Tentative Evidence for Water Vapor in the Atmosphere of the Neptune-sized Exoplanet HD 106315c

We used a custom data reduction pipeline to process the HST transit observations (described in detail in Kreidberg et al. 2018b). The starting point for our reduction was the _ima data product provided by the Space Telescope Science Institute. These images have an intermediate level of processing, with corrections applied for dark current, linearity, and flat fielding. To extract spectra from the images, we used the optimal extraction routine of Horne (1986). This algorithm iteratively masks bad pixels in the image and provides a convenient method to reject cosmic rays from spatial scan data. To estimate the background, we identified a region of pixels that was not contaminated by flux from the target or any nearby stars (rows 10–70 and columns 400–500) and calculated the median count rate in this region. We subtracted the background and extracted the spectra from each up-the-ramp sample separately, and summed them to produce a final spectrum from the exposure. To account for spectral drift, we interpolated each spectrum to the wavelength scale of the first exposure of the first visit. The shift is applied to the final spectrum, not each up-the-ramp sample. We generated spectroscopic light curves by binning the spectra into 22 wavelength channels over the wavelength range 1.125–1.65 μm. This binning corresponds to roughly five pixels in the spectral direction. The binning is about twice as coarse as the native resolution of the grism and was chosen to average over variations in sensitivity between individual pixels. Figure 1 shows the band-integrated light curve, the background counts, and the spectral shifts for each visit.

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We fit the light curves with a joint model of the transit and the instrument systematic trends. In agreement with previous work, we found that the first orbit of every visit and the first exposure in each orbit were strongly affected by a ramp-like systematic (caused by charge traps filling up in the detector; Zhou et al. 2017). This systematic is visible in the raw data, shown in Figure 1. Following past studies, we removed the first orbit of the visit and the first exposure of the remaining orbits in our analysis (e.g., Kreidberg et al. 2014). The trimmed data had three full orbits per visit of out-of-transit baseline, which is sufficient to fit for visit-long trends.

To model the transit signal, we used the batman package (Kreidberg 2015). For the broadband light-curve fit, the free parameters for the transit model were the ratio of planet to stellar radius R_p /R_s , the time of central transit T_c , the orbital inclination i, the ratio of semimajor axis to stellar radius a/R_s . We fixed the eccentricity to zero. We ran an initial fit with free parameters for a linear limb darkening coefficient and found excellent agreement with predictions from a Kurucz ATLAS9 stellar model with T_eff = 6250 K, $\mathrm{log}\ g=4.5$ (cgs), and [Fe/H] = −0.2 (Castelli & Kurucz 2003). We therefore fixed the limb darkening on the predicted quadratic coefficients from the model for the remainder of the analysis. ²⁸ For the spectroscopic channels, we fixed T_c , a/R_s , and i on the best-fit values from the broadband light curve.

To model systematic noise from the instrument, we multiplied the model transit light curve by the analytic model-ramp function, previously used for WFC3 data analysis (Equation (3) in Kreidberg et al. 2018b). Briefly, this function fits an exponential ramp to each orbit, a normalization constant, and a visit-long trend. For the HD 106315c data, there was no significant improvement to the light-curve fit for a quadratic term in the visit-long trend, so we used a linear term only. We also fit for a constant additive offset between scan directions. For both the broadband and spectroscopic light-curve fits, all visits were fit simultaneously. Most of the fit parameters were shared across visits, with the exception of the normalization constant and visit-long slope, which were allowed to vary separately from visit to visit. We determined the best-fit parameters with a least-squares fitting routine and estimated parameter uncertainties with the dynesty package, which uses dynamic nested sampling to evaluate constant likelihood contours over the full prior volume (Speagle 2020). The light curves and best-fit models are shown in Figure 2. To ensure that we did not underestimate the uncertainties, we rescaled the per point errors from the least-squares fit such that the reduced χ² of the best-fit model was unity. The error bars increased by a median (mean) of 9% (12%). The dynesty runs were halted when the remaining contribution to the evidence was estimated to be below 0.01 of the total. The resulting median and 68% credible intervals for the transit depths are listed in Table 1. To test for correlated noise in the light curves, we binned the data in time over a range of bin sizes from 2 to 20 points and calculated the rms for each bin size (see Figure 3). The rms decreases with the square root of the number of points per bin, indicating that the noise is uncorrelated in time.

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3.1.1. Independent Analysis of the WFC3 Data

We also carried out an independent data reduction and analysis. The data were reduced following the methodology previously described by Evans et al. (2016, 2017). Briefly, the spectra were extracted from each _ima frame by summing the difference of successive up-the-ramp samples while masking cross-dispersion regions away from the target to reject cosmic rays and nearby contaminating sources. A wavelength-independent background value was subtracted from each spectrum by taking the median pixel value in a 30 × 250 pixel box away from the target. Broadband light curves were produced for each visit by summing each spectrum along the full dispersion axis. The broadband light curves were fit jointly, with the systematics and transit midtimes allowed to vary separately, and R_p /R_s shared across visits. Other transit parameters such as a/R_s and i were fixed to the median values reported in Crossfield et al. (2017). For the systematics, we adopted the double-exponential ramp treatment described in de Wit et al. (2018) and also allowed the white noise to vary as a free parameter, implemented as an increase above the formal photon noise value.

Following the broadband light-curve fit, we produced spectroscopic light curves in 14 channels spanning the 1.122–1.642 μm wavelength range following the methodology described in Evans et al. (2016), which is based on an original implementation of Deming et al. (2013). This procedure effectively removes the common-mode component of the systematics in each wavelength channel, which is dominated by the ramp systematic. As such, for our spectroscopic light-curve fits, a simple linear time trend and variable white noise level were adequate for modeling the systematics. We also allowed R_p /R_s to vary while holding all other transit parameters fixed to the white light-curve values. In both the white light-curve and spectroscopic light-curve fits, a quadratic limb darkening law was adopted with coefficients held fixed to values determined by fitting the limb darkened profiles of an ATLAS9 stellar model with the same parameters listed in Section 3.1.

The resulting transmission spectrum is compared to that of the first analysis in Figure 4. The two spectra agree to well within 1σ, and the uncertainties on the transit depths are consistent after accounting for the difference in wavelength bin size. The model-ramp fit has a median uncertainty on the transit depth of 23 ppm (for 0.025 μm bins), and the common-mode fit has a median uncertainty of 17 ppm (for 0.037 μm bins). Accounting for the difference in bin size, the uncertainties agree to within 11%. Given the good agreement between the two independent analyses, we used the model-ramp results (listed in Table 1) for the remainder of the analysis.

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In addition to the HST and K2 data, we also analyzed a single transit of HD 106315c observed with Spitzer in the 4.5 μm bandpass. We followed a similar approach to the one described in Berardo et al. (2019), which detrends the data using the Pixel Level Decorrelation method outlined in Deming et al. (2015). For each pixel in a frame, we first generated a time series of its flux across all frames. We then applied a median filter to each of these light curves to remove time-dependent outliers on a pixel-by-pixel basis across the entire observation. We then calculated a background level for each frame by taking the median of the flux in an annulus centered on the point-spread function. We estimated the centroid of each frame by fitting a two-dimensional Gaussian to the image, and obtained a light curve using a fixed radius aperture.

We modeled systematics in the light curve by weighting the nine brightest pixels individually as well as fitting for a quadratic time ramp. We then chose the combination of pixel coefficients, aperture size, and time-series binning that resulted in the smallest rms deviation. Time-series binning was done following the motivation and methods described in Section 3 of Deming et al. (2015). In particular, we fit to the binned data but then examined the residuals of the retrieved model when applied to the unbinned data. A minimum amount of binning is useful in removing short-term variations, which helps when fitting for long-term trends. We did not bin on timescales long enough to distort the transit signal, or where the number of data points approaches the number of free parameters. When fitting we left the photometric uncertainty as a free parameter in the Markov Chain Monte Carlo (MCMC), which accounts for the fact that the number of data points has changed. The optimal aperture radius was found to be 2.4 pixels. We used an MCMC sampler to estimate uncertainties and fit the systematic model simultaneously with a transit model from batman (Kreidberg 2015). We kept the period, inclination, and distance a/R_⋆ fixed to the values 21.0564 days, 88501, and 26.769, respectively (based on the HST white light-curve fit), and allowed the depth and transit center to vary. We also left the uncertainty of the data points as a free parameter, which we found converged to the rms scatter of the raw light curve. We also held fixed the quadratic limb darkening parameters, which were also estimated from a Kurucz ATLAS9 stellar model. The transit light curve and best-fit model are shown in Figure 5, and the fit results are summarized in Table 2.

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Table 2. K2/Spitzer Transit Parameters

Parameter	Units	Value (K2)	Value (Spitzer)
Held fixed:
Rs /a	⋯	0.0373566	0.0373566
i	deg	88.50109	88.50109
u1	⋯	0.365	0.079
u2	⋯	0.244	0.089
Derived values:
T0	BJDTDB − 2,454,833	${2778.1320}_{-0.0017}^{+0.0016}$	3030.8079 ± 0.0012
P	d	21.0564 ± 0.0024	21.0564 (fixed)
Rp /Rs	%	3.208 ± 0.041	3.271 ± 0.11
${({R}_{p}/{R}_{s})}^{2}$	ppm	1030 ± 26	1070 ± 75

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To provide a broadband, optical-wavelength transit depth for comparison with our infrared observations, we reanalyzed the 30 minutes cadence K2 photometry of HD 106315. Although several analyses of these K2 data have already been published (Crossfield et al. 2017; Rodriguez et al. 2017), our reanalysis takes advantage of the tighter constraints on orbital parameters (a/R_s and i) provided by the high-cadence, high-precision HST observations. Our analysis used largely the same approach as described by Crossfield et al. (2017), but with a few changes. First, we used a different set of K2 photometry ²⁹ , which had a substantially lower rms. Second, we fixed two key orbital parameters to the following values: a/R_s = 26.769, and i = 88501. Third, in contrast to the analysis of Crossfield et al. (2017), we allowed no dilution that would potentially decrease the observed transit depth (and so bias the analysis toward larger R_p /R_s ). We neglected dilution because high-resolution imaging and spectroscopy show no nearby stars within 5 magnitudes of HD 106315 at distances of <01 (Kosiarek et al. 2021). Finally, we held the quadratic limb darkening parameters fixed to the values predicted by an ATLAS9 stellar model (u₁ = 0.365 and u₂ = 0.244). The transit parameters derived from this analysis are listed in Table 2.

Unocculted star spots and plages can significantly contaminate exoplanet transmission spectra (Pont et al. 2013; Rackham et al. 2018, 2019). In general, F stars such as HD 106315 have lower spot covering fractions than stars of later spectral types (Rackham et al. 2019). The K2 light curve for HD 106315 shows variability with an amplitude of 0.1% over a timescale of 75 days, a typical value for mid-F stars (Rodriguez et al. 2017). This amplitude corresponds to a covering fraction of 0.1 ± 0.1%. The expected amplitude of the stellar contamination spectrum is 0.0001–0.0002× the transit depth. For the transit depth of HD 106315c (1000 ppm), the expected stellar contamination is 0.1–0.2 parts per million—a negligible contribution.

We used the open-source software package petitRADTRANS (pRT; Mollière et al. 2019), which is a fast spectral synthesis tool for exoplanet atmospheres. We connected pRT to the PyMultiNest tool (Buchner et al. 2014), which is a Python wrapper of the MultiNest (Feroz & Hobson 2008; Feroz et al. 2009, 2013) implementation of nested sampling (Skilling 2004).

The atmosphere was modeled with the vertically constant temperature and absorber mass fractions of H₂O, CH₄, CO₂, CO, and N₂ as free parameters. We also included the cloud-top pressure of a gray cloud deck as a free parameter. The atmospheric mean molecular weight (MMW) was calculated from the parameterized absorber abundances, assuming that the remaining mass is contributed by H₂ and He, with an H₂:He mass ratio of 3:1. Our full model included the line opacities of H₂O, CH₄, CO₂, and CO, as well as the Rayleigh scattering cross sections of these species, in addition to those of H₂, He, and N₂. N₂ may thus be thought of as a proxy for (mostly) invisible species in the atmosphere that can increase its MMW. Instead of retrieving a reference radius at a given pressure we retrieved a reference pressure P₀ at a given radius, where we made sure that the fixed reference radius is chosen at values appropriate for placing the retrieved reference pressure values within the atmospheric pressure domain. We placed log-uniform priors on the absorber mass fractions of H₂O, CH₄, CO₂, CO, and N₂ between 10⁻¹⁰ and 1, requiring that the sum of all mass fractions is below unity. The temperature was allowed to vary between 400 and 1000 K. The cloud and reference pressure could be placed at any location within the atmospheric pressure domain, imposing a log-uniform prior. However, we note that the posterior distribution for the water abundance (which is the only species we detect tentatively) is sensitive to the choice of prior bounds, particularly if regions are explored that do not produce any difference in the model spectrum (for example, very deep clouds). We additionally tested retrieving a scattering haze (${\kappa }_{\mathrm{haze}}={\kappa }_{0}{[\lambda /{\lambda }_{0}]}^{\gamma }$), a cloud patchiness parameter (mixing clear and cloudy terminators), and the planet's gravity within measurement uncertainties, but none of these tests significantly changed our results.

In order to test how reliably water can be detected in our spectrum we followed the approach introduced in Benneke & Seager (2013). Our full model retrieved the abundance of all absorbers listed above. Then, we iteratively removed one absorber at a time and reran the retrieval. Comparing the evidences between the full model and the model lacking a given species allows us to assess whether the observation is in favor of that species being included in the model. The retrieved atmospheric properties for the full model are shown in Figure 6.

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The resulting evidences Z are listed in Table 3. The Bayes factor is the ratio of evidences. Bayes factors greater than 100 are considered decisive, 10–100 are strong, 3.2–10 are substantial, and below 3.2 are insignificant (Kass & Raftery 1995). None of the tested species is substantially favored to be included in our model. However, the full model is slightly favored when compared to a model that removed H₂O, with a Bayes factor of 1.7. The fact that water is the only molecule that can lead to noticeable differences in the fit is not surprising, since WFC3 spectra are predominantly sensitive to absorption from H₂O. Higher precision measurements of the transmission spectrum are needed to uniquely identify absorbing species in the atmosphere of HD 106315c.

Table 3. Bayesian Evidence for Atmospheric Retrievals with PetitRADTRANS

Retrieval model	${\rm{\Delta }}\,\mathrm{ln}(Z)$	Bayes factor for
		molecule present
no H2O	+0.517 ± 0.078	1.68
no CO2	−0.347 ± 0.085	0.71
no CO	−0.490 ± 0.122	0.61
no CH4	−0.482 ± 0.040	0.62
no N2	−0.766 ± 0.237	0.46
no cloud	+0.022 ± 0.067	1.02

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The retrieved spectrum is shown in Figure 7. The amplitude of spectral features in the best-fit model is about 30 ppm (7× smaller than that expected for a solar composition, cloud-free atmosphere). This observed peak-to-trough amplitude corresponds to 0.8 ± 0.04 H₂/He scale heights (assuming μ = 2.3 atomic mass units, T = 800 K, and g = 6.0 m s⁻²). In general, to produce features of this amplitude, models have (1) an enhanced MMW (which decreases the atmospheric scale height and shrinks the spectral features), (2) high-altitude clouds, which truncate the spectral feature at the cloud deck altitude, or (3) both of the above (Benneke & Seager 2013). In the case of HD 106315c, the retrieval prefers scenarios (2) and (3), with the highest posterior probability for moderate cloud coverage. A broad range of H₂O abundances is consistent with the data (3 × 10⁻⁴–290× solar at 1σ). The "solar" water abundance corresponds to the chemical equilibrium water volume mixing ratio for a solar composition gas at 1 mbar pressure and 800 K (2.2 × 10⁻⁴). The cloud-top pressure is in the range P_cloud = 0.04–130 mbar (at 1 σ). There is some degeneracy between ${n}_{{{\rm{H}}}_{2}{\rm{O}}}$ and P_cloud, because a higher water abundance pushes the photosphere to lower pressures. There is also a tail of probability toward water-rich solutions with deep clouds (below the observable photosphere). Very high water abundances cannot be ruled out (${n}_{{{\rm{H}}}_{2}{\rm{O}}}\lt 2100\times$ solar at 2σ confidence, ${n}_{{{\rm{H}}}_{2}{\rm{O}}}\lt 4200\times$ solar at 3σ). At these high metallicities, the atmosphere is no longer dominated by H₂, but rather by H₂O or CO₂ (Moses et al. 2013).

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As an independent check of the results from petitRADTRANS, we also interpreted the transmission spectrum with the SCARLET atmospheric retrieval framework (e.g., Benneke & Seager 2012, 2013; Knutson et al. 2014; Kreidberg et al. 2014; Benneke 2015; Benneke et al. 2019a, 2019b; Wong et al. 2020). Employing SCARLET's free molecular composition mode we defined the mole fractions of H₂O, CH₄, CO₂, CO, and N₂ as free parameters and assumed a well-mixed atmosphere. The remainder of the atmosphere gas was assumed to be composed of H₂ and He in the solar abundance ratio. We included a gray cloud deck using a free parameter describing the cloud-top pressure, and an additional free parameter to capture our prior ignorance of the temperature in the photosphere of HD 106315c near the terminator.

To evaluate the likelihood for a particular set of atmospheric parameters, the SCARLET forward model in free molecular composition mode computes the hydrostatic equilibrium and line-by-line radiative transfer. We considered the latest line opacities of H₂O, CO, and CO₂ from HiTemp (Rothman et al. 1998) and CH₄ from ExoMol (Tennyson et al. 2016), as well as the collision-induced absorption of H₂ and He. We employed log-uniform priors between 10⁻¹⁰ and 10^−0.5 = 31%, but required that the sum of all mass fractions is below unity. We employed log-uniform priors for the cloud-top pressures 10⁻³ and 10⁷ Pa. We used a uniform prior on the photospheric temperature between 620 and 1150 K (70%–130% of the equilibrium temperature).

SCARLET then determined the posterior constraints by combining the SCARLET atmospheric forward model with nested sampling (Skilling 2004). We ran the analyses well beyond formal convergence to obtain a smooth posterior distribution and capture the contours of the wide parameter space in agreement with the transmission spectrum of HD 106315c. As in Section 4.1, we evaluated the presence of individual molecular species in the atmosphere of HD 106315c following the strategy outlined in Benneke & Seager (2013).

The retrieval results are shown in Figure 8. Our analysis reveals a Bayes factor of 2.6 in favor of the presence of water vapor in the atmosphere of HD 106315c, which can be regarded as tentative evidence. No other molecular species is favored by the data. We also tested for the presence of clouds by comparing the full retrieval model to a model that lacks clouds in the hypothesis space, but find no evidence in the observational data. The small variation in evidence computed with SCARLET versus petitRADTRANS is most likely due to the slight differences in prior volume for the two analyses. We performed the final parameter estimation using the full retrieval model including the five molecules (H₂O, CH₄, CO₂, CO, and N₂) and gray clouds. The best-fitting model matches all data points within their 1σ uncertainties. A wide range of models is consistent with the data, in agreement with the results from petitRADTRANS.

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Transmission spectra including the effect of clouds were calculated following the methodology of Morley et al. (2015, 2017). First, 1D cloud-free model temperature profiles were calculated, assuming both radiative–convective and chemical equilibrium, using the approach described in detail in McKay et al. (1989), Marley & McKay (1999), Saumon & Marley (2008), and Fortney et al. (2008). We calculated profiles for metallicities of [M/H] = 0.0, 0.5, 1.0, 1.5, 2.0, and 2.5 (1, 3, 10, 30, 100, and 300× solar). The opacity database is described in detail in Freedman et al. (2008, 2014), with updated chemical equilibrium calculations and opacities as described in Marley et al. (2021).

We included the condensation of Na₂S, KCl, and ZnS, which are expected to condense at the temperature of HD 106315c (T_eq = 800 K). We calculated cloud altitude and height along the cloud-free pressure–temperature profile; the cloud properties were calculated using the methods described in Ackerman & Marley (2001) and Morley et al. (2012) for each metallicity, assuming a range of sedimentation efficiencies (f_sed = 2, 1, 0.5, and 0.1), a parameter which controls the cloud particle size and cloud height. This model calculates the cloud optical depth, single-scattering albedo, and asymmetric parameter for each layer of the atmosphere. Example pressure–temperature profiles with cloud condensation curves are shown in Figure 9.

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To calculate transmission spectra, we used the transmission spectrum model described in the Appendix of Morley et al. (2017). Gas opacity from H₂ collisionally induced absorption, CO₂, H₂O, CH₄, CO, NH₃, PH₃, H₂S, Na, K, TiO, VO, and HCN were included. We calculated models for each metallicity and f_sed combination considered.

Figure 10 shows the goodness of fit for the cloudy model grid compared to the WFC3 transmission spectrum. The K2 and Spitzer data are not precise enough to significantly affect the goodness of fit. The best fits have small water absorption features with an amplitude of around 30 ppm. The amplitude of features in the models is a trade-off between metallicity and cloud altitude: higher metallicity models tend to have a smaller scale height and thus smaller features. A lower sedimentation efficiency also decreases the feature amplitude. Small f_sed values loft cloud particles higher in the atmosphere, obscuring spectral features. As shown in Figure 9, the cloud base is typically below the pressure level sensed by the observations, so f_sed values of ≲0.5 are required to loft the cloud into the observable atmosphere. For the HD 106315c spectrum, the best-fit models are high-metallicity atmospheres (100–300× solar), or lower metallicity with high-altitude clouds (f_sed < 0.5).

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We also calculated transmission spectra for hazy atmospheres using the photochemistry, microphysics, and transmission spectrum models of Kawashima & Ikoma (2018) in the same way as in Kawashima et al. (2019) and Kawashima & Ikoma (2019). We first performed photochemical simulations to derive the steady-state distribution of gaseous species. Then, since the haze monomer production rate is uncertain for exoplanets, we assumed a certain fraction of the sum of the photodissociation rates of the major hydrocarbons in our photochemical model, CH₄, HCN, and C₂H₂, would result in haze monomer production. We call this fraction the haze formation efficiency f_haze following Morley et al. (2013). With this assumption, we derived the steady-state distribution of haze particles by microphysical simulations. Finally, we modeled transmission spectra of the atmospheres with the obtained profiles of haze particles and gaseous species.

For the temperature–pressure profile, we used the online available ³⁰ analytical model of Parmentier & Guillot (2014) assuming an internal temperature of 100 K and their correction factor of 0.25, which corresponds to the case where the irradiation is efficiently redistributed over the entire planetary surface. For the other input parameters, we used the default opacities (Valencia et al. 2013; Parmentier et al. 2015) and Bond albedo. We included convection. Solar elemental abundance ratios were taken from Lodders (2003). For the UV spectrum of HD 106315, we used that of the Sun from Segura et al. (2003) because of its similar stellar type (F5; Houk & Swift 1999). We assumed a constant eddy diffusion coefficient of 10⁷ cm² s⁻¹ throughout the atmosphere for both photochemistry and microphysics calculations. We assumed a monomer radius of 1 nm and an internal density of haze particles of 1 g cm⁻³. The refractive index of haze is uncertain for exoplanets, so we considered two representative cases, tholin (Khare et al. 1984) and soot (Hess et al. 1998).

We calculated spectra for 1, 10, and 100× solar metallicity atmospheres with a range of f_haze from 10⁻⁷ to 1 in 1 dex increments. The integrated monomer production rate for f_haze = 1 (the sum of the photodissociation rates of CH₄, HCN, and C₂H₂) becomes smaller with increasing metallicity: 1.71 × 10⁻¹⁰, 1.20 × 10⁻¹⁰, and 5.51 × 10⁻¹¹ g cm² s⁻¹ for 1, 10, and 100× the solar metallicity atmospheres, respectively.

For the calculation of transmission spectra, we treated the reference radius at 10 bar pressure level as a parameter. We found the appropriate value with a grid of 0.1% of the observed transit radius, which yields the minimum reduced χ² with 18 degrees of freedom (21 data points minus 3 free parameters of metallicity, f_haze, and reference radius), for each case. We accounted for the transmission curve of the WFC3 G141 grism from the SVO Filter Profile Service ³¹ (Rodrigo et al. 2012; Rodrigo & Solano 2013).

The left panel of Figure 11 shows several representative models compared to the measured WFC3 spectrum: models for clear atmospheres of three different metallicities, as well as hazy (tholin) atmospheres with haze formation efficiency tuned to fit the WFC3 data well. The error bars for the K2 and Spitzer points are large and therefore have a negligible effect on the goodness of fit. The right panel of Figure 11 shows the goodness of fit for the model grids. We find that modest haze formation efficiencies of 10⁻³–10⁻⁴ generally match the observed spectra for all the three different metallicities, for both tholins and soots. This is because a smaller scale height due to increasing metallicity can be compensated for by a smaller fiducial monomer production rate. Overall, these haze production efficiencies are orders of magnitude lower than the extreme values required to reproduce the featureless spectrum of GJ 1214b (Morley et al. 2015; Kawashima et al. 2019). As noted above, the near-UV irradiation of HD 106315c is likely higher than that of GJ 1214b, so more haze precursors are present and a lower haze production efficiency is needed. Broadly speaking, the cloud and haze models are qualitatively similar over the wavelength range of our data, and either model can explain the spectrum. However, previous work has shown that clouds and hazes affect the spectrum differently at different wavelengths (Morley et al. 2015). In particular, small haze particles may lead to strong slopes in the optical and larger differences between optical and infrared wavelengths than cloud models. Future observations over a wider wavelength range would help distinguish between the two possibilities for HD 106315c.

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