Determining the prevalence of atmospheres on terrestrial planets is a core objective in exoplanetary science. While M dwarf systems offer a promising opportunity, conclusive observations of terrestrial atmospheres have remained elusive, with many yielding flat transmission spectra. We observe four transits of the hot terrestrial planet TOI-1685 b using James Webb Space Telescope (JWST)'s Near Infrared Spectrograph (NIRSpec) G395H instrument. Combining this with the transit from the previously observed phase curve of the planet with the same instrument, we perform a detailed analysis to determine the possibility of an atmosphere on TOI-1685 b. From our retrievals, the Bayesian evidence favours a simple flat line model, indicating no evidence for an atmosphere on TOI-1685 b, in line with results from the phase curve analysis. Our results show that hydrogen-dominated atmospheres can be confidently ruled out. For heavier, secondary atmospheres we find a lower limit on the mean molecular weight of greater than or similar to 10, at a significance of similar to 5 sigma. Pure CO2, SO2, H2O, and CH4 atmospheres, or a mixed secondary atmosphere (CO + CO2 + SO2) could explain the data (Delta ln Z < 3). However, pure CH4 atmospheres may be physically unlikely, and the pure H2O and CO2 cases require a high-altitude cloud, which could also be interpreted as a thin cloud-free atmosphere. We discuss the theoretical possibility for different types of atmosphere on this planet, and consider the effects of atmospheric escape and stellar activity on the system. Though we find that TOI-1685 b is likely a bare rock, this study also highlights the challenges of detecting secondary atmospheres on rocky planets with JWST.

JWST is transforming our ability to characterize small exoplanets, from sub-Neptunes to rocky worlds. A key open question is whether highly irradiated rocky planets can retain atmospheres or are stripped bare by stellar irradiation-a boundary that remains to be mapped observationally. Here we present the first JWST secondary eclipse observations of the rocky exoplanet GJ 3473 b, obtained with MIRI F1500W photometry. Using four visits, we confidently detect the eclipse at an average depth of 186 +/- 45 ppm, somewhat lower than expected for a blackbody. We test a wide range of data reduction and analysis assumptions and provide new insights into MIRI detector settling behavior that will benefit future observations. We model a suite of airless surfaces with varied compositions, textures, and degrees of space weathering, as well as idealized atmospheric scenarios including the possibility of atmospheric collapse. Both atmospheric and bare-rock interpretations remain consistent with the data, but we exclude thick CO2 atmospheres, placing a 95% credible upper limit of 1.2-6.5 bar on the surface pressure. We also find tentative evidence for visit-to-visit variability in eclipse depth (33-371 ppm), though additional data are required to confirm this. Our results highlight the challenges and intrinsic degeneracies in interpreting MIRI F1500W eclipse measurements of rocky exoplanets, indicating that such observations alone may not uniquely distinguish between bare-rock and atmospheric scenarios. Future spectroscopic or phase-curve observations will be required to determine whether or not GJ 3473 b hosts a substantial atmosphere.

This chapter reviews the current state of observational and theoretical efforts in the characterization of exoplanet atmospheres, with a focus on developments enabled through the Swiss National Centre for Competence in Research (NCCR) PlanetS. It covers the essential physical and chemical processes that govern atmospheric dynamics, radiative transfer, chemistry, and cloud formation in exoplanets and brown dwarfs. The review discusses the modeling approaches used to simulate these processes, ranging from simplified 1D models to fully coupled 3D general circulation models. Atmospheric retrieval frameworks are presented as tools for inferring atmospheric properties from observational data, highlighting both classical Bayesian techniques and emerging machine learning methods. Observational strategies using instruments like HST, JWST, and ground-based high-resolution spectrographs are also examined. Special emphasis is placed on the interplay between theory and observation, and how developments in modeling, data analysis, and instrumentation collectively advance our understanding of planetary atmospheres beyond the Solar System.

Observations of transiting hot Jupiters have revealed a mismatch between the values of the Bond versus geometric albedos. In the planetary science literature, the ratio of these quantities is known as the phase integral. It has been extensively measured for the solar system planets and shown to generally be nonunity in value. We use existing Cassini data on Jupiter to derive bandpass-integrated geometric albedos and phase integrals in the CHEOPS, TESS, and Ariel bandpasses, demonstrating that these quantities vary markedly across these different wavelength ranges. By performing a population study of geometric albedos and phase integrals, we demonstrate that atmospheres with partial cloud cover may be identified using measurements of the phase integral if its measured uncertainty is ∼0.1, which corresponds to an uncertainty of ∼3% on the optical/visible secondary eclipse depth. The upcoming Ariel space mission will conduct an unprecedented statistical survey of cloud cover on hot Jupiters via the simultaneous measurement of ∼100 infrared phase curves and optical secondary eclipses. Whenever available, the shape of optical phase curves of reflected light will directly constrain the phase integral, spherical albedo, degree of cloud cover, and scattering asymmetry factor.

We investigate the geometric albedos of hot Jupiters by comparing observational data from space telescopes TESS, Kepler, CoRoT, and CHEOPS against theoretical models. The study aims to understand the distribution of observed geometric albedos across different bandpasses and how these observations align with or deviate from model predictions. We curated a comprehensive sample of observed geometric albedos, using either existing Spitzer secondary eclipse measurements or a scaling law between the equilibrium and dayside temperature to remove any contaminating thermal planetary emission. We then utilised hierarchical Bayesian modelling to identify trends with planetary properties such as equilibrium temperature, gravity, and stellar metallicity. On a population level, we found no statistical difference in the distributions of geometric albedos measured by TESS compared to those measured by Kepler, CoRoT, and CHEOPS. We confront the geometric albedo sample with a simple but first-principles model that includes Rayleigh scattering by molecular hydrogen and absorption by sodium, water, titanium oxide, and vanadium oxide. We find that the abundance of sodium and water are the key absorbers that influence the geometric albedos of hot Jupiters, whilst the addition of titanium oxide and vanadium oxide (in the absence of condensation) results in vanishing geometric albedos that are inconsistent with the observed distributions.

High-resolution UV spectroscopy serves a diversity of science cases, from small bodies to planets, stars, and galaxies, but is currently limited to the Hubble Space Telescope and bright targets. Major advances require increasing sensitivity by at least one order of magnitude. Here we present the UV science cases for PEGASUS (Planets, Earths, Galaxies, And Stars UV Spectrograph), a UV Échelle high-resolution spectrograph concept, with R = λ/δλ∼ 100 000 (full range 10 000-140 000) and covering 90–400 nm, with a foreseen extension to at least 800 nm. PEGASUS is ideally suited for the Habitable Worlds Observatory (HWO), enabling transformative science across the UV/optical wavelength ranges. PEGASUS will be unique in high sensitivity (effective area) and high spectral resolution – an uncharted territory – as well as robustness, thanks to the simplicity of its design. Its UV science cases include: I) Formation and evolution of planets and their habitability: properties of exoplanets and atmospheres, protoplanetary disks, Solar System bodies; II) Stellar lives and deaths at their extremes: the first stars and the origin of the elements, compact and massive stars, Supernovae; III) Gas and metals in the baryon cycle of galaxies: the interstellar, circumgalactic, and intergalactic medium and their roles in galaxy growth. These are essential for the Astro Decadal 2020 Survey, Voyage 2050, and HWO. While this paper focuses on high-impact science enabled by UV high-resolution spectroscopy, PEGASUS will extend into the optical regime and lower spectral resolution, making it a multi-purpose, widely used, workhorse spectrograph for HWO.

The atmospheres of sub-Neptunes provide a window into their internal structure and history, shedding light on the origin of this common, but enigmatic, class of exoplanets. However, the physical and chemical processes that shape sub-Neptunes' transmission spectra, in particular cloud and haze formation, are not well understood. To identify possible correlations between transmission spectra and UV irradiation, the SPACE (Sub-neptune Planetary Atmosphere Characterization Experiment) Program observed an array of sub-Neptunes and their host stars using the Hubble Space Telescope (HST), measuring the planets' transmission spectra between 1.1 μm and 1.7 μm with the Wide Field Camera 3 (WFC3) and the stars' UV spectra with the Space Telescope Imaging Spectrograph (STIS). Here, we present the observations of HD 191939 b carried out as part of the SPACE Program, which reveal no significant spectral features in the transmission spectrum. The data deliver moderate evidence at significance levels between 2.0 σ and 3.2 σ against a cloud-free atmosphere with solar metallicity, rendering this scenario unlikely, but still possible. A super-solar metallicity of HD 191939 b might be consistent with the known trend of increasing atmospheric metallicity with decreasing planet mass. Both hydrocarbon haze formation and cloud condensation can be efficient at HD 191939 b's zero-albedo equilibrium temperature of (880± 20)K, particularly in atmospheres with super-solar metallicity, possibly additionally muting absorption features.

Context. M-dwarf systems offer an opportunity to study terrestrial exoplanetary atmospheres due to their small size and cool temperatures. However, the extreme conditions imposed by these host stars raise a question about whether their close-in rocky planets are able to retain any atmosphere at all. Aims. The Hot Rocks Survey aims to answer this question by targeting nine different M-dwarf rocky planets spanning a range of planetary and stellar properties. Of these, LHS 1478 b orbits an M3-type star, has an equilibrium temperature of T-eq = 585 K, and receives 21 times Earth's instellation. Methods. We observed two secondary eclipses of LHS 1478 b using photometric imaging at 15 mu m using the Mid-Infrared Instrument on the James Webb Space Telescope (JWST MIRI) to measure thermal emission from the dayside of the planet. We compared these values to atmospheric models to evaluate potential heat transport and CO2 absorption signatures. Results. We find that a secondary eclipse depth of 138 +/- 53 ppm at the expected time for a circular orbit is preferred over a null model at 2.8 sigma, a moderate detection, though dynamical models do favour a non-eccentric orbit for this planet. The second observation results in a non-detection due to significantly larger unexplained systematics. Based on the first observation alone, we can reject the null hypothesis of the dark (zero Bond albedo) no atmosphere bare rock model with a confidence level of 3.3 sigma, though for A(B) = 0.2 the significance decreases to 2.1 sigma. The tentative secondary eclipse depth is consistent with the majority of the atmospheric scenarios we considered, spanning CO2-rich atmospheres with surface pressures from 0.1 to 10 bar. However, we stress that the two observations from our programme do not yield consistent results, and more observations are needed to verify our findings. The Hot Rocks Survey serves as a relevant primer for future endeavours such as the Director's Discretionary Time (DDT) Rocky Worlds programme.

Stellar surface heterogeneities, such as spots and faculae, often contaminate exoplanet transit spectra, hindering precise atmospheric characterization. We demonstrate a novel, epoch-based, model-independent method to mitigate stellar contamination, applicable to multiplanet systems with at least one airless planet. We apply this method using quasi-simultaneous transits of TRAPPIST-1 b and TRAPPIST-1 c observed on 2024 July 9, with JWST/NIRSpec PRISM. These two planets, with nearly identical radii and impact parameters, are likely to either be bare rocks or possess thin, low-pressure atmospheres, making them ideal candidates for this technique, as variations in their transit spectra would be primarily attributed to stellar activity. Our observations reveal their transit spectra exhibit consistent features, indicating similar levels of stellar contamination. We use TRAPPIST-1 b to correct the transit spectrum of TRAPPIST-1 c, achieving a 2.5 × reduction in stellar contamination at shorter wavelengths. At longer wavelengths, lower signal-to-noise ratio prevents clear detection of contamination or full assessment of mitigation. Still, out-of-transit analysis reveals variations across the spectrum, suggesting contamination extends into the longer wavelengths. Based on the success of the correction at shorter wavelengths, we argue that contamination is also reduced at longer wavelengths to a similar extent. This shifts the challenge of detecting atmospheric features to a predominantly white noise issue, which can be addressed by stacking observations. This method enables epoch-specific stellar contamination corrections, allowing coaddition of planetary spectra for reliable searches of secondary atmospheres with signals of 60–250 ppm. Additionally, we identify small-scale cold (∼2000 K) and warm (∼2600 K) regions almost uniformly distributed on TRAPPIST-1, with overall covering fractions varying by ∼0.1% per hour.

Hydrogen- and helium-rich primordial atmospheres of small rocky planets, formed as a result of planetary accretion, are subject to subsequent modifications of geochemical outgassing. Two outcomes are possible: a secondary atmosphere forms if the outgassing completely replaces the primordial atmosphere, or a hybrid atmosphere results if the primordial atmosphere undergoes a partial loss with its leftover reacting with the newly outgassed species. We constructed a zero-dimensional thermodynamic model where both scenarios can be consistently simulated. The model assumes chemical equilibrium and admits input parameters of oxidation and sulfidation states of the mantle, melt temperature, atmospheric nitrogen content, surface pressure (for secondary atmosphere models), and hydrogen partial pressure (for hybrid atmosphere models). It computes the chemical compositions of outgassing, namely, the volume mixing ratios of various gaseous species. Non-ideal gas behaviors are accounted for in the model and the calculated secondary and hybrid atmospheres both exhibit a vast chemical diversity. For example, hydrogen-rich atmospheres, conventionally deemed of primordial origin, can also stem from interior outgassing. By Monte Carlo sampling in the possible ranges of the input parameters, we found that outgassed methane-dominated atmospheres, regardless of secondary or hybrid, require rather specific conditions: (1) a reduced rocky mantle; (2) relatively low melt temperatures in comparison to those of basaltic or peridotitic melts; (3) relatively high atmosphere pressures (> c.a. 10 bar) on the rocky surface. Moreover, we found that the abundance ratio of CO2 and CO can serve as a powerful diagnostic of oxygen fugacity of rocky mantles, which could potentially be constrained by future James Webb Space Telescope spectra. The current model does not consider atmospheric escape, chemical kinetics or photochemistry, which awaits to be incorporated in future works.

In the era of the James Webb Space Telescope (JWST), the dramatic improvement in the spectra of exoplanetary atmospheres demands a corresponding leap forward in our ability to analyze them: atmospheric retrievals need to be performed on thousands of spectra, applying to each large ensembles of models (that explore atmospheric chemistry, thermal profiles, and cloud models) to identify the best one(s). In this limit, traditional Bayesian inference methods such as nested sampling become prohibitively expensive. We introduce Fast Amortized Simulation-based Transiting Exoplanet Retrieval ( FASTER ), a neural-network-based method for performing atmospheric retrieval and Bayesian model comparison at a fraction of the computational cost of classical techniques. We demonstrate that the marginal posterior distributions of all parameters within a model and the posterior probabilities of the models we consider match those computed using nested sampling both on mock spectra and for the real NIRSpec PRISM spectrum of WASP-39b. The true power of the FASTER framework comes from its amortized nature, which allows the trained networks to perform practically instantaneous Bayesian inference and model comparison over ensembles of spectra—real or simulated—at minimal additional computational cost. This offers valuable insight into the expected results of model comparison (e.g., distinguishing cloudy from cloud-free and isothermal from nonisothermal models), as well as their dependence on the underlying parameters, which is computationally unfeasible with nested sampling. This approach will constitute as large a leap in spectral analysis as the original retrieval methods based on Markov Chain Monte Carlo have proven to be.

Photo-evaporation shapes the observed radii of small exoplanets and constrains the underlying distributions of atmospheric and core masses. However, the diversity of atmospheric chemistries corresponding to these distributions remains unelucidated. We develop a first-principles carbon-hydrogen-oxygen-sulfur-silicon (CHOSSi) outgassing model that accounts for non-ideal gas behavior (via fugacities) at high pressures, as well as the tendency for water and hydrogen to dissolve in melt (via solubility laws). We use data-driven radius valley constraints to establish the relationship between the atmospheric surface pressures and melt temperatures of sub-Neptunes. Sub-Neptunes with less massive rocky cores retain less of their primordial hydrogen envelopes, which leads to less heat retention and diminished melt temperatures at the surfaces of these cores. Lower melt temperatures lead thermodynamically to the dominance of carbon-, oxygen-, sulfur- and silicon-bearing molecules over molecular hydrogen, which naturally produce a diversity of mean molecular weights. Our geochemical outgassing calculations robustly predict a gradient of mean molecular weight across the radius valley, where the strength of this gradient is primarily driven by the oxygen fugacity of the molten cores and not by the carbon enrichment (or "metallicity") of the atmosphere. Smaller sub-Neptunes are predicted to have less hydrogen-dominated atmospheres. The precise relationship between the observed and outgassed chemistries requires an understanding of how convection near the core interacts with large-scale atmospheric circulation (driven by stellar heating) near the photosphere, as well as the influence of photochemistry.

The Wide Field Camera 3 (WFC3) instrument on the Hubble Space Telescope has provided an abundance of exoplanet spectra over the years. These spectra have enabled analysis studies using atmospheric retrievals to constrain the properties of these objects. However, follow-up observations from the James Webb Space Telescope have called into question some of the results from these older datasets, and highlighted the need to properly understand the degeneracies associated with retrievals of WFC3 spectra. In this study, we perform atmospheric retrievals of 38 transmission spectra from WFC3 and use model comparison to determine the complexity required to fit the data. We explore the effect of retrieving system parameters such as the stellar radius and planet's surface gravity, and thoroughly investigate the degeneracies between individual model parameters – specifically the temperature, abundance of water, and cloud-top level. We focus on three case studies (HD 209458b, WASP-12b, and WASP-39b) in an attempt to diagnose some of the issues with these retrievals, in particular the low retrieved temperatures when compared to the equilibrium values. Our study advocates for the careful consideration of parameter degeneracies when interpreting retrieval results, as well as the importance of wider wavelength coverage to break these degeneracies, in agreement with previous studies. The combination of data from multiple instruments, as well as analysis from multiple data reductions and retrieval codes, will allow us to robustly characterise the atmosphere of these exoplanets.

Time-series photometry at mid-infrared wavelengths is becoming a common technique to search for atmospheres around rocky exoplanets. This method constrains the brightness temperature of the planet to determine whether heat redistribution is taking place, which would be indicative of the presence of an atmosphere, or whether the heat is reradiated from a low-albedo bare rock. By observing at 15 mu m, we are also highly sensitive to CO2 absorption. We observed three eclipses of the rocky super-Earth LHS 1140c, using MIRI/Imaging with the F1500W filter. We found a significant variation in the initial settling ramp for these observations and identified a potential trend between the detector settling and the previous filter used by MIRI. We analysed our data using aperture photometry, however, we also developed a novel approach, which performs a joint fit of the pixel light curves using a shared eclipse model and a flexible multi-dimensional Gaussian process which can model changes in the PSF over time. Using simulated data, we demonstrate that our method has the ability to weight away from particular pixels that exhibit increased systematics, allowing for the recovery of eclipse depths in a more robust and precise way. Both methods, as well as an independent analysis, have detected the eclipse at >5 sigma, while recovering an eclipse depth consistent with a low-albedo bare rock. We measured a dayside brightness temperature of T-day = 561 +/- 44 K, close to the theoretical maximum of T-day; max = 537 +/- 9 K. We rule out a wide range of atmospheric forward models to >3 sigma, including pure CO2 atmospheres with surface pressure >= 10 mbar and pure H2O atmospheres with surface pressure >= 1 bar. Our strict constraints on potential atmospheric composition, in combination with future observations of the exciting outer planet LHS 1140b, could provide a powerful benchmark for understanding atmospheric escape around M dwarfs.

The European Space Agency has selected PLATO (PLAnetary Transits and Oscillations of stars) for its M3 launch which is scheduled for 2026. With its extremely large field of view, PLATO is designed to obtain photometric measurements over an extended period for bright stars in order to detect and characterise (primarily) rocky planets in the habitable zones of solar type stars. The PLATO measurements will have sufficient sensitivity to determine the mass, radius and age of the host stars with unprecedented accuracy. The PLATO planet database will provide the first large-scale catalogue of accurately and homogeneously characterised small planets at intermediate orbital periods, which will can be used to severely constraint planet formation theories. This would facilitate large scale comparative exo-planetology. In addition the bright PLATO host stars will be ideal targets for atmospheric study with next generation facilities such as the ELT. The PLATO sensitivity will be sufficient to detect pulsations from stars across the HR diagram allowing a deep understanding of stellar structure and evolution to be developed using parameters determined from asteroseismology.

It is an open question whether small planets around M dwarfs are able to maintain atmospheres. The Hot Rocks Survey aims to address this question by observing nine rocky exoplanets orbiting M dwarfs with MIRI emission photometry to constrain the onset of atmospheres. In this paper, we present two MIRI F1500W (15 mu m) eclipses of LTT 3780 b, an ultrashort-period super-Earth (P = 0.768 days, R = 1.325 R circle plus, M = 2.46 M circle plus) that receives 111x Earth's instellation, the highest in the survey. We find a combined eclipse depth of 312 +/- 38 ppm, which is consistent between different data reduction and analysis assumptions, bolstering our confidence in the eclipse detection. This eclipse depth is consistent with the thermal emission from a bare rock surface, with a dayside temperature of Tday=1143-99+104 K, 98% +/- 9% of the maximum temperature predicted for a zero-albedo, zero heat redistribution blackbody. We are able to confidently rule out CO2-based atmospheres down to a 0.01 bar surface pressure to greater than 3 sigma (ruling out an approximately Mars-like atmosphere). We are unable to rule out a pure H2O 1 bar atmosphere, though we argue that this composition is unlikely on such a highly irradiated planet, nor O2 atmospheres due to the lack of features in the bandpass, though we can put constraints on CO2-mixture atmospheres. As a potential bare rock, we consider a variety of surface composition models, but are unable to distinguish between them. However, LTT 3780 b is an excellent target for follow-up JWST observations to determine its surface composition and rule out additional atmospheric compositions.

In the era of the James Webb Space Telescope, inferring the presence and bulk composition of temperate rocky exoplanet atmospheres is now possible. The primary targets typically have equilibrium temperatures ranging from 400 to 1500K, for which a balance between geochemical outgassing and escape is required to maintain an atmosphere. The composition of these exoplanet atmospheres hold crucial information on the redox state of the planetary interior characterized by the oxygen fugacity (fo_2). The relative molecular abundances of volatile species with opposite redox states inferred from observations can help constrain an effective interior fo_2. Using different model complexities from 0D simulations of chemical equilibrium to 1D atmospheric simulations with outgassing and self-consistent iterations of atmospheric chemistry (photochemistry and thermochemistry) and radiative transfer, we assess the reliability of using relative abundances in a C-H-O system to infer fo_2. The CO_2/CO, previously suggested as the most reliable tracer of fo_2, is increased by atmospheric cooling (thermochemical cooling between melt and atmosphere) and photochemistry, which would cause a bias of approximately one to two orders of magnitude on the retrieved fo_2. Constraints on the atmospheric temperature can help correct the effect of atmospheric cooling and improve the retrieval of fo_2. The increase of CO_2/CO driven by photochemistry is dominant for thin atmospheres, although it occurs over long timescales (tens or hundreds of thousands of years) and therefore would be negligible if the atmosphere is continuously replenished by outgassing. The transition between a chemical regime dominated by atmospheric thermochemistry toward a regime dominated by photochemistry is controlled not only by surface pressure and temperature but also by oxygen fugacity itself (via O/H). Inferring CO_2/CO from the data might be challenging given the low contribution of CO in transit and emission spectra for objects with high CO_2 and H_2O abundances. We suggest CO_2/CH_4 as an alternative tracer of fo_2, although high methane abundances are only expected in reducing conditions (i.e., less than the iron-wustite buffer) and high pressure-temperature surface conditions favoring the buildup of CH_4 by atmospheric cooling.

Sub-Neptune exoplanets are the most abundant type of planet known today. As they do not have a Solar System counterpart, many open questions exist about their composition and formation. Previous spectroscopic studies rule out aerosol-free hydrogen-helium-dominated atmospheres for many characterized sub-Neptunes but are inconclusive about their exact atmospheric compositions. Here we characterize the hot (Teq=1311K) sub-Neptune HD 86226 c, which orbits its G-type host star. Its high equilibrium temperature prohibits methane-based haze formation, increasing the chances for a clear atmosphere on this planet. We use HST data taken with WFC3 and STIS from the Sub-neptune Planetary Atmosphere Characterization Experiment (SPACE) Program to perform near-infrared 1.1-1.7micrometer transmission spectroscopy and UV characterization of the host star. We report a featureless transmission spectrum that is consistent within 0.4 sigma with a constant transit depth of 418+-14ppm. The amplitude of this spectrum is only 0.01 scale heights for a H/He-dominated atmosphere, excluding a cloud-free solar-metallicity atmosphere on HD 86226 c with a confidence of 6.5 sigma. Based on an atmospheric retrieval analysis and forward models of cloud and haze formation, we find that the featureless spectrum could be due to a metal enrichment [M/H] above 2.3 (3 sigma confidence lower limit) of a cloudless atmosphere, or silicate (MgSiO3), iron (Fe), or manganese sulfide (MnS) clouds. For these species, we perform an investigation of cloud formation in high-metallicity, high-temperature atmospheres. Our results highlight that HD 86226c does not follow the aerosol trend of sub-Neptunes found by previous studies. Follow-up observations with the JWST could determine whether this planet aligns with the recent detections of metal-enriched atmospheres or if it harbors a cloud species otherwise atypical for sub-Neptunes.

Remote sensing of the atmospheres of distant worlds motivates a firm understanding of radiative transfer. In this review, we provide a pedagogical cookbook that describes the principal ingredients needed to perform a radiative transfer calculation and predict the spectrum of an exoplanet atmosphere, including solving the radiative transfer equation, calculating opacities (and chemistry), iterating for radiative equilibrium (or not), and adapting the output of the calculations to the astronomical observations. A review of the state of the art is performed, focusing on selected milestone papers. Outstanding issues, including the need to understand aerosols or clouds and elucidating the assumptions and caveats behind inversion methods, are discussed. A checklist is provided to assist referees/reviewers in their scrutiny of works involving radiative transfer. A table summarizing the methodology employed by past studies is provided.