Brandt, G. M., Brandt, T. D., Dupuy, T. J., Michalik, D., & Marleau, G.-D., 2021, ApJ, 915, L16

Brown-Sevilla, S. B., Maire, A. L., Mollière, P., et al. 2023, A&A, 673, A98

Buchner, J., Georgakakis, A., Nandra, K., et al. 2014, A&A, 564, A125

Burgasser, A. J., Simcoe, R. A., Bochanski, J. J., et al. 2010, ApJ, 725, 1405

Burningham, B., Marley, M. S., Line, M. R., et al. 2017, MNRAS, 470, 1177

Burningham, B., Faherty, J. K., Gonzales, E. C., et al. 2021, MNRAS, 506, 1944

Burrows, A., & Sharp, C. M. 1999, ApJ, 512, 843

Burrows, A., Sudarsky, D., & Hubeny, I. 2006, ApJ, 640, 1063

Burrows, A., Heng, K., & Nampaisarn, T. 2011, ApJ, 736, 47

Calamari, E., Faherty, J. K., Visscher, C., et al. 2024, ApJ, 963, 67

Cameron, A. G. W. 1978, Moon Planets, 18, 5

Cannon, A. J., & Pickering, E. C. 1993, VizieR Online Data Catalog, III/135A

Cantalloube, F., Mouillet, D., Mugnier, L. M., et al. 2015, A&A, 582, A89

Chabrier, G., Baraffe, I., Allard, F., & Hauschildt, P. 2000, ApJ, 542, 464

Charnay, B., Bézard, B., Baudino, J.-L., et al. 2018, ApJ, 854, 172

Chen, K., Kama, M., Pinilla, P., & Keyte, L. 2024, MNRAS, 527, 2049

Chubb, K. L., Rocchetto, M., Al-Refaie, A. F., et al. 2020, A&A, 646, A21

Coles, P. A., Yurchenko, S. N., & Tennyson, J. 2019, MNRAS, 490, 4638

Contro, B., Wittenmyer, R. A., Horner, J., & Marshall, J. P. 2015, Origins of Life and Evolution of the Biosphere, 45, 41

Covarrubias, S., Blunt, S., & Wang, J. J. 2022, RNAAS, 6, 66

Cridland, A. J., Eistrup, C., & van Dishoeck, E. F. 2019, A&A, 627, A127

Cridland, A. J., van Dishoeck, E. F., Alessi, M., & Pudritz, R. E. 2020, A&A, 642, A229

Currie, T., Burrows, A., Itoh, Y., et al. 2011, ApJ, 729, 128

Currie, T., Fukagawa, M., Thalmann, C., Matsumura, S., & Plavchan, P. 2012, ApJ, 755, L34

Currie, T., Burrows, A., Girard, J. H., et al. 2014, ApJ, 795, 133

Cushing, M. C., Roellig, T. L., Marley, M. S., et al. 2006, ApJ, 648, 614

Cushing, M. C., Marley, M. S., Saumon, D., et al. 2008, ApJ, 678, 1372

Demars, D., Bonnefoy, M., Dougados, C., et al. 2023, A&A, 676, A123

Desgrange, C., Chauvin, G., Christiaens, V., et al. 2022, A&A, 664, A139

Dodson-Robinson, S. E., Veras, D., Ford, E. B., & Beichman, C. A. 2009, ApJ, 707, 79

Doelman, D. S., Stone, J. M., Briesemeister, Z. W., et al. 2022, AJ, 163, 217

Eddington, A. S. 1930, MNRAS, 90, 279

Eistrup, C., Walsh, C., & van Dishoeck, E. F. 2018, A&A, 613, A14

Esposito, S., Mesa, D., Skemer, A., et al. 2013, A&A, 549, A52

Faherty, J. K. 2018, in Handbook of Exoplanets, eds. H. J. Deeg & J. A. Belmonte (Cham: Springer), 188

Faramaz, V., Marino, S., Booth, M., et al. 2021, AJ, 161, 271

Fegley, B. J., & Lodders, K. 1996, ApJ, 472, L37

Feroz, F., & Hobson, M. P. 2008, MNRAS, 384, 449

Feroz, F., Hobson, M. P., Cameron, E., & Pettitt, A. N. 2019, Open J. Astrophys., 2, 10

Flasseur, O., Denis, L., Thiébaut, E., & Langlois, M. 2018, A&A, 618, A138

Flasseur, O., Denis, L., Thiébaut, É., & Langlois, M. 2020, A&A, 637, A9

Fonte, S., Turrini, D., Pacetti, E., et al. 2023, MNRAS, 520, 4683

Fortney, J. J., Ikoma, M., Nettelmann, N., Guillot, T., & Marley, M. S. 2011, ApJ, 729, 32

Fragoso, T. M., Bertoli, W., & Louzada, F. 2018, Int. Stat. Rev., 86, 1

Fukagawa, M., Itoh, Y.,amura, M., et al. 2009, ApJ, 696, L1

Gaia Collaboration 2020, VizieR Online Data Catalog I/350

Galicher, R., Marois, C., Macintosh, B., Barman, T., & Konopacky, Q. 2011, ApJ, 739, L41

Gehren, T. 1977, A&A, 59, 303

Geiler, F., Krivov, A. V., Booth, M., & Löhne, T. 2018, MNRAS, 483, 332

Giacobbe, P., Brogi, M., Gandhi, S., et al. 2021, Nature, 592, 205

Goździewski, K., & Migaszewski, C. 2018, ApJS, 238, 6

GRAVITY Collaboration (Abuter, R., et al.) 2017, A&A, 602, A94

GRAVITY Collaboration (Lacour, S., et al.) 2019, A&A, 623, A11

GRAVITY Collaboration (Nowak, M., et al.) 2020a, A&A, 633, A110

GRAVITY Collaboration (Bauböck, M., et al.) 2020b, A&A, 635, A143

Gray, R. O., & Kaye, A. B. 1999, AJ, 118, 2993

Gray, R. O., Corbally, C. J., Garrison, R. F., McFadden, M. T., & Robinson, P. E. 2003, AJ, 126, 2048

Greco, J. P., & Brandt, T. D. 2016, ApJ, 833, 134

Greenbaum, A. Z., Pueyo, L., Ruffio, J.-B., et al. 2018, AJ, 155, 226

Groff, T. D., Kasdin, N. J., Limbach, M. A., et al. 2015, in Techniques and Instrumentation for Detection of Exoplanets VII, 9605, ed. S. Shaklan (SPIE), 96051C

Groff, T., Chilcote, J., Brandt, T., et al. 2017, SPIE Conf. Ser., 10400, 1040016

Guillot, T. 2005, Annu. Rev. Earth Planet. Sci., 33, 493

Guillot, T. 2010, A&A, 520, A27

Hansen, J. E. 1971, J. Atmos. Sci., 28, 1400

Helled, R., & Bodenheimer, P. 2010, Icarus, 207, 503

Hoch, K. K. W., Konopacky, Q. M., Barman, T. S., et al. 2022, AJ, 164, 155

Hoch, K. K. W., Konopacky, Q. M., Theissen, C. A., et al. 2023, AJ, 166, 85

Ingraham, P., Marley, M. S., Saumon, D., et al. 2014, ApJ, 794, L15

Janson, M., Bergfors, C., Goto, M., Brandner, W., & Lafrenière, D. 2010, ApJ, 710, L35

Jullion, A., & Lambert, P. 2007, Computat. Stat. Data Anal., 51, 2542

Karalidi, T., Marley, M., Fortney, J. J., et al. 2021, ApJ, 923, 269

Kass, R. E., & Raftery, A. E. 1995, J. Am. Stat. Assoc., 90, 773

Kaye, A. B., Handler, G., Krisciunas, K., Poretti, E., & Zerbi, F. M. 1999, PASP, 111, 840

Kirkpatrick, J. D., Reid, I. N., Liebert, J., et al. 1999, ApJ, 519, 802

Kitzmann, D., Heng, K., Oreshenko, M., et al. 2020, ApJ, 890, 174

Konopacky, Q. M., Barman, T. S., Macintosh, B. A., & Marois, C. 2013, Science, 339, 1398

Lacour, S., Wang, J. J., Nowak, M., et al. 2020, SPIE Conf. Ser., 11446, 1144600

Lafrenière, D., Marois, C., Doyon, R., & Barman, T. 2009, ApJ, 694, L148

Lang, S., & Brezger, A. 2004, J. Comput. Graph. Stat., 13, 183

Lapeyrère, V., Kervella, P., Lacour, S., et al. 2014, SPIE Conf. Ser., 9146, 91462D

Larkin, J., Barczys, M., Krabbe, A., et al. 2006, SPIE Conf. Ser., 6269, 62691A

Laughlin, G., & Rozyczka, M. 1996, ApJ, 456, 279

Lavie, B., Mendonça, J. M., Mordasini, C., et al. 2017, AJ, 154, 91

Lee, J.-M., Heng, K., & Irwin, P. G. J. 2013, ApJ, 778, 97

Leggett, S. K., Saumon, D., Albert, L., et al. 2008, ApJ, 682, 1256

Linder, E. F., Mordasini, C., Mollière, P., et al. 2019, A&A, 623, A85

Line, M. R., Teske, J., Burningham, B., Fortney, J. J., & Marley, M. S. 2015, ApJ, 807, 183

Liu, P., Bohn, A. J., Doelman, D. S., et al. 2023, A&A, 674, A115

Lodders, K. 2003, ApJ, 591, 1220

Lodders, K., & Begley, B. 2002, Icarus, 155, 393

Lodders, K., Palme, H., & Gail, H. P. 2009, Landolt-Börnstein, 4B, 712

Looper, D. L., Kirkpatrick, J. D., Cutri, R. M., et al. 2008, ApJ, 686, 528

Luna, J. L., & Morley, C. V. 2021, ApJ, 920, 146

Macintosh, B., Graham, J. R., Ingraham, P., et al. 2014, PNAS, 111, 12661

Madhusudhan, N. 2019, ARA&A, 57, 617

Madhusudhan, N., & Seager, S. 2009, ApJ, 707, 24

Madhusudhan, N., Burrows, A., & Currie, T. 2011, ApJ, 737, 34

Madhusudhan, N., Sarkar, S., Constantinou, S., et al. 2023, ApJ, 956, L13

Maire, A. L., Skemer, A. J., Hinz, P. M., et al. 2015, A&A, 576, A133

Marleau, G.-D., Klahr, H., Kuiper, R., & Mordasini, C. 2017, ApJ, 836, 221

Marleau, G.-D., Mordasini, C., & Kuiper, R. 2019, ApJ, 881, 144

Marley, M. S., Fortney, J. J., Hubickyj, O., Bodenheimer, P., & Lissauer, J. J. 2007, ApJ, 655, 541

Marley, M. S., Saumon, D., & Goldblatt, C. 2010, ApJ, 723, L117

Marley, M. S., Saumon, D., Cushing, M., et al. 2012, ApJ, 754, 135

Marley, M. S., Saumon, D., Visscher, C., et al. 2021, ApJ, 920, 85

Marocco, F., Day-Jones, A. C., Lucas, P. W., et al. 2014, MNRAS, 439, 372

Marois, C., Macintosh, B., Barman, T., et al. 2008, Science, 322, 1348

Marois, C., Zuckerman, B., Konopacky, Q. M., Macintosh, B., & Barman, T. 2010, Nature, 468, 1080

Matthews, B., Kennedy, G., Sibthorpe, B., et al. 2014, ApJ, 780, 97

McCarthy, A. M., Muirhead, P. S., Tamburo, P., et al. 2024, ApJ, 965, 1

McKemmish, L. K., Yurchenko, S. N., & Tennyson, J. 2016, MNRAS, 463, 771

McKemmish, L. K., Masseron, T., Hoeijmakers, H. J., et al. 2019, MNRAS, 488, 2836

Metchev, S., Marois, C., & Zuckerman, B. 2009, ApJ, 705, L204

Miles, B. E., Biller, B. A., Patapis, P., et al. 2023, ApJ, 946, L6

Mollière, P., van Boekel, R., Dullemond, C., Henning, T., & Mordasini, C. 2015, ApJ, 813, 47

Mollière, P., van Boekel, R., Bouwman, J., et al. 2017, A&A, 600, A10

Mollière, P., Wardenier, J. P., van Boekel, R., et al. 2019, A&A, 627, A67

Mollière, P., Stolker, T., Lacour, S., et al. 2020, A&A, 640, A131

Mollière, P., Molyarova, T., Bitsch, B., et al. 2022, ApJ, 934, 74

Mordasini, C., Alibert, Y., Klahr, H., & Henning, T. 2012, A&A, 547, A111

Mordasini, C., Marleau, G.-D., & Mollière, P. 2017, A&A, 608, A72

Morley, C. V., Mukherjee, S., Marley, M. S., et al. 2024, ApJ, submitted [arXiv:2402.00758]

Moses, J. I., Madhusudhan, N., Visscher, C., & Freedman, R. S. 2013, ApJ, 763, 25

Moses, J. I., Marley, M. S., Zahnle, K., et al. 2016, ApJ, 829, 66

Moya, A., Amado, P. J., Barrado, D., et al. 2010a, MNRAS, 405, L81

Moya, A., Amado, P. J., Barrado, D., et al. 2010b, MNRAS, 406, 566

Nasedkin, E., Mollière, P., Wang, J., et al. 2023, A&A, 678, A41

Nasedkin, E., Mollière, P., & Blain, D. 2024, J. Open Source Softw., 9, 5875

Nero, D., & Bjorkman, J. E. 2009, ApJ, 702, L163

Nixon, M. C., Welbanks, L., McGill, P., & Kempton, E. M. R. 2023, ApJ, 966, 2

Nowak, M., Lacour, S., Lagrange, A. M., et al. 2020, A&A, 642, A2

Öberg, K. I., Murray-Clay, R., & Bergin, E. A. 2011, ApJ, 743, L16

Oppenheimer, B. R., Baranec, C., Beichman, C., et al. 2013, ApJ, 768, 24

Pacetti, E., Turrini, D., Schisano, E., et al. 2022, ApJ, 937, 36
Palma-Bifani, P., Chauvin, G., Bonnefoy, M., et al. 2023, A&A, 670, A90

Patapis, P., Nasedkin, E., Cugno, G., et al. 2022, A&A, 658, A72

Patience, J., King, R. R., De Rosa, R. J., et al. 2012, A&A, 540, A85

Perri, F., & Cameron, A. G. W. 1974, Icarus, 22, 416

Petit dit de la Roche, D. J. M., van den Ancker, M. E., Kissler-Patig, M., Ivanov, V. D., & Fedele, D. 2019, MNRAS, 491, 1795

Petrus, S., Bonnefoy, M., Chauvin, G., et al. 2021, A&A, 648, A59

Petrus, S., Chauvin, G., Bonnefoy, M., et al. 2023, A&A, 670, A9

Phillips, M. W., Tremblin, P., Baraffe, I., et al. 2020, A&A, 637, A38

Podolak, M. 2003, Icarus, 165, 428

Pollack, J. B., Hubickyj, O., Bodenheimer, P., et al. 1996, Icarus, 124, 62

Polyansky, O. L., Kyuberis, A. A., Zobov, N. F., et al. 2018, MNRAS, 480, 2597

Pueyo, L. 2016, ApJ, 824, 117

Radigan, J. 2014, ApJ, 797, 120

Radigan, J., Lafrenière, D., Jayawardhana, R., & Artigau, E. 2014, ApJ, 793, 75

Rahman, M. M. 2005, PhD thesis, University of British Columbia, Canada

Rajan, A., Barman, T., Soummer, R., et al. 2015, ApJ, 809, L33

Rhee, J. H., Song, I., Zuckerman, B., & McElwain, M. 2007, ApJ, 660, 1556

Rossow, W. B. 1978, Icarus, 36, 1

Rothman, L. S., Gordon, I. E., Barber, R. J., et al. 2010, J. Quant. Spec. Radiat. Transf., 111, 2139

Rowland, M. J., Morley, C. V., & Line, M. R. 2023, ApJ, 947, 6

Ruffio, J.-B., Macintosh, B., Konopacky, Q. M., et al. 2019, AJ, 158, 200

Ruffio, J.-B., Konopacky, Q. M., Barman, T., et al. 2021, AJ, 162, 290

Ruffio, J.-B., Perrin, M. D., Hoch, K. K. W., et al. 2023, AJ, submitted [arXiv:2310.09902]

Rustamkulov, Z., Sing, D. K., Mukherjee, S., et al. 2023, Nature, 614, 659

Sadakane, K. 2006, PASJ, 58, 1023

Samland, M., Mollière, P., Bonnefoy, M., et al. 2017, A&A, 603, A57

Saumon, D., & Marley, M. S. 2008, ApJ, 689, 1327

Schmidt, T. O. B., Neuhäuser, R., Seifahrt, A., et al. 2008, A&A, 491, 311

Schneider, A. D., & Bitsch, B. 2021a, A&A, 654, A71

Schneider, A. D., & Bitsch, B. 2021b, A&A, 654, A72

Sepulveda, A. G., & Bowler, B. P. 2022, AJ, 163, 52

Sepulveda, A. G., Huber, D., Li, G., et al. 2023, RNAAS, 7, 2

Showman, A. P., & Kaspi, Y. 2013, ApJ, 776, 85

Skemer, A. J., Hinz, P. M., Esposito, S., et al. 2012, ApJ, 753, 14

Skemer, A. J., Marley, M. S., Hinz, P. M., et al. 2014, ApJ, 792, 17

Skemer, A. J., Hinz, P., Montoya, M., et al. 2015, SPIE Conf. Ser., 9605, 96051D

Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163

Soni, V., & Acharyya, K. 2023, ApJ, 946, 29

Soummer, R., Hagan, J. B., Pueyo, L., et al. 2011, ApJ, 741, 55

Soummer, R., Pueyo, L., & Larkin, J. 2012, ApJ, 755, L28

Sousa-Silva, C., Al-Refaie, A. F., Tennyson, J., & Yurchenko, S. N. 2015, MNRAS, 446, 2337

Stephens, D. C., Leggett, S. K., Cushing, M. C., et al. 2009, ApJ, 702, 154

Stolker, T., Bonse, M. J., Quanz, S. P., et al. 2019, A&A, 621, A59

Stolker, T., Quanz, S. P., Todorov, K. O., et al. 2020, A&A, 635, A182

Su, K. Y. L., Rieke, G. H., Stapfelfeldt, K. R., et al. 2009, ApJ, 705, 314

Suárez, G., & Metchev, S. 2022, MNRAS, 513, 5701

Suárez, G., & Metchev, S. 2023, MNRAS, 523, 4739

Suárez, G., Metchev, S., Leggett, S. K., Saumon, D., & Marley, M. S. 2021, ApJ, 920, 99

Suárez, G., Vos, J. M., Metchev, S., Faherty, J. K., & Cruz, K. 2023, ApJ, 954, L6

Szulágyi, J., & Mordasini, C. 2017, MNRAS, 465, L64

Tan, X., & Showman, A. P. 2021a, MNRAS, 502, 678

Tan, X., & Showman, A. P. 2021b, MNRAS, 502, 2198

Tennyson, J., & Yurchenko, S. N. 2012, MNRAS, 425, 21

Thompson, W., Marois, C., Do Ó, C. R., et al. 2023, AJ, 165, 29

Thorngren, D., & Fortney, J. J. 2019, ApJ, 874, L31

Thorngren, D. P., Fortney, J. J., Murray-Clay, R. A., & Lopez, E. D. 2016, ApJ, 831, 64

Tremblin, P., Amundsen, D. S., Mourier, P., et al. 2015, ApJ, 804, L17

Tremblin, P., Amundsen, D. S., Chabrier, G., et al. 2016, ApJ, 817, L19

Tremblin, P., Chabrier, G., Baraffe, I., et al. 2017, ApJ, 850, 46

Tremblin, P., Padioleau, T., Phillips, M. W., et al. 2019, ApJ, 876, 144

Turrini, D., Schisano, E., Fonte, S., et al. 2021, ApJ, 909, 40

Vos, J. M., Biller, B. A., Bonavita, M., et al. 2019, MNRAS, 483, 480

Vos, J. M., Burningham, B., Faherty, J. K., et al. 2023, ApJ, 944, 138

Wahhaj, Z., Milli, J., Romero, C., et al. 2021, A&A, 648, A26

Waldmann, I. P., Rocchetto, M., Tinetti, G., et al. 2015, ApJ, 813, 13

Wang, J. 2023, AAS J., submitted [arXiv:2310.00088]

Wang, J., Mawet, D., Fortney, J. J., et al. 2018a, AJ, 156, 272

Wang, J. J., Graham, J. R., Dawson, R., et al. 2018b, AJ, 156, 192

Wang, J. J., Ginzburg, S., Ren, B., et al. 2020a, AJ, 159, 263

Wang, J., Wang, J. J., Ma, B., et al. 2020b, AJ, 160, 150

Wang, J. J., Vigan, A., Lacour, S., et al. 2021a, AJ, 161, 148

Wang, J. J., Ruffio, J.-B., Morris, E., et al. 2021b, AJ, 162, 148

Wang, J. J., Gao, P., Chilcote, J., et al. 2022, AJ, 164, 143

Wang, J., Wang, J. J., Ruffio, J.-B., et al. 2023, AJ, 165, 4

Wende, S., Reiners, A., Seifahrt, A., & Bernath, P. F. 2010, A&A, 523, A58

Whiteford, N., Glasse, A., Chubb, K. L., et al. 2023, MNRAS, 525,1,1375

Wilcomb, K. K., Konopacky, Q. M., Barman, T. S., et al. 2020, AJ, 160, 207

Wilner, D. J., MacGregor, M. A., Andrews, S. M., et al. 2018, ApJ, 855, 56

Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868

Yurchenko, S. N., Amundsen, D. S., Tennyson, J., & Waldmann, I. P. 2017, A&A, 605, A95

Yurchenko, S. N., Mellor, T. M., Freedman, R. S., & Tennyson, J. 2020, MNRAS, 496, 5282

Zahnle, K. J., & Marley, M. S. 2014, ApJ, 797, 41

Zerbi, F. M., Rodríguez, E., Garrido, R., et al. 1999, MNRAS, 303, 275

Zhang, Y., Snellen, I. A. G., Bohn, A. J., et al. 2021, Nature, 595, 370

Zhang, Z., Mollière, P., Hawkins, K., et al. 2023, AJ, 166, 198

Zuckerman, B., & Song, I. 2004, ARA&A, 42, 685

Zuckerman, B., Rhee, J. H., Song, I., & Bessell, M. S. 2011, ApJ, 732, 61

Zurlo, A., Vigan, A., Galicher, R., et al. 2016, A&A, 587, A57

Zurlo, A., Goździewski, K., Lazzoni, C., et al. 2022, A&A, 666, A133

¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: nasedkin@mpia.de

² LESIA, Observatoire de Paris, PSL, CNRS, Sorbonne Université, Université de Paris, 5 place Janssen, 92195 Meudon, France

³ European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany

⁴ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

⁵ Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands

⁶ Center for Interdisciplinary Exploration and Research in Astro-
physics (CIERA) and Department of Physics and Astronomy,
Northwestern University, Evanston, IL 60208, USA

⁷ Department of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA

⁸ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

⁹ Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße 1, 85748 Garching, Germany

¹⁰ Universidade de Lisboa – Faculdade de Ciências, Campo Grande, 1749-016 Lisboa, Portugal

¹¹ CENTRA – Centro de Astrofísica e Gravitação, IST, Universidade de Lisboa, 1049-001 Lisboa, Portugal

¹² Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France

¹³ Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France

¹⁴ Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, France

¹⁵ STAR Institute, Université de Liège, Allée du Six Août 19c, 4000 Liège, Belgium

¹⁶ Department of Astrophysical & Planetary Sciences, JILA, Duane Physics Bldg., 2000 Colorado Ave, University of Colorado, Boulder, CO 80309, USA

¹⁷ Institute of Physics, University of Cologne, Zülpicher Straße 77, 50937 Cologne, Germany

¹⁸ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany

¹⁹ Universidade do Porto, Faculdade de Engenharia, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

²⁰ School of Physics, University College Dublin, Belfield, Dublin 4, Ireland

²¹ Departments of Physics and Astronomy, Le Conte Hall, University of California, Berkeley, CA 94720, USA

²² European Southern Observatory, Casilla 19001, Santiago 19, Chile

²³ Advanced Concepts Team, European Space Agency, TEC-SF, ESTEC, Keplerlaan 1, NL-2201, AZ Noordwijk, The Netherlands
24 Department of Astronomy and Steward Observatory, University of Arizona, Tucson, AZ, USA

25 University of Exeter, Physics Building, Stocker Road, Exeter EX4 4QL, United Kingdom

26 Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany

27 Institut für Astronomie und Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

28 Physikalisches Institut, Universität Bern, Gesellschaftsstr. 6, 3012 Bern, Switzerland

29 Astronomy Department, University of Michigan, Ann Arbor, MI 48109, USA

30 Academia Sinica, Institute of Astronomy and Astrophysics, 11F Astronomy-Mathematics Building, NTU/AS campus, No. 1, Section 4, Roosevelt Rd., Taipei 10617, Taiwan

31 European Space Agency, ESA Office, Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA

32 Department of Astronomy & Astrophysics, University of California, San Diego, La Jolla, CA 92093, USA

33 Department of Earth & Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218, USA

34 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany

35 Excellence Cluster ORIGINS, Boltzmannstraße 2, 85748 Garching bei München, Germany
## Appendix A: Data logs

<table><caption>**Table A.1.** Near infrared stellar Photometry of HR8799, using apparent flux normalised to 10 pc, retrieved from the Spanish Virtual Observatory (Bayo et al. 2008).</caption><thead><tr><th>Filter</th><th>λ<br>[µm]</th><th>Flux<br>[erg/s/cm²/Å]</th><th>Ref.</th></tr></thead><tbody><tr><td>2MASS J</td><td>1.235</td><td>2.198 ± 0.055 × 10<sup>-12</sup></td><td>S06</td></tr><tr><td>2MASS H</td><td>1.662</td><td>8.754 ± 0.145 × 10<sup>-13</sup></td><td>S06</td></tr><tr><td>2MASS Ks</td><td>2.159</td><td>3.433 ± 0.057 × 10<sup>-13</sup></td><td>S06</td></tr><tr><td>WISE W1</td><td>3.353</td><td>6.840 ± 1.367 × 10<sup>-14</sup></td><td>W10</td></tr><tr><td>WISE W2</td><td>4.603</td><td>2.316 ± 0.166 × 10<sup>-14</sup></td><td>W10</td></tr></tbody></table>

**Notes**

References: S06 Skrutskie et al. (2006); W10 Wright et al. (2010);

<table><caption>**Table A.2.** Photometric data for HR 8799 bcde.</caption><thead><tr><th>Instrument/Filter</th><th>m</th><th>Ref.</th></tr></thead><tbody><tr><td colspan="3">HR 8799 b</td></tr><tr><td>Keck/NIRC2.H</td><td>18.05 ± 0.09</td><td>C12</td></tr><tr><td>Keck/NIRC2.Ks</td><td>17.03 ± 0.08</td><td>M10</td></tr><tr><td>Keck/NIRC2.Ms</td><td>16.05 ± 0.3</td><td>G11</td></tr><tr><td>Paranal/NACO.Lp</td><td>15.52 ± 0.1</td><td>C14</td></tr><tr><td>Paranal/NACO.NB405</td><td>14.82 ± 0.18</td><td>C14</td></tr><tr><td>Paranal/SPHERE/IRDIS.B_J</td><td>19.78 ± 0.09</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_2</td><td>18.08 ± 0.14</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_3</td><td>17.78 ± 0.1</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_1</td><td>17.15 ± 0.06</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_2</td><td>16.97 ± 0.09</td><td>Z16</td></tr><tr><td>Subaru/CIAO.z</td><td>21.22 ± 0.29</td><td>C11</td></tr><tr><td>JWST/MIRI.F1065C</td><td>13.54 ± 0.04</td><td>B23</td></tr><tr><td>JWST/MIRI.F1140C</td><td>13.64 ± 0.07</td><td>B23</td></tr><tr><td>JWST/MIRI.F1550C</td><td>13.49 ± 0.25</td><td>B23</td></tr><tr><td colspan="3">HR 8799 c</td></tr><tr><td>Keck/NIRC2.H</td><td>17.06 ± 0.13</td><td>C12</td></tr><tr><td>Keck/NIRC2.Ks</td><td>16.11 ± 0.08</td><td>M10</td></tr><tr><td>Keck/NIRC2.Ms</td><td>15.03 ± 0.14</td><td>G11</td></tr><tr><td>Paranal/NACO.Lp</td><td>14.65 ± 0.11</td><td>C14</td></tr><tr><td>Paranal/NACO.NB405</td><td>13.97 ± 0.11</td><td>C14</td></tr><tr><td>Paranal/SPHERE/IRDIS.B_J</td><td>18.6 ± 0.13</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_2</td><td>17.09 ± 0.12</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_3</td><td>16.78 ± 0.1</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_1</td><td>16.19 ± 0.05</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_2</td><td>15.86 ± 0.07</td><td>Z16</td></tr><tr><td>JWST/MIRI.F1065C</td><td>12.97 ± 0.18</td><td>B23</td></tr><tr><td>JWST/MIRI.F1140C</td><td>13.59 ± 0.26</td><td>B23</td></tr><tr><td>JWST/MIRI.F1550C</td><td>11.88 ± 0.23</td><td>B23</td></tr><tr><td colspan="3">HR 8799 d</td></tr><tr><td>Keck/NIRC2.H</td><td>16.71 ± 0.24</td><td>C12</td></tr><tr><td>Keck/NIRC2.Ks</td><td>16.09 ± 0.12</td><td>M10</td></tr><tr><td>Keck/NIRC2.Ms</td><td>14.65 ± 0.35</td><td>G11</td></tr><tr><td>Paranal/NACO.Lp</td><td>14.55 ± 0.14</td><td>C14</td></tr><tr><td>Paranal/NACO.NB405</td><td>13.87 ± 0.15</td><td>C14</td></tr><tr><td>Paranal/SPHERE/IRDIS.B_J</td><td>18.59 ± 0.37</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_2</td><td>17.02 ± 0.17</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_3</td><td>16.85 ± 0.16</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_1</td><td>16.2 ± 0.07</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_2</td><td>15.84 ± 0.1</td><td>Z16</td></tr><tr><td>JWST/MIRI.F1065C</td><td>12.98 ± 0.14</td><td>B23</td></tr><tr><td>JWST/MIRI.F1140C</td><td>12.98 ± 0.17</td><td>B23</td></tr><tr><td>JWST/MIRI.F1550C</td><td>11.88 ± 0.23</td><td>B23</td></tr><tr><td colspan="3">HR 8799 e</td></tr><tr><td>Keck/NIRC2.Ks</td><td>15.91 ± 0.22</td><td>C12</td></tr><tr><td>Keck/NACO.Lp</td><td>14.49 ± 0.21</td><td>M10</td></tr><tr><td>Keck/NACO.NB405</td><td>13.72 ± 0.2</td><td>C14</td></tr><tr><td>Paranal/SPHERE/IRDIS.B_J</td><td>18.4 ± 0.21</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_2</td><td>16.91 ± 0.2</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_H23_3</td><td>16.68 ± 0.21</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_1</td><td>16.12 ± 0.1</td><td>Z16</td></tr><tr><td>Paranal/SPHERE/IRDIS.D_K12_2</td><td>15.82 ± 0.11</td><td>Z16</td></tr><tr><td>JWST/MIRI.F1065C</td><td>12.52 ± 0.26</td><td>B23</td></tr><tr><td>JWST/MIRI.F1140C</td><td>12.52 ± 0.23</td><td>B23</td></tr><tr><td>JWST/MIRI.F1550C</td><td>11.01 ± 0.42</td><td>B23</td></tr></tbody></table>

**Notes:**

References: C12 Currie et al. (2012); M10 Marois et al. (2010); G11 Galicher et al. (2011); C14 Currie et al. (2014); Z16 Zurlo et al. (2016); C11 Currie et al. (2011); B23 Boccaletti et al. (2024).
<table><caption>**Table A.3.** Spectroscopic Observation Log.</caption><thead><tr><th>Planet</th><th>Instrument</th><th>Date</th><th>λ</th><th>λ/Δλ<br>[µm]</th><th>ΔPA<br>[°]</th><th>Seeing<br>[as], Med.</th><th>Airmass<br>Min.</th><th>DIT<br>[s]</th><th>NEXP</th><th>Ref.</th></tr></thead><tbody><tr><td rowspan="7">b</td><td>GRAVITY</td><td>2019-11-11</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.98</td><td>1.54</td><td>8x100</td><td>3</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-26</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.88</td><td>1.48</td><td>8x100</td><td>3</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-27</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.86</td><td>1.45</td><td>8x100</td><td>2</td><td>...</td></tr><tr><td>OSIRIS</td><td>2009-07-22</td><td>2.0–2.4</td><td>60</td><td>...</td><td>...</td><td>1.0</td><td>900</td><td>30</td><td>B11</td></tr><tr><td>OSIRIS</td><td>2009-07-23</td><td>1.5–1.8</td><td>60</td><td>...</td><td>...</td><td>1.0</td><td>900</td><td>30</td><td>B11</td></tr><tr><td>OSIRIS</td><td>2009-07-30</td><td>1.5–1.8</td><td>60</td><td>...</td><td>...</td><td>1.0</td><td>900</td><td>30</td><td>B11</td></tr><tr><td>OSIRIS</td><td>2010-07-11</td><td>2.0–2.4</td><td>60</td><td>...</td><td>...</td><td>1.0</td><td>900</td><td>30</td><td>B11</td></tr><tr><td></td><td>OSIRIS</td><td>2010-07-13</td><td>1.5–1.8</td><td>60</td><td>...</td><td>...</td><td>1.0</td><td>900</td><td>30</td><td>B11</td></tr><tr><td rowspan="10">c</td><td>GRAVITY</td><td>2019-11-11</td><td>2.0–2.4</td><td>500</td><td>...</td><td>1.01</td><td>1.62</td><td>8x100</td><td>3</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-26</td><td>2.0–2.4</td><td>500</td><td>...</td><td>1.04</td><td>1.50</td><td>8x100</td><td>3</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-27</td><td>2.0–2.4</td><td>500</td><td>...</td><td>1.00</td><td>1.45</td><td>8x100</td><td>2</td><td>...</td></tr><tr><td>GRAVITY</td><td>2022-08-19</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.64</td><td>1.54</td><td>4x100</td><td>10</td><td>...</td></tr><tr><td>GRAVITY</td><td>2023-07-02</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.75</td><td>1.45</td><td>4x100</td><td>6</td><td>...</td></tr><tr><td>SPHERE</td><td>2015-07-04</td><td>0.9–1.6</td><td>30</td><td>16.4</td><td>1.43</td><td>1.44</td><td>...</td><td>46</td><td>F20</td></tr><tr><td>CHARIS</td><td>2018-09-01</td><td>1.2–2.4</td><td>19</td><td>202.24</td><td>0.47</td><td>1.0</td><td>20</td><td>1201</td><td>W22</td></tr><tr><td>CHARIS</td><td>2018-09-02</td><td>1.2–2.4</td><td>19</td><td>206.55</td><td>0.42</td><td>1.0</td><td>20</td><td>1253</td><td>W22</td></tr><tr><td>GPI</td><td>2016-09-19</td><td>1.5–1.8</td><td>45</td><td>20.93</td><td>0.97</td><td>1.61</td><td>60</td><td>60</td><td>G18</td></tr><tr><td>ALES</td><td>2019-09-18</td><td>2.8–4.2</td><td>35</td><td>85.64</td><td>0.8–1.1</td><td>1.02</td><td>3.934</td><td>1300</td><td>D22</td></tr><tr><td>OSIRIS</td><td>2010-2011</td><td>1.97–2.38</td><td>4000</td><td>...</td><td>...</td><td>...</td><td>600</td><td>33</td><td>K13</td></tr><tr><td rowspan="10">d</td><td>GRAVITY</td><td>2019-11-09</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.85</td><td>1.63</td><td>8x60</td><td>4</td><td>...</td></tr><tr><td>GRAVITY</td><td>2019-11-11</td><td>2.0–2.4</td><td>500</td><td>...</td><td>1.14</td><td>1.70</td><td>8x100</td><td>3</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-26</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.96</td><td>1.54</td><td>8x100</td><td>3</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-27</td><td>2.0–2.4</td><td>500</td><td>...</td><td>1.18</td><td>1.48</td><td>8x100</td><td>2</td><td>...</td></tr><tr><td>GRAVITY</td><td>2022-09-15</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.67</td><td>1.54</td><td>4x100</td><td>12</td><td>...</td></tr><tr><td>SPHERE</td><td>2014-08-12</td><td>0.9–1.6</td><td>30</td><td>29.65</td><td>0.87</td><td>1.43</td><td>100</td><td>32</td><td>Z16</td></tr><tr><td>SPHERE</td><td>2014-08-12</td><td>0.9–1.6</td><td>30</td><td>15.37</td><td>0.87</td><td>1.43</td><td>60</td><td>48</td><td>Z16</td></tr><tr><td>CHARIS</td><td>2018-09-01</td><td>1.2–2.4</td><td>19</td><td>202.24</td><td>0.47</td><td>1.0</td><td>20</td><td>1201</td><td>W22</td></tr><tr><td>CHARIS</td><td>2018-09-02</td><td>1.2–2.4</td><td>19</td><td>206.55</td><td>0.42</td><td>1.0</td><td>20</td><td>1253</td><td>W22</td></tr><tr><td>GPI</td><td>2016-09-19</td><td>1.5–1.8</td><td>45</td><td>20.93</td><td>0.97</td><td>1.61</td><td>60</td><td>60</td><td>G18</td></tr><tr><td>ALES</td><td>2019-09-18</td><td>2.8–4.2</td><td>35</td><td>85.64</td><td>0.8–1.1</td><td>1.02</td><td>3.934</td><td>1300</td><td>D22</td></tr><tr><td rowspan="10">e</td><td>GRAVITY</td><td>2018-08-28</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.67</td><td>1.44</td><td>10x100</td><td>7</td><td>G19</td></tr><tr><td>GRAVITY</td><td>2019-11-09</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.84</td><td>1.55</td><td>8x60</td><td>3</td><td>M20</td></tr><tr><td>GRAVITY</td><td>2019-11-11</td><td>2.0–2.4</td><td>500</td><td>...</td><td>1.15</td><td>1.47</td><td>8x100</td><td>3</td><td>M20</td></tr><tr><td>GRAVITY</td><td>2021-08-26</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.66</td><td>1.50</td><td>8x100</td><td>2</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-08-27</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.67</td><td>1.47</td><td>8x100</td><td>2</td><td>...</td></tr><tr><td>GRAVITY</td><td>2021-09-27</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.82</td><td>1.55</td><td>4x100</td><td>6</td><td>...</td></tr><tr><td>GRAVITY</td><td>2023-07-02</td><td>2.0–2.4</td><td>500</td><td>...</td><td>0.75</td><td>1.46</td><td>4x100</td><td>6</td><td>...</td></tr><tr><td>SPHERE</td><td>2014-08-12</td><td>0.9–1.6</td><td>30</td><td>29.65</td><td>0.87</td><td>1.43</td><td>100</td><td>32</td><td>Z16</td></tr><tr><td>SPHERE</td><td>2014-08-12</td><td>0.9–1.6</td><td>45</td><td>15.37</td><td>0.87</td><td>1.43</td><td>60</td><td>48</td><td>Z16</td></tr><tr><td>CHARIS</td><td>2018-09-01</td><td>1.2–2.4</td><td>19</td><td>202.24</td><td>0.47</td><td>1.0</td><td>20</td><td>1201</td><td>W22</td></tr><tr><td>CHARIS</td><td>2018-09-02</td><td>1.2–2.4</td><td>19</td><td>206.55</td><td>0.42</td><td>1.0</td><td>20</td><td>1253</td><td>W22</td></tr><tr><td>GPI</td><td>2016-09-19</td><td>1.5–1.8</td><td>45</td><td>20.93</td><td>0.97</td><td>1.61</td><td>60</td><td>60</td><td>G18</td></tr><tr><td>ALES</td><td>2019-09-18</td><td>2.8–4.2</td><td>35</td><td>85.64</td><td>0.8–1.1</td><td>1.02</td><td>3.934</td><td>1300</td><td>D22</td></tr></tbody></table>

**Notes**

References: B11: Barman et al. (2011); K13: Konopacky et al. (2013); Z16: Zurlo et al. (2016); G18: Greenbaum et al. (2018); G19: GRAVITY Collaboration (2019); F20: Flasseur et al. (2020); M20: Mollière et al. (2020); Wang et al. (2022); D22: Doelman et al. (2022).
## Appendix B: Reprocessing SPHERE and GPI datasets

To resolve the known discrepancies in the H-band flux between the archival SPHERE and GPI datasets, we reprocessed each using KLIP (Soummer et al. 2012; Pueyo 2016), ANDROMEDA (Cantalloube et al. 2015) and PynPoint (Amara & Quanz 2012; Stolker et al. 2019). We optimised the choice of algorithm parameters through a series of injection/extraction tests into each dataset, as in Nasedkin et al. (2023). Using two different goodness-of-fit metrics on injections representative of the true companion contrast and separation, we choose the number of principal components used in the PSF subtraction in order to extract the companion spectra with minimal bias. Figures B.1 and B.2 shows the extracted spectra for each of HR 8799 c, d, and e, for SPHERE and GPI respectively, compared to published literature spectra from Zurlo et al. (2016), Greenbaum et al. (2018), and Flasseur et al. (2018). As the goodness-of-fit metrics favoured the KLIP extractions, we used these as the basis of our retrieval analysis.

<figure><img src="image_22.png" /><figcaption>**Fig. B.1.** KLIP and ANDROMEDA extractions from SPHERE for HR 8799 c, d, and e compared to the spectra published in Zurlo et al. (2016) and Flasseur et al. (2018).</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>**Fig. B.2.** KLIP and ANDROMEDA extractions from GPI for HR 8799 c, d, and e compared to the spectra published in Greenbaum et al. (2018).</figcaption></figure>

## Appendix C: Retrieval validation

Extensive validation of the pRT retrieval module was performed as part of this work. Following updates described in Nasedkin et al. (2024), we verified that the results of Mollière et al. (2020) could be reproduced. We independently tested updates to the c-k mixing implementation, the adaptive mesh refinement implementation, updated opacity sources for H₂O and CO, bug fixes for convergence on multiple scattering in the clouds, the inclusion of photometric data, the inclusion of scaling factors on the SPHERE and GPI datasets, including or excluding the GPI K-band spectra, updates to each of the SPHERE, GPI, and GRAVITY datasets, different prior widths and the number of live points used in the retrieval. All of the posterior distributions were fully consistent to within $2\sigma$ with most falling well within $1\sigma$ of the published results, apart from the inclusion of new epochs of GRAVITY data, which led to a significantly higher retrieved metallicity ($[M/H]=1.1 \pm 0.32$) and an $f_{\text{sed}}$ of $5 \pm 2.6$.

We verified several model assumptions through retrievals that only include the GRAVITY datasets, or the GRAVITY data and photometry. We find that the GRAVITY data alone could not distinguish between clear and cloudy models ($\Delta \log_{10} Z < 1$), while cloudy models were strongly favoured once the broad wavelength coverage of the photometry was included ($\Delta \log_{10} Z > 10$).

Models that use the dynamical mass estimates as priors for calculating the surface gravity were marginally favoured over those that freely retrieve $\log g$ and $R_{\text{pl}}$, but that the posteriors parameter distributions were generally consistent, with $T_{\text{int}}$ and $R_{\text{pl}}$ showing the greatest discrepancy. Using the dynamical mass as a prior and setting a Gaussian prior on the radius led to more reasonable estimates of the radius of HR 8799 e ($0.97 \pm 0.04$) compared to the free retrieval ($0.79 \pm 0.05$). However, the composition of the planet and the degree of cloudiness did not vary significantly between the two models.

Using the full dataset for HR 8799 b, we verified that retrievals including scattering clouds are strongly favoured over those without scattering ($\Delta \log_{10} Z > 10$). Without scattering, both the temperature and composition ([M/H] and C/O) are significantly discrepant from retrievals that include scattering clouds.
<figure><img src="image_24.png" /></figure>

**Fig. C.1.** Comparison of best-fit disequilibrium models to OSIRIS data from Ruffio et al. (2021). From top to bottom is HR 8799 b, c, and d. In blue are the best-fit disequilibrium models, with the spectra generated using high-resolution line-by-line opacities, before being convolved, binned, and normalised for comparison. In orange is the same, but with the metallicity set to 0.

<figure><img src="image_25.png" /></figure>

**Fig. C.2.** Comparison of best-fit disequilibrium models (black) of HR 8799 c to the data, with residuals shown in the bottom panel. In blue are the same spectra, but without opacity contributions from CH<sub>4</sub>.

<figure><img src="image_26.png" /></figure>

**Fig. C.3.** Comparison of best-fit disequilibrium models (black) of HR 8799 c to the data, with residuals shown in the bottom panel. In blue are the same spectra, but without opacity contributions from HCN.
## Appendix D: Using the Hansen distribution with EDDYSED

The EDDYSED cloud model from Ackerman & Marley (2001) is implemented in pRT, and is the most physically motivated model incorporated to date. Typically, it assumes a log-normal particle size distribution, where the geometric particle radius will vary throughout the atmosphere as a function of the vertical diffusion coefficient $K_{zz}$ and the sedimentation fraction $f_{sed}$. Here, we substitute the log-normal particle size distribution with the Hansen distribution, originally introduced in Hansen (1971), and rederive the calculation for the particle radius as a function of $K_{zz}$ and $f_{sed}$.

We begin with a review of the EDDYSED model: the distribution of the number of particles as a function of particle radius, $n(r)$ is approximated as a log-normal distribution with width $\sigma_g$ and characteristic geometric radius $r_g$.

$$n(r) = \frac{N}{r\sqrt{2\pi}\log\sigma_g} \exp\left(-\frac{\log^2(r/r_g)}{2\log^2\sigma_g}\right), \qquad (D.1)$$

$N$ is the total number of cloud particles.

The goal of the EDDYSED model is to calculate $r_g$ for each layer in the atmosphere, given $K_{zz}$ and $f_{sed}$. It balances the upwards vertical mixing, parameterised by $K_{zz}$ and the particle settling velocity, $v_f$.

$$v_f = w_* \left(\frac{r}{r_w}\right)^\alpha. \qquad (D.2)$$

Here $w_*$ is the convective velocity scale. We note that $r_w \neq r_g$. $r_w$ is the radius at which the particle settling velocity equals the convective velocity scale:

$$w_* = \frac{K_{zz}}{L}, \qquad (D.3)$$

where $L$ is the convective mixing length. Since $w_*$ is known, and $v_f$ can be found analytically as in Ackerman & Marley (2001); Podolak (2003), a linear fit can be used to find both $\alpha$ and $r_w$.

With both of these quantities known, we follow AM01 and define $f_{sed}$ as:

$$f_{sed} = \frac{\int_{0}^{\infty} r^{3+\alpha} n(r) dr}{r_w^{\alpha} \int_{0}^{\infty} r^3 n(r) dr} \qquad (D.4)$$

For the log-normal distribution, one finds:

$$\int_{0}^{\infty} r^{\beta} n(r) dr = N r_g^{\beta} \exp\left(\frac{1}{2}\beta^2 \log^2 \sigma_g\right) \qquad (D.5)$$

Which we can then use to solve for $r_g$:

$$r_g = r_w f_{sed}^{1/\alpha} \exp\left(-\frac{\alpha + 6}{2} \log^2 \sigma_g\right) \qquad (D.6)$$

In order to use the Hansen distribution, we must recalculate the total number of particles $N$, and integrate the distribution for $f_{sed}$. We note here that the Hansen distribution is parameterised by the effective radius, $\bar{r}$, rather than the geometric mean radius. In this derivation we do not correct for this difference in definition, as both act as nuisance parameters in the context of an atmospheric retrieval.

We start by giving the Hansen distribution in full:

$$n_{\text{Hansen}}(r) = \frac{N (\bar{r} v_e)^{(2v_e - 1)/v_e}}{\Gamma[(1 - 2v_e)/v_e]} r^{(1 - 3v_e)/v_e} \exp\left(-\frac{r}{\bar{r} v_e}\right) \qquad (D.7)$$

In Hansen (1971), the authors use the parameters $\alpha$ and $b$ to denote the mean effective radius and effective variance, which we write as $\bar{r}$ and $v_e$ respectively. These differ from the simple mean radius and variance by weighting them by the particle area, as the cloud particle scatters an amount of light proportional to its area. Thus:

$$\bar{r} = \frac{\int_{0}^{\infty} r \pi r^2 n(r) dr}{\int_{0}^{\infty} \pi r^2 n(r) dr} \qquad (D.8)$$

and

$$v_e = \frac{\int_{0}^{\infty} (r - \bar{r})^2 r^2 n(r) dr}{\bar{r}^2 \int_{0}^{\infty} \pi r^2 n(r) dr} \qquad (D.9)$$

As in EDDYSED, we fit for the settling velocity, which will provide us with $\alpha$ and $r_w$, which we can use to find $f_{sed}$, as in D.4. However, we must now integrate the Hansen distribution. We find that:

$$\int_{0}^{\infty} r^{\beta} n_{\text{Hansen}}(r) dr = \frac{v_e^{\beta} (v_e \beta + 2v_e + 1) \left(\frac{1}{\bar{r}}\right)^{-\beta} \Gamma\left(\beta + 1 + \frac{1}{v_e}\right)}{(-v_e + v_e^{\beta+3} + 1) \Gamma\left(1 + \frac{1}{v_e}\right)} \qquad (D.10)$$

We can then use Eqns. D.4 and D.10 to solve for $\bar{r}$:

$$\bar{r} = \left( \frac{f_{sed} r_w^{\alpha} v_e^{-\alpha} \left( v_e^{3+\alpha} - v_e + 1 \right) \Gamma \left( 1 + \frac{1}{v_e} \right)}{(v_e \alpha + 2v_e + 1) \Gamma \left( \alpha + 1 + \frac{1}{v_e} \right)} \right)^{\frac{1}{\alpha}}. \qquad (D.11)$$

Thus for a given $K_{zz}$, $f_{sed}$, and $v_e$, we can find the effective particle radius for every layer in the atmosphere.

However, in order to compute the cloud opacity, we still require the total particle count. For a volume mixing ratio of a given species, $\chi_i$, we can integrate $n(r)$ to find $N$:

$$N = \frac{\chi_i}{(\bar{r}^3 v_e - 1)(2v_e - 1)} \qquad (D.12)$$

## Appendix E: Complete retrieval results

We include in the text abridged tables that present key parameters of interest. The complete set of inferred parameters for every retrieval is available on Zenodo.

Legend: Chemistry/Profile/Clouds/Data/Info.

- Chemistry: (D)isequilibrium or (F)ree.

- Profile: (M)olliere, (Z)hang, (G)uillot or (S)pline(NNodes).

- Clouds: Clear (CLR); (f)ree or (eq)uilibrium condensation location, (species)_(cd/am)_(P)atchy_(h)ansen. '*' indicates $f_{sed}$ was retrieved independently for each cloud species.

- Data: -(not included) or (only included). O indicates OSIRIS data was used in place of GRAVITY data.

- Info: '-' indicates not included. 'mr' indicates mass and radius were used as parameters instead of log $g$ and radius.

In the text, models will be referred to as planet.group.index.
<table><caption>Table E.1. Abridged retrieval results HR 8799 b</caption><thead><tr><th>Planet</th><th>Index</th><th>Model</th><th>Δlog<sub>10</sub> Z</th><th>χ<sup>2</sup>/ν</th><th>T<sub>Eff</sub> [K]</th><th>log g [cgs]</th><th>[M/H]</th><th>C/O</th><th>Radius [R<sub>up</sub>]</th><th>log L/L<sub>☉</sub></th><th>Mass [M<sub>☉</sub>]</th></tr></thead><tbody><tr><td>b</td><td>b.A.0</td><td>F/Z/eq*FeMg_am/ALL/-CH4/</td><td>0</td><td>1.46</td><td>948<sup>+11</sup><sub>-14</sub></td><td>4.11<sup>+0.03</sup><sub>-0.04</sub></td><td>0.94<sup>+0.08</sup><sub>-0.08</sub></td><td>0.78<sup>+0.03</sup><sub>-0.04</sub></td><td>1.1<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.06<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.AB.1</td><td>F/Z/eq*FeMg_am/ALL/</td><td>0</td><td>1.47</td><td>942<sup>+12</sup><sub>-13</sub></td><td>4.1<sup>+0.03</sup><sub>-0.04</sub></td><td>0.96<sup>+0.08</sup><sub>-0.08</sub></td><td>0.78<sup>+0.03</sup><sub>-0.04</sub></td><td>1.1<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.08<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.2</td><td>F/Z/eq*FeMg_am/ALL/-H2S/</td><td>0</td><td>1.49</td><td>958<sup>+13</sup><sub>-15</sub></td><td>4.1<sup>+0.04</sup><sub>-0.04</sub></td><td>1.1<sup>+0.2</sup><sub>-0.1</sub></td><td>0.83<sup>+0.03</sup><sub>-0.04</sub></td><td>1.1<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.05<sup>+0.04</sup><sub>-0.04</sub></td><td>5.9<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.A.3</td><td>F/S1/eqMg_am/ALL/</td><td>-2</td><td>1.48</td><td>977<sup>+11</sup><sub>-10</sub></td><td>4.18<sup>+0.04</sup><sub>-0.04</sub></td><td>1.25<sup>+0.1</sup><sub>-0.1</sub></td><td>0.89<sup>+0.02</sup><sub>-0.02</sub></td><td>1.01<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.07<sup>+0.03</sup><sub>-0.03</sub></td><td>6<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.A.4</td><td>F/S2/eqMg_am/ALL/</td><td>-4</td><td>1.50</td><td>970<sup>+14</sup><sub>-13</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.2<sup>+0.1</sup><sub>-0.1</sub></td><td>0.87<sup>+0.03</sup><sub>-0.03</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.08<sup>+0.04</sup><sub>-0.04</sub></td><td>5.9<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.A.5</td><td>F/S1/CLR/ALL/</td><td>-4</td><td>1.53</td><td>985<sup>+11</sup><sub>-11</sub></td><td>4.18<sup>+0.04</sup><sub>-0.04</sub></td><td>1.43<sup>+0.08</sup><sub>-0.08</sub></td><td>0.92<sup>+0.02</sup><sub>-0.02</sub></td><td>1.01<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.06<sup>+0.03</sup><sub>-0.03</sub></td><td>6<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.AB.6</td><td>D/M/eqNa_P/ALL/</td><td>-4</td><td>1.52</td><td>931<sup>+23</sup><sub>-12</sub></td><td>4.12<sup>+0.05</sup><sub>-0.05</sub></td><td>1.16<sup>+0.08</sup><sub>-0.08</sub></td><td>0.73<sup>+0.02</sup><sub>-0.02</sub></td><td>1.09<sup>+0.04</sup><sub>-0.04</sub></td><td>-5.07<sup>+0.06</sup><sub>-0.06</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.AB.7</td><td>D/M/eqNa/ALL/</td><td>-4</td><td>1.50</td><td>966<sup>+17</sup><sub>-19</sub></td><td>4.19<sup>+0.04</sup><sub>-0.04</sub></td><td>0.95<sup>+0.07</sup><sub>-0.07</sub></td><td>0.78<sup>+0.02</sup><sub>-0.03</sub></td><td>1.0<sup>+0.05</sup><sub>-0.04</sub></td><td>-5.05<sup>+0.05</sup><sub>-0.05</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.AB.8</td><td>F/Z/f*FeMg_am/ALL/</td><td>-4</td><td>1.48</td><td>944<sup>+10</sup><sub>-10</sub></td><td>4.15<sup>+0.03</sup><sub>-0.03</sub></td><td>0.97<sup>+0.08</sup><sub>-0.08</sub></td><td>0.78<sup>+0.03</sup><sub>-0.04</sub></td><td>1.04<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.11<sup>+0.03</sup><sub>-0.03</sub></td><td>5.9<sup>+0.4</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.9</td><td>F/S3/CLR/ALL/</td><td>-4</td><td>1.49</td><td>962<sup>+13</sup><sub>-12</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.85<sup>+0.03</sup><sub>-0.04</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.A.10</td><td>F/S2/CLR/ALL/</td><td>-4</td><td>1.52</td><td>962<sup>+15</sup><sub>-14</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.2<sup>+0.1</sup><sub>-0.1</sub></td><td>0.87<sup>+0.03</sup><sub>-0.04</sub></td><td>1.02<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>5.9<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.AB.11</td><td>F/Z/f*FeMg_cd/ALL/</td><td>-4</td><td>1.48</td><td>942<sup>+11</sup><sub>-11</sub></td><td>4.15<sup>+0.03</sup><sub>-0.03</sub></td><td>0.94<sup>+0.08</sup><sub>-0.08</sub></td><td>0.77<sup>+0.04</sup><sub>-0.04</sub></td><td>1.05<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.11<sup>+0.03</sup><sub>-0.03</sub></td><td>5.9<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.12</td><td>F/S3/eqMg_am/ALL/</td><td>-4</td><td>1.51</td><td>965<sup>+13</sup><sub>-12</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.85<sup>+0.04</sup><sub>-0.04</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.03</sup><sub>-0.03</sub></td><td>6<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.AB.13</td><td>D/M/eq*FeMg_am/ALL/</td><td>-6</td><td>1.54</td><td>944<sup>+11</sup><sub>-10</sub></td><td>4.06<sup>+0.03</sup><sub>-0.03</sub></td><td>1.11<sup>+0.08</sup><sub>-0.08</sub></td><td>0.72<sup>+0.02</sup><sub>-0.02</sub></td><td>1.17<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.03<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.14</td><td>F/S4/CLR/ALL/</td><td>-6</td><td>1.49</td><td>966<sup>+13</sup><sub>-12</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.15<sup>+0.1</sup><sub>-0.1</sub></td><td>0.86<sup>+0.03</sup><sub>-0.04</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.A.15</td><td>F/S4/eqMg_am/ALL/</td><td>-6</td><td>1.52</td><td>968<sup>+12</sup><sub>-12</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.15<sup>+0.09</sup><sub>-0.09</sub></td><td>0.86<sup>+0.03</sup><sub>-0.03</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.08<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.AB.16</td><td>D/M/eq*FeMg_cd/ALL/</td><td>-6</td><td>1.55</td><td>911<sup>+14</sup><sub>-13</sub></td><td>4.05<sup>+0.04</sup><sub>-0.04</sub></td><td>1.16<sup>+0.08</sup><sub>-0.08</sub></td><td>0.73<sup>+0.02</sup><sub>-0.02</sub></td><td>1.18<sup>+0.04</sup><sub>-0.04</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.AB.17</td><td>D/M/eq*FeMg_am/ALL/</td><td>-7</td><td>1.55</td><td>941<sup>+12</sup><sub>-12</sub></td><td>4.07<sup>+0.03</sup><sub>-0.03</sub></td><td>1.08<sup>+0.08</sup><sub>-0.08</sub></td><td>0.73<sup>+0.02</sup><sub>-0.02</sub></td><td>1.16<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.05<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.AB.18</td><td>D/Z/eq*FeMg_am/ALL/</td><td>-7</td><td>1.57</td><td>934<sup>+10</sup><sub>-10</sub></td><td>4.06<sup>+0.03</sup><sub>-0.03</sub></td><td>1.06<sup>+0.07</sup><sub>-0.07</sub></td><td>0.73<sup>+0.02</sup><sub>-0.02</sub></td><td>1.17<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.05<sup>+0.03</sup><sub>-0.03</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.19</td><td>F/S5/CLR/ALL/</td><td>-7</td><td>1.50</td><td>955<sup>+13</sup><sub>-14</sub></td><td>4.16<sup>+0.04</sup><sub>-0.04</sub></td><td>1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.84<sup>+0.04</sup><sub>-0.05</sub></td><td>1.03<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.A.20</td><td>F/S5/eqMg_am/ALL/</td><td>-7</td><td>1.51</td><td>958<sup>+13</sup><sub>-14</sub></td><td>4.17<sup>+0.03</sup><sub>-0.03</sub></td><td>1.09<sup>+0.1</sup><sub>-0.1</sub></td><td>0.84<sup>+0.03</sup><sub>-0.04</sub></td><td>1.03<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.AB.21</td><td>D/M/eqKCI/ALL/</td><td>-8</td><td>1.56</td><td>906<sup>+12</sup><sub>-13</sub></td><td>4.08<sup>+0.03</sup><sub>-0.03</sub></td><td>1.22<sup>+0.08</sup><sub>-0.08</sub></td><td>0.7<sup>+0.02</sup><sub>-0.02</sub></td><td>1.13<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.13<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.2</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.22</td><td>F/S6/CLR/ALL/</td><td>-9</td><td>1.50</td><td>960<sup>+13</sup><sub>-13</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.83<sup>+0.04</sup><sub>-0.05</sub></td><td>1.03<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.AB.23</td><td>D/Z/f*FeMg_am/ALL/</td><td>-9</td><td>1.53</td><td>954<sup>+45</sup><sub>-59</sub></td><td>4.17<sup>+0.03</sup><sub>-0.03</sub></td><td>1.22<sup>+0.06</sup><sub>-0.02</sub></td><td>0.76<sup>+0.01</sup><sub>-0.02</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.1<sup>+0.08</sup><sub>-0.11</sub></td><td>5.9<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.24</td><td>F/S6/eqMg_am/ALL/</td><td>-9</td><td>1.49</td><td>928<sup>+17</sup><sub>-15</sub></td><td>4.01<sup>+0.04</sup><sub>-0.04</sub></td><td>0.82<sup>+0.07</sup><sub>-0.05</sub></td><td>0.63<sup>+0.05</sup><sub>-0.05</sub></td><td>1.21<sup>+0.04</sup><sub>-0.04</sub></td><td>-5.03<sup>+0.04</sup><sub>-0.04</sub></td><td>5.8<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.AB.25</td><td>D/S4/eq*FeMg_am/ALL/</td><td>-10</td><td>1.53</td><td>867<sup>+45</sup><sub>-15</sub></td><td>4.03<sup>+0.03</sup><sub>-0.03</sub></td><td>1.13<sup>+0.07</sup><sub>-0.07</sub></td><td>0.67<sup>+0.04</sup><sub>-0.04</sub></td><td>1.21<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.15<sup>+0.1</sup><sub>-0.1</sub></td><td>6<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.A.26</td><td>F/S7/CLR/ALL/</td><td>-10</td><td>1.52</td><td>964<sup>+13</sup><sub>-15</sub></td><td>4.17<sup>+0.04</sup><sub>-0.04</sub></td><td>1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.85<sup>+0.04</sup><sub>-0.04</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.AB.27</td><td>D/M/Na/ALL/</td><td>-11</td><td>1.56</td><td>918<sup>+46</sup><sub>-57</sub></td><td>4.13<sup>+0.03</sup><sub>-0.03</sub></td><td>1.18<sup>+0.06</sup><sub>-0.06</sub></td><td>0.7<sup>+0.02</sup><sub>-0.02</sub></td><td>1.07<sup>+0.03</sup><sub>-0.02</sub></td><td>-5.1<sup>+0.09</sup><sub>-0.1</sub></td><td>6<sup>+0.2</sup><sub>-0.3</sub></td></tr><tr><td>b</td><td>b.AB.28</td><td>F/S8/CLR/ALL/</td><td>-11</td><td>1.52</td><td>955<sup>+14</sup><sub>-14</sub></td><td>4.16<sup>+0.04</sup><sub>-0.04</sub></td><td>0.98<sup>+0.1</sup><sub>-0.1</sub></td><td>0.79<sup>+0.05</sup><sub>-0.1</sub></td><td>1.03<sup>+0.03</sup><sub>-0.03</sub></td><td>-5.1<sup>+0.04</sup><sub>-0.04</sub></td><td>6<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.A.29</td><td>F/S9/CLR/ALL/</td><td>-12</td><td>1.52</td><td>965<sup>+13</sup><sub>-12</sub></td><td>4.18<sup>+0.04</sup><sub>-0.04</sub></td><td>0.95<sup>+0.1</sup><sub>-0.1</sub></td><td>0.57<sup>+0.2</sup><sub>-0.1</sub></td><td>1.02<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.09<sup>+0.04</sup><sub>-0.04</sub></td><td>6.1<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>b</td><td>b.A.30</td><td>F/S0/CLR/ALL/</td><td>-21</td><td>1.84</td><td>1020<sup>+12</sup><sub>-12</sub></td><td>4.24<sup>+0.04</sup><sub>-0.04</sub></td><td>1.92<sup>+0.04</sup><sub>-0.04</sub></td><td>0.97<sup>+0.05</sup><sub>-0.05</sub></td><td>0.93<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.08<sup>+0.04</sup><sub>-0.04</sub></td><td>5.8<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.A.31</td><td>F/S0/eqMg_am/ALL/</td><td>-21</td><td>1.83</td><td>1022<sup>+13</sup><sub>-11</sub></td><td>4.24<sup>+0.04</sup><sub>-0.04</sub></td><td>1.93<sup>+0.04</sup><sub>-0.06</sub></td><td>0.97<sup>+0.005</sup><sub>-0.005</sub></td><td>0.93<sup>+0.02</sup><sub>-0.02</sub></td><td>-5.08<sup>+0.04</sup><sub>-0.04</sub></td><td>5.8<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>b</td><td>b.A.32</td><td>D/Z/eq*FeMg_am/Gr/</td><td>-948</td><td>0.74</td><td>891<sup>+30</sup><sub>-27</sub></td><td>4.18<sup>+0.07</sup><sub>-0.07</sub></td><td>1.4<sup>+0.3</sup><sub>-0.4</sub></td><td>0.42<sup>+0.1</sup><sub>-0.2</sub></td><td>0.99<sup>+0.08</sup><sub>-0.08</sub></td><td>-5.3<sup>+0.09</sup><sub>-0.1</sub></td><td>5.8<sup>+0.3</sup><sub>-0.3</sub></td></tr></tbody></table>

Notes

All values presented are the median values from the fits, with uncertainties given as the ±34.1% percentiles.
<table><caption>Table E.2. Abridged retrieval results HR 8799 c</caption><thead><tr><th>Planet</th><th>Index</th><th>Model</th><th>Δ log<sub>10</sub> Z</th><th>χ<sup>2</sup>/ν</th><th>T<sub>Eff</sub> [K]</th><th>log g [cgs]</th><th>[M/H]</th><th>C/O</th><th>Radius [R<sub>Jup</sub>]</th><th>log L/L<sub>☉</sub></th><th>Mass [M<sub>Jup</sub>]</th></tr></thead><tbody><tr><td rowspan="10">c</td><td>c.A.0</td><td>F/Z/eq*FeMg_am/O-Gr/mr</td><td>0</td><td>1.72</td><td>1145<sup>+14</sup><sub>-15</sub></td><td>4.27<sup>+0.03</sup><sub>-0.04</sub></td><td>0.95<sup>+0.1</sup><sub>-0.1</sub></td><td>0.6<sup>+0.09</sup><sub>-0.1</sub></td><td>1.06<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.75<sup>+0.03</sup><sub>-0.03</sub></td><td>8<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>c.A.1</td><td>D/M/eq*FeMg_cd/O-Gr/mr</td><td>-1</td><td>1.83</td><td>1207<sup>+11</sup><sub>-10</sub></td><td>4.34<sup>+0.03</sup><sub>-0.03</sub></td><td>1.89<sup>+0.06</sup><sub>-0.06</sub></td><td>0.87<sup>+0.005</sup><sub>-0.006</sub></td><td>0.99<sup>+0.02</sup><sub>-0.02</sub></td><td>-4.73<sup>+0.03</sup><sub>-0.03</sub></td><td>8.2<sup>+0.5</sup><sub>-0.5</sub></td></tr><tr><td>c.AB.2</td><td>F/Z/eq*FeMg_am/ALL/mr</td><td>-430</td><td>2.88</td><td>1158<sup>+12</sup><sub>-12</sub></td><td>4.26<sup>+0.02</sup><sub>-0.03</sub></td><td>1.27<sup>+0.06</sup><sub>-0.06</sub></td><td>0.66<sup>+0.01</sup><sub>-0.01</sub></td><td>1.1<sup>+0.01</sup><sub>-0.01</sub></td><td>-4.71<sup>+0.02</sup><sub>-0.02</sub></td><td>8.5<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>c.AB.3</td><td>F/G/f*FeMg_am/ALL/mr</td><td>-432</td><td>2.87</td><td>1173<sup>+18</sup><sub>-8</sub></td><td>4.26<sup>+0.02</sup><sub>-0.02</sub></td><td>1.3<sup>+0.06</sup><sub>-0.06</sub></td><td>0.67<sup>+0.01</sup><sub>-0.01</sub></td><td>1.09<sup>+0.01</sup><sub>-0.01</sub></td><td>-4.71<sup>+0.03</sup><sub>-0.02</sub></td><td>8.3<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>c.AB.4</td><td>F/Z/f*FeMg_am/ALL/mr</td><td>-435</td><td>2.91</td><td>1173<sup>+5</sup><sub>-6</sub></td><td>4.28<sup>+0.02</sup><sub>-0.02</sub></td><td>1.27<sup>+0.05</sup><sub>-0.07</sub></td><td>0.67<sup>+0.01</sup><sub>-0.01</sub></td><td>1.07<sup>+0.01</sup><sub>-0.01</sub></td><td>-4.71<sup>+0.01</sup><sub>-0.01</sub></td><td>8.5<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>c.AB.5</td><td>D/M/eq*FeMg_cd/ALL/mr</td><td>-443</td><td>2.93</td><td>1057<sup>+14</sup><sub>-13</sub></td><td>4.05<sup>+0.02</sup><sub>-0.02</sub></td><td>1.05<sup>+0.04</sup><sub>-0.04</sub></td><td>0.62<sup>+0.01</sup><sub>-0.01</sub></td><td>1.4<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.69<sup>+0.03</sup><sub>-0.03</sub></td><td>8.6<sup>+0.3</sup><sub>-0.4</sub></td></tr><tr><td>c.A.6</td><td>F/G/f*FeMg_am/ALL/-CH4/mr</td><td>-444</td><td>3.02</td><td>1191<sup>+40</sup><sub>-12</sub></td><td>4.28<sup>+0.02</sup><sub>-0.02</sub></td><td>1.2<sup>+0.06</sup><sub>-0.06</sub></td><td>0.7<sup>+0.01</sup><sub>-0.01</sub></td><td>1.07<sup>+0.01</sup><sub>-0.01</sub></td><td>-4.69<sup>+0.05</sup><sub>-0.02</sub></td><td>8.4<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>c.AB.7</td><td>D/S4/eq*FeMg_am/ALL/-CH4/mr</td><td>-464</td><td>3.10</td><td>1198<sup>+23</sup><sub>-11</sub></td><td>4.29<sup>+0.02</sup><sub>-0.02</sub></td><td>1.02<sup>+0.03</sup><sub>-0.03</sub></td><td>0.6<sup>+0.01</sup><sub>-0.01</sub></td><td>1.08<sup>+0.01</sup><sub>-0.01</sub></td><td>-4.67<sup>+0.03</sup><sub>-0.02</sub></td><td>8.8<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>c.A.8</td><td>F/G/f*FeMg_am/ALL/-HCN/mr</td><td>-465</td><td>3.14</td><td>1197<sup>+45</sup><sub>-33</sub></td><td>4.27<sup>+0.03</sup><sub>-0.04</sub></td><td>1.36<sup>+0.05</sup><sub>-0.06</sub></td><td>0.69<sup>+0.01</sup><sub>-0.01</sub></td><td>1.1<sup>+0.05</sup><sub>-0.03</sub></td><td>-4.62<sup>+0.04</sup><sub>-0.05</sub></td><td>8.7<sup>+0.2</sup><sub>-0.2</sub></td></tr><tr><td>c.AB.9</td><td>D/M/eq*FeMg_am_P/ALL/mr</td><td>-468</td><td>3.25</td><td>1099<sup>+15</sup><sub>-16</sub></td><td>4.14<sup>+0.03</sup><sub>-0.03</sub></td><td>1.1<sup>+0.05</sup><sub>-0.05</sub></td><td>0.61<sup>+0.01</sup><sub>-0.01</sub></td><td>1.28<sup>+0.04</sup><sub>-0.05</sub></td><td>-4.72<sup>+0.03</sup><sub>-0.03</sub></td><td>8.9<sup>+0.4</sup><sub>-0.4</sub></td></tr><tr><td>c.AB.10</td><td>D/Z/f*FeMg_am/ALL/mr</td><td>-478</td><td>3.38</td><td>1145<sup>+9</sup><sub>-7</sub></td><td>4.23<sup>+0.02</sup><sub>-0.02</sub></td><td>1.18<sup>+0.03</sup><sub>-0.03</sub></td><td>0.62<sup>+0.01</sup><sub>-0.009</sub></td><td>1.16<sup>+0.01</sup><sub>-0.01</sub></td><td>-4.69<sup>+0.02</sup><sub>-0.01</sub></td><td>8.8<sup>+0.3</sup><sub>-0.3</sub></td></tr><tr><td>c.A.11</td><td>D/Z/eq*FeMg_am/Gr/mr</td><td>-2678</td><td>0.84</td><td>1234<sup>+18</sup><sub>-17</sub></td><td>4.29<sup>+0.04</sup><sub>-0.03</sub></td><td>0.79<sup>+0.1</sup><sub>-0.2</sub></td><td>0.69<sup>+0.02</sup><sub>-0.02</sub></td><td>1.01<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.66<sup>+0.04</sup><sub>-0.03</sub></td><td>7.6<sup>+0.4</sup><sub>-0.4</sub></td></tr></tbody></table>

Notes

All values presented are the median values from the fits, with uncertainties given as the ±34.1% percentiles.
<table><caption>Table E.3. Abridged retrieval results HR 8799 d</caption><thead><tr><th>Planet</th><th>Index</th><th>Model</th><th>Δlog<sub>10</sub> Z</th><th>χ<sup>2</sup>/ν</th><th>T<sub>Eff</sub> [K]</th><th>log g [cgs]</th><th>[M/H]</th><th>C/O</th><th>Radius [R<sub>lim</sub>]</th><th>log L/L<sub>☉</sub></th><th>Mass [M<sub>☉</sub>]</th></tr></thead><tbody><tr><td>d</td><td>d.AB.0</td><td>D/M/eq*FeMg_am/ALL/mr</td><td>0</td><td>1.42</td><td>1177<sup>+21</sup><sub>-21</sub></td><td>4.18<sup>+0.04</sup><sub>-0.03</sub></td><td>1.2<sup>+0.2</sup><sub>-0.1</sub></td><td>0.61<sup>+0.03</sup><sub>-0.04</sub></td><td>1.26<sup>+0.05</sup><sub>-0.06</sub></td><td>-4.63<sup>+0.04</sup><sub>-0.04</sub></td><td>9.19<sup>+0.08</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.AB.1</td><td>D/Z/f*FeMg_am/ALL/mr</td><td>0</td><td>1.39</td><td>1139<sup>+38</sup><sub>-19</sub></td><td>4.13<sup>+0.02</sup><sub>-0.02</sub></td><td>1.3<sup>+0.1</sup><sub>-0.1</sub></td><td>0.6<sup>+0.03</sup><sub>-0.04</sub></td><td>1.34<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.6<sup>+0.06</sup><sub>-0.03</sub></td><td>9.2<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.AB.2</td><td>D/M/eq*FeMg_am_P/ALL/mr</td><td>-1</td><td>1.47</td><td>1220<sup>+10</sup><sub>-10</sub></td><td>4.25<sup>+0.02</sup><sub>-0.02</sub></td><td>1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.49<sup>+0.04</sup><sub>-0.04</sub></td><td>1.16<sup>+0.02</sup><sub>-0.02</sub></td><td>-4.58<sup>+0.03</sup><sub>-0.03</sub></td><td>9.2<sup>+0.09</sup><sub>-0.09</sub></td></tr><tr><td>d</td><td>d.AB.3</td><td>D/M/eq*FeMg_cd/ALL/mr</td><td>-1</td><td>1.47</td><td>1220<sup>+9</sup><sub>-9</sub></td><td>4.25<sup>+0.02</sup><sub>-0.02</sub></td><td>1.1<sup>+0.1</sup><sub>-0.1</sub></td><td>0.49<sup>+0.04</sup><sub>-0.04</sub></td><td>1.16<sup>+0.02</sup><sub>-0.02</sub></td><td>-4.58<sup>+0.03</sup><sub>-0.03</sub></td><td>9.21<sup>+0.09</sup><sub>-0.09</sub></td></tr><tr><td>d</td><td>d.AB.4</td><td>F/G/f*FeMg_cd/ALL/mr</td><td>-3</td><td>1.43</td><td>1194<sup>+18</sup><sub>-15</sub></td><td>4.18<sup>+0.02</sup><sub>-0.02</sub></td><td>1.5<sup>+0.2</sup><sub>-0.2</sub></td><td>0.68<sup>+0.03</sup><sub>-0.04</sub></td><td>1.26<sup>+0.02</sup><sub>-0.03</sub></td><td>-4.58<sup>+0.03</sup><sub>-0.03</sub></td><td>9.2<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.AB.5</td><td>F/G/f*FeMg_am/ALL/mr</td><td>-3</td><td>1.42</td><td>1196<sup>+20</sup><sub>-17</sub></td><td>4.18<sup>+0.03</sup><sub>-0.02</sub></td><td>1.5<sup>+0.2</sup><sub>-0.2</sub></td><td>0.67<sup>+0.03</sup><sub>-0.04</sub></td><td>1.26<sup>+0.03</sup><sub>-0.04</sub></td><td>-4.58<sup>+0.03</sup><sub>-0.03</sub></td><td>9.2<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.AB.6</td><td>F/Z/eq*FeMg_am/ALL/mr</td><td>-4</td><td>1.46</td><td>1146<sup>+13</sup><sub>-13</sub></td><td>4.17<sup>+0.02</sup><sub>-0.02</sub></td><td>1.6<sup>+0.2</sup><sub>-0.1</sub></td><td>0.67<sup>+0.04</sup><sub>-0.05</sub></td><td>1.27<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.62<sup>+0.03</sup><sub>-0.03</sub></td><td>9.19<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.AB.7</td><td>D/Z/eq*FeMg_am/ALL/mr</td><td>-4</td><td>1.47</td><td>1150<sup>+21</sup><sub>-16</sub></td><td>4.17<sup>+0.04</sup><sub>-0.03</sub></td><td>0.95<sup>+0.1</sup><sub>-0.1</sub></td><td>0.5<sup>+0.04</sup><sub>-0.04</sub></td><td>1.27<sup>+0.05</sup><sub>-0.06</sub></td><td>-4.67<sup>+0.04</sup><sub>-0.04</sub></td><td>9.18<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.AB.8</td><td>D/Z/eq*FeMg_am/ALL/mr</td><td>-5</td><td>1.49</td><td>1166<sup>+19</sup><sub>-16</sub></td><td>4.21<sup>+0.03</sup><sub>-0.03</sub></td><td>0.98<sup>+0.1</sup><sub>-0.1</sub></td><td>0.48<sup>+0.04</sup><sub>-0.04</sub></td><td>1.22<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.66<sup>+0.04</sup><sub>-0.04</sub></td><td>9.19<sup>+0.07</sup><sub>-0.06</sub></td></tr><tr><td>d</td><td>d.AB.9</td><td>D/Z/eq*FeMg_am/ALL/mr</td><td>-6</td><td>1.50</td><td>1158<sup>+30</sup><sub>-30</sub></td><td>4.5<sup>+0.3</sup><sub>-0.3</sub></td><td>1.3<sup>+0.3</sup><sub>-0.3</sub></td><td>0.48<sup>+0.04</sup><sub>-0.04</sub></td><td>1.23<sup>+0.08</sup><sub>-0.06</sub></td><td>-4.61<sup>+0.06</sup><sub>-0.06</sub></td><td>20.70<sup>+19</sup><sub>-10</sub></td></tr><tr><td>d</td><td>d.AB.10</td><td>F/Z/f*FeMg_am/ALL/mr</td><td>-6</td><td>1.44</td><td>1157<sup>+30</sup><sub>-16</sub></td><td>4.16<sup>+0.01</sup><sub>-0.01</sub></td><td>1.7<sup>+0.1</sup><sub>-0.1</sub></td><td>0.64<sup>+0.04</sup><sub>-0.04</sub></td><td>1.29<sup>+0.02</sup><sub>-0.02</sub></td><td>-4.57<sup>+0.04</sup><sub>-0.03</sub></td><td>9.22<sup>+0.05</sup><sub>-0.05</sub></td></tr><tr><td>d</td><td>d.AB.11</td><td>D/S4/eq*FeMg_am/ALL/mr</td><td>-12</td><td>1.51</td><td>1198<sup>+21</sup><sub>-20</sub></td><td>4.24<sup>+0.03</sup><sub>-0.04</sub></td><td>0.71<sup>+0.2</sup><sub>-0.1</sub></td><td>0.34<sup>+0.07</sup><sub>-0.06</sub></td><td>1.17<sup>+0.05</sup><sub>-0.04</sub></td><td>-4.62<sup>+0.04</sup><sub>-0.04</sub></td><td>9.19<sup>+0.07</sup><sub>-0.07</sub></td></tr><tr><td>d</td><td>d.A.12</td><td>D/Z/eq*FeMg_am/Gir/mr</td><td>-2276</td><td>0.79</td><td>1172<sup>+18</sup><sub>-18</sub></td><td>4.18<sup>+0.03</sup><sub>-0.03</sub></td><td>2<sup>+0.2</sup><sub>-0.2</sub></td><td>0.78<sup>+0.02</sup><sub>-0.03</sub></td><td>1.25<sup>+0.04</sup><sub>-0.04</sub></td><td>-4.61<sup>+0.04</sup><sub>-0.04</sub></td><td>9.19<sup>+0.08</sup><sub>-0.08</sub></td></tr><tr><td>d</td><td>d.A.13</td><td>D/Z/eq*FeMg_am/-Gir/mr</td><td>-3498</td><td>1.03</td><td>1162<sup>+28</sup><sub>-28</sub></td><td>4.22<sup>+0.04</sup><sub>-0.04</sub></td><td>0.46<sup>+0.7</sup><sub>-0.7</sub></td><td>0.31<sup>+0.1</sup><sub>-0.1</sub></td><td>1.19<sup>+0.06</sup><sub>-0.06</sub></td><td>-4.68<sup>+0.06</sup><sub>-0.06</sub></td><td>9.2<sup>+0.08</sup><sub>-0.08</sub></td></tr></tbody></table>

Notes

All values presented are the median values from the fits, with uncertainties given as the ±34.1% percentiles.
<table><caption>Table E.4. Abridged retrieval results HR 8799 e</caption><thead><tr><th>Planet</th><th>Index</th><th>Model</th><th>Δlog<sub>10</sub> Z</th><th>χ<sup>2</sup>/ν</th><th>T<sub>Eff</sub> [K]</th><th>log g [cgs]</th><th>[M/H]</th><th>C/O</th><th>Radius [R<sub>up</sub>]</th><th>log L/L<sub>O</sub></th><th>Mass [M<sub>up</sub>]</th></tr></thead><tbody><tr><td>e</td><td>e.A.0</td><td>F/Z/eq*FeMg_am/ALL/-CH4/mr</td><td>0</td><td>1.23</td><td>1139<sup>+21</sup><sub>-20</sub></td><td>4.18<sup>+0.05</sup><sub>-0.05</sub></td><td>1.9<sup>+0.1</sup><sub>-0.1</sub></td><td>0.88<sup>+0.01</sup><sub>-0.02</sub></td><td>1.13<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.73<sup>+0.05</sup><sub>-0.05</sub></td><td>7.5<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.1</td><td>F/G/eq*FeMg_am/ALL/mr</td><td>0</td><td>1.22</td><td>1172<sup>+27</sup><sub>-29</sub></td><td>4.2<sup>+0.06</sup><sub>-0.06</sub></td><td>1.8<sup>+0.1</sup><sub>-0.2</sub></td><td>0.88<sup>+0.02</sup><sub>-0.02</sub></td><td>1.1<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.71<sup>+0.06</sup><sub>-0.05</sub></td><td>7.5<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.2</td><td>F/Z/eq*FeMg_am/ALL/mr</td><td>0</td><td>1.23</td><td>1134<sup>+24</sup><sub>-20</sub></td><td>4.18<sup>+0.05</sup><sub>-0.05</sub></td><td>1.9<sup>+0.1</sup><sub>-0.1</sub></td><td>0.87<sup>+0.02</sup><sub>-0.02</sub></td><td>1.14<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.74<sup>+0.06</sup><sub>-0.05</sub></td><td>7.5<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.3</td><td>F/G/Fe/ALL/mr</td><td>-1</td><td>1.22</td><td>1206<sup>+27</sup><sub>-23</sub></td><td>4.24<sup>+0.05</sup><sub>-0.05</sub></td><td>1.8<sup>+0.1</sup><sub>-0.2</sub></td><td>0.88<sup>+0.02</sup><sub>-0.02</sub></td><td>1.06<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.67<sup>+0.05</sup><sub>-0.05</sub></td><td>7.6<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.4</td><td>F/G/grey_P/ALL/mr</td><td>-2</td><td>1.22</td><td>1203<sup>+23</sup><sub>-28</sub></td><td>4.24<sup>+0.05</sup><sub>-0.05</sub></td><td>1.8<sup>+0.1</sup><sub>-0.2</sub></td><td>0.89<sup>+0.02</sup><sub>-0.02</sub></td><td>1.07<sup>+0.03</sup><sub>-0.04</sub></td><td>-4.69<sup>+0.06</sup><sub>-0.05</sub></td><td>7.6<sup>+0.7</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.5</td><td>F/G/grey_P/ALL/mr</td><td>-3</td><td>1.23</td><td>1261<sup>+18</sup><sub>-18</sub></td><td>4.35<sup>+0.05</sup><sub>-0.06</sub></td><td>1.7<sup>+0.2</sup><sub>-0.3</sub></td><td>0.89<sup>+0.02</sup><sub>-0.03</sub></td><td>0.94<sup>+0.04</sup><sub>-0.03</sub></td><td>-4.64<sup>+0.04</sup><sub>-0.05</sub></td><td>7.6<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.6</td><td>F/G/Fe/FeMg_am/ALL/mr</td><td>-3</td><td>1.23</td><td>1214<sup>+23</sup><sub>-23</sub></td><td>4.25<sup>+0.04</sup><sub>-0.04</sub></td><td>1.8<sup>+0.2</sup><sub>-0.2</sub></td><td>0.89<sup>+0.02</sup><sub>-0.02</sub></td><td>1.05<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.69<sup>+0.04</sup><sub>-0.04</sub></td><td>7.5<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.7</td><td>F/S4/eq*FeMg_am/ALL/mr</td><td>-6</td><td>1.26</td><td>1202<sup>+19</sup><sub>-20</sub></td><td>4.28<sup>+0.05</sup><sub>-0.05</sub></td><td>1.8<sup>+0.1</sup><sub>-0.2</sub></td><td>0.9<sup>+0.02</sup><sub>-0.03</sub></td><td>1.01<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.7<sup>+0.05</sup><sub>-0.05</sub></td><td>7.6<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.8</td><td>D/M/eqFeMg_cd_P/ALL/mr</td><td>-6</td><td>1.32</td><td>1215<sup>+19</sup><sub>-18</sub></td><td>4.31<sup>+0.05</sup><sub>-0.05</sub></td><td>2.1<sup>+0.2</sup><sub>-0.3</sub></td><td>0.83<sup>+0.01</sup><sub>-0.02</sub></td><td>1.0<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.68<sup>+0.04</sup><sub>-0.05</sub></td><td>7.9<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.9</td><td>D/Z/eq*FeMg_cd/ALL/mr</td><td>-7</td><td>1.27</td><td>1084<sup>+23</sup><sub>-23</sub></td><td>4.09<sup>+0.06</sup><sub>-0.06</sub></td><td>1.3<sup>+0.1</sup><sub>-0.1</sub></td><td>0.77<sup>+0.03</sup><sub>-0.03</sub></td><td>1.29<sup>+0.06</sup><sub>-0.07</sub></td><td>-4.82<sup>+0.06</sup><sub>-0.05</sub></td><td>7.9<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.10</td><td>D/M/eq*FeMg_cd_P/ALL/mr</td><td>-7</td><td>1.32</td><td>1215<sup>+17</sup><sub>-18</sub></td><td>4.31<sup>+0.05</sup><sub>-0.05</sub></td><td>2.1<sup>+0.2</sup><sub>-0.3</sub></td><td>0.83<sup>+0.01</sup><sub>-0.02</sub></td><td>1.0<sup>+0.03</sup><sub>-0.05</sub></td><td>-4.68<sup>+0.05</sup><sub>-0.05</sub></td><td>7.9<sup>+0.6</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.11</td><td>D/M/eq*FeMg_cd/ALL/mr</td><td>-7</td><td>1.28</td><td>1106<sup>+33</sup><sub>-28</sub></td><td>4.11<sup>+0.06</sup><sub>-0.06</sub></td><td>1.3<sup>+0.2</sup><sub>-0.1</sub></td><td>0.78<sup>+0.03</sup><sub>-0.03</sub></td><td>1.26<sup>+0.07</sup><sub>-0.09</sub></td><td>-4.82<sup>+0.07</sup><sub>-0.07</sub></td><td>7.9<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.A.12</td><td>F/Z/eq*FeMg_am/ALL-HCN/mr</td><td>-8</td><td>1.30</td><td>1148<sup>+24</sup><sub>-23</sub></td><td>4.15<sup>+0.06</sup><sub>-0.06</sub></td><td>1.91<sup>+0.07</sup><sub>-0.1</sub></td><td>0.87<sup>+0.02</sup><sub>-0.02</sub></td><td>1.17<sup>+0.06</sup><sub>-0.06</sub></td><td>-4.73<sup>+0.06</sup><sub>-0.06</sub></td><td>7.5<sup>+0.7</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.13</td><td>D/Z/eq*FeMg_am/ALL/mr</td><td>-9</td><td>1.33</td><td>1187<sup>+50</sup><sub>-30</sub></td><td>4.26<sup>+0.04</sup><sub>-0.04</sub></td><td>2<sup>+0.3</sup><sub>-0.3</sub></td><td>0.83<sup>+0.02</sup><sub>-0.02</sub></td><td>1.08<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.69<sup>+0.07</sup><sub>-0.06</sub></td><td>8.1<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.14</td><td>D/Z/eq*FeMg2/Gr/mr</td><td>-9</td><td>1.35</td><td>1170<sup>+26</sup><sub>-27</sub></td><td>4.26<sup>+0.06</sup><sub>-0.06</sub></td><td>1.3<sup>+0.2</sup><sub>-0.2</sub></td><td>0.76<sup>+0.02</sup><sub>-0.03</sub></td><td>1.06<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.77<sup>+0.05</sup><sub>-0.06</sub></td><td>7.8<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.15</td><td>F/Z/eq*FeMg_am/ALL/mr</td><td>-10</td><td>1.29</td><td>1143<sup>+12</sup><sub>-18</sub></td><td>4.19<sup>+0.05</sup><sub>-0.05</sub></td><td>1.99<sup>+0.05</sup><sub>-0.05</sub></td><td>0.86<sup>+0.02</sup><sub>-0.02</sub></td><td>1.09<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.73<sup>+0.04</sup><sub>-0.04</sub></td><td>7<sup>+0.6</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.A.16</td><td>D/Z/eqFeMg_am/ALL/Fe-H15mr</td><td>-10</td><td>1.37</td><td>1202<sup>+20</sup><sub>-17</sub></td><td>4.32<sup>+0.05</sup><sub>-0.05</sub></td><td>1.5<sup>+0</sup><sub>-0</sub></td><td>0.76<sup>+0.02</sup><sub>-0.02</sub></td><td>0.99<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.73<sup>+0.05</sup><sub>-0.05</sub></td><td>7.8<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.A.17</td><td>D/Z/eqFeMg_am/ALL/Fe-H20mr</td><td>-10</td><td>1.33</td><td>1179<sup>+29</sup><sub>-28</sub></td><td>4.25<sup>+0.06</sup><sub>-0.06</sub></td><td>2.0<sup>+0</sup><sub>-0</sub></td><td>0.82<sup>+0.01</sup><sub>-0.01</sub></td><td>1.08<sup>+0.07</sup><sub>-0.07</sub></td><td>-4.77<sup>+0.06</sup><sub>-0.05</sub></td><td>8<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.A.18</td><td>D/M/grey_P/ALL/mr</td><td>-10</td><td>1.38</td><td>1245<sup>+16</sup><sub>-16</sub></td><td>4.36<sup>+0.05</sup><sub>-0.05</sub></td><td>1.5<sup>+0.1</sup><sub>-0.1</sub></td><td>0.63<sup>+0.02</sup><sub>-0.02</sub></td><td>0.95<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.68<sup>+0.04</sup><sub>-0.04</sub></td><td>8<sup>+0.8</sup><sub>-0.8</sub></td></tr><tr><td></td><td>e.AB.19</td><td>D/M/eq*FeMg_am/ALL/mr</td><td>-11</td><td>1.33</td><td>1206<sup>+22</sup><sub>-22</sub></td><td>4.3<sup>+0.05</sup><sub>-0.05</sub></td><td>2.1<sup>+0.2</sup><sub>-0.2</sub></td><td>0.83<sup>+0.02</sup><sub>-0.02</sub></td><td>1.02<sup>+0.04</sup><sub>-0.05</sub></td><td>-4.69<sup>+0.06</sup><sub>-0.06</sub></td><td>8.1<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.20</td><td>D/Z/eq*FeMg_am_P/ALL/mr</td><td>-11</td><td>1.33</td><td>1129<sup>+27</sup><sub>-27</sub></td><td>4.15<sup>+0.06</sup><sub>-0.05</sub></td><td>1.4<sup>+0.1</sup><sub>-0.1</sub></td><td>0.78<sup>+0.03</sup><sub>-0.03</sub></td><td>1.21<sup>+0.06</sup><sub>-0.06</sub></td><td>-4.77<sup>+0.07</sup><sub>-0.07</sub></td><td>7.9<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.21</td><td>D/M/grey_P/ALL/mr</td><td>-11</td><td>1.37</td><td>1245<sup>+15</sup><sub>-15</sub></td><td>4.34<sup>+0.05</sup><sub>-0.07</sub></td><td>1.5<sup>+0.1</sup><sub>-0.1</sub></td><td>0.63<sup>+0.02</sup><sub>-0.02</sub></td><td>0.97<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.64<sup>+0.08</sup><sub>-0.06</sub></td><td>8<sup>+0.8</sup><sub>-0.8</sub></td></tr><tr><td></td><td>e.A.22</td><td>D/Z/eqFeMg_am/ALL/Fe-H10mr</td><td>-11</td><td>1.41</td><td>1208<sup>+21</sup><sub>-19</sub></td><td>4.29<sup>+0.05</sup><sub>-0.05</sub></td><td>1.0<sup>+0</sup><sub>-0</sub></td><td>0.69<sup>+0.02</sup><sub>-0.02</sub></td><td>0.98<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.72<sup>+0.05</sup><sub>-0.05</sub></td><td>7.3<sup>+0.7</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.A.23</td><td>D/Z/eqFeMg_am/ALL/mr</td><td>-11</td><td>1.36</td><td>1209<sup>+20</sup><sub>-17</sub></td><td>4.32<sup>+0.04</sup><sub>-0.05</sub></td><td>1.7<sup>+0.7</sup><sub>-0.3</sub></td><td>0.79<sup>+0.03</sup><sub>-0.05</sub></td><td>0.99<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.72<sup>+0.05</sup><sub>-0.05</sub></td><td>7.9<sup>+0.6</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.24</td><td>D/Z/eqAl2O3/ALL/mr</td><td>-11</td><td>1.34</td><td>1235<sup>+17</sup><sub>-14</sub></td><td>4.36<sup>+0.04</sup><sub>-0.05</sub></td><td>2.3<sup>+0.1</sup><sub>-0.3</sub></td><td>0.82<sup>+0.01</sup><sub>-0.01</sub></td><td>0.94<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.73<sup>+0.04</sup><sub>-0.04</sub></td><td>7.9<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.AB.25</td><td>D/Z/eq*FeMg_am/ALL/mr</td><td>-11</td><td>1.36</td><td>1207<sup>+19</sup><sub>-17</sub></td><td>4.32<sup>+0.04</sup><sub>-0.04</sub></td><td>2.1<sup>+0.3</sup><sub>-0.6</sub></td><td>0.81<sup>+0.01</sup><sub>-0.01</sub></td><td>0.99<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.72<sup>+0.05</sup><sub>-0.05</sub></td><td>8<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.AB.26</td><td>D/Z/eq*FeMg_am/ALL/Fe/Gr/mr</td><td>-12</td><td>1.36</td><td>1224<sup>+21</sup><sub>-22</sub></td><td>4.8<sup>+0.2</sup><sub>-0.2</sub></td><td>2<sup>+0.3</sup><sub>-0.3</sub></td><td>0.76<sup>+0.05</sup><sub>-0.03</sub></td><td>0.96<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.78<sup>+0.06</sup><sub>-0.06</sub></td><td>19.91<sup>+13</sup><sub>-7</sub></td></tr><tr><td></td><td>e.AB.27</td><td>F/G/grey/ALL/mr</td><td>-12</td><td>1.37</td><td>1245<sup>+58</sup><sub>-31</sub></td><td>4.24<sup>+0.06</sup><sub>-0.06</sub></td><td>2.05<sup>+0.09</sup><sub>-0.08</sub></td><td>0.91<sup>+0.02</sup><sub>-0.02</sub></td><td>1.04<sup>+0.04</sup><sub>-0.04</sub></td><td>-4.6<sup>+0.09</sup><sub>-0.07</sub></td><td>7.4<sup>+0.8</sup><sub>-0.8</sub></td></tr><tr><td></td><td>e.AB.28</td><td>D/S4/eq*FeMg_cd/ALL/mr</td><td>-12</td><td>1.27</td><td>1093<sup>+27</sup><sub>-24</sub></td><td>4.08<sup>+0.05</sup><sub>-0.05</sub></td><td>1.4<sup>+0.1</sup><sub>-0.1</sub></td><td>0.78<sup>+0.02</sup><sub>-0.03</sub></td><td>1.3<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.73<sup>+0.06</sup><sub>-0.06</sub></td><td>7.8<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.A.29</td><td>D/Z/eqFeMg_am/ALL/Fe-H05mr</td><td>-17</td><td>1.49</td><td>1217<sup>+20</sup><sub>-18</sub></td><td>4.29<sup>+0.05</sup><sub>-0.05</sub></td><td>0.5<sup>+0</sup><sub>-0</sub></td><td>0.52<sup>+0.03</sup><sub>-0.04</sub></td><td>0.97<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.71<sup>+0.04</sup><sub>-0.05</sub></td><td>7.1<sup>+0.7</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.A.30</td><td>D/Z/eqFeMg_am/ALL/Fe-H00mr</td><td>-26</td><td>1.58</td><td>1227<sup>+17</sup><sub>-16</sub></td><td>4.29<sup>+0.05</sup><sub>-0.05</sub></td><td>0.0<sup>+0</sup><sub>-0</sub></td><td>0.21<sup>+0.02</sup><sub>-0.02</sub></td><td>0.95<sup>+0.03</sup><sub>-0.03</sub></td><td>-4.72<sup>+0.04</sup><sub>-0.05</sub></td><td>6.9<sup>+0.6</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.A.31</td><td>D/Z/eq*FeMg_am/Gr/mr</td><td>-2294</td><td>0.72</td><td>1173<sup>+28</sup><sub>-28</sub></td><td>4.24<sup>+0.06</sup><sub>-0.06</sub></td><td>1.8<sup>+0.4</sup><sub>-0.5</sub></td><td>0.85<sup>+0.02</sup><sub>-0.02</sub></td><td>1.06<sup>+0.06</sup><sub>-0.06</sub></td><td>-4.71<sup>+0.07</sup><sub>-0.07</sub></td><td>7.5<sup>+0.7</sup><sub>-0.7</sub></td></tr><tr><td></td><td>e.A.32</td><td>D/Z/CLR/Gr/mr</td><td>-2301</td><td>0.79</td><td>1339<sup>+36</sup><sub>-38</sub></td><td>4.3<sup>+0.07</sup><sub>-0.07</sub></td><td>0.65<sup>+0.2</sup><sub>-0.2</sub></td><td>0.71<sup>+0.07</sup><sub>-0.07</sub></td><td>0.94<sup>+0.05</sup><sub>-0.05</sub></td><td>-4.53<sup>+0.08</sup><sub>-0.08</sub></td><td>6.9<sup>+0.8</sup><sub>-0.6</sub></td></tr><tr><td></td><td>e.A.33</td><td>D/Z/eq*FeMg_am/Gr/mr</td><td>-3496</td><td>1.88</td><td>1143<sup>+32</sup><sub>-32</sub></td><td>4.17<sup>+0.08</sup><sub>-0.08</sub></td><td>2<sup>+0.3</sup><sub>-0.4</sub></td><td>0.71<sup>+0.08</sup><sub>-0.2</sub></td><td>1.15<sup>+0.09</sup><sub>-0.09</sub></td><td>-4.79<sup>+0.08</sup><sub>-0.09</sub></td><td>7.5<sup>+0.7</sup><sub>-0.7</sub></td></tr></tbody></table>

Notes

All values presented are the median values from the fits, with uncertainties given as the ±34.1% percentiles.