Community Targets of JWST's Early Release Science Program: Evaluation of WASP-63b

We apply the transit models from Howe & Burrows (2012), which adopt chemical-equilibrium abundances for molecular species from Burrows & Sharp (1999) and opacities from Sharp & Burrows (2007). The atmospheric models consider an isothermal temperature profile and gray haze opacity with cross sections of 0.001–0.005 cm²g⁻¹ from 10⁻⁶ bar to 1 bar.

By exploring a range of temperatures, haze opacities, metallicities, and nonequilibrium CO/CH₄ abundances, the best-fitting solutions pointed to solar-abundance atmospheres at a temperature of 1000 K, with a haze/cloud muting the water absorption feature at 1.4 μm (Figure 4, top panel). There is no indication of significant CH₄. There is a slight degeneracy between the cloud thickness and temperature, but it is clear that the atmosphere is cloudy. These models do not show a significant metallicity dependence. Finally, a high CO abundance excess (∼100 times solar) can help to fit the data at 1.5 μm, but it does not seem realistic.

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As a complementary approach to the full retrieval calculations, we fit the data with a three-parameter analytical model (Heng & Kitzmann 2017). In that study, it was demonstrated that this isothermal, isobaric model matched full numerical calculations at the ∼0.1% level over the WFC3 wavelength range. The model has three parameters: temperature, water abundance, and a constant cloud opacity. The constant cloud opacity assumes that the cloud particles are large over the wavelength range probed by WFC3 (i.e., micron-sized or larger radius). Water opacities are computed using the HELIOS-K opacity calculator (Grimm & Heng 2015) and the HITEMP spectroscopic database. This procedure confronts the data with a simple model, which has a minimal number of parameters, to serve as a plausibility check.

Following the approach of Kreidberg et al. (2015), we equate the reference transit radius to the white-light radius and set the reference pressure to 10 bar. We assume a hydrogen-dominated atmosphere and set the mean molecular weight to 2.4. The top panel of Figure 4 shows the best-fit model to the WFC3 WASP-63b data. Our general conclusion mirrors that of the retrieval calculations: water is present in the atmosphere of WASP-63b, but its presence is muted by a continuum, which in this case is attributed to a constant cloud opacity. The values of our fitting parameters span a temperature range from 500 to 1000 K, a water mixing ratio from ∼10⁻⁸ to 10⁻⁷, and a cloud opacity ∼10⁻⁸ to 10⁻⁷ cm² g⁻¹.

In order to determine the clouds that are predicted to form in the atmosphere of WASP-63b and their effect on the planet's transmission spectrum, we ran self-consistent models including the effects of cloud condensation. These models solve for the temperature structure of the atmosphere in radiative-convective and chemical equilibrium and are more extensively described in McKay et al. (1989), Marley et al. (1996, 1999, 2002), Burrows et al. (1997), Fortney (2005), Saumon & Marley (2008), Fortney et al. (2008), Morley et al. (2015). Our opacity database for gases is described in Freedman et al. (2008, 2014), and we calculate the effect of cloud opacity using Mie theory, assuming spherical particles. We include iron and silicate clouds and vary the cloud sedimentation efficiency f_sed from 0.1 to 1, and find that these clouds do indeed form at high altitudes and damp the size of the signal for low sedimentation efficiencies (i.e., lofted clouds of small particles). Figure 4 top panel shows a representative transmission model for WASP-63b.

In order to understand how the three-dimensional structure of the planet might affect our interpretation of the planet's transmission spectrum, we model WASP-63b with the three-dimensional global circulation model SPARC/MITgcm described in Showman et al. (2009). Our model solves for the three-dimensional temperature structure of the atmosphere assuming a cloud-free, solar-composition atmosphere. We then use the temperature map to predict the position of the clouds at the limb of the planet by comparing the partial pressure and the saturation pressure of the cloud gaseous constituents as described in Parmentier et al. (2016). The cloud-top level and size of the cloud particles are free parameters representing vertical mixing and microphysics respectively. We then compute the transmission spectrum of the whole atmosphere by combining the transmission spectrum obtained with the temperature and cloud profile at each latitude around the limb (Parmentier et al. 2016).

Our global circulation model predicts a temperature difference of 400 K between the east and west limb at the 10 mbar level. As a consequence some cloud species are predicted to be condensed all over the limb of the planet whereas others should condense only on the morning limb and be evaporated on the other one, leading to a partially cloudy atmosphere (Line & Parmentier 2016). We computed models assuming the presence of enstatite clouds (MgSiO₃) or manganese sulfide clouds (MnS) corresponding to a fully cloudy and partially cloud case respectively. Our best-fit spectrum with enstatite clouds is very similar to the Morley model of Figure 4. It has a cloud-top pressure of 1 mbar and no constraints on the particle size. Our best-fit model with MnS clouds is the Parmentier model of Figure 4. It has a limb that is ≈60% cloudy, resulting in a qualitatively different spectrum than the other, one-dimensional models shown here. For this model, the cloud-top pressure is ≈0.1 mbar and the particle size is ≈1 μm. We conclude that the atmosphere of WASP-63b is unlikely to be clear with a solar-composition abundance of water. Both fully cloudy and partially cloudy atmospheres can exist, depending on the cloud composition. A higher signal-to-noise spectrum should be able to disentangle between the two scenarios.

To model the atmosphere and spectrum of WASP-63b, we use the Python Radiative Transfer in a Bayesian framework (Pyrat Bay) package¹⁹ (J. Blecic et al. 2018, in preparation; P. E. Cubillos et al. 2018, in preparation). Pyrat Bay is an open-source reproducible code, based on the Bayesian Atmospheric Radiative Transfer package (Blecic 2016; Cubillos 2016). The code provides a line-by-line radiative-transfer and a thermochemical-equilibrium abundances (Blecic et al. 2016) module, which can be use in forward or retrieval mode, via a Differential-evolution MCMC sampler (Cubillos et al. 2017). The atmospheric model consist of a 1D set of concentric shell layers, in hydrostatic equilibrium, spanning from 10⁻⁸ to 100 bar. For the temperature profile we consider either the three-channel Eddington approximation parameterization (TCEA; Line et al. 2013b) or an isothermal profile.

The Pyrat Bay code considers molecular opacities for H₂O from HITEMP (Rothman et al. 2010), NH₃ and CH₄ from HITRAN (Rothman et al. 2013), and HCN from Exomol (Barber et al. 2014). We compressed these line-by-line data files using the repack package (Cubillos 2017) to extract only the strong lines that dominate the spectrum, speeding up the radiative-transfer calculation. Additionally, Pyrat Bay considers collision induced absorption (CIA) from H₂–H₂ (Borysow et al. 2001; Borysow 2002) and H₂–He (Borysow et al. 1988, 1989; Borysow & Frommhold 1989); and H₂ Rayleigh scattering (Lecavelier Des Etangs et al. 2008). We also consider two cloud parameterizations, a simple gray-cloud opacity with constant cross section (cm⁻² molec⁻¹) below 10⁻⁵ bars, and a thermal-stability cloud model based on the approach described in Ackerman & Marley (2001) and Benneke (2015), with additional flexibility (J. Blecic et al. 2018, in preparation). We compute the opacity for either Fe or MgSiO₃ condensates using Mie-scattering theory (Toon & Ackerman 1981).

The retrieval parameterization includes free scale factors for the mixing ratios of H₂O, NH₃, CH₄, and HCN (vertical-constant values) and the mean molecular mass of the atmosphere; either the isothermal temperature or the κ, γ, and β parameters of the TCEA model (see Line et al. 2013b); the gray-cloud cross section or the Mie-scattering cloud profile shape, condensate mole fraction, particle-size distribution, and gas number fraction just below the cloud deck.; and the planetary radius at 0.1 bar.

We explored several cases, obtaining qualitatively good fits in all gray-cloud, complex-cloud, and clear-atmosphere cases. As expected for transmission spectroscopy, the retrieval returned largely unconstrained parameters for the TCEA temperature model, suggesting that the data does not justify more complex models than an isothermal profile. In all cases, the MCMC favors lower temperatures (T < 1000 K) than equilibrium temperature (1500 K) at the pressures probed by the observations. We constrain the water abundance, ranging from solar to ∼0.1 times solar values (Figure 6). The observed water absorption feature is muted relative to a clear atmosphere with solar abundances. This is caused by a sub-solar water abundance, an absorbing cloud opacity, or a high mean molecular mass, which reflects in a strong correlation between the water abundance and the cloud cross section. When we compare retrievals with the gray and complex-cloud model, we find similar best-fitting spectra between the two cases. The complex-cloud retrieval does not constrain any of the cloud parameters when we set all four species abundances free. In the case when we set the water abundance as the only abundance free parameter, we find a somewhat better condensate-fraction constraint. Since the cloud opacity dominates only a limited region of the observed spectrum (∼1.2–1.3 μm), we conclude that there is no need for a more complex-cloud model for this study. The Reproducible Research Compendium for the Pyrat Bay models is available at https://github.com/pcubillos/KilpatrickEtal2018_WASP63b.

We use the CHIMERA transmission model (Line et al. 2013a; Kreidberg et al. 2014a, 2015; Swain et al. 2014; Greene et al. 2016; Line et al. 2016). For transit geometry, the code solves the radiative-transfer equation for parallel rays across the terminator of the planet (Brown 2001; Tinetti et al. 2012). The code integrates atmospheric opacities from either correlated-K or sampled "line-by-line" absorption cross sections. To explore the parameter space, the transmission model is coupled with the PyMultiNest (Buchner et al. 2014) multimodal nested-sampling algorithm (Feroz & Hobson 2008). The atmosphere is in hydrostatic equilibrium with height-dependent gravity, temperature, and molecular weight. The temperature profile comes from either the radiative-equilibrium model from Guillot (2010) or an isothermal profile, spanning from 10⁻⁷ to 30 bar. The atmosphere uses "thermochemically consistent" molecular abundances (as defined in Kreidberg et al. 2015), computed using the NASA CEA2 model for given elemental abundances (Lodders 2009).

The CHIMERA code considers molecular opacities for H₂O, CH₄, CO, CO2, NH₃, Na, K, TiO, VO, C₂H₂, HCN, and FeH (Freedman et al. 2014); CIA from H₂–H₂ and H₂–He Richard et al. (2012); a Rayleigh power-law haze (Lecavelier Des Etangs et al. 2008); and either an opaque gray patchy cloud model (Line & Parmentier 2016) or a more complex, Mie-cloud model (Lee et al. 2013).

The retrieval parameterization includes the metallicity [M/H], the carbon-to-oxygen ratio $\mathrm{log}({\rm{C}}/{\rm{O}})$, and the carbon- and nitrogen-species quench pressures (Kreidberg et al. 2015; Morley et al. 2017) to set the elemental abundances; either the isothermal temperature or the κ_IR, γ_v, T_irr parameters of Guillot (2010); the top-pressure boundary and a "patchy terminator" parameter for the gray patchy cloud model, or the Q₀ and r (see Lee et al. 2013) and profile shape (mixing ratio, cloud base pressure, pressure fall off index; M R. Line et al. 2017, in preparation) for the Mie-cloud model; and a radius scale factor to set the reference altitude at 10 bar.

The "chemically consistent" retrieval detects the water spectral feature at 3.6σ confidence (Figure 7). This is consistent with a hard upper limit on C/O near 1. The water band is muted relative to solar composition. The retrieval posterior shows two "composition" modes: low metallicity ([M/H] ≲ 1.3 (20×)) degenerate with a cloud and high metallicity (peak near ∼300 × solar). There is a turn-over degeneracy in cloud top versus [M/H] (due to the effect on the mean molecular weight) resulting in the bi-modal marginalized metallicity distribution. Clouds can be present, but are not required to fit the spectra as given by the Bayes factor (0.45) and result in a much lower value for the low-metallicity mode (<0.1 × solar), while the high-metallicity mode remains. The highest of the sampled metallicities (greater than ∼50 times solar) are possibly implausible given mass and radius of WASP-63b.

Further tests found negligible variations when imposing a temperature prior or no patchy-cloud factor. A comparison between correlated-K and line-by-line sampling opacities produced nearly identical results. Likewise, the more complex Mie-cloud model produced qualitatively similar main conclusions (with unconstrained cloud particle sizes, vertical extent, or cloud composition).

We use the nested-sampling retrieval algorithm POSEIDON (MacDonald & Madhusudhan 2017) to analyze the WFC3 observations of WASP-63b. The code pre-computes line-by-line molecular cross sections following the methodology of Hedges & Madhusudhan (2016) and & Madhusudhan (2017). To compute detection significances we conduct nested Bayesian model comparisons. For simplicity, we model the atmosphere assuming an isothermal temperature–pressure profile, with 100 layers uniformly spaced in log-pressure from 10⁻⁶ to 100 bar, in hydrostatic equilibrium.

The POSEIDON code considers molecular opacities for H₂O from HITEMP (Rothman et al. 2010) and CH₄, NH₃, and HCN from Exomol (Tennyson et al. 2016); CIA from H₂–H₂ and H₂–He (Richard et al. 2012); Rayleigh scattering (Lecavelier Des Etangs et al. 2008); and a uniform-in-altitude gray-opacity cloud model.

The retrieval parameterization includes free scale factors for the mixing ratio of H₂O, CH₄, NH₃, and HCN; the isothermal temperature; the gray-cloud opacity; and the reference pressure at the transit radius (Figure 8).

The model comparison test marginally prefer the gray-opacity case (${\chi }_{\mathrm{red}}^{2}=1.21$) over a cloud-free case (${\chi }_{\mathrm{red}}^{2}=1.46$), with a Bayes factor of 2.2. Adopting the gray-opacity model, we detect H₂O at 4.0σ (Bayes factor = 601), HCN at 3.1σ (Bayes factor = 27.6), and "nitrogen chemistry" (combination of HCN and NH₃) at 3.3σ (Bayes factor = 53.7). We do not detect CH₄.

We retrieved the HST/WFC3 spectrum of WASP-63b using the Tau-REx atmospheric retrieval framework (Waldmann et al. 2015a, 2015b; Waldmann 2016). Based on the Tau code transmission forward models by Hollis et al. (2013), Tau-REx employs Nested Sampling (Feroz & Hobson 2008) to solve the full Bayesian argument. Tau-REx can use high-resolution absorption cross section or correlated-k tables as opacity inputs. Here we used the latter but find both to yield equivalent results for the wavelength ranges and sensitivities of the data at hand. We include pressure-dependent line broadening where such information is available, taking into account the J quantum number dependence on pressure broadening coefficients. In this study, we assume an isothermal atmospheric temperature–pressure profile, spanning from to 10⁻⁹ to 10 bar.

The Tau-REx code considers molecular opacities for H₂O, CH₄, NH₃, HCN, TiO, and VO from Exomol (Tennyson & Yurchenko 2012), CO and CO2 from HITEMP (Rothman et al. 2010), and O₂, O₃, NO₂, NO, HCOOH, C₂H₆, and C₂H₂ from HITRAN (Rothman et al. 2009, 2013); CIA from H₂–H₂ (Borysow et al. 2001; Borysow 2002) and H₂–He (Abel et al. 2012); Rayleigh scattering (Lecavelier Des Etangs et al. 2008); and clouds using a hybrid model of gray-cloud opacities and a phenomenological Mie scattering (Lee et al. 2013).

We run two types of retrievals, a "free" retrieval with abundances of H₂O, CH₄, CO, CO₂, NH₃, (Figure 9) as well as a chemical-equilibrium retrieval using an implementation of the ACE model by Agúndez et al. (2012), with the C/O ratio and atmospheric metallicity as free parameters. The rest of the retrieval parameters are the isothermal temperature; the top pressure of the gray-cloud model and the particle size, composition and mixing ratio of the Mie-cloud model; and the planet reference radius at 10 bar.

We detect water with a 3.5σ significance (Bayes factor = 103) compared with a family of pure-cloud or featureless atmosphere models. We obtain $\mathrm{log}({{\rm{H}}}_{2}{\rm{O}})=-{4.84}_{-1.53}^{+1.04}$. We do not find any evidence of an extended Rayleigh curve due to hazes but found a gray-cloud model to be sufficient. We constrain the cloud-top pressure to $\mathrm{log}(p)={3.08}_{-0.93}^{+1.48}$ Pa. The chemically consistent retrieval yielded two results. The first result yields a high-metallicity atmosphere at 370 times solar. The second result yields a low-metallicity atmosphere at 0.24 times solar. Both solutions feature comparable log-evidences and result in upper bounds of C/O at 0.49. A ratio of C/O < 0.7 is expected as only water is retrieved in this data set and is therefore consistent with the "free" retrieval approach above. The atmospheric metallicity is poorly constrained due to the presence of clouds, which has the effect of muting the water feature and biasing the chemical-consistent model to either compensate with unrealistically high mean molecular weight atmospheres or unrealistically low trace gas abundances.