studies it was successfully characterised in eclipse (Beatty et al., 2014,
2017a), suggesting a monotonically decreasing temperature-pressure profile.
However, more recent work has suggested the atmosphere presents indications of
a localised thermal inversion associated with VO, FeH and H- (Changeat et al.,
2022).

We find that, due to it’s high mass which leads to it being classified as a
brown dwarf, there is no evidence for atmospheric species in transit spectrum.
We note that expected transit depth modulation due to one scale height of
atmosphere is far below the size of the error bars, explaining why a flat
spectrum is recovered.

### Kepler-9 b and Kepler-9 c

The Kepler-9 system was discovered in 2010 and planets b and c were the first
planets to be confirmed via transit timing variations Holman et al. (2010).
These TTVs allowed the masses of the planets to be measured (e.g. Dreizler &
Ofir, 2014) and these masses were later verified by radial velocity
observations Borsato et al. (2019).

The two transit observations of Kepler-9 b, as well as the two transit
observations of Kepler-9 c, were taken in staring mode using the GRISM256
aperture. The SPARS10 sampling sequence was utilised, with 12 up-the-ramp
reads, leading to an exposure time of 73.742661 s. These were taken as part of
GO-12482 (PI: Jean-Michel Desert).

For Kepler-9 b, the free retrievals did not provide more preferable fit to the
data than the flat model. However, the GGChem retrieval did provide a
preferable fit, albeit to only 1.89$\sigma$. In the case of Kepler-9 c, the
opposite was true: the flat model was preferred to the GGChem retrieval but
not to the free chemistry retrievals. However, the preferred free chemistry
model did not detect features, rather a slope in the spectrum. Neither
atmospheric “detection” is convincing, but this is unsurprising given the size
of the error bars with respect to the expected atmospheric modulation due to a
single scale height of atmosphere.

### Kepler-51 b & Kepler-51 d

Each of the three planets which are known to be orbiting Kepler-51 have low
densities (Masuda, 2014). Kepler-51 c has only a grazing transit, making
constraints on its size difficult. However, Kepler-51 b and Kepler-51 d were
originally determined to have radii of 7.1$\pm$0.3 R⊕ and 9.7$\pm$0.5 R⊕,
respectively (Masuda, 2014). Their masses, derived from transit timing
variations, gave them both densities of less than 0.05 gcm-3 (Masuda, 2014).

Two HST WFC3 G141 observations were taken of each planet (PN: 14218, PI: Zach
Berta-Thompson) and these were analysed by Libby-Roberts et al. (2020). In
this study, the radii and masses of the planets were updated and they found
that the densities were slightly higher than previously thought. However, they
were still low at 0.064 gcm-3 and 0.038 gcm-3, respectively. Despite the low
density, and thus large atmospheric scale height, the transmission spectra
uncovered by Libby-Roberts et al. (2020) did not yield any spectral features.

The observations of HST WFC3 G141 were taken with the following settings. The
GRISM256 aperture and the SPARS10 readout sequence were utilised, with 15 up-
the-ramp reads resulting in exposure time of 103 seconds. Due to the faintness
of the host star (J = 13.56), the staring mode was used as it offered a higher
efficiency and precision than the now common scanning mode (Libby-Roberts et
al., 2020).

We analysed all four observations but had issues with the extraction of data
for one of the Kepler-51 b visits. We show a comparison between our spectra
and those from Libby-Roberts et al. (2020). As we could only analyse a single
visit of Kepler-51 b with Iraclis, we use the spectrum from Libby-Roberts et
al. (2020) for this planet. However, we note the good comparison between the
single visit and there spectrum and also clarify that we utilise our fitting
of the Kepler-51 d data.

### LTT 9779 b

LTT 9779 b is an ultra-hot Neptune discovered using data from TESS Jenkins et
al. (2020). With a period of less than a day, LTT 9779 b lies within the
Neptune desert: there is a dearth of planets between 2 and 10 R⊕ in these very
short orbits. Photometric eclipse observations of LTT 9779 b with Spitzer
revealed a spectrum which is best-fitted by a non-inverted atmosphere and
evidence was found for the presence of CO (Dragomir et al., 2020). Phase curve
observations with TESS and Spitzer have also been made, which found a large (
1100 K) day-night brightness contrast and suggestions of a super-solar
atmospheric metallicity (Crossfield et al., 2020). The transit observations
from these phase curves were not precise enough to constrain the atmosphere in
transmission.

HST WFC3 G141 observations of LTT 9779 b’s transit were taken as part of
proposal GO-16457 (PI: Billy Edwards, Edwards et al., 2020a), with an
additional dataset using the G102 grism also taken. The data were taken using
the SPARS10 sequence and the GRISM256 aperture. The total exposure time was
103.13 seconds, with 16 samples being taken per exposure. To avoid
contamination by a background star, we used this up-the-ramp reads, using
Iraclis’s splitting mode to extract these individually.

Assuming a H/He dominated atmosphere (mmw = 2.3), the derived spectrum has
error bars that are just below the expected atmospheric modulation due to one
scale height of atmosphere. The spectrum has an increasing transit depth with
wavelength, which is best fitted by the model with no absorbers (flat model)
where the slope is caused by CIA. The bluest spectral point is significantly
higher than the subsequent data points and the retrieval including optical
absorbers suggests this could be due to TiO. However, as the detection is
based off of a single data point it is unreliable and the G102 data will be
required to ascertain the presence of this molecule. However, we don’t analyse
it here to maintain homogeneity across the planets studied.

###  5.1 TrES-2 b

TrES-2 b was among the first transiting exoplanets to be discovered (O’Donovan
et al., 2006). The 1.2 RJ planet orbits its host star in roughly 2.47 days,
giving it an equilibrium temperature of around 1700 K. It was among the
planets considered for the JWST Early Release Science (ERS) Transiting
Exoplanet programme (Stevenson et al., 2016b) but ultimately not selected
(Bean et al., 2018). Turner et al. (2016) obtained a ground-based UV transit
of TrES-2 b to search for asymmetries in the light curve but no such phenomena
was observed. Given the large transit depth, the planet has also been
regularly followed-up from the ground with numerous studies updating the
ephemerides and searching for non-linear periods (Rabus et al., 2009; Raetz et
al., 2014; Edwards et al., 2020c; Öztürk & Erdem, 2019, e.g.). Additionally, a
K-band eclipse was detected by Croll et al. (2010) which, when combined with
Spitzer eclipses of the planet (O’Donovan et al., 2010), suggested the dayside
could be represented by a blackbody and confirmed the planet’s orbit was
circular.

The HST WFC3 G141 transmission spectrum was obtained using the staring mode.
The RAPID readout mode was used for the GRISM512 aperture, with 16 sample
being taken per exposure to give an exposure time of 12.8 seconds. The data
was previously analysed by Ranjan et al. (2014) who found that the spectrum
was not precise enough to constrain the atmosphere. We reanalyse this data
here, using Iraclis, and yield the same result: the uncertainites on each data
point are several scale heights in size. The comparison between our spectrum
and the one from Ranjan et al. (2014) is given in Figure 20.

Figure 20: Comparison of the transit spectrum of TrES-2 b obtained here, to
the spectrum from Ranjan et al. (2014).

###  5.2 TrES-4 b

TrES-4 b is a short-period (3.5539268 days), hot Jupiter (R = 1.706 RJ)
(Mandushev et al., 2007). The planet has been observed in eclipse, with data
from the Spitzer space telescope suggested a thermal inversion (Knutson et
al., 2009) while attempts have also been made to measure the thermal emission
from the ground (Martioli et al., 2018).

As with TrES-2 b, the HST WFC3 G141 transmission spectrum was obtained using
the staring mode. Again the RAPID readout mode was used for the GRISM512
aperture, with 16 sample being taken per exposure to give an exposure time of
12.8 seconds. The data also was previously analysed by Ranjan et al. (2014)
who found that the spectrum was not precise enough to constrain the
atmosphere. We reanalyse this data here and find that the recovered error bars
are tens of scale heights in size, therefore offering no information on the
atmosphere. A comparison of the spectra is shown in Figure 21.

Figure 21: Comparison of the transit spectrum of TrES-4 b obtained here, to
the spectrum from Ranjan et al. (2014).

### TOI-270 c and TOI-270 d

TOI-270 c is part of a three planet system, consisting of two sub-Neptunes and
a Super-Earth (Günther et al., 2019), found by TESS. The planets orbit a
bright (K=8.25) M-dwarf (TEff $\sim$3500 K) and the masses of the planets were
subsequently measured using radial velocity measurements (Van Eylen et al.,
2021).

Three transit observations were taken of TOI-270 c, each constituting three
orbits which meant the first orbit was not, in this case, discarded. Despite
having larger ramps than subsequent orbits, fitting the light curve using
these orbits still led to good fits to the data. For these observations, the
GRISM512 subarray was used, with 8 up-the-ramp reads using the SPARS25
sampling sequence, and an exposure time of 138.380508 s, combined with a scan
rate of 0.111 ”/s. Additionally, a single transit of TOI-270 d was acquired
using the same setup. These observations were taken as part of GO-15814 (PI:
Thomas Mikal-Evans).

We find that the white light curve depth for TOI-270 c varies drastically,
with a 1000 ppm difference between visits 2 and 3. On the other hand, the
spectral shape of these visits is consistent, as shown in Figure 22. However,
the spectral shape is itself strange: there is a significant drop at bluer
wavelengths. Atmospheric scenarios seem unlikely because of the size of the
feature ($~{}3.5$ scale heights) leaving two hypotheses. Firstly, it could be
due to the fitting of the data but this seems unlikely as the effect is
recovered in all three visits. Furthermore, no significant residuals within
any of the fittings and there are no indications that the fittings are, in any
way, poor.

Figure 22: Left: Uncorrected transit spectra for each visit of TOI-270 c. The
shaded regions indicate the white light curve depth, and 1 sigma uncertainty,
for each visit. Right: Normalised transit spectra for each visit of TOI-270 c.
The averaged transit spectrum, which was used in the analysis here, is given
in black.

Figure 23: Comparison of the transit depths obtained here to those from Van
Eylen et al. (2021) for TOI-270 c (left) and TOI-270 d (right). As previously
noted, we find a large variance in the transit depth obtained for each visit
of TOI-270 c and only one of these is of a similar depth to the TESS data.

The second possible explanation is that the feature could be due the transit
light source effect as stellar spots or facuale can cause significant spectral
modulation. While no spot crossing events were found in the light curves,
unocculted spots could be to blame and these could also explain the large
difference between the averaged HST data and the TESS transit depth from Van
Eylen et al. (2021). Surprisingly, the HST data for TOI-270 d has no such
feature. The observation of TOI-270 d was taken between 4 days after the third
visit of TOI-270 c, with the observations of TOI-270 c data being taken over a
period of roughly 7 months. There are 56.61 days between visits 1 and 2, while
visits 2 and 3 were separated by 164.16 days. Van Eylen et al. (2021)
estimated that the rotation period of the star was around 58 days, which would
imply that approximately the same face of the star was visible for each
observation of TOI-270 c. Nevertheless, the visible portion of the star would
have only changed by around 7% between the third visit of TOI-270 c and the
transit of TOI-270 d. The transit chords of these planets is different as they
have slightly different inclinations, but this would not affect the transit
light source effect from unocculted spots.

We attempted atmospheric retrievals on both planets, but could find no model
which would adequately fit the data for TOI-270 c. Meanwhile, for TOI-270 d,
our retrievals uncovered evidence for H2O.

### TOI-674 b

The discovery of the Neptune-sized planet TOI-674 b (R = 5.25 R⊕, M = 23.6
M⊕,) was recently announced (Murgas et al., 2021). The planet has a period of
only 1.977143 days, but orbits an M-dwarf (Teff=3514 K) and thus has a
equilibrium temperature of around 650 K. Three transits of TOI-674 b were
taken as part of GO-15333 (PI: Ian Crossfield). These have previously been
presented in Brande et al. (2022) where the discovery of a water feature was
announced. Their study also utilised data from TESS and Spitzer, but the
retrieved water abundance in their study (log(vmr) = -3.00$\pm$1.00) is
consistent with ours (log(vmr) = -3.12${}^{+0.78}_{-1.04}$). We note that a
small vertical offset is present between our HST WFC3 G141 spectrum and that
of Brande et al. (2022). As such offsets are a common occurrence, this is not
concerning except when combining instruments without wavelength overlap.
Finding such an offset further motivates our choice to only consider data from
HST WFC3 G141 instead of combining all available datasets without being able
to verify their compatibility.

### V1298 Tau b & c

V1298 Tau b, a warm Jupiter-sized planet with an orbital period of 24.148
days, was detected around a young solar analogue by David et al. (2019b).
Further analysis of the K2 data unveiled three additional planets in the
system (David et al., 2019a), with planets b and c having orbital periods of
8.25 and 12.4 days, respectively. However, the period of V1298 Tau e could not
be constrained as it only transited once in the K2 data. A second transit was
later observed by TESS, which helped constrain potential orbital periods with
the highest probability orbit placing V1298 Tau e close to a 2:1 resonance
with V1298 Tau b (Feinstein et al., 2022).

Measuring the masses of these planets has proved difficult due to the intense
activity of the host star. Beichman et al. (2019) placed a 3$\sigma$ upper-
limit on the mass of V1298 Tau b of 2.2 MJ while dynamical arguments have
placed constraints on the total masses of the planet pairs (David et al.,
2019a). Further radial velocity measurements were taken and lead to the first
mass measurements in the system Suárez Mascareño et al. (2021). Their work
concluded that V1298 Tau b had a mass of 0.64 MJ while V1298 Tau e had a mass
of 1.16 MJ, making it much denser than typical giant exoplanets. However, the
period of V1298 Tau e derived by Suárez Mascareño et al. (2021) disagrees to
4$\sigma$ with the value from (Feinstein et al., 2022).

Figure 24: White light curve fits for the observations of V1298 Tau b (top)
and V1298 Tau c (bottom). We note the non-Gaussian residuals in each case,
potentially due to stellar activity.

Two datasets have been taken with Hubble WFC3 G141 to probe the atmospheres of
worlds in the V1298 Tau system. The transit of V1298 Tau b utilised ten Hubble
orbits and was taken as part of GO-16083 (PI: Kamen Todorov). For these
observations, the GRISM256 subarray was used, with 5 up-the-ramp reads using
the SPARS25 sampling sequence, leading to an exposure time of 89.661957 s,. S
scan rate of 0.230 ”/s was used, which gave a scan length of around 170
pixels. The observation of V1298 Tau c (GO-16462, Vatsal Panwar) required only
eight orbits but used the same detector setup as the transit of V1298 Tau b.

The white light curves fits for the two planets are shown in Figure 24. In
both cases, non-Gaussian residuals can be seen and these are likely due to the
high variability of the host star. Nevertheless, thanks to the divide-by-white
method, the residuals on the spectral light curves were Gaussian. The spectra
recovered showed clear evidence of spectral modulation and we conducted
retrievals to attempt to constrain the chemistry. As note above, there are
disagreements about the orbital period of V1298 Tau e. As the total radial
velocity signal is a combination of components from all planets in the system,
an error in the derivation of the period of one planet can lead to an
inaccurate mass measurement of both it and another planet in the system.
Additionally, V1298 Tau c doesn’t have a measured mass. Therefore, for both
planets we attempted retrievals in which we fitted for the mass (Changeat et
al., 2020c). For V1298 Tau b, we also ran retrievals with the mass fixed to
the value from Suárez Mascareño et al. (2021).

Figure 25: Top: spectrum of V1298 Tau b recovered with Iraclis and the
preferred models from our retrievals. Bottom: the probability distributions
for the planetary mass when it was fitted for. We note that, while it gives a
preferable fit to the data, the fitted mass is extremely low (a value of 0.64
MJ was recovered by Suárez Mascareño et al., 2021). The optical absorber model
is unlikely for this planet given the equilibrium temperature ($\sim$1000 K).
Figure 26: Top: spectrum of V1298 Tau b recovered with Iraclis and the
preferred models from our retrievals. Bottom: the probability distributions
for the planetary mass when it was fitted for. The optical absorber model is
preferred, but it is unlikely that FeH and e- are present in the atmosphere of
this planet given the equilibrium temperature ($\sim$700 K).

In the case of V1298 Tau b, the fixed-mass retrievals did not lead to models
which well-fitted the data. As can be seen in Figure 25, the retrievals were
unable to recreate the strong water seen at 1.4 $\mu$m. When we fitted for the
mass, the retrieval was subsequently able to fit this feature but the
retrieved mass was extremely low. We had placed a lower bound on the mass at
0.1 MJ, which is far below the 0.64 MJ from Suárez Mascareño et al. (2021).

For V1298 Tau c, the both retrievals fitted for the mass as there are
currently no constraints on it from radial velocities or transit timing
variations. As seen in Figure 26, the retrieval without optical absorbers
struggles to fit the spectrum. However, when they are included a combination
of FeH and e- help to create the features seen yet the cool temperature of the
planet makes the existence of these species unlikely.

Given the issues with fitting of these spectra it is possible that the stellar
activity has affected the spectrum recovered with Iraclis. Iraclis can fit the
long-term trend using a linear or quadratic model, but in these cases a
different model might be preferable (e.g. a sinusoid). However, we leave such
an exploration for future work which should also aim to resolve the
discrepancy in the period of V1298 Tau e to increase the accuracy and
confidence in the mass measurements. Some transit timing variations have
already been seen in the system and future transit measurements may also led
to mass constraints. Due to the poor fitting of the spectra of V1298 Tau b and
c, we do not include them in the primary analyses of this paper (e.g. any of
the trend fitting) but include them for completeness and to highlight the
issue with the data.

### WASP-6 b

Discovered by Gillon et al. (2009), WASP-6 b has a mass around half that of
Jupiter but is inflated and has an equilibrium temperature of 1200 K. The
atmosphere of the planet has been widely studied, with Nikolov et al. (2015)
presenting the HST STIS and Spitzer IRAC transmission spectrum which showed
signs of scattering in the optical. The same data was later analysed by Sing
et al. (2016a) before Carter et al. (2020) present the HST WFC3 G141 spectrum.
Carter et al. (2020) also took data with the VLT and other ground-based
spectra of WASP-6 b have been also been obtained, all of which have concluded
the atmosphere is hazy due to a lack of spectral features due to Na or K
(Jordán et al., 2013; Carter et al., 2020).

The HST WFC3 G141 data for WASP-6 b was taken for proposal GO-14767 (PI: David
Sing, Sing et al., 2016b). For these observations, the GRISM512 subarray was
used, with 8 up-the-ramp reads using the SPARS25 sampling sequence, and an
exposure time of 138.380508 s, combined with a scan rate of 0.06 ”/s. The data
was previously presented in Carter et al. (2020) where it was combined with
data from the VLT. The analysis by Carter et al. (2020) again found the
atmosphere to be hazy and they also noted that corrections for the stellar
heterogeneity could have significant effect on the Na and K abundances. We
find a highly similar HST WFC G141 spectrum to this work, as shown in Figure
27.

Figure 27: Comparison of the transit spectrum of WASP-6 b obtained here to the
spectrum from Carter et al. (2020).

### WASP-18 b

WASP-18 b (Hellier et al., 2009) has been thoroughly studied since its
discovery in 2008. Spitzer, Hubble WFC3 and ground-based eclipses have been
taken (Nymeyer et al., 2011; Kedziora-Chudczer et al., 2019; Sheppard et al.,
2017; Arcangeli et al., 2018; Manjavacas et al., 2019; Iro & Maxted, 2013;
Gandhi et al., 2020) as well as phase curves with Hubble WFC3 and TESS
(Arcangeli et al., 2019; Shporer et al., 2019). These have revealed a low
albedo, poor redistribution of energy to the night-side and evidence for an
inverted day-side temperature-pressure profile. In particular, the analysis
from Sheppard et al. (2017) considered a similar data-set to us and detected a
strong thermal inversion, associated with the presence of H2O and CO.

The HST transmission spectrum was taken, along with two eclipses, as part of a
phase curve (GO-13467, PI: Bean). These observations had an exposure time of
73.74 seconds having used the GRISM256 aperture and the SPARS10 sampling
sequence with 12 up-the-ramp reads. Due to the high mass of WASP-18 b,
1$\sigma$ uncertainties on the recover transit spectrum were equivalent to
around 5 scale heights, denying any chance of recovering spectral features.

### WASP-19 b

WASP-19 b orbits its bright host star on a very short orbit (0.94 days) and
its high temperature, and large size, make it an excellent target for
atmospheric studies (Hellier et al., 2011a). WASP-19 b has been the subject of
a number of investigations, from both the ground and from space. Work by
Anderson et al. (2013) analysed four Spitzer eclipses, taken across 3.6-8 $\mu
m$, and constructed a spectral energy distribution of the planet’s day-side
atmosphere. They found no stratosphere, supporting the hypothesis that hot
Jupiters orbiting active stars have suppressed thermal inversions (Knutson et
al., 2010). Analysis of the TESS optical phase curve showed moderately
efficient day-night heat transport, with a day-side temperature of 2240 K and
a day to night contrast of around 1000 K (Wong et al., 2019). This study also
utilised a host of ground-based observations by Anderson et al. (2010b);
Burton et al. (2012); Abe et al. (2013); Bean et al. (2013).

WASP-19 b has also been studied via transmission spectroscopy. The retrievals
of the STIS-G430L, G750L, WFC-G141 and Spitzer-IRAC observations suggest the
presence of water at log(H2O) $\approx$ 4 but show no evidence for optical
absorbers (Sing et al., 2016a; Barstow et al., 2017; Pinhas et al., 2019).
Those results do not match the ground-based transits that were acquired with
the European Southern Observatory’s Very Large Telescope (VLT), using the low-
resolution FORS2 spectrograph which covers the entire visible-wavelength
domain (0.43–1.04 $\mu m$). When analysing this data, Sedaghati et al. (2017)
detected the presence of TiO to a confidence level of 7.7$\sigma$. However,
data from Magellan/IMACS did not find any evidence for TiO or Na as a
featureless transmission spectrum was recovered (Espinoza et al., 2019).

Two transit observations of WASP-19 b have been acquired. The first, in
staring mode, as part of Proposal GO-12181 (PI: Drake Deming, Deming, 2010)
has previously been presented in another studies (e.g. Sing et al., 2016a).
The scanning mode data were taken with the GRISM512 aperture and consisted of
4 up-the-ramp reads with the SPARS25 sequence. This gave an exposure time of
46.695518 s scan rate was 0.026 ”/s. These observations were part of a phase
curve and, while guide star acquisition issues were incurred, the failure in
pointing happened long after the transit had occurred, meaning the data
analysed here was unaffected.

### WASP-103 b

WASP-103 b is an ultra-short period planet ($P$ = 22.2 hr) whose orbital
distance is less than 20% larger than its Roche radius, resulting in the
possibility of tidal distortions and mass-loss via Roche-lobe overflow (Gillon
et al., 2014). Given its size, temperature, and the brightness of its host
star it is a great target for atmospheric studies and has been observed with
numerous instruments.

WASP-103 b’s HST WFC3 emission spectrum was found to be featureless down to a
sensitivity of 175 ppm, showing a shallow slope toward the red (Cartier et
al., 2017). Work by Manjavacas et al. (2019), which performed a reanalysis of
the same data-set, found that the emission spectrum of WASP-103 b was
comparable to that of an M-3 dwarf. Delrez et al. (2018) obtained several
ground-based high-precision photometric eclipse observations which, when added
to the HST data, could be fit with an isothermal black-body or with a low
water abundance atmosphere with a thermal inversion. However, their Ks band
observation showed an excess of emission compared to both these models. More
recently, a phase-curve analysis of the planet was taken and reported in
Kreidberg et al. (2018b). The study also utilized the previous HST emission
spectra and confirmed a seemingly featureless day-side. A later study on the
same data employed a unified phase-curve retrieval technique to obtain a more
complex picture of the planet (Changeat, 2022). It confirmed the presence of
thermal inversion and dissociation processes on the day-side of the planet and
found signature of FeH emission. The study also constrained water vapour
across the entire atmosphere. Furthermore, ground-based transmission
observations found strong evidence for sodium and potassium (Lendl et al.,
2017). Later observations by Wilson et al. (2020) yielded a featureless
spectrum while a comprehensive analysis of 11 transmission spectra by Kirk et
al. (2021) found evidence for unocculted regions or the star as well as weak
evidence for TiO.

Two HST G141 phase curves of WASP-103 b were obtained (PN: 14050, PI:
Kreidberg et al., 2014a) which each contained a single transit and eclipse. We
analysed these two transits and observed that the slope in the final spectrum
is well fit by VO. Other optical absorbers might be present (TiO, H-) but the
data does not allow verification of this. The solution found possesses a wide
range of metallicities; sub-solar in nature. We note that Kirk et al. (2021)
found that VO could only account for their spectrum if present in extremely
high quantities.

### WASP-107 b

A sub-Saturn around a solar-metallicity K6 star, WASP-107 b was immediately
noted as an excellent target for atmospheric studies (Anderson et al., 2017).
Soon after its discovery, the transmission spectrum of WASP-107 b was taken
with HST WFC3 G141 as part of proposal GO-14915 (PI: Laura Kreidberg). The
data was previously presented in Kreidberg et al. (2018a), showing strong
evidence for the presence of water but a possible methane depletion. The study
also noted that the features seen were smaller than would be expected for a
cloud-free atmosphere, inferring the presence of high-altitude aerosols. In
line with the results from Kreidberg et al. (2018a), we found strong evidence
for water but muted features compared to a clear atmosphere.

Additionally, an observation was taken with the G102 grism of HST WFC3
(GO-14916, PI: Jessica Spake) which was used to demonstrate that the
atmosphere of WASP-107 b was eroding as the G102 data gave access to the 1.083
$\mu$m Helium line (Spake et al., 2018). High-resolution observations have
since confirmed this detection (Allart et al., 2019; Kirk et al., 2020). We do
not fit the G102 data as part of this study to ensure homogeneity across our
datasets. We show a comparison between the spectrum from previous studies and
ours in Figure 28.

Figure 28: Comparison of the transit spectrum of WASP-107 b obtained here to
the spectrum from Kreidberg et al. (2018a) and Spake et al. (2018).

### WASP-121 b

Significant observational time has been spent on WASP-121 b. In transmission,
the analyses of ground-based observations, Hubble STIS and Hubble WFC3 have
shown the presence of H2O and optical absorption attributed to VO and/or FeH
(Evans et al., 2016, 2018). The authors of these studies note that chemical
equilibrium models with solar abundances cannot reproduce the spectrum seen,
while free chemical retrievals can only do so by converging to high abundances
of VO and FeH. In parallel, high resolution ground-based observations of the
transit have put upper limits on the abundances of TiO and VO at the
terminator with log(VMR) $<$ -7.3 and 7.9 respectively, suggesting these
cannot be causing the inversion seen (Merritt et al., 2020). However, the
study highlighted that these limits are largely degenerate with other
atmospheric properties such as the scattering properties or the altitude of
clouds on WASP-121 b. Another study found a host of atomic metals, including
V, which are predicted to exist if a planet is in equilibrium and has a
significant quantity of VO (Hoeijmakers et al., 2020). They too noted the
absence of TiO which could support the hypothesis that Ti is depleted via a
cold-trap. Furthermore, various high resolution studies have found evidence
for absorption due to metallic lines (e.g. Borsa et al., 2021; Cabot et al.,
2020; Gibson et al., 2020).

Here, we fit three transit observations. Two of these were obtained as part of
a phase curve (PN: 15134, PI: Thomas Mikal-Evans, Evans, 2017) which was
recently published, showing evidence for a diurnal water cycle (Mikal-Evans et
al., 2022). The other transit (PN: 14468, PI: Evans, 2015) was previously
analysed, both with Iraclis (Tsiaras et al., 2018) and by Evans et al. (2016).
We choose to refit this observation to ensure the methodology, parameters and
limb-darkening coefficients were the same across all three transit fits.

### WASP-178 b

WASP-178 b, also known as KELT-26 b, is an ultra-hot Jupiter orbiting an A1V
host star (Hellier et al., 2019). The planet appears to be in a highly
misaligned orbit and has a mass of 1.93${}^{+0.14}_{-0.16}$ MJ (Rodríguez
Martínez et al., 2020), making it one of the heaviest planets in our sample.

A single transit was taken as part of proposal GO-16450 (PI: Joshua
Lothringer). For these observations, the GRISM256 subarray was used, with 8
up-the-ramp reads using the SPARS25 sampling sequence, and an exposure time of
138.354034 s, combined with a scan rate of 0.07597 ”/s. We note that WFC3 data
with the UVIS and G102 grisms has also been taken for this planet but was not
included in this study due to the need to ensure homogeneity across the planet
sample.

We fitted the data with Iraclis and the preferred atmospheric model for this
finds strong evidence for water in the atmosphere. The increasing absorption
at shorter wavelengths is best fit with a large abundance of TiO as well as
absorption by H-. The result is consistent with the expected chemistry given
the equilibrium temperature of around 2400 K, although we note that the
retrieved temperature is cooler than expected ($\sim$1250 K). We note that
analysis of the HST WFC3 UVIS data by Lothringer et al. (2022) found evidence
for SiO. To understand this planet fully, an analysis of all three HST
datasets is required.

## Appendix 2: Fixed CO retrievals

One set of retrievals conducted in this study fitted equilibrium chemistry
models to the data, with the C/O ratio and metallicity as free parameters
controlling the chemistry. Despite the large uncertainties on the retrieved
C/O ratio, we noted that the majority of planets were not consistent with C/O
ratios larger than 1. To explore this further we attempted chemical
equilibrium retrievals with fixed C/O ratios of 0.5 or 1.

Figure 29: The comparison of the retrieved metallicity when the C/O ratio is a
free parameter to when it is fixed to 0.5 (top) and 1 (bottom). We only show
planets with our sample which have a strong ($>$3$\sigma$) atmosphere
detection.

We then compared the metallicities retrieved in each case, as well as the
goodness of the fit. We find that, forcing the C/O to be equal to 1 led to the
metallicities of the planets generally being retrieved as solar but that these
models provided a poorer fit to the data than when the C/O ratio was free to
vary. On the other hand, we find fixing the C/O to 0.5 generally leads to only
minor differences in the metallicity and goodness of fit in comparison to the
free C/O case. The results of these retrievals are displayed in Figure 29 and
provide further suggestions that high C/O ratio atmospheres are not compatible
with the spectra derived in this work. However, we caution that the narrow
wavelength coverage of HST WFC3 G141 does not provide strong constrains on
carbon-bearing species so the robustness of the finding is questionable.

Figure 30: Comparison of the Bayesian evidence for the fixed C/O ratio
retrievals when it is fixed to 0.5 (top) and 1 (bottom). The dotted line shows
the 3$\sigma$ region.

## Appendix 3: Bayesian Hierarchical Modelling

The following derivation is based primarily the work of Lustig-Yaeger et al.
(2022) so, while we will provide a brief discussion on the method, interested
readers can refer to Section 2.2 in Lustig-Yaeger et al. (2022) for more
detailed discussion. Consider that we have obtained $N$ exoplanets, each with
$M_{n}$ observations $\bm{D}_{n}$. For our case $M_{n}=1$ but it can be more
than 1. For each of these planets we can infer the joint posterior
distribution of a pre-defined set of parameters $\bm{\theta}_{n}$ given
$\bm{D}_{n}$, $P(\bm{\theta}_{n}|\bm{D}_{n})$ via standard Bayesian
formulation:

$P(\bm{\theta}_{n}|\bm{D}_{n})=\frac{P(\bm{D}_{n}|\bm{\theta}_{n})P(\bm{\theta}_{n})}{P(\bm{D}_{n})}$
(5)

where $P(\bm{D}_{n}|\bm{\theta}_{n}$) is the likelihood of observing $D$ given
the specific set of parameters $\theta$. $P(\bm{D})$ is the marginal
likelihood over all possible sets of $\bm{\theta}_{n}$, also known as the
evidence. The prior function, $P(\bm{\theta}_{n})$ is taken to be flat or
uninformative.

Suppose we would like to derive the population level trend of planetary
temperature against some molecular abundance. If we assume the trend can be
parameterised by a set of hyper-parameters $\bm{\alpha}$, we can compute the
(population level) likelihood of the entire data ensemble
$\mathcal{L}_{\alpha}$ as

$\mathcal{L}_{\alpha}=P(\\{\bm{D}\\}_{n=1}^{N}|\bm{\alpha})$ (6)

If we further assume that there is no likelihood covariance between parameters
of different exoplanets $n$, we can express Equation Appendix 3: Bayesian
Hierarchical Modelling as the product of $N$ marginalised integral over
parameters $\bm{\theta}_{n}$.

$\displaystyle\mathcal{L}_{\alpha}$ $\displaystyle=\prod^{N}_{n=1}\int
P(\bm{D}_{n},\bm{\theta}_{n}|\bm{\alpha}_{n})d\bm{\theta}_{n}$
$\displaystyle=\prod^{N}_{n=1}\int
P(\bm{D}_{n}|\bm{\theta}_{n},\bm{\alpha})P(\bm{\theta}_{n}|\bm{\alpha})d\bm{\theta}_{n}$

assuming $\bm{D}_{n}$ is related to $\alpha_{n}$ through $\bm{\theta}_{n}$.
The first term is simply the likelihood function for each individual
observations (nth planet) and the second term act as a re-weighting function.

We can further manipulate Equation Appendix 3: Bayesian Hierarchical Modelling
by recognising that the second term is a ratio between the new prior
$P_{\alpha}(f_{n,T})$, that depends solely on $\alpha$ and the original prior
$P_{0}(f_{n,T})$ , multiples the prior function of the parameters
$P(\bm{\theta}_{n})$:

$\mathcal{L}_{\alpha}=\prod^{N}_{n=1}\int
P(\bm{\theta}_{n}|\bm{D}_{n})\frac{P_{\alpha}(f_{T,n})}{P_{0}(f_{T,n})})d\bm{\theta}_{n}$
(7)

Note that we have combined $P(\bm{D}_{n}|\bm{\theta}_{n})$ and
$P(\bm{\theta}_{n})$ to get the posterior $P(\bm{\theta}_{n}|\bm{D}_{n})$. We
have also omitted the evidence term here since it is merely a constant in this
context. In our implementation, we have assumed a linear trend for the
temperature, hence:

$f_{T}(m,c,X_{mol})=mX_{mol}+c$ (8)

where $m$ and $c$ represent the slope and intercept of the straight line, and
$X_{mol}$ represent the molecular abundance of the chemical species.

We can simplify the integral in Equation 7 by summing over all the samples in
the posterior traces:

$\mathcal{L}_{\alpha}\approx\prod_{n=1}^{N}\frac{1}{K}\sum_{k=1}^{K}\frac{P_{\alpha}(f_{T,n,k})}{P_{0}(f_{T,n,k})}$
(9)

The new prior function $P_{\alpha}(f_{T,n,k})$, is assumed to be a Gassuian
distribution, and therefore we can compute the probability analytically by
comparing $f_{T,n,k}$ with $f_{T}(m,c,X_{mol})$:

$P_{\alpha}(f_{T,n,k})=\mathcal{N}(f_{T,n,k}-f_{T}(m,c,X_{mol}),\sigma)$ (10)

Similar to Lustig-Yaeger et al. (2022), we have added an additional term
$\sigma$ to account for the variability in the traces. The hyperparameter
$\alpha$ has in total 3 free parameters, i.e. $\alpha\equiv[m,c,\sigma]$ that
we can infer from the posterior traces

Once the likelihood function $\mathcal{L}_{\alpha}$ is computed, the posterior
on the hyperparameter $\bm{\alpha}$ can be inferred simply by referring to
Equation 5:

$P(\bm{\alpha}|\\{\bm{D}_{n}\\}_{n=1}^{N})\propto\mathcal{L}_{\alpha}P(\bm{\alpha})$
(11)

where $P(\bm{\alpha})$ is the (hyper-)prior function for the hyperparameters
$\bm{\alpha}$. In this paper we have fixed all the hyper-priors as uniform
distribution.

To infer the hyperparameters, we have used MultiNest algorithm (Feroz et al.,
2009; Buchner et al., 2014) to compute the preferred BHM importance sampling
model. Using the log-evidence provided by MultiNest, we are able to compare
the different models and assess the evidence for a particular trend when
compared to a null hypothesis.

In the main text we showed the linear models as well as providing the evidence
for these and the null hypothesis. Here we show the models for these linear
models again, but also show the model, as well as the traces, for the null
hypothesis in each case. For H2O, CH4, HCN and NH3, these are given in Figure
31. The associated log-evidence, and best-fit parameters, are shown in Table
11.

Molecule | m | c | $\sigma$ | ln(E)
---|---|---|---|---
H2O | 0.000 ${}^{+0.001}_{-0.001}$ | -2.08 ${}^{+0.84}_{-0.88}$ | -0.01 ${}^{+0.12}_{-0.13}$ | -213.22
- | -2.43 ${}^{+0.31}_{-0.31}$ | -0.03 ${}^{+0.12}_{-0.11}$ | -208.81
CH4 | 0.000 ${}^{+0.001}_{-0.001}$ | -8.31 ${}^{+2.27}_{-2.12}$ | -1.11 ${}^{+0.8}_{-0.83}$ | -185.25
- | -8.25 ${}^{+1.0}_{-1.05}$ | -1.16 ${}^{+0.82}_{-0.78}$ | -181.26
HCN | 0.000 ${}^{+0.001}_{-0.001}$ | -8.09 ${}^{+2.17}_{-2.19}$ | -1.04 ${}^{+0.8}_{-0.84}$ | -186.24
- | -7.94 ${}^{+1.14}_{-1.03}$ | -1.1 ${}^{+0.81}_{-0.83}$ | -181.94
NH3 | -0.001 ${}^{+0.001}_{-0.001}$ | -5.35 ${}^{+1.64}_{-1.61}$ | -0.06 ${}^{+0.42}_{-0.44}$ | -190.77
- | -6.61 ${}^{+0.8}_{-0.88}$ | -0.1 ${}^{+0.46}_{-0.58}$ | -187.37
Table 11: Hyperparameters for the BHM fits for each molecule. In each case,
the null hypothesis (i.e. constant abundance with temperature) yielded a
preferable fit to the data.

In the main text we fitted the trends for the optical absorbers on all
retrievals which, when optical absorber were included, led to an atmospheric
detection of $>3\sigma$, even if the model without optical absorbers was
preferred. We did this because we have no reason to expect these planets
aren’t drawn from the same distribution as the others and so we want to test
how applicable the GGChem predictions are too all planets. However, in this
Appendix we also show the fits to only those planets where the retrieval with
optical absorbers gave a preferable fit.

When all optical absorbers retrievals are taken, we found evidence for an
increasing abundance of e- with increasing temperature. The fits to these are
given in Figures 32, 33, 34 and 35. Additionally, the associated evidence is
given in Table 12. Similarly, the fits to only retrievals which preferred the
presence of optical absorbers are given in the same figures. In this case, no
statistically viable trend was uncovered and the log-evidence for the models
is given in Table 13.

Molecule | m | c | $\sigma$ | ln(E)
---|---|---|---|---
TiO | 0.000 ${}^{+0.002}_{-0.002}$ | -8.09 ${}^{+2.25}_{-2.24}$ | -1.02 ${}^{+0.83}_{-0.82}$ | -189.48
- | -7.81 ${}^{+0.91}_{-0.87}$ | -1.05 ${}^{+0.85}_{-0.86}$ | -185.62
VO | 0.001 ${}^{+0.001}_{-0.001}$ | -9.97 ${}^{+1.52}_{-1.54}$ | -1.19 ${}^{+0.8}_{-0.82}$ | -185.37
- | -9.13 ${}^{+0.59}_{-0.65}$ | -1.16 ${}^{+0.81}_{-0.82}$ | -181.23
FeH | 0.001 ${}^{+0.001}_{-0.001}$ | -10.23 ${}^{+1.66}_{-1.69}$ | -0.62 ${}^{+0.86}_{-0.97}$ | -190.95
- | -8.68 ${}^{+0.96}_{-0.82}$ | -0.55 ${}^{+0.82}_{-1.03}$ | -187.19
e- | 0.003 ${}^{+0.001}_{-0.001}$ | -12.47 ${}^{+0.88}_{-0.81}$ | -1.04 ${}^{+0.78}_{-0.84}$ | -186.94
- | -8.8 ${}^{+0.72}_{-0.72}$ | -0.24 ${}^{+0.49}_{-0.63}$ | -188.19
Table 12: Hyperparameters for the BHM fits for each molecule when using all retrievals where optical abosrbers were preferred to the flat model by $>3\sigma$. Only the fit to e- provided evidence of a trend with temperature (at a 2.28$\sigma$ level). In the other cases, the null hypothesis (i.e. constant abundance with temperature) was preferred. Molecule | m | c | $\sigma$ | ln(E)
---|---|---|---|---
TiO | 0.000 ${}^{+0.002}_{-0.002}$ | -7.6 ${}^{+3.88}_{-4.01}$ | -1.13 ${}^{+1.03}_{-1.04}$ | -74.27
- | -7.16 ${}^{+1.86}_{-1.88}$ | -1.02 ${}^{+0.97}_{-1.03}$ | -71.01
VO | -0.001 ${}^{+0.002}_{-0.002}$ | -6.57 ${}^{+3.17}_{-3.56}$ | -1.13 ${}^{+1.04}_{-1.04}$ | -74.1
- | -7.41 ${}^{+1.33}_{-1.56}$ | -1.08 ${}^{+1.0}_{-1.01}$ | -70.13
FeH | 0.002 ${}^{+0.002}_{-0.002}$ | -9.72 ${}^{+3.64}_{-3.34}$ | 0.01 ${}^{+0.55}_{-0.75}$ | -76.95
- | -7.29 ${}^{+1.68}_{-1.79}$ | 0.14 ${}^{+0.4}_{-0.26}$ | -73.63
e- | 0.004 ${}^{+0.001}_{-0.001}$ | -12.16 ${}^{+2.18}_{-2.05}$ | -1.12 ${}^{+1.05}_{-1.07}$ | -73.99
- | -7.07 ${}^{+1.06}_{-1.08}$ | -0.17 ${}^{+0.64}_{-0.91}$ | -73.48
Table 13: Hyperparameters for the BHM fits for each molecule when using all retrievals where optical absorbers were preferred to the model without them. In each cases, the null hypothesis (i.e. constant abundance with temperature) was preferred. m | c | $\sigma$ | ln(E)
---|---|---|---
-0.57 ${}^{+0.62}_{-0.6}$ | 1.09 ${}^{+0.45}_{-0.47}$ | -0.15 ${}^{+0.14}_{-0.13}$ | -153.93
- | 0.76 +0.34 -0.32 | -0.15 ${}^{+0.14}_{-0.09}$ | -152.46
-0.07 ${}^{+0.17}_{-0.18}$ | 0.74 ${}^{+0.36}_{-0.34}$ | -0.18 ${}^{+0.14}_{-0.08}$ | -204.16
- | 0.66 ${}^{+0.34}_{-0.33}$ | -0.2 ${}^{+0.15}_{-0.07}$ | -200.41
Table 14: Hyperparameters for the BHM fits for a mass-metallicity trend when
the stellar metallicity was not accounted for. In each case, the null
hypothesis (i.e. constant abundance with temperature) yielded a preferable fit
to the data.

For the mass-metallicity fits, in the main text we explored the impact of
using only $>3\sigma$ atmospheric detections or using those at 2-3$\sigma$
too. We provide here the full set of models, both for the linear trend and the
null hypothesis and these are given in Figure 36.

With the metallicity for the GGChem retrievals, we used the host star’s
metallicity [Fe/H] to infer the relative planet-star metallicity and fit our
trend to this data. Here we also explore fitting to just the recovered planet
metallicity. When only retrievals which led to strong ($>3\sigma$) atmospheric
detections are used, we again find the linear model has a negative slope
(implying a decreasing metallicity with increasing mass, es expected).
However, the null hypothesis again has a higher Bayesian evidence.
Furthermore, no trend, or even a positive slope, is within the 1$\sigma$
bounds of the best fitting model. When the retrievals which provided a fit
which was preferred to 2-3$\sigma$ over the flat model are utilised, the BHM
shows even less evidence for a mass-metallicity trend. The results are shown
in Figure 37 and the hyper-parameters, as well as the log-evidence, are given
in Table 14.

For completeness we also show the fits for the water-to-hydrogen case. Again,
there is no evidence for a mass-metallicity trend within the data. The plots
are given in Figure 38 while Table 5 contains the log-evidence for each fit.
We provide the retrieved metallicities and water abundances in Tables 15 and
16.

Figure 31: Retrieved abundances of H2O, CH4, HCN and NH3 against planet
equilibrium temperature. In some cases, only an upper bound on the presence of
the molecule could be placed and, for these, the error bar extends to
log10(vmr) = -12. The filled regions bounded by dashed grey lines indicate the
predicted abundances from GGchem chemical equilibrium models (assuming C/O =
0.54 and solar metallicity) across 1e2 to 1e5 Pa (1e-3 to 1 Bar). Left: The
thick coloured line on each plot indicates the linear trend from the BHM while
the thinner colours lines represent the traces from the fit that were within
the 1$\sigma$ errors of the best-fit model. Right: the same except for the
flat model (i.e. the null hypothesis).

Figure 32: Retrieved abundances of TiO against planet equilibrium temperature.
In some cases, only an upper bound on the presence of the molecule could be
placed and, for these, the error bar extends to log10(vmr) = -12. The filled
regions bounded by dashed grey lines indicate the predicted abundances from
GGchem chemical equilibrium models (assuming C/O = 0.54 and solar metallicity)
across 1e2 to 1e5 Pa (1e-3 to 1 Bar). Left: The thick coloured line on each
plot indicates the linear trend from the BHM while the thinner colours lines
represent the traces from the fit that were within the 1$\sigma$ errors of the
best-fit model. Right: the same except for the flat model (i.e. the null
hypothesis). Top: black data points indicate planets for which the retrieval
model with optical absorbers is preferred while grey point represent those for
which a preferable fit is obtained without them. In these plots, all these
retrieval traces were used in the BHM. Bottom: only the retrievals for which
the optical absorb model was preferred.

Figure 33: Same as Figure 32 but for VO.

Figure 34: Same as Figure 32 but for FeH.

Figure 35: Same as Figure 32 but for e-.

Figure 36: Retrieved metallicity from our GGChem runs. Left: BHM applied to
retrievals which yielded a fit which was preferred to $>$3 sigma compared to
the flat model. Right: BHM applied to retrievals which yielded a fit which was
preferred to $>$2 sigma compared to the flat model. The fits for a linear
trend fit (top) and flat trend (i.e. constant with mass, bottom) are shown
with the thick line indicating the best-fit model and the thinner lines
representing the traces from the fit that fell within 1 sigma of the best-fit
model. In both cases, the flat model is preferred, implying we cannot conclude
there is a trend between planet mass and the metallicity from these data.

Figure 37: Same as Figure 36 but without accounting for the stellar
metallicity. Again there is no evidence for a mass-metallicity trend in these
data as the constant metallicity model provides a preferable fit to these
data.

Figure 38: Fits from our BHM to the water ratio which was determined using the methods of Welbanks et al. (2019). Left: BHM applied to retrievals which yielded a fit which was preferred to $>$3 sigma compared to the flat model. Right: BHM applied to retrievals which yielded a fit which was preferred to $>$2 sigma compared to the flat model. The fits for a linear trend fit (top) and flat trend (i.e. constant with mass, bottom) are shown with he thick line indicating the best-fit model and the thinner lines representing the traces from the fit that fell within 1 sigma of the best-fit model. In both cases, the flat model is preferred, implying we cannot conclude there is a trend between planet mass and the water-to-hydrogen ratio from these data. Table 15: Results of our chemical equilibrium retrievals. The C/O ratio and metallicity were free parameters in these retrievals, with the planet to star metallicity ratio (log10(ZP/ZS)) calculated from the retrieved metallicity value and the star’s Fe/H as described in the text. The sigma column refers to the significance of the model with respect to the flat model. Where the preference for the atmospheric model was below 2$\sigma$, we do not report the significance and assume that, from our retrieval, there is no meaningful evidence for atmospheric modulation. For completeness, we report the C/O and metallicity in all cases. Planet Name | C/O | log10(ZP) | log10(ZP/ZS) | Sigma | Planet Name | C/O | log10(ZP) | log10(ZP/ZS) | Sigma
---|---|---|---|---|---|---|---|---|---
CoRoT-1 b | 1.09${}^{+0.6}_{-0.65}$ | 0.56${}^{+0.82}_{-0.96}$ | 2.71${}^{+0.82}_{-0.96}$ | 1.99 | LTT 9779 b | 1.39${}^{+0.41}_{-0.65}$ | 0.83${}^{+0.97}_{-1.03}$ | 2.42${}^{+0.97}_{-1.03}$ | -
GJ 436 b | 1.04${}^{+0.59}_{-0.52}$ | 0.32${}^{+1.03}_{-0.81}$ | 2.16${}^{+1.03}_{-0.81}$ | - | TOI-270 c | 0.57${}^{+0.52}_{-0.3}$ | 0.19${}^{+1.21}_{-0.78}$ | 2.22${}^{+1.21}_{-0.78}$ | -
GJ 1214 b | 0.53${}^{+0.5}_{-0.28}$ | 0.03${}^{+0.97}_{-0.62}$ | 1.49${}^{+0.97}_{-0.62}$ | 2.38 | TOI-270 d | 0.51${}^{+0.39}_{-0.28}$ | 0.35${}^{+1.19}_{-0.95}$ | 2.38${}^{+1.19}_{-0.95}$ | 3.67
GJ 3470 b | 0.57${}^{+0.36}_{-0.3}$ | 0.02${}^{+0.91}_{-0.64}$ | 1.69${}^{+0.91}_{-0.64}$ | 2.27 | TOI-674 b | 0.48${}^{+0.25}_{-0.52}$ | 0.12${}^{+0.83}_{-0.68}$ | 2.7${}^{+0.83}_{-0.68}$ | 4.94
HAT-P-1 b | 0.64${}^{+0.2}_{-0.31}$ | 1.73${}^{+0.2}_{-1.0}$ | 3.46${}^{+0.2}_{-1.0}$ | 4.53 | TrES-2 b | 0.97${}^{+0.6}_{-0.31}$ | 0.46${}^{+0.91}_{-0.88}$ | 2.46${}^{+0.91}_{-0.88}$ | -
HAT-P-2 b | 1.09${}^{+0.56}_{-0.64}$ | 0.39${}^{+1.0}_{-0.86}$ | 2.1${}^{+1.0}_{-0.86}$ | - | TrES-4 b | 1.18${}^{+0.5}_{-0.24}$ | 0.49${}^{+0.92}_{-0.94}$ | 2.2${}^{+0.92}_{-0.94}$ | -
HAT-P-3 b | 1.04${}^{+0.59}_{-0.54}$ | 0.51${}^{+0.92}_{-0.82}$ | 2.1${}^{+0.92}_{-0.82}$ | - | V1298 Tau b | 0.23${}^{+0.17}_{-0.41}$ | -0.01${}^{+0.36}_{-0.39}$ | 1.7${}^{+0.36}_{-0.39}$ | 18.48
HAT-P-7 b | 0.93${}^{+0.64}_{-0.53}$ | 0.56${}^{+0.96}_{-0.95}$ | 2.15${}^{+0.96}_{-0.95}$ | - | V1298 Tau c | 0.23${}^{+0.17}_{-0.45}$ | -0.01${}^{+0.36}_{-0.39}$ | 1.7${}^{+0.36}_{-0.39}$ | 14.56
HAT-P-11 b | 0.47${}^{+0.34}_{-0.24}$ | 1.59${}^{+0.27}_{-1.4}$ | 3.13${}^{+0.27}_{-1.4}$ | 4.77 | WASP-6 b | 0.42${}^{+0.28}_{-0.0}$ | 0.31${}^{+0.94}_{-0.8}$ | 2.37${}^{+0.94}_{-0.8}$ | 4.99
HAT-P-12 b | 0.72${}^{+0.79}_{-0.41}$ | 0.39${}^{+1.07}_{-0.85}$ | 2.53${}^{+1.07}_{-0.85}$ | - | WASP-12 b | 0.46${}^{+0.29}_{-0.24}$ | -0.07${}^{+0.63}_{-0.49}$ | 1.45${}^{+0.63}_{-0.49}$ | 6.02
HAT-P-17 b | 0.82${}^{+0.76}_{-0.45}$ | 0.41${}^{+0.95}_{-0.84}$ | 2.26${}^{+0.95}_{-0.84}$ | - | WASP-17 b | 0.32${}^{+0.27}_{-0.53}$ | 1.74${}^{+0.18}_{-0.9}$ | 3.79${}^{+0.18}_{-0.9}$ | 8.77
HAT-P-18 b | 1.05${}^{+0.65}_{-0.68}$ | 0.84${}^{+0.91}_{-1.17}$ | 2.59${}^{+0.91}_{-1.17}$ | 3.2 | WASP-18 b | 1.12${}^{+0.52}_{-0.37}$ | 0.41${}^{+0.94}_{-0.9}$ | 2.16${}^{+0.94}_{-0.9}$ | -
HAT-P-26 b | 0.32${}^{+0.27}_{-0.16}$ | 0.32${}^{+0.85}_{-0.82}$ | 2.22${}^{+0.85}_{-0.82}$ | 9.29 | WASP-19 b | 0.47${}^{+0.26}_{-0.28}$ | 0.95${}^{+0.57}_{-1.11}$ | 2.65${}^{+0.57}_{-1.11}$ | 4.65
HAT-P-32 b | 0.47${}^{+0.29}_{-0.24}$ | 0.23${}^{+1.23}_{-0.75}$ | 2.12${}^{+1.23}_{-0.75}$ | 7.31 | WASP-29 b | 1.02${}^{+0.61}_{-0.23}$ | 0.27${}^{+1.03}_{-0.84}$ | 2.02${}^{+1.03}_{-0.84}$ | -
HAT-P-38 b | 0.51${}^{+0.27}_{-0.26}$ | 1.59${}^{+0.25}_{-0.65}$ | 3.38${}^{+0.25}_{-0.65}$ | 2.87 | WASP-31 b | 0.79${}^{+0.71}_{-0.47}$ | 0.17${}^{+1.02}_{-0.76}$ | 2.23${}^{+1.02}_{-0.76}$ | 2.4
HAT-P-41 b | 0.46${}^{+0.25}_{-0.23}$ | 1.32${}^{+0.37}_{-1.34}$ | 2.96${}^{+0.37}_{-1.34}$ | 4.89 | WASP-39 b | 0.32${}^{+0.29}_{-0.86}$ | 1.87${}^{+0.1}_{-0.24}$ | 3.84${}^{+0.1}_{-0.24}$ | 9.24
HD 3167 c | 1.36${}^{+0.45}_{-0.86}$ | 1.74${}^{+0.21}_{-1.66}$ | 3.56${}^{+0.21}_{-1.66}$ | 3.34 | WASP-43 b | 0.63${}^{+0.79}_{-0.07}$ | 0.6${}^{+0.83}_{-0.98}$ | 2.51${}^{+0.83}_{-0.98}$ | 2.6
HD 97658 b | 0.86${}^{+0.04}_{-0.07}$ | 1.95${}^{+0.04}_{-0.07}$ | 4.03${}^{+0.04}_{-0.07}$ | 5.3 | WASP-52 b | 0.41${}^{+0.46}_{-0.48}$ | 0.33${}^{+0.91}_{-0.82}$ | 2.15${}^{+0.91}_{-0.82}$ | 6.8
HD 106315 c | 0.51${}^{+0.26}_{-0.26}$ | 1.61${}^{+0.31}_{-1.74}$ | 3.74${}^{+0.31}_{-1.74}$ | 5.58 | WASP-62 b | 0.43${}^{+0.25}_{-0.43}$ | 0.19${}^{+0.63}_{-0.67}$ | 2.01${}^{+0.63}_{-0.67}$ | 5.56
HD 149026 b | 0.69${}^{+0.62}_{-0.37}$ | 0.58${}^{+1.04}_{-1.01}$ | 2.08${}^{+1.04}_{-1.01}$ | - | WASP-63 b | 0.7${}^{+0.73}_{-0.65}$ | 0.49${}^{+0.85}_{-0.88}$ | 2.26${}^{+0.85}_{-0.88}$ | -
HD 189733 b | 0.5${}^{+0.49}_{-0.28}$ | 0.89${}^{+0.62}_{-0.97}$ | 2.77${}^{+0.62}_{-0.97}$ | 4.95 | WASP-67 b | 0.83${}^{+0.73}_{-0.53}$ | 0.5${}^{+0.91}_{-0.92}$ | 2.43${}^{+0.91}_{-0.92}$ | 2.33
HD 209458 b | 0.42${}^{+0.29}_{-0.23}$ | -0.04${}^{+0.83}_{-0.62}$ | 1.81${}^{+0.83}_{-0.62}$ | 6.78 | WASP-69 b | 0.42${}^{+0.77}_{-0.19}$ | -0.13${}^{+0.86}_{-0.57}$ | 1.58${}^{+0.86}_{-0.57}$ | 4.98
HD 219666 b | 0.89${}^{+0.69}_{-0.47}$ | 0.46${}^{+1.02}_{-1.0}$ | 2.27${}^{+1.02}_{-1.0}$ | 2.66 | WASP-74 b | 0.64${}^{+0.74}_{-0.31}$ | 0.69${}^{+0.84}_{-0.96}$ | 2.15${}^{+0.84}_{-0.96}$ | 1.93
HIP 41378 b | 0.87${}^{+0.74}_{-0.48}$ | 0.68${}^{+1.0}_{-1.06}$ | 2.65${}^{+1.0}_{-1.06}$ | - | WASP-76 b | 0.5${}^{+0.26}_{-0.62}$ | 1.75${}^{+0.15}_{-0.21}$ | 3.24${}^{+0.15}_{-0.21}$ | 8.11
HIP 41378 f | 0.11${}^{+0.01}_{-0.0}$ | -0.49${}^{+0.48}_{-0.32}$ | 1.48${}^{+0.48}_{-0.32}$ | 6.3 | WASP-79 b | 0.37${}^{+0.24}_{-0.57}$ | 0.06${}^{+0.97}_{-0.68}$ | 1.89${}^{+0.97}_{-0.68}$ | 5.49
K2-18 b | 0.77${}^{+0.75}_{-0.43}$ | 0.34${}^{+1.18}_{-0.87}$ | 2.07${}^{+1.18}_{-0.87}$ | 3.05 | WASP-80 b | 0.71${}^{+0.75}_{-0.63}$ | 0.29${}^{+1.0}_{-0.82}$ | 2.28${}^{+1.0}_{-0.82}$ | 2.96
K2-24 b | 1.14${}^{+0.52}_{-0.65}$ | 0.34${}^{+1.01}_{-0.86}$ | 1.85${}^{+1.01}_{-0.86}$ | - | WASP-96 b | 0.78${}^{+0.77}_{-0.56}$ | 0.53${}^{+0.7}_{-0.8}$ | 2.24${}^{+0.7}_{-0.8}$ | 3.84
KELT-1 b | 0.99${}^{+0.6}_{-0.53}$ | 0.53${}^{+0.91}_{-0.96}$ | 2.38${}^{+0.91}_{-0.96}$ | - | WASP-101 b | 1.01${}^{+0.59}_{-0.68}$ | 0.06${}^{+0.82}_{-0.67}$ | 1.71${}^{+0.82}_{-0.67}$ | 2.27
KELT-7 b | 0.6${}^{+0.53}_{-0.31}$ | -0.15${}^{+0.67}_{-0.49}$ | 1.57${}^{+0.67}_{-0.49}$ | 3.46 | WASP-103 b | 1.03${}^{+0.52}_{-0.64}$ | -0.3${}^{+0.48}_{-0.42}$ | 1.49${}^{+0.48}_{-0.42}$ | 6.54
KELT-11 b | 0.58${}^{+0.17}_{-0.19}$ | -0.09${}^{+0.14}_{-0.17}$ | 1.6${}^{+0.14}_{-0.17}$ | 10.4 | WASP-107 b | 0.25${}^{+0.18}_{-0.16}$ | 1.4${}^{+0.45}_{-1.28}$ | 3.24${}^{+0.45}_{-1.28}$ | 9.95
Kepler-9 b | 0.96${}^{+0.68}_{-0.55}$ | 0.64${}^{+0.89}_{-1.09}$ | 2.45${}^{+0.89}_{-1.09}$ | 1.89 | WASP-117 b | 0.9${}^{+0.69}_{-0.54}$ | 0.61${}^{+0.98}_{-1.03}$ | 2.57${}^{+0.98}_{-1.03}$ | 2.8
Kepler-9 c | 1.04${}^{+0.59}_{-0.56}$ | 0.25${}^{+1.07}_{-0.78}$ | 2.06${}^{+1.07}_{-0.78}$ | - | WASP-121 b | 0.46${}^{+0.25}_{-0.26}$ | 1.76${}^{+0.18}_{-2.12}$ | 3.48${}^{+0.18}_{-2.12}$ | 5.68
Kepler-51 b | 1.13${}^{+0.56}_{-0.62}$ | 0.58${}^{+1.04}_{-1.09}$ | 2.38${}^{+1.04}_{-1.09}$ | - | WASP-127 b | 0.29${}^{+0.21}_{-0.23}$ | -0.12${}^{+0.7}_{-0.57}$ | 1.91${}^{+0.7}_{-0.57}$ | 18.17
Kepler-51 d | 0.9${}^{+0.63}_{-0.57}$ | 0.5${}^{+1.09}_{-0.98}$ | 2.3${}^{+1.09}_{-0.98}$ | - | WASP-178 b | 0.57${}^{+0.56}_{-0.26}$ | 0.08${}^{+0.83}_{-0.65}$ | 2.0${}^{+0.83}_{-0.65}$ | 3.41
Kepler-79 d | 1.09${}^{+0.58}_{-0.63}$ | 0.56${}^{+1.03}_{-1.01}$ | 2.49${}^{+1.03}_{-1.01}$ | - | XO-1 b | 0.76${}^{+0.19}_{-0.55}$ | 0.97${}^{+0.7}_{-1.21}$ | 2.8${}^{+0.7}_{-1.21}$ | 3.28
Table 16: Retrieved volume mixing ratios of water from our free chemistry retrievals. The H2O/H ratio was subsequently derived as described in the text. The sigma column refers to the significance of the preferred model with respect to the flat model. Where the preference for the atmospheric model was below 2$\sigma$, we do not report the significance and assume that, from our retrieval, there is no meaningful evidence for atmospheric modulation. For completeness, we report the H2O abundance in all cases. Planet Name | log10(H2O) | log10(H2O/H) | Sigma | Planet Name | log10(H2O) | log10(H2O/H) | Sigma
---|---|---|---|---|---|---|---
CoRoT-1 b | -5.33${}^{+2.81}_{-3.81}$ | -1.65${}^{+2.81}_{-3.81}$ | 2.36 | LTT 9779 b | -8.23${}^{+2.37}_{-2.33}$ | -5.12${}^{+2.37}_{-2.33}$ | -
GJ 1214 b | -2.98${}^{+1.03}_{-1.39}$ | -0.33${}^{+1.03}_{-1.39}$ | 2.41 | TOI-270 c | -3.73${}^{+1.56}_{-3.78}$ | -0.52${}^{+1.56}_{-3.78}$ | -
GJ 3470 b | -3.34${}^{+1.09}_{-1.93}$ | -0.48${}^{+1.09}_{-1.93}$ | 2.16 | TOI-270 d | -2.63${}^{+0.93}_{-1.06}$ | 0.58${}^{+0.94}_{-1.06}$ | 4.0
GJ 436 b | -6.89${}^{+2.83}_{-2.86}$ | -3.87${}^{+2.83}_{-2.86}$ | - | TOI-674 b | -3.12${}^{+0.78}_{-1.04}$ | 0.65${}^{+0.78}_{-1.04}$ | 4.96
HAT-P-1 b | -1.67${}^{+0.53}_{-1.07}$ | 1.58${}^{+0.55}_{-1.07}$ | 4.4 | TrES-2 b | -6.47${}^{+3.24}_{-3.07}$ | -2.94${}^{+3.24}_{-3.07}$ | -
HAT-P-2 b | -7.23${}^{+2.8}_{-2.83}$ | -4.0${}^{+2.8}_{-2.83}$ | 2.87 | TrES-4 b | -6.85${}^{+3.14}_{-2.96}$ | -3.62${}^{+3.14}_{-2.96}$ | -
HAT-P-3 b | -6.72${}^{+3.08}_{-3.13}$ | -3.61${}^{+3.08}_{-3.13}$ | - | V1298 Tau b | -2.51${}^{+0.41}_{-0.54}$ | 0.39${}^{+0.41}_{-0.54}$ | 19.4
HAT-P-7 b | -6.48${}^{+3.4}_{-3.2}$ | -3.36${}^{+3.41}_{-3.2}$ | - | V1298 Tau c | -1.56${}^{+0.32}_{-0.52}$ | 1.64${}^{+0.34}_{-0.52}$ | 14.53
HAT-P-11 b | -1.94${}^{+0.68}_{-1.26}$ | 0.89${}^{+0.7}_{-1.27}$ | 4.62 | WASP-6 b | -2.83${}^{+0.87}_{-1.14}$ | 0.75${}^{+0.88}_{-1.14}$ | 4.88
HAT-P-12 b | -3.72${}^{+1.61}_{-3.33}$ | -0.15${}^{+1.62}_{-3.33}$ | - | WASP-12 b | -2.89${}^{+0.53}_{-0.63}$ | 0.22${}^{+0.53}_{-0.63}$ | 8.3
HAT-P-17 b | -6.0${}^{+3.41}_{-3.44}$ | -2.96${}^{+3.41}_{-3.44}$ | - | WASP-17 b | -1.87${}^{+0.57}_{-0.67}$ | 1.7${}^{+0.59}_{-0.67}$ | 9.15
HAT-P-18 b | -1.89${}^{+0.63}_{-1.39}$ | 1.11${}^{+0.65}_{-1.4}$ | 3.57 | WASP-18 b | -6.75${}^{+3.46}_{-3.27}$ | -3.46${}^{+3.46}_{-3.27}$ | -
HAT-P-26 b | -2.5${}^{+0.89}_{-0.97}$ | 0.88${}^{+0.9}_{-0.97}$ | 9.35 | WASP-19 b | -1.88${}^{+0.52}_{-1.03}$ | 1.36${}^{+0.53}_{-1.04}$ | 4.56
HAT-P-32 b | -1.18${}^{+0.12}_{-0.32}$ | 2.27${}^{+0.12}_{-0.33}$ | 7.35 | WASP-29 b | -6.51${}^{+2.95}_{-3.03}$ | -3.29${}^{+2.95}_{-3.03}$ | -
HAT-P-38 b | -3.07${}^{+1.12}_{-2.27}$ | 0.24${}^{+1.13}_{-2.27}$ | 2.25 | WASP-31 b | -3.29${}^{+1.36}_{-3.44}$ | 0.28${}^{+1.36}_{-3.44}$ | 2.01
HAT-P-41 b | -2.55${}^{+0.92}_{-1.36}$ | 0.62${}^{+0.93}_{-1.36}$ | 4.72 | WASP-39 b | -1.13${}^{+0.09}_{-0.24}$ | 2.39${}^{+0.1}_{-0.25}$ | 9.47
HD 3167 c | -3.73${}^{+1.07}_{-0.97}$ | -0.73${}^{+1.07}_{-0.97}$ | 4.61 | WASP-43 b | -3.14${}^{+1.41}_{-5.5}$ | 0.29${}^{+1.42}_{-5.5}$ | 3.63
HD 97658 b | -3.49${}^{+0.35}_{-0.53}$ | -0.23${}^{+0.35}_{-0.53}$ | 13.25 | WASP-52 b | -2.61${}^{+0.78}_{-0.93}$ | 0.73${}^{+0.79}_{-0.93}$ | 7.1
HD 106315 c | -1.92${}^{+0.58}_{-1.01}$ | 1.51${}^{+0.59}_{-1.02}$ | 5.61 | WASP-62 b | -1.4${}^{+0.23}_{-0.51}$ | 1.95${}^{+0.24}_{-0.52}$ | 5.81
HD 149026 b | -4.54${}^{+2.45}_{-4.12}$ | -1.53${}^{+2.45}_{-4.12}$ | - | WASP-63 b | -3.49${}^{+1.48}_{-4.05}$ | -0.2${}^{+1.48}_{-4.05}$ | -
HD 189733 b | -2.01${}^{+0.56}_{-0.86}$ | 1.4${}^{+0.57}_{-0.87}$ | 4.98 | WASP-67 b | -3.6${}^{+1.51}_{-2.75}$ | -0.17${}^{+1.51}_{-2.75}$ | 2.21
HD 209458 b | -3.1${}^{+0.95}_{-1.17}$ | 0.28${}^{+0.95}_{-1.17}$ | 6.76 | WASP-69 b | -2.48${}^{+0.69}_{-0.94}$ | 0.71${}^{+0.7}_{-0.94}$ | 5.32
HD 219666 b | -3.23${}^{+1.57}_{-4.21}$ | 0.1${}^{+1.58}_{-4.21}$ | 2.33 | WASP-74 b | -3.88${}^{+2.13}_{-4.79}$ | -0.9${}^{+2.14}_{-4.79}$ | 1.98
HIP 41378 b | -4.03${}^{+2.34}_{-4.79}$ | -0.65${}^{+2.35}_{-4.79}$ | - | WASP-76 b | -2.96${}^{+0.84}_{-1.33}$ | 0.06${}^{+0.84}_{-1.33}$ | 7.49
HIP 41378 f | -8.8${}^{+1.14}_{-1.77}$ | -5.65${}^{+1.14}_{-1.77}$ | 16.77 | WASP-79 b | -2.05${}^{+0.4}_{-0.6}$ | 1.3${}^{+0.41}_{-0.6}$ | 6.44
K2-18 b | -3.19${}^{+1.28}_{-1.71}$ | -0.28${}^{+1.28}_{-1.71}$ | 2.98 | WASP-80 b | -2.97${}^{+0.93}_{-1.59}$ | 0.21${}^{+0.93}_{-1.59}$ | 2.69
K2-24 b | -7.83${}^{+2.92}_{-2.64}$ | -5.13${}^{+2.92}_{-2.64}$ | 2.46 | WASP-96 b | -2.77${}^{+1.01}_{-1.47}$ | 0.47${}^{+1.02}_{-1.47}$ | 3.72
KELT-1 b | -6.63${}^{+3.23}_{-3.08}$ | -3.23${}^{+3.23}_{-3.08}$ | - | WASP-101 b | -6.72${}^{+3.18}_{-3.07}$ | -3.54${}^{+3.18}_{-3.07}$ | 3.56
KELT-7 b | -4.33${}^{+1.5}_{-4.78}$ | -1.09${}^{+1.5}_{-4.78}$ | 5.97 | WASP-103 b | -7.71${}^{+2.86}_{-2.59}$ | -4.35${}^{+2.86}_{-2.59}$ | 6.78
KELT-11 b | -5.09${}^{+1.57}_{-0.87}$ | -1.89${}^{+1.57}_{-0.87}$ | 10.87 | WASP-107 b | -2.0${}^{+0.53}_{-0.83}$ | 1.02${}^{+0.54}_{-0.84}$ | 10.33
Kepler-9 b | -4.71${}^{+2.51}_{-4.19}$ | -1.73${}^{+2.51}_{-4.19}$ | - | WASP-117 b | -3.1${}^{+1.38}_{-2.85}$ | 0.37${}^{+1.38}_{-2.85}$ | 2.6
Kepler-9 c | -5.99${}^{+2.22}_{-3.25}$ | -3.0${}^{+2.22}_{-3.25}$ | 2.78 | WASP-121 b | -3.14${}^{+0.9}_{-1.25}$ | 0.12${}^{+0.9}_{-1.25}$ | 5.6
Kepler-51 b | -6.1${}^{+3.13}_{-3.32}$ | -3.11${}^{+3.13}_{-3.32}$ | - | WASP-127 b | -1.14${}^{+0.08}_{-0.12}$ | 2.44${}^{+0.09}_{-0.13}$ | 18.44
Kepler-51 d | -6.92${}^{+2.9}_{-3.04}$ | -3.93${}^{+2.9}_{-3.04}$ | - | WASP-178 b | -3.01${}^{+0.67}_{-0.95}$ | 0.45${}^{+0.67}_{-0.96}$ | 4.85
Kepler-79 d | -6.82${}^{+2.9}_{-3.04}$ | -3.71${}^{+2.9}_{-3.04}$ | 2.03 | XO-1 b | -1.39${}^{+0.27}_{-0.69}$ | 1.98${}^{+0.29}_{-0.7}$ | 3.2

## Appendix 4: Fitting The WFC3 G141 Spectral Feature Size

The key spectral feature within the HST WFC3 G141 band is the 1.4 $\mu$m water
feature and, instead of preforming retrievals in an attempt to recover the
abundance of this molecule, several studies have instead measured the size of
the feature in relation to other bands within WFC3’s spectral range (Fu et
al., 2017; Wakeford et al., 2019). While the information gained in the
approach is limited, we nonetheless explored its use to compare our results to
other studies which have previously used this metric. We achieved this by
first modelling a cloud-free atmosphere where water in the only molecular
opacity. We also include scattering due to Rayleigh and Collision Induced
Absorption (CIA). The model is then scaled using:

$y(\lambda)=ax(\lambda)+bx+c,$ (12)

where $x(\lambda)$ is the original spectrum model, $a$ is a scaling factor,
$b$ is the wavelength coefficient for the baseline slope, and $c$ is a
constant offset (Fu et al., 2017). The scaling factor, $a$, moderates the size
of the water feature, acting as proxy for clouds while $b$ can be used to
account for slopes within the spectrum (e.g. due to H- opacity). We fit the
model using Nestle444https://github.com/kbarbary/nestle (Skilling, 2004;
Mukherjee et al., 2006; Shaw et al., 2007) and we follow the methodology of
Stevenson (2016), computing the difference between the minimum in the J band
(1.22-1.30) and the maximum in the H2O band (1.36-1.44) from the preferred
model spectrum after removing the slope.

By dividing the feature size by the expected transit depth modulation from one
scale height of atmosphere, one can determine the magnitude of atmospheric
absorption in an way which easily facilitates comparisons across a broad
parameter space. The change in the transit depth due to one scale height of
atmosphere was determined by:

$\Delta D=\frac{2HR_{p}}{R^{2}_{s}}$ (13)

where $R_{p}$ is the planet’s radius, $R_{s}$ is the radius of the host star
and $H$ is the atmospheric scale height, calculated from:

$H=\frac{kT}{\mu g}$ (14)

where $k$ is the Boltzmann constant, $T$ is the planet’s equilibrium
temperature, $\mu$ is the atmospheric mean molecular weight (set to 2.3), and
$g$ is the planet’s surface gravity.

Figure 39: Posteriors and best-fit spectrum for amplitude fitting of WASP-107
b.

An example fit for WASP-107 b is given in Figure 39. We provide the feature
size for all planets studied here in Table 17. The spectral feature size has
often been used to infer the presence of clouds and proposed as a way of
guiding observers as to the spectral modulation that could be expected when
planning future observations. Across the population, we recover an average
feature size of 0.92 scale heights, a comparable value to previous studies:
1.4 H (Fu et al., 2017) and 0.89 H (Wakeford et al., 2019). The amplitude of
this feature is far below what would be expect from a clear, solar metallicity
atmosphere. However, we note that the magnitude of the atmospheric absorption
is only valid across the HST WFC3 G141 range and that other instruments,
particularly those that probe further into the infrared, will see larger
feature sizes.

Extending the models used to derive the 1.4 $\mu$m feature size in the HST
WFC3 G141 data, we estimate the amplitude of features seen in observations
with future instruments by studying the minimum and maximum transit depth
across their spectral coverage. For JWST NIRISS GR700XD (0.6-2.8 $\mu$m, Doyon
et al., 2012) and JWST NIRSpec G395H (2.8-5.1 $\mu$m, Birkmann et al., 2016))
we predict average feature sizes of 2.52 and 1.65 scale heights respectively.
Combining both instruments, observing with the JWST NIRSpec PRISM (0.6-5.3
$\mu$m), or with Twinkle (0.5-4.5 $\mu$m, Edwards et al., 2019)), gives an
amplitude of 2.57 scale heights. Finally, the expected amplitude across the
spectral coverage of Ariel (0.5-7.8 $\mu$m, Tinetti et al., 2018)) is 3.13
scale heights.

Therefore, while clouds and hazes obviously need to be accounted for during
the planning of observations with future facilities, current data shows the
expected amplitude should, on average, be greater than a single scale height.
However, we note also that the methodology used to measure the amplitude of
absorption features is somewhat flawed. While the parameters in Equation 12
allow the spectrum to be modulated to fit the data, and account for the
features seen, the final fit does not provide a robust analysis of the nature
of the atmosphere. The presence, and effect, of clouds can be better
understood by fitting physical models to the data via atmospheric retrievals.

Table 17: 1.4$\mu$m feature size, in scale heights, of the planets studied here. In this table we report all fitted values but, in the figures, we only plot those where the uncertainty of the feature size is less than 2 scale heights. Planet Name | Feature Size | Planet Name | Feature Size
---|---|---|---
CoRoT-1 b | 5.3 $\pm$ 2.08 | LTT 9779 b | 0.32 $\pm$ 0.68
GJ 1214 b | 0.12 $\pm$ 0.04 | TOI-270 c | 0.27 $\pm$ 0.366
GJ 3470 b | 0.68 $\pm$ 0.24 | TOI-270 d | 2.66 $\pm$ 0.
GJ 436 b | 0.02 $\pm$ 0.36 | TOI-674 b | 1.38 $\pm$ 0.26
HAT-P-1 b | 1.89 $\pm$ 0.37 | TrES-2 b | 1.5 $\pm$ 2.47
HAT-P-2 b | 6.04 $\pm$ 3.74 | TrES-4 b | -5.75 $\pm$ 3.61
HAT-P-3 b | 0.61 $\pm$ 0.62 | V1298Tau b | 10.66 $\pm$ 0.57
HAT-P-7 b | 3.31 $\pm$ 4.36 | V1298Tau c | 14.24 $\pm$ 0.71
HAT-P-11 b | 2.0 $\pm$ 0.39 | WASP-6 b | 1.78 $\pm$ 0.36
HAT-P-12 b | 0.46 $\pm$ 0.21 | WASP-12 b | 2.42 $\pm$ 0.34
HAT-P-17 b | 0.97 $\pm$ 0.61 | WASP-17 b | 1.88 $\pm$ 0.2
HAT-P-18 b | 0.81 $\pm$ 0.19 | WASP-18 b | -1.31 $\pm$ 3.01
HAT-P-26 b | 2.52 $\pm$ 0.27 | WASP-19 b | 2.29 $\pm$ 0.46
HAT-P-32 b | 1.89 $\pm$ 0.25 | WASP-29 b | -0.15 $\pm$ 0.36
HAT-P-38 b | 1.56 $\pm$ 0.61 | WASP-31 b | 1.07 $\pm$ 0.38
HAT-P-41 b | 2.06 $\pm$ 0.45 | WASP-39 b | 1.58 $\pm$ 0.15
HD 3167 c | 1.22 $\pm$ 0.31 | WASP-43 b | 1.45 $\pm$ 0.43
HD 97658 b | 1.98 $\pm$ 0.64 | WASP-52 b | 1.6 $\pm$ 0.24
HD 106315 c | 2.42 $\pm$ 0.4 | WASP-62 b | 1.37 $\pm$ 0.26
HD 149026 b | 1.08 $\pm$ 0.54 | WASP-63 b | 0.64 $\pm$ 0.28
HD 189733 b | 2.09 $\pm$ 0.38 | WASP-67 b | 1.16 $\pm$ 0.51
HD 209458 b | 0.98 $\pm$ 0.15 | WASP-69 b | 0.61 $\pm$ 0.12
HD 219666 b | 2.05 $\pm$ 0.62 | WASP-74 b | 0.96 $\pm$ 0.44
HIP 41378 b | 2.25 $\pm$ 0.97 | WASP-76 b | 1.39 $\pm$ 0.19
HIP 41378 f | -2.41 $\pm$ 0.68 | WASP-79 b | 2.41 $\pm$ 0.38
K2-18 b | 2.33 $\pm$ 0.67 | WASP-80 b | 0.44 $\pm$ 0.21
K2-24 b | -1.04 $\pm$ 0.68 | WASP-96 b | 2.36 $\pm$ 0.66
KELT-1 b | -1.19 $\pm$ 4.63 | WASP-101 b | 0.11 $\pm$ 0.29
KELT-7 b | 1.35 $\pm$ 0.46 | WASP-103 b | 1.97 $\pm$ 0.64
KELT-11 b | 1.12 $\pm$ 0.14 | WASP-107 b | 0.79 $\pm$ 0.08
Kepler-9 b | 3.26 $\pm$ 1.57 | WASP-117 b | 0.99 $\pm$ 0.31
Kepler-9 c | -0.9 $\pm$ 1.86 | WASP-121 b | 1.05 $\pm$ 0.18
Kepler-51 b | 0.14 $\pm$ 0.48 | WASP-127 b | 2.47 $\pm$ 0.15
Kepler-51 d | 0.08 $\pm$ 0.47 | WASP-178 b | 1.6 $\pm$ 0.44
Kepler-79 d | -2.46 $\pm$ 1.58 | XO-1 b | 2.72 $\pm$ 0.69

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