The Hubble Space Telescope PanCET Program: An Optical to Infrared Transmission Spectrum of HAT-P-32Ab

We obtained time-series spectroscopy during two transits of HAT-P-32Ab using HST's STIS on UT 2017 March 6 and UT 2017 March 11 with the G430L grating, which provides low-resolution (R ∼ 500) spectroscopy from 2892 to 5700 Å. We observed an additional transit with the G750L grating on UT 2017 June 22, which covers the 5240–10270 Å wavelength range at R ∼ 500. The visits were scheduled to include the transit event in the third orbit and provide sufficient out-of-transit baseline flux as well as good coverage between the second and third contact. Each visit consisted of five consecutive 96 minute orbits, during which 48 stellar spectra were obtained over exposure times of 253 s. To decrease the readout times between exposures, we used a 128 pixel wide subarray. The data were taken with the 52 × 2 arcsec² slit to minimize slit light losses. This narrow slit is small enough to exclude any flux contribution from the M-dwarf companion to HAT-P-32A, located ∼29 away from the target (Zhao et al. 2014).

We reduced the STIS G430L and G750L spectra using the techniques described in Nikolov et al. (2014, 2015) and Alam et al. (2018), which we summarize briefly here. We used the CALSTIS pipeline (version 3.4) to bias-, dark-, and flat-field correct the raw 2D data frames. To identify and correct for cosmic-ray events, we used median-combined difference images to flag bad pixels and interpolate over them. We then extracted 1D spectra from the calibrated .flt files and extracted light curves using aperture widths of 6 to 18 pixels, with a step size of 1. Based on the lowest photometric dispersion in the out-of-transit baseline flux, we selected an aperture of 13 pixels for use in our analysis. We computed the mid-exposure time in MJD for each exposure. From the x1d files, we resampled all of the extracted spectra and cross-correlated them to a common rest frame to obtain a wavelength solution. Since the cross-correlation measures the shift of each stellar spectrum with respect to the first spectrum of the time series, we resampled the spectra to align them and remove subpixel drifts associated with the different locations of the spacecraft on its orbit (Huitson et al. 2013). Example spectra for the G430L and G750L gratings are shown in Figure 1.

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We observed a single transit of HAT-P-32Ab with the Wide Field Camera 3 (WFC3) instrument on UT 2016 January 21. The transit observation consisted of five consecutive HST orbits, with 18 spectra taken during each orbit. At the beginning of the first orbit, we took an image of the target using the F139M filter with an exposure time of 29.664 s. We then obtained time-series spectroscopy with the G141 grism (1.1–1.7 μm). Following standard procedures for WFC3 observations of bright targets (e.g., Deming et al. 2013; Kreidberg et al. 2014; Evans et al. 2016; Wakeford et al. 2017a), we used the spatial scan observing mode to slew the telescope in the spatial direction during an exposure. This technique allows for longer exposures without saturating the detector (McCullough & MacKenty 2012). We read out using the SPARS10 sampling sequence with five nondestructive reads per exposure (NSAMP = 5), which resulted in integration times of 89 s.

We started our analysis of the WFC3 spectra using the flat-fielded and bias-subtracted ima files produced by the CALWF3 pipeline¹⁶ (version 3.3). We extracted the flux for each exposure by taking the difference between successive reads and then subtracting the median flux in a box 32 pixels away from the stellar spectrum. This background subtraction technique masks the area surrounding the 2D spectrum to suppress contamination from nearby stars and companions, including the M-dwarf companion to HAT-P-32A. We then corrected for cosmic-ray events using the method of Nikolov et al. (2014).

Stellar spectra were extracted by summing the flux within a rectangular aperture centered on the scanned spectrum along the full dispersion axis and along the cross-dispersion direction ranging from 48 to 88 pixels. We determined the wavelength solution by cross-correlating each stellar spectrum to a grid of simulated spectra from the WFC3 Exposure Time Calculator (ETC) with temperatures ranging from 4060 to 9230 K. The closest matching model spectrum to HAT-P-32A (T_eff = 6000 K) was the 5860 K model. We used this process to determine shifts along the dispersion axis over the course of the observations.

We obtained two transit observations of HAT-P-32Ab on UT 2012 November 18 and UT 2013 March 19 with the Spitzer IRAC 3.6 μm and 4.5 μm channels, respectively (Fazio et al. 2004; Werner et al. 2004). Each IRAC exposure was taken over integration times of 2 s in the 32 × 32 pixel subarray mode. We reduced the 3.6 and 4.5 μm Spitzer/IRAC data using a custom data analysis pipeline which implements pixel-level decorrelation (PLD; Deming et al. 2015), described fully in C. Baxter et al. (2020, in preparation). In summary, the pipeline performs a full search of the data reduction parameter space in order to determine the optimum aperture photometry, background subtraction, and centroiding. The resulting photometric light curve is normalized to the out-of-transit flux, and errors are scaled with the photon noise. We clipped outliers with a sliding 4σ median filter.

Stellar activity can mimic planetary signals and imprint spectral slopes and spurious absorption features in transmission spectra (e.g., Pont et al. 2013; McCullough et al. 2014). To assess whether stellar activity might impact the transit observations, we inspected available ground-based photometry from the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2014; Kochanek et al. 2017; Rackham et al. 2017) and the Tennessee State University (TSU) Celestron 14 inch (C14) automated imaging telescope (AIT) at Fairborn Observatory. Since the ASAS-SN data set exhibits large scatter (σ ∼ 10 mmag) and is dominated by noise, we only use the AIT observations in our analysis of the host star's activity levels.

We acquired a total of 270 nightly observations of HAT-P-32A over the past five observing seasons from 2014–2015 to 2018–2019 (see, e.g., Henry 1999; Eaton et al. 2003). The first three observing seasons were discussed in Nikolov et al. (2018b), where they provide details about the observing and data reduction procedures. On the basis of those three observing seasons, we concluded that HAT-P-32A is constant on night-to-night timescales within the precision (∼2 mmag) of our observations and likely to be constant on year-to-year timescales.

The SBIG STL-1001E CCD camera on the AIT suffered a failure early in the 2017–2018 observing season and had to be replaced, resulting in an abbreviated fourth observing season. The camera was replaced with another SBIG STL-1001E CCD to minimize instrumental shifts in the long-term data. Nonetheless, we found that the 2017–2018 and 2018–2019 observing seasons had seasonal-mean differential magnitudes several millimagnitudes different from the earlier data. The observations are summarized in Table 1, but we have not included measurements of the seasonal-mean magnitudes because of the calibration uncertainties. We note that the small nightly scatter in the new data is consistent with the star remaining constant within the precision of our data on night-to-night timescales.

The complete HAT-P-32A AIT data set is plotted in the top panel of Figure 2, where the data have been normalized so that each seasonal-mean differential magnitude is the same as the first observing season. The bottom panel shows a Lomb-Scargle periodogram (Lomb 1976; Scargle 1982) of our complete data set, which shows no evidence for any coherent periodicity between 1 and 100 days.

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We further consider XMM-Newton observations taken on UT 2019 August 30 (PI: Sanz-Forcada). These observations reveal an X-ray flux of ${L}_{{\rm{X}}}=2\times {10}^{29}$ erg s⁻¹ in the European Photon Imaging Camera (EPIC) cameras using d = 291.5 pc (Gaia DR2), in addition to the presence of two small flares (see further details in J. Sanz-Forcada et al. 2020, in preparation). EPIC cannot separate the A and B components of the HAT-P-32 system; so although the emission most likely comes from the A component, part of it might originate from the M-dwarf companion. Considering this possibility, we checked observations from the optical monitor (OM) onboard XMM-Newton with the UVW2 filter (λ = 1870–2370 Å). These observations indicate a low-level of activity in HAT-P-32A while the companion is not detected, reinforcing the idea that most of the X-ray emission originates from the A component of the system. The UV and X-ray observations, which are most sensitive to the star's chromosphere, reveal some level of activity, while HAT-P-32A's photosphere (probed by the optical ground-based monitoring) appears quiet. Given these discrepant results, we decided to fit for activity in our retrievals as described in more detail in Section 4.3.

We produced the white light curves for the HST and Spitzer data sets by summing the flux of the stellar spectra across the full spectrum. We fit the white light curves using a complete analytic transit model (Mandel & Agol 2002) parameterized by the mid-transit time T₀, orbital period P, inclination i, normalized planet semimajor axis a/R_⋆, and planet-to-star radius ratio R_p/R_⋆ (see Sections 3.1.1 and 3.1.2). The raw and detrended white light curves are shown in Figures 3 and 4. The derived system parameters for HAT-P-32Ab from these fits are given in Table 2.

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3.1.1. STIS

3.1.2. WFC3

3.1.3. IRAC

We fit the cleaned and normalized IRAC light curves with a batman transit model (Kreidberg 2015) in combination with the PLD systematic model and temporal ramp, resulting in 14 free parameters (four batman, nine PLD, and one temporal ramp). Furthermore, we fixed the eccentricity e to zero and the orbital period P to the literature value of 2.15 days (Hartman et al. 2011), and fit for i, a/R_⋆, T₀, and R_p/R_star. We used the linear limb-darkening law to calculate the theoretical limb-darkening coefficients using the 1D ATLAS code presented in Sing (2010). Posteriors for all 14 free parameters were calculated using the Markov Chain Monte Carlo (MCMC) script emcee (Foreman-Mackey et al. 2013). The final transit parameters presented in Table 2 are the result of a second MCMC, where the semimajor axis a/R_⋆ and the inclination i were varied within Gaussian priors from the median and standard deviation of the initial fits.

From these fits, we derive R_p/R_⋆ values of 0.14663 ± 0.00034 and 0.14866 ± 0.00067 for the 3.6 μm and 4.5 μm IRAC channels, respectively. Considering the 12 × 12 pixel size for the Spitzer 32 × 32 subarray images, we must correct for dilution from the M-dwarf companion to HAT-P-32A. We applied the dilution correction derived in Stevenson et al. (2014),

$$\begin{eqnarray}&&{\delta }_{\mathrm{true}}(\lambda )={\delta }_{\mathrm{obs}}(\lambda )\left[1+g(\beta ,\lambda )\displaystyle \frac{{F}_{B}}{{F}_{A}}\right],\end{eqnarray} \tag{ 1 }$$

where δ_true(λ) is the true (undiluted) transit depth, δ_obs(λ) is the observed (diluted) transit depth, g(β, λ) is wavelength-dependent companion flux fraction inside a photometric aperture of size β, F_B is the flux of the companion star, and F_A is the in-transit flux of the primary star. To account for the third light contribution in the Spitzer images, we use the dilution factors of ${({F}_{B}/{F}_{A})}_{3.6}=0.050$ ± 0.020 and ${({F}_{B}/{F}_{A})}_{4.5}=0.053$ ±  0.020 from Zhao et al. (2014) and estimate g(β, λ) for an aperture radius of 2.5 pixels using the IRAC point response function¹⁷ at 1/5 pixel sampling. The resulting R_p/R_⋆ values corrected for dilution are reported in Tables 2 and 3.

Table 3.  Broadband HST+Spitzer Transmission Spectrum for HAT-P-32Ab and Adopted Nonlinear (HST) and Linear (Spitzer) Limb-darkening Coefficients

λ (Å)	Rp/R*	c1	c2	c3	c4
2900–3300	0.15466 ± 0.00158	0.3152	0.4420	0.4813	−0.3167
3300–3700	0.15281 ± 0.00088	0.4052	0.6943	−0.2319	0.0273
3700–3950	0.15203 ± 0.00073	0.4069	0.5814	0.0073	−0.1117
3950–4200	0.15225 ± 0.00054	0.3991	0.5794	0.0046	−0.0954
4200–4350	0.15084 ± 0.00093	0.4025	0.5039	0.0782	−0.1137
4350–4500	0.15104 ± 0.00068	0.4998	0.3418	0.1836	−0.1546
4500–4650	0.15126 ± 0.00066	0.5702	0.2601	0.0992	−0.0640
4650–4800	0.15104 ± 0.00063	0.5660	0.3170	−0.0081	−0.0204
4800–4950	0.15083 ± 0.00065	0.6888	0.1103	0.1042	−0.0767
4950–5100	0.15093 ± 0.00049	0.6243	0.1792	0.0510	−0.0290
5100–5250	0.15137 ± 0.00059	0.6077	0.1870	0.0812	−0.0633
5250–5400	0.15183 ± 0.00049	0.6782	0.0034	0.2548	−0.1367
5400–5550	0.15080 ± 0.00051	0.7363	−0.0980	0.2614	−0.1063
5550–5700	0.15128 ± 0.00060	0.7356	−0.1217	0.2683	−0.1016
5700–6000	0.15077 ± 0.00070	0.7728	−0.2053	0.3104	−0.1130
6000–6300	0.15105 ± 0.00058	0.7964	−0.2947	0.3789	−0.1381
6300–6500	0.15057 ± 0.00122	0.8037	−0.3285	0.4036	−0.1533
6500−6700	0.14924 ± 0.00075	0.8718	−0.4706	0.4820	−0.1819
6700–6900	0.14933 ± 0.00072	0.8333	−0.4336	0.4641	−0.1631
6900–7100	0.15066 ± 0.00069	0.8462	−0.4889	0.5201	−0.1886
7100–7300	0.15121 ± 0.00097	0.8461	−0.4985	0.5090	−0.1780
7300–7500	0.15022 ± 0.00058	0.8321	−0.4776	0.4849	−0.1740
7500–7700	0.15084 ± 0.00071	0.8520	−0.5558	0.5665	−0.2086
7700–8100	0.14905 ± 0.00073	0.8573	−0.5815	0.5666	−0.2010
8100–8350	0.15021 ± 0.00110	0.8645	−0.6135	0.5794	−0.2024
8350–8600	0.15080 ± 0.00122	0.8574	−0.6348	0.6070	−0.2167
8600–8850	0.15013 ± 0.00110	0.8560	−0.6383	0.5907	−0.2071
8850–9100	0.15105 ± 0.00189	0.8622	−0.6681	0.6155	−0.2188
9100–9500	0.14906 ± 0.00146	0.8598	−0.6768	0.6389	−0.2305
9500–10200	0.14939 ± 0.00113	0.8479	−0.6659	0.6118	−0.2182
11190–11470	0.15071 ± 0.00035	0.6341	−0.2157	0.1764	−0.0625
11470–11750	0.15068 ± 0.00031	0.6336	−0.2103	0.1587	−0.0553
11750–12020	0.15136 ± 0.00033	0.6311	−0.2011	0.1333	−0.0413
12020–12300	0.15119 ± 0.00030	0.6282	−0.1673	0.0809	−0.0204
12300–12580	0.15055 ± 0.00028	0.6318	−0.1698	0.0748	−0.0191
12580–12860	0.15065 ± 0.00032	0.6566	−0.1844	0.0366	−0.0005
12860–13140	0.15048 ± 0.00035	0.6480	−0.1651	0.0284	0.0051
13140–13420	0.15148 ± 0.00027	0.6588	−0.1768	0.0249	0.0089
13420–13700	0.15204 ± 0.00033	0.6724	−0.1969	0.0252	0.0125
13700–13980	0.15168 ± 0.00030	0.6987	−0.2291	0.0299	0.0157
13980–14260	0.15182 ± 0.00030	0.7189	−0.2589	0.0426	0.0140
14260–14540	0.15202 ± 0.00029	0.7400	−0.3024	0.0668	0.0091
14540–14820	0.15122 ± 0.00039	0.7750	−0.3619	0.1059	−0.0025
14820–15090	0.15180 ± 0.00034	0.8033	−0.4316	0.1561	−0.0152
15090–15370	0.15067 ± 0.00036	0.8629	−0.5486	0.2411	−0.0365
15370–15650	0.15172 ± 0.00039	0.8773	−0.6057	0.3004	−0.0586
15650–15930	0.15114 ± 0.00036	0.8491	−0.5982	0.3194	−0.0704
15930–16210	0.15015 ± 0.00039	0.9445	−0.8091	0.5039	−0.1343
16210–16490	0.14947 ± 0.00042	0.9501	−0.8296	0.5057	−0.1253
36000	0.14820 ± 0.00078	0.1816 ±  0.0048	⋯	⋯	⋯
45000	0.15020 ± 0.00087	0.1614 ±  0.0051	⋯	⋯	⋯

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To produce the spectroscopic light curves, we binned the STIS and WFC3 spectra into 49 spectrophotometric channels between 0.3 and 1.7 μm. The resulting binned light curves are shown in Figures 5–8. We produced 30 STIS spectrophotometric light curves by summing the flux of the stellar spectra in bins with widths ranging from 0.015 to 0.04 μm. We used a range of bin widths to achieve similar fluxes in each spectroscopic channel as well as avoid stellar absorption lines. To generate the 19 WFC3 spectroscopic light curves, we summed the flux of the stellar spectra in uniformly sized bins of six pixels (0.028 μm) each.

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We performed a common mode correction to remove wavelength-independent systematic trends from each spectroscopic channel and reduce the amplitude of the observed HST breathing systematics. Common mode trends are computed by dividing the raw flux of the white light curve in each grating by the best-fitting transit model. We applied the common mode correction by dividing each spectrophotometric light curve by the computed common mode flux, which may cause offsets between the independent data sets. We then fit each spectroscopic light curve following the same procedure as the white light curves (see Sections 3.1.1 and 3.1.2 for details), but fixed T₀ to the white light curve best-fit value. We also fixed i and $a/{R}_{\star }$ to the values from Hartman et al. (2011) to reduce the effect of instrumental offsets between the different data sets. The limb-darkening coefficients were fixed to the computed theoretical values for each wavelength bin (see Table 3). The measured R_p/R_⋆ values for each spectroscopic channel are presented in Table 3.

The optical to infrared transmission spectrum of HAT-P-32Ab is characterized by a weak H₂O absorption feature at 1.4 μm, no evidence of Na i or K i alkali absorption features, and a steep slope in the blue optical. This continuum slope may be due to the presence of an optical opacity source in the atmosphere of this planet, which Mallonn & Wakeford (2017) predict could be magnesium silicate aerosols. Additionally, we note that the reddest spectroscopic channels of the WFC3 observations (∼1.57–1.65 μm) present a steep slope in the H₂O bandhead at ∼1.6 μm. This feature is also present in the independently reduced WFC3 results of Damiano et al. (2017), suggesting that it may be physical in nature and not an artifact of the data reduction process. This feature is not well modeled by the best-fitting ATMO models (Section 4.2) or PLATON retrievals (Section 4.3) and we note that it has been observed for other planets, such as the HAT-P-26b (Wakeford et al. 2017a) and WASP-79b (Sotzen et al. 2020).

There are several other measured transmission spectra for HAT-P-32Ab in addition to the HST spectrum reported here, including observations from Gemini/Gemini Multi-Object Spectrograph (GMOS; Gibson et al. 2013), Large Binocular Telescope/Multi-Object Double Spectrograph (LBT/MODS; Mallonn et al. 2016), Gran Telescopio Canarias/Optical System for Imaging and low-Intermediate Resolution Integrated Spectroscopy (GTC/OSIRIS; Nortmann et al. 2016), and Large Binocular Telescope/Large Binocular Camera (LBT/LBC; Mallonn & Wakeford 2017). Figure 9 shows our results compared to previously published optical and near-infrared transmission spectra. Cloud-free atmospheric models predict Na i at 5893 Å and K i at 7665 Å, but ground-based optical transmission spectra of HAT-P-32Ab show no evidence of these pressure-broadened absorption features in addition to a Rayleigh-scattering slope (Gibson et al. 2013; Mallonn et al. 2016; Mallonn & Strassmeier 2016; Nortmann et al. 2016; Tregloan-Reed et al. 2018). We varied the size of the spectroscopic channels centered on Na i and K i to search for absorption signatures from these species and confirm no evidence of these features in the spectrum at the precision level of our data.

Our STIS, WFC3, and Spitzer measurements are consistent with these previous ground-based observations in terms of the slope and shape of the transmission spectrum, as well as the R_p/R_⋆ baseline. Small offsets among data sets can be attributed to systematic errors, different data reduction techniques, and the challenges of measuring absolute transit depths from observations taken during different epochs as the stellar photosphere evolves (e.g., Stevenson et al. 2014; Kreidberg et al. 2015). The agreement in the HAT-P-32Ab absolute transit depth measurements over several epochs, using ground-based as well as space-borne facilities, and with different instruments susceptible to different systematic effects reiterates the lack of variability in the photosphere of the stellar host (Section 2.4).

We compare our observed HST+Spitzer transmission spectrum (Figure 9) to the publicly available generic grid of forward-model transmission spectra presented in Goyal et al. (2018, 2019). The 1D radiative-convective equilibrium models are produced using ATMO (Amundsen et al. 2014; Tremblin et al. 2015, 2016; Drummond et al. 2016), computed assuming isothermal pressure–temperature (P–T) profiles and condensation without rainout (local condensation). The models include opacities due to H₂–H₂, H₂–He collision induced absorption, H₂O, CO₂, CO, CH₄, NH₃, Na, K, Li, Rb, Cs, TiO, VO, FeH, CrH, PH₃, HCN, C₂H₂, H₂S, and SO₂. The pressure broadening sources for these species are tabulated in Goyal et al. (2018).

The entire generic ATMO grid comprises 56,320 forward-model transmission spectra for 22 equilibrium temperatures (400–2600 K in steps of 100 K), four planetary gravities (5, 10, 20, 50 m s⁻²), five metallicities (1, 10, 50, 100, 200 × solar), and four C/O ratios (0.35, 0.56, 0.7, 1.0), as well as varying degrees of haziness (1, 10, 150, 1100) and cloudiness (0.0, 0.06, 0.20, 1.0). Gray scattering clouds are included in the models using the H₂ cross-section at 350 nm as a reference wavelength; the varying degrees of cloudiness are a multiplicative factor to this value.

We fit the generic ATMO model grid scaled to g = 5 m s⁻² to the observed spectrum by computing the mean model prediction for the wavelength range of each spectroscopic channel (see Table 3) and performing a least-squares fit of the band-averaged model to the spectrum. In the fitting procedure, we preserved the shape of the model by allowing the vertical offset in R_p/R_⋆ between the spectrum and model to vary while holding all other parameters fixed. The number of degrees of freedom for each model is n–m, where n is the number of data points and m is the number of fitted parameters. Since n = 51 and m = 1, the number of degrees of freedom for each model is constant. From the fits, we quantified our model selection by computing the χ² statistic.

The best-fitting model is shown in the bottom panel of Figure 9, which also shows a flat model, and representative cloudy and clear atmosphere models for reference. The best-fitting model (${\chi }_{r}^{2}=1.7$) corresponds to a cloudy (α_cloud = 1.0) and slightly hazy (α_haze= 150) atmosphere, with a temperature of T = 1000 K, super-solar metallicity ([Fe/H] = +1.7), and subsolar C/O (C/O = 0.35). The selected clear (${\chi }_{r}^{2}$ = 4.5) and cloudy models (${\chi }_{r}^{2}$ = 2.3) are similar to the best-fitting model, but with no clouds or hazes (α_haze = 0.0, α_cloud = 0.0) and extreme cloudiness (α_cloud = 1.0), respectively. The flat model (${\chi }_{r}^{2}$ = 2.7) represents a gray (featureless) spectrum. The models shown here do not predict that Na i or K i should be present in the transmission spectrum, indicating that these species may be depleted in the atmosphere of HAT-P-32Ab (Burrows & Sharp 1999).

Although the forward-model fits described in Section 4.2 well match the red optical and near-infrared portions of the transmission spectrum, the best-fitting model poorly constrains the data in the blue optical. We therefore retrieve the atmospheric properties of our HST+Spitzer transmission spectrum using the Python-based PLanetary Atmospheric Transmission for Observer Noobs (PLATON)¹⁸ (Zhang et al. 2019) code to better constrain HAT-P-32Ab's atmosphere.¹⁹ The results of the full optical to infrared retrieval analysis for this planet are shown in Figure 10 and Table 4.

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Table 4.  PLATON Atmospheric Retrieval Results for HAT-P-32Ab

Parameter	HST+Spitzer
Planetary radius, Rp [RJ]	${1.96}_{-0.00}^{+0.00}$
Isothermal temperature, T [K]	${1248}_{-92}^{+92}$
Metallicity, log(Z)	${2.41}_{-0.07}^{+0.06}$
Carbon-to-oxygen ratio, C/O	${0.12}_{-0.04}^{+0.08}$
Cloud-top pressure, log(Pcloud [Pa])	${3.61}_{-1.03}^{+0.91}$
Scattering, log(scattering factor)	${1.00}_{-0.28}^{+0.37}$
Scattering slope	${9.02}_{-1.00}^{+0.58}$

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We constrain the planetary radius R_p, temperature of the isothermal part of the atmosphere T_p, atmospheric metallicity log(Z), carbon-to-oxygen ratio C/O, cloud-top pressure P_cloud, the factor by which the absorption coefficient is stronger than Rayleigh scattering at the reference wavelength of 1 μm (log(scattering factor)), and the scattering slope. We use flat priors for R_p, T_p, log(Z), and C/O, with upper and lower bounds for R_p and T_p from Tregloan-Reed et al. (2018). Our metallicity and C/O priors are set by PLATON's precomputed equilibrium chemistry grid (Zhang et al. 2019). The pairs plots showing the distributions of retrieved parameters are presented in Figure 11. We initially performed our retrievals including activity in our fits (parameterized by spot size and temperature contrast), but found that the model with no stellar heterogeneities was preferred. This finding is consistent with the star appearing quiet in the optical photometry as described in Section 2.4. We therefore adopt the results from the fits without activity henceforth in the paper.

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The results of our retrieval fits to the HST+Spitzer spectrum are summarized in Table 4. The best-fit retrieved spectrum is consistent with an isothermal temperature of ${1248}_{-92}^{+92}$ K, a thick cloud deck, enhanced Rayleigh scattering, and ∼10× H₂O abundance. The inferred atmospheric metallicity is ${2.41}_{-0.07}^{+0.06}$ x solar. We also retrieve a subsolar C/O of ${0.12}_{-0.04}^{+0.08}$, a log cloud-top pressure of ${3.61}_{-1.03}^{+0.91}$, a scattering factor of ${1.00}_{-0.28}^{+0.37}$, and a scattering slope of ${9.02}_{-1.00}^{+0.58}$.

In comparison with the best-fitting ATMO forward-model (Section 4.2), we note that the estimated subsolar values for C/O from our ATMO and PLATON fits confirm the presence of clouds in the atmosphere of this planet (Helling et al. 2019). The atmospheric metallicity from ATMO (log(Z) ∼ −0.04; Bertelli et al. 1994), however, does not well match the constrained PLATON metallicity for the broadband HST+Spitzer spectrum.

The retrieved limb temperature from PLATON is lower than the equilibrium temperature of HAT-P-32Ab. This finding is in accordance with other retrieval results from the literature in which retrieved temperatures have been found to be notably cooler (∼200–600 K) than planetary equilibrium temperatures (see Table 1 of MacDonald et al. 2020). These lower retrieved temperatures appear to be the result of applying 1D atmospheric models to planetary spectra with different morning–evening terminator compositions (MacDonald et al. 2020). Although 1D retrievals provide an acceptable fit to observations, they artificially shift atmospheric parameters away from terminator-averaged properties. As a result, the retrieved temperature profiles are hundreds of degrees cooler and have weaker temperature gradients than reality.

Furthermore, our retrieval and forward-model fits confirm a cloudy atmosphere for this planet. Our findings also corroborate previous PanCET results for this planet suggesting a Bond albedo of A_B < 0.4 and poor atmospheric re-circulation (Nikolov et al. 2018b), consistent with the measured geometric albedo of A_g < 0.2 for this planet by Mallonn et al. (2019), as well as previous studies showing that planets with higher stellar irradiation levels have greater day–night temperature contrasts and lower re-efficiencies (e.g., Schwartz & Cowan 2015; Kataria et al. 2016; Schwartz et al. 2017).