Recognition: unknown
On the Information Content of Ariel Transmission Spectra: Reassessing the Tier System
Pith reviewed 2026-05-10 16:51 UTC · model grok-4.3
The pith
Ariel's Tier 1 survey data already constrains water and carbon dioxide abundances in giant exoplanet atmospheres to useful levels even with clouds.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Simulations of Ariel transmission spectra for a hot-Saturn, warm-Neptune, and temperate sub-Neptune at different tiers, followed by retrievals, show that Tier 1-quality observations suffice for constraints better than 1.5 dex on H2O and CO2 in giant planets irrespective of clouds. Higher tiers yield incremental precision gains and enable detections of additional molecules such as H2S and CO in certain scenarios. Tier 1 data constrains CH4 in a cloud-free temperate sub-Neptune, but at least Tier 2 precision is needed if clouds are present, and the transit count required may prove prohibitive for Tier 1 inclusion.
What carries the argument
Atmospheric retrievals performed on simulated Ariel transmission spectra generated at Tier 1, 2, and 3 precisions for three benchmark planets.
If this is right
- Important chemical insights on H2O and CO2 abundances are already obtainable from the Tier 1 survey for giant planets.
- Tiers 2 and 3 provide incremental increases in precision and enable detection of additional molecules like H2S and CO in some cases.
- Tier 1 observations suffice to constrain CH4 in cloud-free temperate sub-Neptunes but require at least Tier 2 precision if clouds are present.
- The number of transits needed for adequate precision on temperate sub-Neptunes may limit their inclusion even in the Tier 1 survey.
Where Pith is reading between the lines
- Survey planners could consider allocating more Tier 1 targets to giant planets to maximize early chemical returns.
- Similar tiered missions might benefit from testing whether lower-precision data suffices for population-level trends in specific planet types.
- Clouds appear as the dominant factor limiting characterization of smaller planets, suggesting targeted cloud studies could improve tier planning.
- Validation against actual Ariel data will be essential to confirm that simulated noise and degeneracy assumptions hold in practice.
Load-bearing premise
The forward-model spectra and retrieval framework accurately represent Ariel's real noise properties, cloud effects, and parameter degeneracies for the chosen benchmark planets.
What would settle it
Performing the same retrieval analysis on real Ariel Tier 1 observations of a hot-Saturn and checking whether the resulting H2O and CO2 abundance uncertainties fall below 1.5 dex.
Figures
read the original abstract
The European Space Agency's Ariel mission will conduct a survey of the atmospheric properties of exoplanets around bright stars. The mission is nominally divided into three Tiers. The Tier 1 survey will consist of low-precision observations of ~1000 planets, with a subset of these included in the higher-precision Tier 2 survey expected to be necessary for atmospheric characterization. Tier 3 will be repeated observations of a small number of benchmark planets. Though previous studies have assessed the ability of Ariel to uncover population-level trends, they have generally presupposed a given Tier. Here we interrogate this assumption and assess the information content of Ariel transmission spectra as a function of Tier for three benchmark planets: a hot-Saturn, warm-Neptune, and temperate sub-Neptune. We simulate a grid of Ariel transit spectra at different Tiers for each target and use retrievals to assess which chemical species are detectable. We find that for giant planets like a hot-Saturn or warm-Neptune, Tier 1-quality observations are sufficient for <1.5dex constraints on H2O and CO2, irrespective of the presence of clouds -- meaning important chemical insights are already obtainable in the Tier 1 survey. Moving to Tiers 2 and 3 result in an incremental increase in precision as well as other molecules becoming detectable in certain scenarios (e.g., H2S, CO). Tier 1 observations are also sufficient to constrain CH4 in a cloud-free, temperate sub-Neptune, whereas observations with at least Tier 2 precision are necessary if the atmosphere is cloudy. The number of transits necessary to reach this precision, however, may be prohibitive for the inclusion of temperate sub-Neptunes in even the Tier 1 survey.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper simulates a grid of Ariel transmission spectra for three benchmark planets (hot-Saturn, warm-Neptune, temperate sub-Neptune) across the mission's Tier 1-3 precision levels and performs atmospheric retrievals to quantify the detectability and abundance constraints on key molecules (H2O, CO2, CH4, etc.). It concludes that Tier 1-quality data suffice for <1.5 dex constraints on H2O and CO2 in the giant-planet cases irrespective of clouds, with higher tiers yielding incremental gains and additional species (e.g., H2S, CO); for the temperate sub-Neptune, Tier 1 works for CH4 only if cloud-free, otherwise Tier 2 is required, though the necessary transit numbers may limit inclusion.
Significance. If the quantitative results hold, the work is significant for Ariel mission planning: it shows that the low-precision Tier 1 survey can already deliver chemically meaningful constraints on giant planets, potentially allowing reallocation of higher-tier resources and refining target selection. The use of forward simulations followed by retrievals on synthetic data provides a direct, tier-by-tier comparison that is reproducible in principle and tests a falsifiable claim about information content versus precision.
major comments (2)
- [Methods and Results sections describing the forward model and retrieval framework] The central claim that Tier 1 observations deliver <1.5 dex constraints on H2O and CO2 'irrespective of the presence of clouds' (abstract) rests on retrievals that employ the same forward model used to generate the spectra. This self-consistent setup omits biases from model incompleteness (wavelength-dependent cloud scattering, unmodeled trace gases, 3D effects) that would broaden posteriors in real data, directly weakening the Tier-1 sufficiency conclusion for the hot-Saturn and warm-Neptune cases.
- [Methods] Full details on the noise model (including Tier-specific floors and precision targets), cloud parameterization, retrieval priors, and validation metrics are not provided. Without these, the reported precision values cannot be independently assessed or reproduced, leaving the quantitative thresholds (<1.5 dex, number of transits) on unexamined assumptions.
minor comments (2)
- [Introduction] The abstract and main text would benefit from explicit comparison to prior Ariel tier studies cited in the introduction, to clarify what is new versus confirmatory.
- [Figures] Figure captions and axis labels should more clearly distinguish the three benchmark planets and the cloud-free versus cloudy cases to aid quick reading of the tier-dependent results.
Simulated Author's Rebuttal
We thank the referee for their constructive comments, which have prompted us to clarify key aspects of our analysis and improve the manuscript's transparency. We address each major comment point by point below.
read point-by-point responses
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Referee: The central claim that Tier 1 observations deliver <1.5 dex constraints on H2O and CO2 'irrespective of the presence of clouds' (abstract) rests on retrievals that employ the same forward model used to generate the spectra. This self-consistent setup omits biases from model incompleteness (wavelength-dependent cloud scattering, unmodeled trace gases, 3D effects) that would broaden posteriors in real data, directly weakening the Tier-1 sufficiency conclusion for the hot-Saturn and warm-Neptune cases.
Authors: We agree that the self-consistent forward-model/retrieval framework represents an idealized scenario and does not incorporate biases arising from model incompleteness, such as wavelength-dependent cloud scattering, missing trace gases, or 3D atmospheric effects. These omissions could indeed broaden the retrieved posteriors in real data. Our study is designed to isolate the information content as a function of spectral precision under controlled conditions, establishing a theoretical baseline for what Tier 1 data can deliver. To address the referee's concern, we have added a new paragraph in the Discussion section explicitly acknowledging this limitation, stating that the quoted constraints are best-case values, and noting that higher tiers may provide greater robustness against such systematics. The relative comparison across tiers remains a useful guide for mission planning. revision: partial
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Referee: Full details on the noise model (including Tier-specific floors and precision targets), cloud parameterization, retrieval priors, and validation metrics are not provided. Without these, the reported precision values cannot be independently assessed or reproduced, leaving the quantitative thresholds (<1.5 dex, number of transits) on unexamined assumptions.
Authors: We thank the referee for highlighting this omission. While the Methods section outlines the overall retrieval framework, it does not provide the granular parameters needed for full reproducibility. We have revised the manuscript by expanding the Methods section with a dedicated subsection and accompanying tables that specify: (i) the complete noise model, including Tier-specific noise floors and precision targets; (ii) the cloud parameterization, including the functional form, free parameters, and scattering properties; (iii) the full set of retrieval priors and their ranges; and (iv) the validation metrics, such as convergence criteria and goodness-of-fit diagnostics. These additions enable independent assessment and reproduction of the reported thresholds. revision: yes
Circularity Check
No significant circularity; results derive from independent forward simulations and retrievals on synthetic data
full rationale
The paper generates synthetic Ariel transmission spectra via forward modeling for three benchmark planets across Tiers 1-3, then performs retrievals to quantify chemical constraints (e.g., <1.5 dex on H2O/CO2 for giants irrespective of clouds). This chain relies on external noise models, opacity databases, and retrieval frameworks applied to simulated data; no step reduces a claimed prediction to a quantity defined by the authors' own prior fits, self-definitions, or load-bearing self-citations. The derivation remains self-contained and falsifiable against real Ariel data or alternative models.
Axiom & Free-Parameter Ledger
free parameters (2)
- Tier-specific noise floors and precision targets
- Number of transits per target
axioms (1)
- domain assumption Atmospheric retrieval codes recover true parameters from noise-free and noisy spectra without major systematic bias
Reference graph
Works this paper leans on
-
[1]
3 https://zenodo.org/records/19443323 10Radica et al. 4 3 2 log XH2O Tier 1 Tier 2 Tier 3 Cloud Free 1 mbar Cloud 0.5 1.0Precision [dex] 1 3 5 7 10 15 20 Number of Transits 0.0 0.5 1.0 1.5MSE Figure 6.Same as Figure 3, but showing trends for H 2O in HAT-P-11 b. 3.0 2.5 2.0 1.5 log XCO Tier 1 Tier 2 Tier 3 Cloud Free 1 mbar Cloud 0.5 1.0Precision [dex] 1 3...
-
[2]
Ahrer, E.-M., Stevenson, K. B., Mansfield, M., et al. 2023, Nature, 614, 653, doi: 10.1038/s41586-022-05590-4
-
[3]
Alderson, L., Batalha, N. E., Wakeford, H. R., et al. 2024, AJ, 167, 216, doi: 10.3847/1538-3881/ad32c9
-
[4]
2026, AJ, 171, 215, doi: 10.3847/1538-3881/ae4494
Ashtari, R., Collins, S., Splinter, J., et al. 2026, AJ, 171, 215, doi: 10.3847/1538-3881/ae4494
-
[5]
Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, Annu. Rev. Astron. Astrophys., 47, 481, doi: 10.1146/annurev.astro.46.060407.145222 Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33, doi: 10.1051/0004-6361/201322068 Astropy Collaboration, Price-Whelan, A. M., Sip˝ ocz, B. M., et al. 2018, AJ, 156, 123, doi: ...
-
[6]
Naumenko, O. V. 2016, MNRAS, 460, 4063, doi: 10.1093/mnras/stw1133
-
[7]
Baraffe, I., Homeier, D., Allard, F., & Chabrier, G. 2015, Astronomy & Astrophysics, 577, doi: 10.1051/0004-6361/201425481 On the Ariel Tier System11 3 2 1 log XCH4 Tier 1 Tier 2 Tier 3 Cloud Free 1 mbar Cloud 0.0 0.5 1.0Precision [dex] 0 25 50 75 100 125 150 175 200 Number of Transits 0 1 2 3MSE Figure 8.Same as Figure 7, but showing trends for CH 4 in K...
-
[8]
” Rothman et al. (2010) Polyansky et al. (2018) “
Barber, R. J., Strange, J. K., Hill, C., et al. 2014, MNRAS, 437, 1828, doi: 10.1093/mnras/stt2011
-
[9]
Barstow, J. K., Changeat, Q., Chubb, K. L., et al. 2022, Experimental Astronomy, 53, 447, doi: 10.1007/s10686-021-09821-w
-
[10]
2013, ApJ, 778, 153, doi: 10.1088/0004-637X/778/2/153
Benneke, B., & Seager, S. 2013, ApJ, 778, 153, doi: 10.1088/0004-637X/778/2/153
-
[11]
2017, ApJ, 834, 187, doi: 10.3847/1538-4357/834/2/187
Benneke, B., Werner, M., Petigura, E., et al. 2017, ApJ, 834, 187, doi: 10.3847/1538-4357/834/2/187
-
[12]
2016, Stat Comput, 26, 383, doi: 10.1007/s11222-014-9512-y
Buchner, J. 2016, Stat Comput, 26, 383, doi: 10.1007/s11222-014-9512-y
-
[13]
Winn, J. N. 2008, The Astrophysical Journal, 689, 499–512, doi: 10.1086/592321
-
[14]
Changeat, Q., Al-Refaie, A., Mugnai, L. V., et al. 2020, AJ, 160, 80, doi: 10.3847/1538-3881/ab9a53 12Radica et al. T able 3.Retrieval Priors Parameter Prior Range log VMR U[−12,−1] log Pcloud [bar] U[−6, 3] αRay U[0, 10] γRay U[−5, 5] ×Rp U[0.75×Rp, 1.25×Rp] Tiso [K] U[100, 2000] Note—Udenotes a uniform prior on the specified range. VMR prior ranges for ...
-
[15]
Changeat, Q., Lagage, P.-O., Tinetti, G., et al. 2025, On the synergetic use of Ariel and JWST for exoplanet atmospheric science, arXiv, doi: 10.48550/arXiv.2509.02657
-
[16]
Charnay, B., Mendon¸ ca, J. M., Kreidberg, L., et al. 2022, Experimental Astronomy, 53, 417, doi: 10.1007/s10686-021-09715-x
-
[17]
Christiansen, J. L., McElroy, D. L., Harbut, M., et al. 2025, Planet. Sci. J., 6, 186, doi: 10.3847/PSJ/ade3c2
-
[18]
and Rocchetto, Marco and Yurchenko, Sergei N
Chubb, K. L., Rocchetto, M., Yurchenko, S. N., et al. 2021, A&A, 646, A21, doi: 10.1051/0004-6361/202038350
-
[19]
Claringbold, A. B., Fisher, C. E., Kirk, J., et al. 2026, MNRAS, 546, stag143, doi: 10.1093/mnras/stag143
-
[20]
2017, A&A, 608, A35, doi: 10.1051/0004-6361/201731558
Cloutier, R., Astudillo-Defru, N., Doyon, R., et al. 2017, A&A, 608, A35, doi: 10.1051/0004-6361/201731558
-
[21]
Coles, P. A., Yurchenko, S. N., & Tennyson, J. 2019, MNRAS, 490, 4638, doi: 10.1093/mnras/stz2778
-
[22]
2023, ApJL, 943, L10, doi: 10.3847/2041-8213/acaead
Constantinou, S., Madhusudhan, N., & Gandhi, S. 2023, ApJL, 943, L10, doi: 10.3847/2041-8213/acaead
-
[23]
Cowan, N. B., & Coull-Neveu, B. 2025, The Open Journal of Astrophysics, 8, doi: 10.33232/001c.146656
-
[24]
Crossfield, I. J. M., Ciardi, D. R., Petigura, E. A., et al. 2016, ApJS, 226, 7, doi: 10.3847/0067-0049/226/1/7 D’Aoust, L., Coull-Neveu, B., Lee, E. J., & Cowan, N. B. 2025, The Astrophysical Journal, 995, 144, doi: 10.3847/1538-4357/ae10ac
-
[25]
Davey, J. J., Yip, K. H., Al-Refaie, A. F., & Waldmann, I. P. 2024, Monthly Notices of the Royal Astronomical Society, 536, 2618, doi: 10.1093/mnras/stae2731
-
[26]
2019, AJ, 157, 242, doi: 10.3847/1538-3881/ab1cb9
Edwards, B., Mugnai, L., Tinetti, G., Pascale, E., & Sarkar, S. 2019, AJ, 157, 242, doi: 10.3847/1538-3881/ab1cb9
-
[27]
2022, AJ, 164, 15, doi: 10.3847/1538-3881/ac6bf9
Edwards, B., & Tinetti, G. 2022, AJ, 164, 15, doi: 10.3847/1538-3881/ac6bf9
-
[28]
Faedi, F., Barros, S. C. C., Anderson, D. R., et al. 2011, A&A, 531, A40, doi: 10.1051/0004-6361/201116671
-
[29]
D., Radica, M., Welbanks, L., et al
Feinstein, A. D., Radica, M., Welbanks, L., et al. 2023, Nature, 614, 670, doi: 10.1038/s41586-022-05674-1
-
[30]
F., Capozziello, S., & Dainotti, M
Feroz, F., Hobson, M. P., & Bridges, M. 2009, Monthly Notices of the Royal Astronomical Society, 398, 1601, doi: 10.1111/j.1365-2966.2009.14548.x
-
[31]
Fortney, J. J. 2005, Monthly Notices of the Royal Astronomical Society, 364, 649, doi: 10.1111/j.1365-2966.2005.09587.x
-
[32]
Greene, T. P., Line, M. R., Montero, C., et al. 2016, ApJ, 817, 17, doi: 10.3847/0004-637X/817/1/17
-
[33]
Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357, doi: 10.1038/s41586-020-2649-2
-
[34]
Hunter, J. D. 2007, Computing in Science & Engineering, 9, 90, doi: 10.1109/MCSE.2007.55
-
[35]
2013, A&A, 553, A6, doi: 10.1051/0004-6361/201219058
Husser, T.-O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6, doi: 10.1051/0004-6361/201219058
-
[36]
Kirk, J., Ahrer, E.-M., Claringbold, A. B., et al. 2025, Monthly Notices of the Royal Astronomical Society, 537, 3027, doi: 10.1093/mnras/staf208
-
[37]
Li, G., Gordon, I. E., Rothman, L. S., et al. 2015, ApJS, 216, 15, doi: 10.1088/0067-0049/216/1/15
-
[38]
R., Zhang, X., Vasisht, G., et al
Line, M. R., Zhang, X., Vasisht, G., et al. 2012, The Astrophysical Journal, 749, 93, doi: 10.1088/0004-637X/749/1/93
-
[39]
MacDonald, R. J. 2023, JOSS, 8, 4873, doi: 10.21105/joss.04873
-
[40]
MacDonald, R. J., & Madhusudhan, N. 2017, Monthly Notices of the Royal Astronomical Society, 469, 1979, doi: 10.1093/mnras/stx804
-
[41]
2012, ApJ, 758, 36, doi: 10.1088/0004-637X/758/1/36
Madhusudhan, N. 2012, ApJ, 758, 36, doi: 10.1088/0004-637X/758/1/36
-
[42]
2023b, The Astrophysical Journal Letters, 956, L13, doi: 10.3847/2041-8213/acf577
Madhusudhan, N., Sarkar, S., Constantinou, S., et al. 2023, ApJL, 956, L13, doi: 10.3847/2041-8213/acf577
-
[43]
Mahajan, A. S., Eastman, J. D., & Kirk, J. 2024, The Astrophysical Journal Letters, 963, doi: 10.3847/2041-8213/ad29f3 On the Ariel Tier System13
-
[44]
2018, A&A, 613, A41, doi: 10.1051/0004-6361/201732234
Mancini, L., Esposito, M., Covino, E., et al. 2018, A&A, 613, A41, doi: 10.1051/0004-6361/201732234
-
[45]
Meech, A., Claringbold, A. B., Ahrer, E.-M., et al. 2025, Monthly Notices of the Royal Astronomical Society, 539, 1381, doi: 10.1093/mnras/staf530
-
[46]
Moses, J. I., Visscher, C., Fortney, J. J., et al. 2011, ApJ, 737, 15, doi: 10.1088/0004-637X/737/1/15
-
[47]
Moses, J. I., Line, M. R., Visscher, C., et al. 2013, ApJ, 777, 34, doi: 10.1088/0004-637X/777/1/34
-
[48]
V., Al-Refaie, A., Bocchieri, A., et al
Mugnai, L. V., Al-Refaie, A., Bocchieri, A., et al. 2021, AJ, 162, 288, doi: 10.3847/1538-3881/ac2e92
-
[49]
V., Pascale, E., Edwards, B., Papageorgiou, A., & Sarkar, S
Mugnai, L. V., Pascale, E., Edwards, B., Papageorgiou, A., & Sarkar, S. 2020, Experimental Astronomy, 50, 303–328, doi: 10.1007/s10686-020-09676-7
-
[50]
Cowan, N. B. 2026, arXiv e-prints, arXiv:2601.21020, doi: 10.48550/arXiv.2601.21020 P´ erez, F., & Granger, B. E. 2007, Computing in Science and Engineering, 9, 21, doi: 10.1109/MCSE.2007.53
-
[51]
V., Madhusudhan, N., & Apai, D
Pinhas, A., Rackham, B. V., Madhusudhan, N., & Apai, D. 2018, Monthly Notices of the Royal Astronomical Society, 480, 5314, doi: 10.1093/mnras/sty2209
-
[52]
Polyansky, O. L., Kyuberis, A. A., Zobov, N. F., et al. 2018, MNRAS, 480, 2597, doi: 10.1093/mnras/sty1877
-
[53]
Powell, D., Feinstein, A. D., Lee, E. K. H., et al. 2024, Nature, 626, 979, doi: 10.1038/s41586-024-07040-9
-
[54]
2022b, Monthly Notices of the Royal Astronomical Society, 517, 5050, doi: 10.1093/mnras/stac3024
Radica, M., Artigau, E., Lafreni´ ere, D., et al. 2022, Monthly Notices of the Royal Astronomical Society, 517, 5050, doi: 10.1093/mnras/stac3024
-
[55]
2023, Monthly Notices of the Royal Astronomical Society, 524, 835, doi: 10.1093/mnras/stad1762
Radica, M., Welbanks, L., Espinoza, N., et al. 2023, Monthly Notices of the Royal Astronomical Society, 524, 835, doi: 10.1093/mnras/stad1762
-
[56]
2024, ApJL, 962, L20, doi: 10.3847/2041-8213/ad20e4
Radica, M., Coulombe, L.-P., Taylor, J., et al. 2024, ApJL, 962, L20, doi: 10.3847/2041-8213/ad20e4
-
[57]
Radica, M., Taylor, J., Rotman, Y., et al. 2026, Super-Solar Metallicity and Tentative Evidence for Photochemistry on WASP-96b from JWST and Ground-Based VLT Transmission Spectroscopy, arXiv, doi: 10.48550/arXiv.2604.05049
work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2604.05049 2026
-
[58]
The Astrophysical Journal , author =
Rotman, Y., Welbanks, L., Line, M. R., et al. 2025, ApJ, 989, 201, doi: 10.3847/1538-4357/adef04
-
[59]
, year = 2015, month = may, volume =
Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, PhyS, 90, 054005, doi: 10.1088/0031-8949/90/5/054005
-
[60]
Stassun, K. G., Collins, K. A., & Gaudi, B. S. 2017, The Astronomical Journal, 153, 136, doi: 10.3847/1538-3881/aa5df3
-
[61]
Stock, J. W., Kitzmann, D., Patzer, A. B. C., & Sedlmayr, E. 2018, MNRAS, 479, 865, doi: 10.1093/mnras/sty1531
-
[62]
Thorngren, D. P., Sing, D. K., & Mukherjee, S. 2026, ApJS, 283, 10, doi: 10.3847/1538-4365/ae0e71
-
[63]
European Planetary Science Congress , year = 2022, month = sep, eid =
Tinetti, G., Eccleston, P., Lueftinger, T., et al. 2022, in European Planetary Science Congress, EPSC2022–1114, doi: 10.5194/epsc2022-1114
-
[64]
2018, Experimental Astronomy, 46, 135, doi: 10.1007/s10686-018-9598-x
Tinetti, G., Drossart, P., Eccleston, P., et al. 2018, Exp Astron, 46, 135, doi: 10.1007/s10686-018-9598-x
-
[65]
Tsai, S.-M., Lee, E. K. H., Powell, D., et al. 2023, Nature, 617, 483, doi: 10.1038/s41586-023-05902-2
-
[66]
S., Tennyson, J., Yurchenko, S
Underwood, D. S., Tennyson, J., Yurchenko, S. N., et al. 2016, MNRAS, 459, 3890, doi: 10.1093/mnras/stw849
-
[67]
Valentine, D., Wakeford, H. R., Hammond, M., et al. 2025, Monthly Notices of the Royal Astronomical Society, 544, 3647, doi: 10.1093/mnras/staf1721
-
[68]
Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261, doi: 10.1038/s41592-019-0686-2
-
[69]
2019, AJ, 157, 206, doi: 10.3847/1538-3881/ab14de
Welbanks, L., & Madhusudhan, N. 2019, The Astronomical Journal, 157, 206, doi: 10.3847/1538-3881/ab14de
-
[70]
Welbanks, L., Madhusudhan, N., Allard, N. F., et al. 2019, ApJ, 887, L20, doi: 10.3847/2041-8213/ab5a89
-
[71]
Tennyson, J. 2020, MNRAS, 496, 5282, doi: 10.1093/mnras/staa1874
-
[72]
N., Owens, A., Kefala, K., & Tennyson, J
Yurchenko, S. N., Owens, A., Kefala, K., & Tennyson, J. 2024, MNRAS, 528, 3719, doi: 10.1093/mnras/stae148
-
[73]
Zellem, R. T., Swain, M. R., Cowan, N. B., et al. 2019, Publications of the Astronomical Society of the Pacific, 131, 094401, doi: 10.1088/1538-3873/ab2d54
-
[74]
2018, Experimental Astronomy, 46, 67, doi: 10.1007/s10686-018-9572-7
Zingales, T., Tinetti, G., Pillitteri, I., et al. 2018, Experimental Astronomy, 46, 67, doi: 10.1007/s10686-018-9572-7
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