A Temperature Trend for Clouds and Hazes in Exoplanet Atmospheres

NASA's Hubble Space Telescope (HST) has been used to observe exoplanet transits at wavelengths ranging from the ultraviolet (UV) to the visible to the near-infrared (NIR) as long as 2.4 μm (Charbonneau et al. 2002; Vidal-Madjar et al. 2003; Deming et al. 2013; Swain et al. 2021). However, the majority of HST transiting-exoplanet spectroscopic observations have been conducted with the Wide Field Camera 3 (WFC3) instrument using the spatial-scan mode and the G141 grism covering wavelengths from 1.1 to 1.6 μm. Comparative planetology studies based on these observations show that the spectral modulation seen in the transmission spectra indicate atmospheres can vary from obscured to clear (Sing et al. 2016). The nature of the obscuring aerosols, which we will term "clouds and hazes," is an area of active investigation, and possible candidates range from various condensed species to photochemically produced hazes. The cloudy and hazy atmospheres are associated with a weaker absorption feature in the NIR portion of the transmission spectrum of the planet or a featureless spectra (Knutson et al. 2014a, 2014b; Kreidberg et al. 2014). Although some of the low spectral amplitudes could also be associated with low water abundances, as has been pointed out by previous works (Barstow et al. 2017; Pinhas et al. 2019; Welbanks et al. 2019). While in the optical spectra, clouds/hazes can cause Rayleigh scattering–like opacity seen in several planets (Pont et al. 2008, 2013; McCullough et al. 2014; Sing et al. 2016; Estrela et al. 2021). These clouds are generally attributed to atmospheric condensates of salt, silicate, and metal vapors (Morley et al. 2012; Gao et al. 2020; Zhang 2020), or to photochemically produced hazes due to energy input or energetic particle bombardment (Lavvas & Koskinen 2017; Lavvas et al. 2019; Gao et al. 2020; Lavvas & Arfaux 2021). Clouds and hazes can have a critical role in planetary atmospheres. They can affect the amount of light reflected by the atmosphere of the planet, which determines the Bond albedo and consequently the equilibrium temperature of the planet (Cahoy et al. 2010). They can also control the thermal structure, chemistry, and dynamics in the atmosphere (Tomasko & West 2010; Müller-Wodarg et al. 2014).

A wide range of potential cloud compositions may be plausible due to the significant possibility of condensate materials (Zhang 2020) and because of exoplanet properties, the potential for migration, and differences in formation/evolutionary scenarios. Particularly, cloud composition depends on the temperature of the atmosphere. Various scenarios using temperature dependence to infer cloud composition have been modeled (Burrows & Sharp 1999; Morley et al. 2013; Parmentier et al. 2016). Some molecules will condense at high temperatures (e.g., TiO/VO, Al, and Ca), while others prefer moderate temperatures (e.g., Fe, Mg, Si, Cr, and Mn) or lower temperatures (e.g., K and Na) (Gao et al. 2021). Observations of exoplanet atmospheres illustrate this diversity. Many species, such as TiO/VO and metals, have been suggested to be present in ultrahot Jupiters (Ben-Yami et al. 2020; Cabot et al. 2020; Changeat et al. 2022), while smaller and cooler planets (sub-Neptunes and super-Earths) also have indicated the presence of high-altitude aerosols in their atmospheres (Ehrenreich et al. 2014; Wakeford et al. 2017; Kreidberg et al. 2022). Other planets have shown very steep optical slope in their spectra (Alderson et al. 2020; Chen et al. 2021; Estrela et al. 2021) due to scattering in the atmosphere, which could be explained by sulfide clouds (MnS, ZnS, Na₂S; Pinhas & Madhusudhan 2017). High-altitude photochemical hazes could also lead to super-Rayleigh optical slope, depending on their mixing and formation rate (Ohno & Kawashima 2020). Advances in laboratory experiments are helping to better constrain cloud formations, and simulations for hot Jupiters' atmospheres and even smaller planets' atmospheres have shown photochemical haze production (Hörst et al. 2018; Fleury et al. 2019, 2020; Yu et al. 2021).

In addition to understanding cloud formation, the overall level of "cloudiness" in exoplanet atmospheres is a topic of great interest for planning exoplanet observations because of the potential for strong clouds to dampen spectral features and thus compromise the study of atmospheric composition (Kreidberg et al. 2014). A robust method of predicting the likelihood and impact of clouds and hazes in the detection of exoplanet atmospheres is of great value for planning observations. For example, the Ariel mission (Tinetti et al. 2018; Zellem et al. 2019) will conduct a transit spectroscopy survey of hundreds of exoplanets, and the ability to estimate cloud properties could be an important factor in planning the mission observations. Also, the detectability of molecular features on smaller planets with the James Webb Space Telescope (JWST) could be significantly compromised due to the presence of clouds/hazes (Fauchez et al. 2019). Several studies have used HST/WFC3-G141 transmission spectra to conduct statistical analysis using the amplitude of the water feature to identify planets affected by the presence of clouds/hazes. Based on the HST/WFC3-G141 catalog of Tsiaras et al. (2018), Iyer et al. (2016), Fu et al. (2017), Fisher & Heng (2018), and Gao et al. (2020) have found that most planets had their amplitude diminished by aerosols when compared to a clear atmosphere. Wakeford et al. (2019) show that 30% of the time the amplitude of the water spectral feature is found to be below 0.5Hs which deviates from a cloud-free scenario. An analysis by Stevenson (2016) suggests that there is a threshold for cloudiness level at a surface gravity of 2.8 dex. More recently, Dymont et al. (2022) have searched for correlations between cloudiness metrics and other physical parameters such as temperature using sample sizes of 23 planets. However, as noted by Dymont et al. (2022), the lack of a uniform data reduction was a less-than-ideal aspect of the sample they studied.

Given the importance of clouds and hazes for establishing planet properties and their impact on characterization using the transit spectroscopy method, additional investigation into the properties of exoplanet clouds and hazes is a priority. Rapid progress in exoplanet observations is leading to the ability to improve sample size with respect to previous works. Here, we report on an analysis of clouds and hazes using the largest uniformly processed exoplanet transmission spectra catalog available in Roudier et al. (2021).

Detection of clouds and hazes is typically done through measuring the degree of spectral modulation (Sing et al. 2016), which can then be compared to estimates of the theoretical possible values (Iyer et al. 2016; Gao et al. 2020) or plotted against various physical parameters to search for correlations (Stevenson 2016; Fu et al. 2017; Fisher & Heng 2018; Gao et al. 2020; Dymont et al. 2022). Here, we perform this analysis using the catalog from Roudier et al. (2021) that consists of 62 planets observed with the WFC3 instrument on board the HST using the G141 infrared (IR) grism (1.1–1.6 μm) spatial-scan observations. Compared with previous works, this exoplanet catalog has three important advantages for the study of clouds. First, this catalog is the largest uniformly processed catalog of HST transmission spectra that has been published. In this case, the data have all been processed though the same pipeline, and they have all been analyzed with the same spectral retrieval code. A uniformly processed catalog is particularly important when performing comparative planetology because differences in planetary spectra can be attributed to differences in astrophysics rather than analysis methods. Second, this catalog is based on the EXoplanet CALIbration and Bayesian Unified Retrieval (EXCALIBUR) pipeline (Estrela et al. 2021; Roudier et al. 2021; Swain et al. 2021; Huber-Feely et al. 2022), which processes HST/WFC3-G141 data at the full spectral resolution of the instrument. Using the full G141 spectral resolution avoids the potential reduction in spectral feature amplitude that can be caused by additional spectral averaging. Third, the CERBERUS spectral retrieval code, used for modeling the transmission spectra in this catalog, is capable of modeling atmospheres assuming both thermal equilibrium chemistry (TEC) and disequilibrium chemistry (DisEQ). The majority of previous works interpreted planet populations observed with the HST/WFC3 instrument as being consistent only with bulk TEC conditions, while atmospheres can undergo DisEQ due to photochemistry, which can be associated with a water-depleted spectrum. The DisEQ atmosphere assumed by Roudier et al. (2021) does not fully exclude water but includes water as a subdominant feature and brings the possibility of other dominant signatures such as CH₄, C₂H₂, HCN, and CO₂. Roudier et al. (2021) identify a third category of planets that could not be determined, based on the model selection criteria, to be either DisEQ or TEC. We term this category "Indeterminate" and divide this group into those that have spectral modulation greater than 1H_s and those that do not.

To estimate the amplitude of the spectral modulation in the transmission spectra, we take the difference between the maximum and minimum of the CERBERUS preferred model (henceforth referred to as CMM) in the NIR range between 1.15 and 1.6 μm (see Figure 2). This method is based on the approach of Iyer et al. (2016) and has the advantage of naturally debiasing the impact of individual spectral channel values on estimates of spectral modulation. In the case of TEC models, the CMM will measure the strength of the water feature, while for the DisEQ planets it will measure the strength of the other possible dominant features (CH₄, C₂H₂, HCN, and CO₂). To facilitate the analysis, we convert the CMM to units of planetary scale height H_s :

$$\begin{eqnarray}&&{H}_{s}=\displaystyle \frac{{k}_{B}{T}_{\mathrm{eq}}}{\mu g},\end{eqnarray} \tag{ 1 }$$

where k_B is the Boltzmann constant, μ is the mean molecular weight of an atmosphere in solar composition (μ = 2.3 amu), g is the surface gravity, and T_eq is the calculated equilibrium temperature.

Next, we build an index of the spectral modulation that represents a fraction of the potential modulation a planet achieves. This index is obtained by dividing the difference between the CMM of the spectral modulation of the regular retrieved model (CMM_CRB) by the CMM of the cloud-/haze-free model (CMM_FREE) of each individual target:

$$\begin{eqnarray}&&{\mathrm{Spec}}_{\mathrm{index}}=\displaystyle \frac{{\mathrm{CMM}}_{\mathrm{CRB}}}{{\mathrm{CMM}}_{\mathrm{FREE}}}.\end{eqnarray} \tag{ 2 }$$

This index varies from 0 to 1, where 0 accounts for cloudy/hazy and 1 represents a clear atmosphere. The cloud-/haze-free model is obtained by setting the haze/cloud parameters to zero (see Figure 1 for comparison between the retrieved model and the cloud-/haze-free model).

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2.1. Clouds and Hazes

The estimated amplitude of the spectral modulation of the TEC, DisEQ, and Indeterminate targets is shown in Figure 2 and their respective values are shown in Tables A1, A2, and A3.The Indeterminate targets are classified into two groups: those with minimal to no spectral modulation and those with detected modulation > = 1H_s . Targets in these groups are indecisive between TEC and DisEQ because the evidence of the model is not strong enough, and the model cannot decide between TEC or DisEQ to explain any modulation there. Figure 2 shows that our sample is very diverse in terms of equilibrium temperature. The distribution of the modulation varies from planets that have large modulation and are potentially cloud/haze free to those with minimal spectral modulation that could be in a completely aerosol-dominated scenarios or have high molecular weight atmospheres. See the Appendix for values of the spectral amplitude presented in Figure 2.

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The planets' range of cloudiness/haziness level is also well illustrated in Figure 3 through the spectral modulation index (see the description in Section 2). We identify two groups in Figure 3. One group is cloud/haze free (blue region) with spectral modulation indexes above 0.9 that are distributed across different temperatures. Within this group, there are a few "Indeterminate" targets that have indexes greater than 1.3 due to steep slopes toward short wavelengths. We exclude these particular targets because their slopes could be associated to Rayleigh scattering by clouds/hazes or atmospheric escape. The second group has some level of cloudiness/haziness and we identified them as "partial cloud/haze" region (in gray). If we exclude the completely cloud-/haze-dominated (blue targets in Figure 2) and the cloud-/haze-free targets, the partial cloud/haze targets show a rise in the spectral modulation index between 500 and 1500 K, indicating that we expect more clear atmospheres for planets with temperatures between ∼1200 and 1500 K. This trend is consistent with laboratory studies (Yu et al. 2021) that show that in the temperature range of 500–800 K, hazes can be removed more efficiently by direct deposition to the surface or deep atmosphere. Also, the trend seen from 500 to 1500 K is also in agreement with the cloudy-to-clear trend from 500 to 1000 K seen in previous observational studies (Crossfield & Kreidberg 2017; Libby-Roberts et al. 2020; Guilluy et al. 2021) for warm Neptunes. Planets with higher temperatures (>1700 K) seem to indicate more cloudy/hazy atmospheres, although we lack sufficient data to make firm conclusions. However, it is possible that heat transport is very inefficient above 1600 K, which would allow the nightside to cool and clouds to advect to the dayside (Parmentier et al. 2021). The temperature trend in the spectral modulation is well fitted using a second-order polynomial. The fit gives the relationship

$$\begin{eqnarray}&&y=-2.9e-{7}_{-7.1e-8}^{+7.1e-8}{x}^{2}+8.4e-{4}_{-2e-4}^{+2e-4}x+1.4e-{2}_{-0.13}^{+0.13}.\end{eqnarray} \tag{ 4 }$$

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If we fit a fourth-order polynomial to the data (dashed blue line in Figure 3), we see a trend rising toward reduced cloud/hazy atmospheres at low-temperature planets (<270 K) in the habitable zone (HZ), K2-18b and LHS 1140b, where liquid water can exist and condense. This trend is also explained by laboratory studies (Yu et al. 2021), which has shown that high surface energy hazes can be formed in these planets and they are efficiently removed by cloud droplets formed through water condensation. However, any conclusions cannot be made due the lack of targets at lower temperatures. In addition, the second-order polynomial is still the best fit for the partial cloud/haze population (although the fourth order is not excluded), as shown by the Bayesian information criterion (BIC). The BIC for each fit is calculated by

$$\begin{eqnarray}&&\mathrm{BIC}={\chi }^{2}+k\mathrm{ln}(n),\end{eqnarray} \tag{ 5 }$$

where k is the number of free parameters, represented by the polynomial order plus 1, and n is the number of data points. The best model is the one with the lowest BIC, which is the quadratic model, as shown in Table 1. We also estimated the ΔBIC with respect to the best model, and found a value of 0.6 for the fourth-order model, which provides weak evidence that the quadratic model is better. On the other hand, the linear model has a ΔBIC greater than 10, which represents strong evidence that the quadratic model is better.

Considering that future missions would largely benefit from a forecast of spectral modulation for planning observations, we note that the second-order polynomial trend can be used to make a spectral modulation forecast. Including the forecast for the temperature dependence for spectral modulation has the potential to increase the fidelity of planning observations with JWST and Ariel, and based on the results of this study, we would anticipate that plenty of targets would likely show modulation in their spectra.

3.1. Aerosol Properties

Another key result that comes from the analysis of the Roudier et al. (2021) exoplanet catalog of TEC and DisEQ targets relies on the aerosol properties. To infer the aerosol properties, we take the best solution obtained with the CERBERUS atmospheric retrieval code by parameterizing the Jupiter aerosol layer (see Section 2). We find that this sample of exoplanets has a much more extended haze layer than Jupiter, and it is widely distributed throughout the atmosphere. The CTP is very similar in both TEC and DisEQ targets, showing pressures of ∼0.05 bar, which means that any atmospheric column below that pressure is blocked by the cloud layer and not sampled by transmission spectroscopy. These results are summarized in Table 2 and illustrated in Figure 4, where the thickness of the haze layer, the location of the peak density, and the multiplicative factor of the haze opacity (with respect to Jupiter's opacity) are shown.

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Table 2. Median Values of the Aerosol Properties (HScale, HLoc, HThick) and the Cloud-top Pressure (CTP) of the TEC and DisEQ Population Obtained with the Atmospheric Retrieval CERBERUS

Aerosol and Cloud Properties of the TEC and DisEQ Exoplanets in the Sample
	TEC	DisEQ	Indeterminate
HScale	0.008	0.0006	0.70
HLoc	0.005 bar	0.006 bars	0.003 bar
HThick	5.8 × 109	5.5 × 109	4.7 × 1010
CTP	0.03 bar	0.06 bars	0.002 bar

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We caution that our haze model parameters are a parametric scaling of Jupiter's haze properties and thus do not capture the detailed microphysics of haze formation in these much hotter exoplanets. Our modeling suggests that haze in exoplanet atmospheres is typically distributed widely throughout the atmospheric column, similar to what was found for HD 209458b by Lavvas & Koskinen (2017) based on a microphysics model for haze formation. Similarly, our modeling suggests that the presence of a bottom cloud is detectable and influences the interpretation of WFC3/G141 observations. However, detailed physical conclusions about the vertical distribution of the haze and bottom cloud properties will need to be addressed with models that appropriately represent the chemistry and physics of these atmospheres—and we identify this as an area for further investigation.

4.1. Cloudy/Hazy to Clear Atmospheres

4.2. Extended Aerosol Layer in Exoplanets

4.3. Forecasting Spectral Modulation

4.4. Differences between EXCALIBUR and Previous Works

This work performs comparative planetology of a large, uniformly observed and processed catalog of transit spectra that were obtained at the full spectral resolution of the HST/WFC3 instrument. Our method is consistent for a large range of planet properties, and the sample is larger than those used in previous works. Another differentiating aspect of this work when compared with previous studies is that the spectral catalog used here is modeled with both TEC and DisEQ atmospheric composition scenarios. This implies that the spectral modulation in exoplanet spectra is modeled assuming not only H₂O but also other dominant spectral features due to disequilibrium chemistry. The amplitude of the spectral modulation in our catalog reveals that exoplanet atmospheres vary from cloudy to clear, with most of the planets typically lying in between. This suggests that transiting-exoplanet atmospheres contain detectable spectral features that are partially muted. From the analysis of the haze properties, we find that haze layer is partially transparent and widely extended throughout the atmospheric column.

In addition, we estimated a spectral modulation index that quantifies the cloudiness/haziness in each target. We observe that there are two groups of planets, one is completely cloud/haze free spanning a wide temperature range. The other group, denominated "partial cloud/haze," follows a trend from cloudy/hazy to clear within 500–1500 K in the spectral modulation, with the least cloudy atmospheres lying at 1460.86 K${}_{-405}^{+316}$. This trend is consistent with previous observational samples and laboratory studies from Yu et al. (2021) that indicate efficient haze removal in that temperature range. We find that a quadratic polynomial is the best fit for the trend seen in the spectral modulation indexes. However, a fourth-order polynomial trend shows a rise of reduced hazy/cloudy atmospheres for planets with temperatures lower than 270K, including those in the HZ. At these temperatures, water can condense and hazes can be removed by wet deposition (Yu et al. 2021). The empirical quadratic polynomial trend can be used for predicting cloudiness/haziness for modeling large-scale surveys. This is particularly beneficial for forecasting potential targets that could have their atmospheres observed by JWST or future missions devoted to the the observation of exoplanet atmospheres, such as Ariel. A potentially more robust improvement in the estimation of the spectral modulation index could be achieved by including the measurements on the optical wavelengths from HST/STIS in future catalogs. HST/STIS can give information on scattering due to haze and clouds, and would provide a more definitive picture of the range of cloudiness in exoplanet atmospheres.

We would like to thank the anonymous reviewer for their constructive feedback that helped to improve this manuscript. We also thank Robert West for useful comments that provided a valuable addition to improve this manuscript. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. R.E., M.S., and G.R. acknowledge support for a portion of this effort from NASA ADAP award 907524. This work has been supported in part by the Jet Propulsion Laboratory, California Institute of Technology Exoplanet Science Initiative. This research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). ©2022 California Institute of Technology. Government sponsorship acknowledged.

The values of the spectral modulation amplitudes for the planets from the Roudier et al. (2021) catalog are shown in Table A1 for TEC, Table A2 for DisEQ, and Table A3 for the Indeterminate planets.