A CHARACTERISTIC TRANSMISSION SPECTRUM DOMINATED BY H₂O APPLIES TO THE MAJORITY OF HST/WFC3 EXOPLANET OBSERVATIONS

The search for H₂O in exoplanet atmospheres has been dominated by transmission measurements obtained with space-based instruments. Although the early detections of H₂O in an exoplanet atmosphere were made with the Hubble and Spitzer instruments STIS, IRAC, and NICMOS (Tinetti et al. 2007; Barman 2008; Grillmair et al. 2008; Swain et al. 2008), the leading instrument in this area is NASA's Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) using the G141 IR grism (1.1–1.7 μm) to obtain spectra of the transit event. The scope of the collective work is impressive and constitutes the largest collection, 19, of similarly observed exoplanets presently available. These 19 transmission spectra are drawn from 16 papers by 13 authors, a majority (10 of 19) of which report a detection of H₂O (Table 1; Deming et al. 2013; Huitson et al. 2013; Line et al. 2013a; Mandell et al. 2013; Wakeford et al. 2013; Ehrenreich et al. 2014; Fraine et al. 2014; Knutson et al. 2014a, 2014b; Kreidberg et al. 2014a, 2014b, 2015; McCullough et al. 2014; Ranjan et al. 2014; Wilkins et al. 2014; Sing et al. 2015). As a whole, this sample represents a heterogeneous collection of data reduction methods, spectral resolution, observational, and model interpretation approaches. Given these differences, we focus our analysis on the H₂O absorption feature, which occurs in the near-infrared at ∼1.2–1.6 μm. Here we report the trends for both spectral modulation and spectral shape and discuss the possible implications of these findings.

Given a heterogeneous collection of measurements presently, we adopt a template-fitting approach to determine the spectral modulation due to H₂O opacity. We define spectral modulation as the amplitude of the H₂O feature between 1.2–1.4 μm. We generate H₂O template spectra that include the opacities due to Rayleigh scattering and H₂/H₂ and H₂/He using the CHIMERA forward model routine for transmission spectra (Line et al. 2013b; Kreidberg et al. 2014b, 2015; Swain et al. 2014) over the spectral range of the G141 grism (1.1–1.7 μm). These H₂O templates cover abundances from 0.1 to 100 ppm, the range over which the shape of the H₂O spectral modulation changes. H₂O mixing ratios below 0.1 ppm are difficult to detect and abundances above 100 ppm produce spectra that have nearly the same shape when normalized. These templates are then fit to the HST/WFC3 data (Figure 1) with a Levenburg–Markwardt least-squares minimization routine (e.g., Markwardt 2009) by linearly scaling the model amplitudes and vertical offsets. This exercise is carried out to debias the estimate for spectral modulation from single-point outliers and to create a consistent method to treat data reported spectral resolutions that differ by ∼5.

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To facilitate further analysis, all of the HST/WFC3 data and their corresponding best-fit radiative transfer models are converted to units of planetary scale height H_s:

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

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. We adopt the planetary parameters listed on exoplanets.org (Han et al. 2014) for all of these variables except the equilibrium temperature. Assuming efficient heat redistribution from the dayside to the nightside and an albedo of zero, we calculate the equilibrium temperature for each planet via the equation (Mendez 2014)

$$\begin{eqnarray}&&{T}_{\mathrm{eq}}=\displaystyle \frac{{T}_{\ast }{f}^{\prime \tfrac{1}{4}}}{{(a/{R}_{\ast })}^{\tfrac{1}{2}}}\sqrt{1+\left(\displaystyle \frac{8}{{\pi }^{2}}-1\right){e}^{\tfrac{5}{2}}},\end{eqnarray} \tag{ 2 }$$

where T_* and R_* are the stellar temperature and radius, a is the semimajor axis, and e is the eccentricity.

The modulation of each planet's H₂O feature (∼1.2–1.4 μm) is determined by the amplitude of the best-fit model template to prevent any outliers in each data set from skewing the spectral fit. This parameter is then plotted versus the data uncertainty, defined as the mean uncertainty in each spectra scaled by the square root of the change in resolution. The error bars on the spectral modulation are defined as the standard deviation of the residuals of the best-fit template model (Figure 2) and all values here are in units of H_s.

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The major outlying points of TrES-2b, TrES-4b, and CoRoT-1b show a large uncertainty in their spectra as well as significant spectral modulation (Figure 2). However, their poor fit to the water templates indicate that caution should be used in interpreting modulation results for these planets.

We then search for a "representative" spectrum shared among the exoplanets published with H₂O detections. A similar approach to analyze Spitzer data is used by Schwartz & Cowan (2015). We construct a cumulative H₂O-detection transmission spectrum by normalizing the 10 published H₂O-detected spectra between 0 and 1, linearly interpolating them to a common wavelength grid, and then combining them with a weighted average. Unbiased uncertainties of this weighted average spectrum are calculated using the standard expression for the error in the weighted mean. The resultant spectrum (Figure 3) has a characteristic shape that is representative of this group of HST/WFC3 planets, with H₂O as the dominating feature.

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To test the validity of this H₂O-detected "representative" spectrum and to understand the emerging patterns pertaining to this group, we compare it with four single-planet clear (cloud and haze-free) atmosphere models with H₂O abundances of 0.1, 1, 10, and 100 ppm. We include Rayleigh scattering and H₂/H₂ and H₂/He collisionally induced absorption as additional opacity sources in these models, as the planets in our sample are predominantly hot Jupiters with hydrogen and helium atmospheres. These models are also normalized between 0 and 1 to facilitate the comparison of their shape to that of the representative spectrum (the top panel of Figure 4). We find that the amplitude of the representative spectrum is consistent with H₂O abundances of 10–100 ppm.

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Additionally, we also explore the effect of clouds on the H₂O spectral modulation amplitude to explain the shape of the representative spectrum. We compare the representative spectrum with a forward model with [H₂O] = 1000 ppm and a cloud top at 100 mbar, alongside a cloud-free model with [H₂O] = 100 ppm (the bottom panel of Figure 4). The choice of H₂O mixing ratio and cloud-top pressure were selected to match best to the representative spectrum. Both models show a good qualitative fit relative to the representative spectrum, indicating a degeneracy between the cloud-free and cloudy solutions.

To explore the range of values for the water mixing ratio that are consistent with the data, we perform a ${\rm{\Delta }}{\chi }^{2}$ search of the parameter space by computing forward models and comparing their shape with the representative spectrum (the left panel of Figure 5). To generate these forward models we use parameters of a "representative planet" by computing the average T_eq, R_p, R_s, and log(g) of all the water-hosting planets in our sample. Cloud-free models with cloud-top pressure of ≥1 bar, where they do not interact with the transmission spectrum can be consistent with the data. Larger values for the H₂O mixing ratio can also be consistent with the data, but are degenerate with cloud-top pressure (Benneke 2015; Kreidberg et al. 2015). However, we can estimate the degree to which clouds block portions of the atmosphere that would otherwise be sampled in a transmission spectrum. Using the representative spectrum'(s) best-fit cloud-free water abundance of ${17}_{-6}^{+12}$ ppm (the left panel of Figure 5), we compute the spectral modulation for all of the planets in our sample in the following way. We run 1000 Monte-Carlo iterations per planet to generate cloud-free forward models with [H₂O] abundance sampled from the asymmetrical distribution (the left panel of Figure 5). Planet parameters of T_eq, R_p, R_s, and log(g) unique to each planet are used in the CHIMERA radiative transfer code (Line et al. 2013b; Kreidberg et al. 2014b, 2015; Swain et al. 2014). We then calculate the theoretical cloud-free H₂O spectral modulation derived from the MC for each planet, which is plotted against the measured spectral modulation (the right panel Figure 5). By averaging the results for the water-detected planets, we find that clouds likely remove at least half and possibly more of the observable atmospheric modulation from participating in a transit measurement.

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The H₂O spectral modulation of the HST/WFC3 H₂O-detected exoplanets spans 0.9–2.9 H_s with a mean modulation of 1.8 ± 0.5 H_s. This mean value differs significantly from the expectations for the cloud-free H₂O spectral modulation as compared with idealized models which predict ∼7 scale heights of spectral modulation (Seager & Sasselov 2000; Brown 2001). This reduced H₂O modulation implies the presence of some additional opacity source such as clouds or aerosol haze to reduce the true spectral modulation due to H₂O. Aerosol haze has been reported in the atmosphere of the H₂O-hosting hot Jupiter, HD 189733b (Lecavelier Des Etangs et al. 2008; Pont et al. 2008; Sing et al. 2009) and clouds have been discussed by Brown (2001) and Morley et al. (2012). Quite literally, we are likely seeing the effects of H₂O above the haze and clouds, which are opaque for transit viewing geometry, but may not be so for vertical paths observed during eclipse. This hypothesis agrees with recent findings for some of the planets in our sample by Benneke (2015), Kreidberg et al. (2015), and Sing et al. (2016).

The presence of a cloud deck as a common feature of the hot Jupiter H₂O-hosting planets has implications for recent work that found a measurable difference (∼100×) in the H₂O mixing ratio for the dayside and terminator regions of HD 189733b (Line et al. 2014; Madhusudhan et al. 2014). The spectral modulation due to H₂O in the terminator region is 2.0 ± 0.5 H_s. In a scenario where terminator-region clouds are ubiquitous, the dayside measurement can be understood as probing a region in which dayside perpendicular viewing potentially samples 1.3 H_s of additional atmospheric path in deeper, higher-pressure regions of the atmosphere. This geometry allows for more H₂O opacity to be present in the emission spectrum and a correspondingly large value is determined for the H₂O mixing ratio.

Although we now possess the observational evidence to support the conclusion that H₂O is a common constituent in the atmospheres of hot Jupiter exoplanets, much of the water these atmospheres contain may be hidden beneath clouds. When the spectral modulation due to H₂O is measured in units of the atmospheric scale height, we find that the average H₂O-induced modulation is 1.8 ± 0.5 H_s and never exceeds 2.9 H_s. The shape of the spectral modulation is also inconsistent with extremely low H₂O abundances and suggests that a cloud layer may obscure a significant portion of the otherwise observable atmosphere. We also find that the sample of H₂O-hosting planets possesses a representative spectral shape dominated by opacity due to H₂O. The fact that the individual spectra coherently average to a consistent shape for the H₂O-hosting planets, which is reproducible with simple forward models, gives confidence that there is a representative spectrum for at least a significant portion of the hot Jupiter exoplanet population.

We are grateful to Dr. Yan Betremieux, Dr. David Crisp, Dr. Wladimir Lyra, and Dr. Yuk L. Yung for several insightful discussions on our analysis and suggestions for edits on the paper draft.

This research is based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555.

We thank the JPL Exoplanet Science Initiative for partial support of this work. The research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. © 2015. All rights reserved.

This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org.

We thank the anonymous referee for their helpful comments.