbeni<sup>29</sup>, G. Olofsson<sup>13</sup>, R. Ottensamer<sup>14</sup>, I. Pagano<sup>27 ID</sup>, E. Pallé<sup>11,38 ID</sup>, G. Peter<sup>36</sup>, D. Piazza<sup>44</sup>, G. Piotto<sup>18,29 ID</sup>, D. Pollacco<sup>15</sup>, D. Queloz<sup>6,22</sup>, R. Ragazzoni<sup>18,29</sup>, N. Rando<sup>23,24</sup>, H. Rauer<sup>33,50 ID</sup>, I. Ribas<sup>31,32 ID</sup>, M. Rieder<sup>7,49</sup>, S. Salmon<sup>43</sup>, N. C. Santos<sup>12,39 ID</sup>, G. Scandariato<sup>27 ID</sup>, A. E. Simon<sup>7,49 ID</sup>, V. Singh<sup>27 ID</sup>, A. M. S. Smith<sup>37 ID</sup>, S. G. Sousa<sup>39 ID</sup>, M. Stalport<sup>3,46</sup>, Gy. M. Szabó<sup>20,25</sup>, D. Ségransan<sup>43 ID</sup>, N. Thomas<sup>49</sup>, S. Udry<sup>43 ID</sup>, V. Van Grootel<sup>46 ID</sup>, J. Venturini<sup>43</sup>, E. Villaver<sup>11,38</sup>, N. A. Walton<sup>35 ID</sup>, T. G. Wilson<sup>15</sup>, and T. Zingales<sup>18,29 ID</sup>

(Affiliations can be found after the references)

A&A, 684, A27 (2024), https://doi.org/10.1051/0004-6361/202348270

A&A, 685, A63 (2024), https://doi.org/10.1051/0004-6361/202348502

**Key words.** techniques: photometric – planets and satellites: atmospheres – planets and satellites: composition – errata, addenda

This is a corrigendum to Akinsanmi et al. (2024) and Demangeon et al. (2024). The retrieval code used in these works omitted a factor of $\lambda$ in the integration of the stellar ($F_*$) and planetary emission ($F_p$) necessary to obtain the planet-to-star flux ratio ($F_d/F_*$) at each observing band of the atmospheric retrievals (see, for example, Eq. (13) of Akinsanmi et al. 2024). The $\lambda$ factor is needed because the passband response functions ($T_{inst}$) are photon counters. The corrected calculation of the thermal planet-to-star flux ratio is

$$ \frac{F_d}{F_*} = \left(\frac{R_p}{R_*}\right)^2 \frac{\int \mathcal{F}_p(\lambda) T_{inst}(\lambda) \, \lambda \, d\lambda}{\int \mathcal{F}_*(\lambda) T_{inst}(\lambda) \, \lambda \, d\lambda}, \quad (1) $$

where $R_p$ and $R_*$ are the planet and star radii.

However, we note that the general analysis, results, and conclusions of the articles are not affected by this error. The omission of the $\lambda$ factors is only relevant for broad bands and when the emission spectra vary significantly over the bands. This means that in our analyses, only the CHEOPS (CHaracterising ExOPlanet Satellite, Benz et al. 2021) and TESS (Transiting Exoplanet Survey Satellite, Ricker et al. 2015) bands were significantly affected. The revised values, tables, and figures are given below.

## 1. WASP-12 b

In Akinsanmi et al. (2024), the atmospheric retrievals only included infrared eclipse observations as constraints (Sect. 5.2.1). Thus, the retrieval results were not affected in a statistically significant manner. We confirmed this by re-running the analysis with the corrected passband calculation.

The thermal contributions inferred from the retrieval to the eclipse depths in the CHEOPS and TESS passbands are revised from 205 ± 10 and 480 ± 19 ppm (Sect. 5.3) to 270 ± 11 and 511 ± 18 ppm, respectively. This led to updated geometric albedos, from $A_g = 0.083 \pm 0.015$ and $0.010 \pm 0.023$ to $A_g = 0.042 \pm 0.018$ and $-0.010 \pm 0.024$ in the CHEOPS and TESS bands, respectively. This correction does not alter our general conclusion that WASP-12 b has a low geometric albedo, which is consistent with the low reflectivity observed in other ultra-hot Jupiters.

## 2. WASP-76 b

Similarly to what was done for WASP-12 b, the atmospheric retrievals of WASP-76 b performed in Demangeon et al. (2024) only included the infrared eclipse observations as constraints (Sect. 5.1.1). The retrieval results were thus not affected in a statistically significant manner. The retrieval-inferred thermal eclipse depths over the CHEOPS and TESS bands have increased

<footnote>* Corresponding authors: Patricio.Cubillos@oeaw.ac.at; olivier.demangeon@astro.up.pt; Tunde.Akinsanmi@unige.ch</footnote>
<table><caption>**Table 1.** WASP-76b's $A_g$ estimates.</caption><thead><tr><th rowspan="2">Bandpass</th><th rowspan="2">Optical species</th><th colspan="3">Datasets</th></tr><tr><th>D1<sup>a</sup>: HST</th><th>D2<sup>b</sup>: HST + Spitzer</th><th>D3<sup>c</sup>: HST + Spitzer</th></tr></thead><tbody><tr><td rowspan="3">CHEOPS</td><td>With TiO/VO</td><td>&lt;0.107</td><td>0.079 ± 0.014</td><td>0.118 ± 0.014</td></tr><tr><td>Without TiO</td><td>0.072 ± 0.021</td><td>0.079 ± 0.014</td><td>0.119 ± 0.014</td></tr><tr><td>Without TiO/VO</td><td>0.073 ± 0.021</td><td>0.078 ± 0.013</td><td>0.119 ± 0.014</td></tr><tr><td rowspan="3">TESS</td><td>With TiO/VO</td><td>&lt;0.13</td><td>0.093 ± 0.017</td><td>0.172 ± 0.018</td></tr><tr><td>Without TiO</td><td>0.082 ± 0.033</td><td>0.093 ± 0.018</td><td>0.173 ± 0.019</td></tr><tr><td>Without TiO/VO</td><td>0.085 ± 0.032</td><td>0.092 ± 0.017</td><td>0.172 ± 0.018</td></tr></tbody></table>

**Notes.** Shown values and uncertainties correspond to the posterior distributions' median and 16th-to-84th percentile span, respectively. Upper limits correspond to the 99.7th percentile of the posterior distribution. (a) HST (Hubble Space Telescope) eclipse depths from Edwards et al. (2020). (b) HST eclipse depths from Edwards et al. (2020), Spitzer eclipse depths from Demangeon et al. (2024). (c) HST and Spitzer eclipse depths from Fu et al. (2021).

<figure><img src="image_2.png" /></figure>

**Fig. 1.** Corrected reproduction of the insets of Figs. 4 and C1 of Demangeon et al. (2024): WASP-76 b occultation atmospheric retrievals for a model including the TiO and VO optical absorbers (left panel), including only VO (middle), and excluding both TiO and VO (right). The light blue, dark blue, and orange curves and their associated shaded areas show the retrieved spectra and 68% credible intervals when fitting the D1, D2, and D3 occultation observations, respectively (see the legend and notes in Table 1). The grey markers show the CHEOPS and TESS occultation measurements, although the fits are not constrained by these observations. The coloured square markers show the corrected model eclipse-depths integrated over the CHEOPS and TESS bands (see the passband response functions in grey at the bottom of the panels).

from their original values. Figure 1 shows the corrected band-integrated eclipse depths inferred from each retrieval model (correction of the insets in Figs. 4 and C1 of Demangeon et al. 2024). Table 1 shows the corrected geometric albedos (correction of Table 3 of Demangeon et al. 2024). This correction (lower geometric albedo values) does not change the conclusions (Sect. 6.1 of Demangeon et al. 2024), that WASP-76b has a low geometric albedo, consistent with that of other ultra-hot Jupiters. Taking the different composition hypotheses and the different reductions of the infrared datasets into account, we can set a 1-sigma upper limit of 0.13 and 0.19 in the CHEOPS and TESS bandpasses, respectively (correction of the values provided in Table 6).

## References

Akinsanmi, B., Barros, S. C. C., Lendl, M., et al. 2024, A&A, 685, A63

Benz, W., Broeg, C., Fortier, A., et al. 2021, Exp. Ast., 51, 109

Demangeon, O. D. S., Cubillos, P. E., Singh, V., et al. 2024, A&A, 684, A27

Edwards, B., Changeat, Q., Baeyens, R., et al. 2020, AJ, 160, 8

Fu, G., Deming, D., Lothringer, J., et al. 2021, AJ, 162, 108

Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, J. Astron. Teles. Instrum. Syst., 1, 014003

<footnote n="1">1 Admatis, 5. Kandó Kálmán Street, 3534 Miskolc, Hungary</footnote>

<footnote n="2">2 Aix Marseille Univ, CNRS, CNES, LAM, 38 rue Frédéric Joliot-Curie, 13388 Marseille, France</footnote>

<footnote n="3">3 Astrobiology Research Unit, Université de Liège, Allée du 6 Août 19C, 4000 Liège, Belgium</footnote>

<footnote n="4">4 Astrophysics Group, Lennard Jones Building, Keele University, Staffordshire, ST5 5BG, UK</footnote>

<footnote n="5">5 CFisUC, Departamento de Física, Universidade de Coimbra, 3004-516 Coimbra, Portugal</footnote>
⁶ Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, UK

⁷ Center for Space and Habitability, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland

⁸ Centre Vie dans l'Univers, Faculté des sciences, Université de Genève, Quai Ernest-Ansermet 30, 1211 Genève 4, Switzerland

⁹ Centre for Exoplanet Science, SUPA School of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK

¹⁰ Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden

¹¹ Departamento de Astrofísica, Universidad de La Laguna, Astrofísico Francisco Sanchez s/n, 38206 La Laguna, Tenerife, Spain

¹² Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal

¹³ Department of Astronomy, Stockholm University, AlbaNova University Center, 10691 Stockholm, Sweden

¹⁴ Department of Astrophysics, University of Vienna, Türkenschanzstrasse 17, 1180 Vienna, Austria

¹⁵ Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK

¹⁶ Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden

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¹⁸ Dipartimento di Fisica e Astronomia "Galileo Galilei", Università degli Studi di Padova, Vicolo dell'Osservatorio 3, 35122 Padova, Italy

¹⁹ Dipartimento di Fisica, Università degli Studi di Torino, via Pietro Giuria 1, 10125 Torino, Italy

²⁰ ELTE Eötvös Loránd University, Gothard Astrophysical Observatory, 9700 Szombathely, Szent Imre h. u. 112, Hungary

²¹ ELTE Eötvös Loránd University, Institute of Physics, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary

²² ETH Zurich, Department of Physics, Wolfgang-Pauli-Strasse 2, 8093 Zurich, Switzerland

²³ European Space Agency (ESA), ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

²⁴ European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

²⁵ HUN-REN-ELTE Exoplanet Research Group, Szent Imre h. u. 112., Szombathely 9700, Hungary

²⁶ IMCCE, UMR8028 CNRS, Observatoire de Paris, PSL Univ., Sorbonne Univ., 77 av. Denfert-Rochereau, 75014 Paris, France

²⁷ INAF, Osservatorio Astrofisico di Catania, Via S. Sofia 78, 95123 Catania, Italy

²⁸ INAF, Osservatorio Astrofisico di Torino, Via Osservatorio, 20, 10025 Pino Torinese To, Italy

²⁹ INAF, Osservatorio Astronomico di Padova, Vicolo dell'Osservatorio 5, 35122 Padova, Italy

³⁰ Institut d'astrophysique de Paris, UMR7095 CNRS, Université Pierre & Marie Curie, 98bis blvd. Arago, 75014 Paris, France

³¹ Institut de Ciencies de l'Espai (ICE, CSIC), Campus UAB, Can Magrans s/n, 08193 Bellaterra, Spain

³² Institut d'Estudis Espacials de Catalunya (IEEC), Gran Capità 2-4, 08034 Barcelona, Spain

³³ Institut fuer Geologische Wissenschaften, Freie Universitaet Berlin, Maltheserstrasse 74-100,12249 Berlin, Germany

³⁴ Institute for Theoretical Physics and Computational Physics, Graz University of Technology, Petersgasse 16, 8010 Graz, Austria

³⁵ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK

³⁶ Institute of Optical Sensor Systems, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

³⁷ Institute of Space Research, German Aerospace Center (DLR), Rutherfordstrasse 2, 12489 Berlin, Germany

³⁸ Instituto de Astrofísica de Canarias, Via Lactea s/n, 38200 La Laguna, Tenerife, Spain

³⁹ Instituto de Astrofísica e Ciencias do Espaco, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal

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⁴¹ Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA Leiden, The Netherlands

⁴² Max Planck Institute for Extraterrestrial Physics, Gießenbachstraße, 85748 Garching, Germany

⁴³ Observatoire astronomique de l'Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland

⁴⁴ Physikalisches Institut, University of Bern, Gesellschaftsstrasse 6, 3012 Bern, Switzerland

⁴⁵ Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria

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