With a new generation of observatories coming online this decade, the process of characterizing exoplanet atmospheres will need to be reinvented. Currently mostly on the instrumental side, characterization bottlenecks will soon appear at the models used to translate spectra into atmospheric properties. Limitations stemming from our stellar and atmospheric models have already been highlighted. Here, we show that the current limitations of the opacity models used to decode exoplanet spectra propagate into an accuracy wall at ~0.5–1.0 dex (that is, three- to tenfold) on the atmospheric properties, which is an order of magnitude above the precision targeted by James Webb Space Telescope Cycle 1 programmes and needed, for example, for meaningful C/O-ratio constraints and biosignature identification. We perform a sensitivity analysis using nine different opacity models and find that most of the retrievals produce harmonious fits owing to compensations in the form of >5σ biases on the derived atmospheric parameters translating into the aforementioned accuracy wall. We suggest a two-tier approach to alleviate this problem, involving a new retrieval procedure and guided improvements in opacity data, their standardization and optimal dissemination.
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This paper makes use of the opacity data from the HITRAN201620, HITEMP201022 and ExoMol21 databases. The perturbed opacity cross-sections and the synthetic exoplanet transmission spectra are available from the corresponding author upon request and can be (re)generated using the tierraCrossSection and tierra codes (Code availability), respectively. Source data are provided with this paper.
This work makes use of the following publicly available codes: emcee69, ExoCross42 and HAPI19. Additionally, it is based on tierra, which is now publicly available at https://github.com/disruptiveplanets/tierra, and tierraCrossSection, which is also available, at https://github.com/disruptiveplanets/tierraCrossSection.
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P.N. acknowledges the support of the Grayce B. Kerr Fellowship Fund and Elliot Fellowship at MIT. We thank B. V. Rackham, E. K. Conway and S. Seager for discussions on various topics presented in this paper. P.N. thanks P. Molliere for benchmark testing with petitRADTRANS. We acknowledge the MIT Supercloud and Lincoln Laboratory Supercomputing Center for providing (high-performance computing, database, consultation) resources that have contributed to the research results reported within this Article.
The authors declare no competing interests.
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Extended Data Fig. 1 Framework for sensitivity analysis of retrieved atmospheric properties to opacity model.
The four building blocks of the transmission spectra are shown in green, analysis techniques are marked in blue, and the orange parallelogram highlights the remote sensing technique at the center of this perturbation/sensitivity analysis. The arrows are shown to indicate the direction of the information flow. We perform self- and cross-retrieval for two planetary cases (a super-Earth around M-dwarf and a Jupiter-sized planet around K-dwarf, see Supplementary Table 2) with nine distinct sets of cross-sections (see Supplementary Table 1) to access their impacts.
Uncertainties on the line parameters vs line intensities as reported in HITRAN for methane (red), water (yellow), ozone (blue), and carbon dioxide (brown). For each uncertainty range reported (y axis), the mean and median line intensity values are shown as empty and full diamonds, with the 1 and 2σ intensity ranges. The number of lines in each uncertainty range is reported on the right side of its 2σ interval. These uncertainties are used to perturb the four different parameters in the generation of CS-1SUP and CS-1SDN. The parameters of the strongest lines are reported with the smallest uncertainties. a: Uncertainty on the line position. b: Uncertainty on the line intensity. c: Uncertainty on the air broadening coefficient. d: Uncertainty on the temperature dependency of the air broadening coefficient. The uncertainty codes (average, default, unreported) are introduced in Ref. 41.
Benchmarking of tierra (R=100,000) against petitRadtrans for a Jupiter-sized planet around a K dwarf (0.55 R⊙) for 365 K isothermal temperature with base pressure of 1 atm containing water at mixing ratio of 10−5 for a combined NIRSpec and MIRI observation. We use the cross-sections from petitRadtrans, which present a lower resolution on their temperature and pressure grids, to focus this benchmarking on tierra rather than possible difference on underlying cross-sections. The median absolute deviation between two models is 1.95 p.p.m. and RMS is 4.4 ppm which is marginal in comparison to the deviations seen in the model comparisons (Fig. 2).
Extended Data Fig. 4 Corner plot of the posterior probability distribution of the atmospheric parameters for a super-Earth.
Corner plot showing the PPDs of the retrieved parameters for the case of the super-Earth for self-retrieval (CS-DFLT, red) and cross-retrieval (CS-MAXB, green). The only difference between the two cross-sections relate to broadening; CS-DFLT assumes air-broadening (geocentric) while CS-MAXB assumes twice the maximum between air- and self-broadening. Strong biases are seen in the retrieved value of water (-6.97σ), carbon dioxide (-6.23σ), methane (-6.23σ), and ozone (-6.23σ). (Top Right) 500 random PT profiles constructed from the posteriors are shown for comparison against the true profile shown in black. The dotted line shows the contribution factor can change substantially due to the changes in the broadening values.
Extended Data Fig. 5 Propagation of the ensemble of opacity-model perturbations to the level of retrieved atmospheric properties for the warm-Jupiter scenario.
Posterior probability distributions (PPDs) of the retrieved atmospheric parameters for the warm-Jupiter scenario highlighting the biases induced by perturbations to the opacity model (see Methods). Each cross-section is identified by its color and label on the right. The dotted black vertical lines represent the true values used in generating the synthetic spectrum. Deviations with a statistical significance of up to 20σ and physical significance of over 1 dex are reported.
Extended Data Fig. 6 Corner plot of the posterior probability distribution of the atmospheric parameters for a warm-Jupiter.
Corner plot showing the PPDs of the retrieved parameters for the case of the warm-Jupiter for self-retrieval (CS-DFLT, red) and cross-retrieval (CS-SELF, blue). The only difference between the two cross-sections relate to self-broadening; CS-DFLT assumes air-broadening (geocentric) while CS-SELF assumes only self-broadening. Strong biases are seen in the retrieved value of T0 (7.32σ), T∞ (2.64σ), carbon dioxide (7.32σ), methane (7.32σ), water (5.55σ), ozone (-5.57σ), and hydrogen (-3.97σ). (Top Right) 500 random PT profiles constructed from the posteriors are shown for comparison against the true profile shown in black. The dotted line shows the contribution factor can change substantially due to the changes in the pressure broadening values.
Plot highlighting the difference in sensitivity to CO’s number density between CS-DFLT (red) and CS-HTMP (gray) for the super-Earth case. (Top) Best-fit models are shown as solid lines while the models perturbed by -0.25 on Log10NCO are shown as dashed lines. (Bottom) Difference between best-fit and perturbed models, highlighting that the primary effect of a change in CO abundance is a change in scale height (all molecular features are affected). While a 0.25 change on Log10NCO from its best-fit value for CS-DFLT increases the χ2 by ~ 1,000, it does increases the χ2 for CS-HTMP by ~ 3,500 which explained the tighter constraint on CO reported in Fig. 3 and Supplementary Table 1.
Parameters and line-list sources used in the generation of our set of nine different cross-sections.
Parameters used for the generation of synthetic models.
Retrieved parameters† and their observed biases‡ for the case of a super-Earth.
Retrieved parameters† and their observed biases‡ for the case of a warm Jupiter.
Opacity cross-sections for water line/band around 1.37 μm.
Transmission spectra for a warm Jupiter using nine different opacity models.
Best-fit model for the cross-retrieval of a warm Jupiter from its synthetic transmission spectrum simulated with nominal cross-section CS-DFLT and retrieved with cross-section CS-SELF.
Raw MCMC output for the atmospheric retrieval of the super-Earth scenario used to build the posterior distributions of the atmospheric parameters shown in Fig. 4.
Spectrum statistical distance versus parametric statistical distance versus parametric physical distance for the nine different opacity models.
Statistics on the measurement uncertainties on absorption line parameters reported in HITRAN.
Benchmarking of tierra against petitRadtrans.
Raw MCMC output for the atmospheric retrieval of the super-Earth scenario used to build the posterior distributions of the atmospheric parameters shown in Extended Data Fig. 4.
Raw MCMC output for the atmospheric retrieval of the warm-Jupiter scenario used to build the posterior distributions of the atmospheric parameters shown in Extended Data Fig. 5.
Raw MCMC output for the atmospheric retrieval of the warm-Jupiter scenario used to build the posterior distributions of the atmospheric parameters shown in Extended Data Fig. 6.
Spectra of the models presented in Extended Data Fig. 7.
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Niraula, P., de Wit, J., Gordon, I.E. et al. The impending opacity challenge in exoplanet atmospheric characterization. Nat Astron 6, 1287–1295 (2022). https://doi.org/10.1038/s41550-022-01773-1