# Exploring the Ability of HST WFC3 G141 to Uncover Trends in Populations of
Exoplanet Atmospheres Through a Homogeneous Transmission Survey of 70 Gaseous
Planets

Billy Edwards Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM,
91191, Gif-sur-Yvette, France  Department of Physics and Astronomy, University
College London, Gower Street, London, WC1E 6BT, United Kingdom  Quentin
Changeat Department of Physics and Astronomy, University College London, Gower
Street, London, WC1E 6BT, United Kingdom  European Space Agency (ESA), ESA
Baltimore Office, 3700 San Martin Drive, Baltimore, MD 21218, United States of
America  Space Telescope Science Institute (STScI), 3700 San Martin Drive,
Baltimore, MD 21218, United States of America  Angelos Tsiaras INAF,
Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
Department of Physics and Astronomy, University College London, Gower Street,
London, WC1E 6BT, United Kingdom  Kai Hou Yip Department of Physics and
Astronomy, University College London, Gower Street, London, WC1E 6BT, United
Kingdom  Ahmed F. Al-Refaie Department of Physics and Astronomy, University
College London, Gower Street, London, WC1E 6BT, United Kingdom  Lara Anisman
Department of Physics and Astronomy, University College London, Gower Street,
London, WC1E 6BT, United Kingdom  Michelle F. Bieger College of Engineering,
Mathematics and Physical Sciences, University of Exeter, North Park Road,
Exeter, UK  Amélie Gressier  LATMOS, CNRS, Sorbonne Université UVSQ, 11
boulevard d’Alembert, F-78280 Guyancourt, France  Sorbonne Universités, UPMC
Université Paris 6 et CNRS, UMR 7095, Institut d’Astrophysique de Paris,
Paris, France  LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne
Université, Université de Paris, Meudon, France  Sho Shibata Institute for
Computational Science, Center for Theoretical Astrophysics & Cosmology,
University of Zurich, Winterthurerstr. 190, 8057 Zurich, Switzerland  Nour
Skaf LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université,
Université de Paris, Meudon, France  Subaru Telescope, National Astronomical
Observatory of Japan, 650 North A’ohoku Place, Hilo, HI 96720, USA  Department
of Physics and Astronomy, University College London, Gower Street, London,
WC1E 6BT, United Kingdom  Jeroen Bouwman  Max-Planck-Institut für Astronomie,
Königstuhl 17, 69117 Heidelberg, Germany  James Y-K. Cho Center for
Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY
10010, USA  Masahiro Ikoma Division of Science, National Astronomical
Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Department
of Astronomical Science, The Graduate University for Advanced Studies
(SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  Olivia Venot
Université de Paris Cité and Univ Paris Est Creteil, CNRS, LISA, F-75013
Paris, France  Ingo Waldmann Department of Physics and Astronomy, University
College London, Gower Street, London, WC1E 6BT, United Kingdom  Pierre-Olivier
Lagage  Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191,
Gif-sur-Yvette, France  Giovanna Tinetti Department of Physics and Astronomy,
University College London, Gower Street, London, WC1E 6BT, United Kingdom

(Received 5th April 2022; Revised 8th September 2022; Accepted 17th September
2022)

###### Abstract

We present the analysis of the atmospheres of 70 gaseous extrasolar planets
via transit spectroscopy with Hubble’s Wide Field Camera 3 (WFC3). For over
half of these, we statistically detect spectral modulation which our
retrievals attribute to molecular species. Among these, we use Bayesian
Hierarchical Modelling to search for chemical trends with bulk parameters. We
use the extracted water abundance to infer the atmospheric metallicity and
compare it to the planet’s mass. We also run chemical equilibrium retrievals,
fitting for the atmospheric metallicity directly. However, although previous
studies have found evidence of a mass-metallicity trend, we find no such
relation within our data. For the hotter planets within our sample, we find
evidence for thermal dissociation of dihydrogen and water via the H- opacity.
We suggest that the general lack of trends seen across this population study
could be due to i) the insufficient spectral coverage offered by HST WFC3
G141, ii) the lack of a simple trend across the whole population, iii) the
essentially random nature of the target selection for this study or iv) a
combination of all the above. We set out how we can learn from this vast
dataset going forward in an attempt to ensure comparative planetology can be
undertaken in the future with facilities such as JWST, Twinkle and Ariel. We
conclude that a wider simultaneous spectral coverage is required as well as a
more structured approach to target selection.

Exoplanet atmospheres (487); Hubble Space Telescope (761); Surveys (1671)

††journal: ApJS††thanks: These authors contributed equally to this
work.††thanks: These authors contributed equally to this work.

##  1 Introduction

The exoplanet field has rapidly expanded, with thousands of planets currently-
known today and thousands more anticipated in the coming decade. The vast
number of detected worlds has allowed us to begin to further characterise a
diverse selection. While direct imaging has provided high-quality thermal
emission spectra for a handful of planets (e.g. Samland et al., 2017; Zhou et
al., 2020; Wang et al., 2022), the bulk of atmospheric characterisation has
been undertaken using transit or eclipse spectroscopy. Ground-based high
resolution observations have been used to detect atomic metals and their ions
(e.g. Birkby, 2018; Ehrenreich et al., 2020; Kawauchi et al., 2022; Kesseli et
al., 2022; Prinoth et al., 2022; Yan et al., 2022) as well as evidence of
high-speed winds in the terminator region (e.g. Seidel et al., 2020; Cauley et
al., 2021).

While lower resolution space-based data is not capable of distinguishing
individual absorption or emission lines, molecular species have been detected
via their broadband features, giving insights into the atmospheric diversity
of extrasolar planets (e.g. Tinetti et al., 2007; Swain et al., 2008).
Although most research papers have focused on individual objects, some have
begun to conduct population style studies (e.g. Cowan & Agol, 2011; Sing et
al., 2016a; Tsiaras et al., 2018; Changeat et al., 2022). For instance, the
infrared array camera (IRAC) on-board Spitzer was used extensively before the
end of the observatory’s life in 2019 and Spitzer eclipses and phase-curves
have been used to search for trends in the day-night temperatures of hot-
Jupiters (e.g. Garhart et al., 2020; Baxter et al., 2020; Bell et al., 2021;
Keating & Cowan, 2022; May et al., 2022). While the Space Telescope Imaging
Spectrograph (STIS) has studied a number of planets, leading to a detection of
a variety of spectral features in the visible and UV (e.g. Von Essen et al.,
2020; Evans et al., 2018), Hubble’s Wide Field Camera 3 (WFC3) has been the
workhorse of infra-red space-based spectroscopy, initially using staring mode
observations (e.g. Berta et al., 2012; Mandell et al., 2013; Ranjan et al.,
2014). The later development of the spatial scanning technique (McCullough &
MacKenty, 2012) led to far greater efficiencies and thus more precise spectra
(e.g. Deming et al., 2013; Kreidberg et al., 2014b; Changeat & Edwards, 2021).

Using this technique, groups of planets began to be analysed in transmission
and Sing et al. (2016a) combined Hubble STIS/WFC3 and Spitzer IRAC data of 10
hot-Jupiters, finding a range of atmospheric feature sizes indicative of
different cloud levels within the selected planets. The dataset from Sing et
al. (2016a) was later used in a number of different retrieval studies (Barstow
et al., 2017; Pinhas et al., 2019). 19 HST WFC3 G141 transmission spectra were
analysed by (Iyer et al., 2016) who also concluded that clouds were common in
the atmospheres of hot-Jupiters. Tsiaras et al. (2018) conducted a larger
population analysis which included 30 planets. The study used data purely from
HST WFC3 G141, finding that around half the datasets showed significant
evidence for atmospheric features. Tsiaras et al. (2018) did not search for
trend between chemistry and the bulk characteristics of a planet but their
data was later used by Fisher & Heng (2018), who also included data for the
TRAPPIST-1 system from (de Wit et al., 2018) and several other studies
(Mandell et al., 2013; Huitson et al., 2013; Kreidberg et al., 2014b; Knutson
et al., 2014). In their study, they found no trends between water abundance
and planet mass or temperature. However, the analysis of 19 planets by
Welbanks et al. (2019) suggested a mass–metallicity trend where the water
abundance increased with decreasing mass. They also noted that the
metallicities implied by these water abundances were generally below those of
the giants planets in our Solar System (Atreya et al., 2016). Additionally,
many other studies have performed retrieval analyses of planets by taking
spectral data from the literature (e.g. Barstow et al., 2017; Pinhas et al.,
2019; Cubillos & Blecic, 2021; Kawashima & Min, 2021). For smaller planets
within the sub-Neptune or Neptune regime ($\sim$2-6R⊕), a study of 6 planets
showed a strong correlation between the amplitude of the water feature and the
equilibrium temperature of the planet or its bulk mass fraction of H/He
(Crossfield & Kreidberg, 2017).

Population studies have also been undertaken in emission. For instance, data
from Spitzer IRAC channels 1 and 2 have been utilised to study tens of planets
(e.g. Garhart et al., 2020; Baxter et al., 2020; Keating & Cowan, 2022).
Mansfield et al. (2021) presented a simplistic metric which was designed to
indicate whether the spectrum showed evidence for a thermal inversion by
measuring if the water feature in the HST WFC3 G141 band was in absorption or
emission, applying it to 19 planets and comparing the values to a fiducial
model. Finally, Changeat et al. (2022) presented an analysis of 25 hot and
ultra-hot Jupiters in emission with HST and Spitzer and, by using atmospheric
retrievals, observationally uncovered an apparent link between the abundance
of optical absorbers in their atmospheres and the temperature structure.

In many studies in the literature, data from multiple instruments in combined
to expand the wavelength coverage. However, there are many potential issues
when trying to infer atmospheric properties based off these merged datasets.
Firstly, the wavelength region probed determines the sensitivity of the data
to each molecular opacity. Therefore, studying the same planet but with
different instruments can often lead to differing constraints on the abundance
of a species (Pinhas et al., 2019; Pluriel et al., 2020). Applying this to
different planets implies that, if the datasets are not homogeneous, then the
cause of any trends seen in the retrievals cannot be determined: the
underlying abundances could be different or the datasets could have differing
sensitivities to these molecules. Combining instruments can also lead to
inconsistencies, as the datasets are not necessarily compatible (Yip et al.,
2020, 2021). Hence, while a longer spectral baseline may give precise
atmospheric abundances (e.g. Wakeford et al., 2018), these constraints could
be wholly inaccurate. Hence, by combining a menagerie of datasets, biases can
be introduced onto the analysis of a single planet as well as a population as
a whole. Several works have attempted to overcome the vertical offsets often
seen between datasets by adding an offset parameter to the retrieval model
(e.g. Luque et al., 2020; Murgas et al., 2020; Wilson et al., 2020; Yan et
al., 2020; Yip et al., 2021; McGruder et al., 2022). However, it is unclear
how well this works and the issue of varying sensitivity could still apply and
temporal changes (e.g. Bruno et al., 2020; Saba et al., 2022) provide an
additional challenge.

Here we conduct a spectroscopic population study of 70 gaseous exoplanetary
atmospheres, using a methodology which is standardised and applied uniformly
to all targets to try to ensure the extraction of robust trends. In an attempt
to avoid the aforementioned biases, we restrict ourselves to using data from
HST WFC3 G141 only. To further seek homogeneity, the data were extracted using
the same pipeline: Iraclis (Tsiaras et al., 2016b, c). By performing
standardised atmospheric retrievals using the TauREx 3 code (Al-Refaie et al.,
2021) within the Alfnoor pipeline (Changeat et al., 2020a), we search for
trends within these datasets. We attempt to find correlations between the
water abundance recovered and the planet’s bulk parameters, such as mass and
temperature, comparing our findings to those from literature. We also
investigate the amplitude of the spectral features seen, searching for trends
with the planet’s temperature, surface gravity and, for smaller planets, H/He
mass fraction. At each stage we attempt to understand the limitations of our
approach, including the potential biases that could be introduced. As we stand
at the dawn of a new era of increased data quality, consideration of the these
will be crucial to avoid misinterpreting these datasets.

##  2 Observations

To ensure homogeneity in our study, we wished all data to be analysed with a
single pipeline: Iraclis (Tsiaras et al., 2016b). The pipeline has previously
been used in a number of studies and so we acquired a number of spectra from
these. Many of these were taken from the population study by Tsiaras et al.
(2018) and the papers resulting from the Ariel Retrieval of Exoplanets School
(ARES, Edwards et al., 2020b; Skaf et al., 2020; Pluriel et al., 2020; Guilluy
et al., 2021). We constrain ourselves to planets which are likely to possess
an atmosphere containing significant amounts of hydrogen and helium (R $>$ 2
R⊕, Fulton & Petigura, 2018). Therefore, we do not include HST WFC3 data of 55
Cnc e (Tsiaras et al., 2016c), LHS 1140 b (Edwards et al., 2021a), GJ 1132 b
(Mugnai et al., 2021; Libby-Roberts et al., 2021; Swain et al., 2021) or
TRAPPIST-1 b-h (de Wit et al., 2018; Gressier et al., 2022; Garcia et al.,
2022).

A list of all sources of previous datasets analysed with Iraclis are given in
Table 1 along with the proposal numbers and principal investigators of the
observing proposals. Meanwhile, the observations analysed in this work are
given in Table 2. These account for 28 new planets though we note that many of
these datasets have been analysed using other pipelines (Ranjan et al., 2014;
Mandell et al., 2013; Huitson et al., 2013; Kreidberg et al., 2014b; Knutson
et al., 2014; Ranjan et al., 2014; Evans et al., 2016; Kreidberg et al.,
2018a, b; Spake et al., 2018; Carter et al., 2020; Libby-Roberts et al., 2020;
Chachan et al., 2020; Guo et al., 2020; Alam et al., 2022; Brande et al.,
2022; Glidic et al., 2022) meaning that only 16 datasets have not previously
been published at the time of writing. The distribution of our targets, in
terms of the planet’s semi-major axis and mass, is shown in Figure 1.

Figure 1: For the planets studied here, the distribution of their semi-major axis and mass (gold). The entire currently-known transiting population with mass measurements is shown in grey. Table 1: References for data taken from other studies which utilised the Iraclis pipeline. Planet Name | Proposal ID | Proposal PI | Reference
---|---|---|---
GJ 436 b | 11622 | Heather Knutson | T18
GJ 3470 b | 13665 | Björn Benneke | T18
HAT-P-1 b | 12473 | David Sing | T18
HAT-P-3 b | 14260 | Drake Deming | T18
HAT-P-11 b | 12449 | Drake Deming | T18
HAT-P-12 b | 14260 | Drake Deming | T18
HAT-P-17 b | 12956 | Catherine Huitson | T18
HAT-P-18 b | 14260 | Drake Deming | T18
HAT-P-26 b | 14260 | Drake Deming | T18
HAT-P-32 b | 14260 | Drake Deming | T18
HAT-P-38 b | 14260 | Drake Deming | T18
HAT-P-41 b | 14767 | David Sing | T18
HD 3167 c | 15333 | Ian Crossfield | G20
HD 106315 c | 15333 | Ian Crossfield | G20
HD 149026 b | 14260 | Drake Deming | T18
HD 189733 b | 12881 | Peter McCullough | T18
HD 209458 b | 12181 | Drake Deming | T18
KELT-7 b | 14767 | David Sing | P20
KELT-11 b | 15255 | Knicole Colon | C20
K2-18 b | 14682 | Björn Benneke | T19
WASP-12 b | 13467 | Jacob Bean | T18
WASP-17 b | 14918 | Hannah Wakeford | S21
WASP-29 b | 14260 | Drake Deming | T18
WASP-31 b | 12473 | David Sing | T18
WASP-39 b | 14260 | Drake Deming | T18
WASP-43 b | 13467 | Jacob Bean | T18
WASP-52 b | 14260 | Drake Deming | T18
WASP-62 b | 14767 | David Sing | S20
WASP-63 b | 14642 | Kevin Stevenson | T18
WASP-67 b | 14260 | Drake Deming | T18
WASP-69 b | 14260 | Drake Deming | T18
WASP-74 b | 14767 | David Sing | T18
WASP-76 b | 14260 | Drake Deming | E20
WASP-79 b | 14767 | David Sing | S20
WASP-80 b | 14260 | Drake Deming | T18
WASP-96 b | 15469 | Nikolay Nikolov | Y20
WASP-101 b | 14767 | David Sing | T18
WASP-117 b | 15301 | Ludmila Carone | A20
WASP-127 b | 14619 | Jessica Spake | S20
XO-1 b | 12181 | Drake Deming | T18
A20: Anisman et al. (2020); C20: Changeat et al. (2020b)
E20: Edwards et al. (2020b); G20: Guilluy et al. (2021)
S20: Skaf et al. (2020); P20: Pluriel et al. (2020)
S21: Saba et al. (2022); T18: Tsiaras et al. (2018)
T19: Tsiaras et al. (2019); Y20: Yip et al. (2021)
Table 2: Proposal information for data analysed in this study using the
Iraclis pipeline. Spatial Scanning
---
Planet Name | Proposal ID | Proposal PI
GJ 1214 b∗ | 13021 | Jacob Bean
HAT-P-2 b | 16194 | Jean-Michel Desert
HD 97658 b∗ | 13501 | Heather Knutson
13665 | Björn Benneke
HIP 41378 b | 15333 | Ian Crossfield
HIP 41378 f∗ | 16267 | Courtney Dressing
HD 219666 b | 15698 | Thomas Beatty
KELT-1 b | 14664 | Thomas Beatty
K2-24 b | 14455 | Erik Petigura
LTT 9779 b | 16457 | Billy Edwards
TOI-270 c | 15814 | Thomas Mikal-Evans
TOI-270 d | 15814 | Thomas Mikal-Evans
TOI-674 b∗ | 15333 | Ian Crossfield
V1298 Tau b | 16083 | Kamen Todorov
V1298 Tau c | 16462 | Vatsal Panwar
WASP-6 b∗ | 14767 | David Sing
WASP-18 b | 13467 | Jacob Bean
WASP-19 b | 13431 | Catherine Huitson
WASP-103 b∗ | 14050 | Laura Kreidberg
WASP-107 b∗ | 14915 | Laura Kreidberg
WASP-121 b∗ | 14468 | Thomas Mikal-Evans
15134 | Thomas Mikal-Evans
WASP-178 b | 16450 | Joshua Lothringer
|  |
Staring
Planet Name | Proposal ID | Proposal PI
CoRoT-1 b∗ | 12181 | Drake Deming
HAT-P-7 b | 12181 | Drake Deming
Kepler-9 b | 12482 | Jean-Michel Desert
Kepler-9 c | 12482 | Jean-Michel Desert
Kepler-51 d∗ | 14218 | Zach Berta-Thompson
TrES-2 b∗ | 12181 | Drake Deming
TrES-4 b∗ | 12181 | Drake Deming
WASP-19 b∗ | 12181 | Drake Deming
∗Data previously published with another pipeline
Table 3: Proposal information for data for which a good fit could not be achieved with Iraclis and the reference for the spectrum analysed in this study.  Planet Name | Proposal ID | Proposal PI | Reference
---|---|---|---
Kepler-51 b | 14218 | Zach Berta-Thompson | L20
Kepler-79 d | 15138 | Daniel Jontof-Hutter | C20
C20: Chachan et al. (2020), L20: Libby-Roberts et al. (2020)

We detail the methodology of our Iraclis analysis in the Appendix as well as
discussing the results of each individual fitting and comparisons to previous
works. For two planets where reasonable fits could not be obtained with the
Iraclis pipeline, we took values from the literature which are noted in Table
3. We also attempted to fit the transit observation of K2-33 b (PN: 14887, PI:
Björn Benneke, Benneke et al., 2016a) but it did not have a post-egress orbit
and reliable constrains on the transit depth could not be achieved.
Furthermore, a staring mode observation of WASP-18 b (PN: 12181, PI: Drake
Deming, Deming, 2010) was analysed but the precision achieved on the transit
depth was far lower than that of the scanning mode observation. It was
therefore discarded. Similarly, we also analysed the staring mode data of GJ
1214 b (PN: 12251, PI: Zach Berta-Thompson, Berta et al., 2012) but did not
use it in our final analysis due to the better sensitivity offered by the
scanning mode data.

In total we analyse the HST WFC3 G141 transmission spectra of 70 planets, 68
of which have been reduced with the Iraclis pipeline. We note that neither of
the spectra that were taken from the literature, and therefore not reduced
using the Iraclis pipeline, led to detections of atmospheric features.

##  3 Data Analysis

Having created a database of HST WFC3 G141 spectra, we set about analysing
them in search of trends within the population. The analysis included Bayesian
retrievals as well as studying the strength of the 1.4 $\mu$m water feature.

###  3.1 Retrieval Setup

Atmospheric retrievals were performed on the transmission spectra using the
population analysis tool Alfnoor (Changeat et al., 2020a). Alfnoor extends the
capabilities of the publicly available retrieval suite TauREx 3 (Al-Refaie et
al., 2021)111https://github.com/ucl-exoplanets/TauREx3_public to populations
of exo-atmospheres. The atmospheres of the planets analysed here were
simulated to range from 10-4 to 106 Pa (10-9 to 10 Bar) and sampled uniformly
in log-space by 100 atmospheric layers. For the spectra taken from other
studies, the star and planet parameters are given in Tables 6 and 7. For
spectra derived here, the star parameters we used the values listed in Table 8
while the planet parameters are given in Table 9.

In our retrievals we assumed that all planets possess a primary atmosphere
with a solar ratio of helium to hydrogen (He/H2 = 0.17). To this we added
trace gases and included the molecular opacities from the ExoMol (Tennyson et
al., 2016), HITRAN (Gordon et al., 2016) and HITEMP (Rothman & Gordon, 2014)
databases.

The key molecular absorption within the WFC3 range is H2O. However, in a free
chemical retrieval, the other molecules chosen can affect the resulting
abundance of H2O (e.g. Changeat et al., 2020b). Therefore, we attempted
several different retrievals to test the robustness of our results. These
were:

  1. 1.

Standard retrieval: In this setup we included the opacities of H2O (Polyansky
et al., 2018), CH4 (Yurchenko & Tennyson, 2014), CO (Li et al., 2015), CO2
(Rothman et al., 2010), HCN (Barber et al., 2013) and NH3 (Yurchenko et al.,
2011). On top of this, we also included Collision Induced Absorption (CIA)
from H2-H2 (Abel et al., 2011; Fletcher et al., 2018) and H2-He (Abel et al.,
2012) as well as Rayleigh scattering for all molecules. We modelled two sets
of clouds. Firstly, as a uniform opaque deck, fitting only the cloud-top
pressure (i.e. grey clouds). Additionally, we added wavelength dependent Mie
scattering using the approximation from Lee et al. (2013).

  2. 2.

Optical absorbers: A number of previous WFC3 studies have found evidence for
hydrides or oxides (e.g. Evans et al., 2016; Skaf et al., 2020; Pluriel et
al., 2020). Hence, in this setup, we included all the opacity sources from our
standard retrieval with the addition of TiO (McKemmish et al., 2019), VO
(McKemmish et al., 2016), FeH (Wende et al., 2010) and H- (John, 1988;
Lothringer et al., 2018; Edwards et al., 2020b).

  3. 3.

Equilibrium Chemistry: For these retrievals we used the equilibrium chemistry
code GGchem (Woitke et al., 2018) via the recently developed TauREx plugin
(Al-Refaie et al., 2022). As with the free chemistry retrievals, we included
Rayleigh scattering and CIA as well as both simple grey clouds and Mie
scattering. We ran these retrievals with optical absorbers and without, with
the free parameters being the atmospheric metallicity and C/O ratio.

  4. 4.

Fixed C/O Equilibrium Chemistry: As the HST WFC3 band only really allows for
the confident detection of H2O, chemical equilibrium retrievals are
essentially fitting two free parameters (metallicity and C/O ratio) to a
single observable (the H2O abundance). Therefore, the results are generally
highly degenerate, particularly given the lack of sensitivity to carbon-
bearing species. Hence, we attempted several retrievals with the C/O ratio
fixed to various values in an attempt to see whether the metallicity could be
well constrained.

  5. 5.

Flat model: In this retrieval, no molecular opacities were included. Instead,
the only fitted parameters were the planet’s temperature and radius as well as
the pressure of a grey cloud deck. CIA and Rayleigh scattering were also
included. To quantify the significance of our molecular detections, we compare
the Bayesian evidence (Kass & Raftery, 1995) from each of the retrievals to
this flat model. We use this as a baseline from which to calculate the
significance of any apparent atmospheric detections.

In each free chemistry case, all molecular abundances were allowed to vary
from log(VMR) = -1 to log(VMR) = -12. Higher mixing are not expected in the
majority of these atmospheres and these would also necessitate accounting for
self-broadening of the molecular lines (Anisman et al., 2022a, b). For the
equilibrium chemistry retrievals, the metallicity was allowed to vary from 0.1
to 100 and the C/O ratio had bounds of 0.1 and 2. For the Mie clouds we
followed the methodology of Tsiaras et al. (2018) and fixed Q0 to 50 who found
that uncertainty induced by either varying or fixing Q0 is negligible given
the quality of the data at hand. We set a log-uniform prior of $\chi_{0}$
ranging from 10-40 to 10-10, particle size from 10-5 to 10 $\mu$m and cloud-
top pressure from 10-4 to 106 Pa (Lee et al., 2013).

For each planet, the equilibrium temperature was calculated from:

$T_{eq}=T_{s}\left(\frac{(1-A)R_{s}^{2}}{4a^{2}e}\right)^{\frac{1}{4}},$ (1)

where $T_{s}$ is the host star’s temperature, $R_{s}$ is the host star’s
radius, $a$ is the planet’s semi-major axis and the albedo and heat
redistribution factor are set to $A$ = 0.2 and $e$ = 0.8, respectively. An
isothermal temperature–pressure profile was assumed. While this is an
oversimplification and can lead to retrieval biases (Rocchetto et al., 2016),
the restrictive wavelength range does not allow for the differentiation of an
isothermal from a more complex profile. The temperature bounds of the
retrieved were set to $\pm$500 K of the planet’s equilibrium temperature while
the planet’s radius was allowed to vary between $\pm$50 % of its literature
value. The planet’s mass was fixed to the value in Tables 7 and 9 (Changeat et
al., 2020c).

Finally, we explored the parameter space using the nested sampling algorithm
Multinest (Feroz et al., 2009; Buchner et al., 2014) with 1000 live points and
an evidence tolerance of 0.5.

###  3.2 Atmospheric Detectability

Tsiaras et al. (2018) introduced the Atmospheric Detectability Index (ADI),
which compares the Bayesian evidence of an atmospheric retrieval to a flat
model. Using this metric, they concluded that 16 of the 30 planets analysed
had detectable atmospheres before searching for trends with different bulk
parameters, finding a correlation with the planet’s radius. Given that we have
taken the planets studied in Tsiaras et al. (2018) and expanded upon their
sample, we also explored the detectability of atmospheres and searched for
links with planet parameters.

We used the Bayesian evidence to determine the preferred atmospheric model,
comparing this to the evidence from the flat model to calculate the
significance of any atmospheric detection. Instead of using the ADI, we
instead transformed the difference in the Bayesian evidence into a sigma
detection and used these values to search for trends with planetary
parameters. However, we note that these systems of identifying atmosphere
detections are analogous, with an ADI of 3 being equivalent to a 3$\sigma$
detection (Tsiaras et al., 2018).

###  3.3 Search For Atmospheric Trends

Large gaseous planets are thought to initially form via solid core accretion
before undergoing runaway gas accretion and, in the case of the planets
studied here, migration is also likely (Mizuno, 1980; Bodenheimer & Pollack,
1986; Ikoma et al., 2000). In the core-accretion model, lower mass planets are
incapable of accreting substantial gaseous envelopes, instead preferentially
accreting higher-metallicity solids (Mordasini et al., 2012; Fortney et al.,
2013). Therefore the metallicity, the ratio of the elements heavier than
helium to all the elements, can act as a key test of this theory and studies
of methane content of the gaseous planets within our own Solar System are in
agreement with the predictions of the core-accretion scenario. Over the last
decade, exoplanet observations have expanded the search for a mass-metallicity
trend to other planetary systems. Previous observational studies with HST have
found some indications of a mass-metallicity trend within exoplanets
atmospheres (e.g. Wakeford et al., 2017b; Welbanks et al., 2019). Furthermore,
by comparing the bulk characteristics of exoplanets to structural evolution
models, there is evidence that a exoplanet mass-metallicity trend is likely
but could differ for that seen in our own solar-system (Thorngren et al.,
2016).

The targets studied here cover a wide mass range, from the ultra-low density
Kepler-51 b (M = 0.0166 MJ) to the brown dwarf KELT-1 b (M = 27.23 MJ). We
utilised both our free chemistry retrievals, and those conducted assuming
equilibrium chemistry, to search for an enrichment trend. The planet
metallicities extracted by the chemical equilibrium retrievals were compared
to the trend found in Thorngren et al. (2016). They found the strongest
correlation was not between the planet’s mass and the planet’s metallicity but
between the mass and the ratio of the planet-to-star metallicity. Hence we,
like them, calculated the host star metallicity from:

$Z_{S}=0.014\times 10^{[Fe/H]},$ (2)

using the Fe/H values given in Tables 6 and 8. We then divided our retrieval
metallicities by these values to ascertain the ratio of the metallicities and
search for a trend against the planet’s mass.

In the free chemistry case, we attempted to constrain a multitude of molecular
species. However, due to the wavelength coverage of HST WFC3 G141, only the
abundance of water can be convincing constrained in each case. Taking the
water abundance from the preferred atmospheric model (i.e. one with or without
optical absorbers) we followed the methodology of Welbanks et al. (2019) to
get the ratio of water to hydrogen with respect to solar values. For each
planet, the expected water-based metallicity was determined by computing the
theoretical abundance at 1e-3 Pa (0.1 Bar) in thermochemical equilibrium
assuming C/O = 0.54 and a metallicity equivalent to the that of the host star
(Fe/H). The expected water to hydrogen ratio was then compared to the
retrieved one to give the relative level of enrichment.

In addition to searching for trends with mass, we also investigated the
dependence of the retrieved abundances of molecules on temperature. For these,
we computed the expected abundance of H2O, CH4, TiO, VO, FeH and H- using
GGchem over a temperature grid of 100-3000 K at pressures between 1e2 to 1e5
Pa (1e-3 to 1 Bar).

###  3.4 Bayesian Hierarchical Modelling

So far, atmospheric retrievals have been limited to a case-by-case basis,
where each observations yield their own atmospheric parameters of interest
(such as molecular abundance in the atmosphere). With 70 observations
available in our study, we would like to seek trends within our samples. The
conventional approach is to fit a trend to a set of error bars, where the mean
and sigma values are those computed from the individual posterior
distributions. The mean and sigma fall short when attempting to capture the
statistics presented by the rich and often non-Gaussian posterior
distribution. Bayesian Hierarchical Modelling (BHM) is a principled way to
estimate the (hyper-)parameter of the trends that may exist within a
population. BHM does this by first treating the posterior distribution from
each observation as a sub-model and together these sub-models help to infer
the hyper-parameters of the global trend across different datasets. The multi-
stage approach accounts for the planet-to-planet variability presented in each
observation and properly propagates the uncertainty from each observation to
the next layer in the hierarchical model (Gelman et al., 2013).

While Bayesian retrievals have been common in the exoplanetary field for
sometime, and are now the standard methodology, BHM has not been so widely
utilised, perhaps partly due to the general lack of sufficient number of
datasets. However, a number of studies have employed it (e.g. Hogg et al.,
2010; Wang et al., 2011; Wolfgang et al., 2016), including works focused on
seeking trends in exoplanet atmospheres (Keating & Cowan, 2022; Lustig-Yaeger
et al., 2022).

When searching for temperature-related trends using the abundances from our
retrievals we compared two models: a linear trend and a flat trend (i.e. a
null hypothesis). We again utilised Multinest for this fitting and used the
Bayesian evidence from these fits to determine which gave the best
representation of the data. We discuss our implementation of BHM in more depth
in Appendix 3.

##  4 Results

For each transmission spectrum analysed, we determined the best fitting models
using the Bayesian evidence of our retrievals. For the free chemistry cases,
four models were compared as well as a flat model. These spectra, and their
best fitting models, are shown in Figure 2. In each case, two or three models
are shown: the flat model, the preferred free chemistry model that does not
include optical absorbers, and, for planets above 1500 K, the preferred free
chemistry model that does include optical absorbers. The preferred overall
model is shown by the solid line while dashed lines show the other models. In
the following sections, we place the results of these retrievals in the
context of the findings of previous studies.

Figure 2: HST/WFC3/G141 datasets utilised in this study. For each planet, the
preferred model is denoted by the solid line while the dotted lines show other
models which provide a poorer fit. Models including optical absorbers (red)
are only shown if they provide a preferable fit to the data than those without
(blue). In each case, the grey line denotes the flat model. The error bar in
the top right corner of each plot highlights the transit depth variation due
to one scale height of atmosphere. Planets have been ordered in terms of their
equilibrium temperature, from coolest (top left) to hottest (bottom right).

###  4.1 Atmospheric Detectability

We find that, of our sample of 70 planets, 37 have strong evidence
($>3\sigma$) of atmospheric modulation. We note that, for several planets
(KELT-1 b, HAT-P-2 b, WASP-18 b) the error bars are too large to detect even a
completely clear atmosphere. Therefore, we conclude that, of those for which
an atmosphere could have been statistically detected, we find evidence for
atmospheric detections on 57% of the population studied here, similar to the
53% from Tsiaras et al. (2018).

To explore the concept further, we computed the expected SNR on a single scale
height of atmospheric signal for each planet, comparing this to the achieved
detection significance. We find that while there is evidently a correlation
between the anticipated SNR and the significance of the detection, for some
planets no detection is made even though the precise of the observations is
high enough to expect one. GJ 1214 b provides the perfect example of this as
it has the highest predicted SNR based on a H/He dominated atmosphere yet
there is not strong evidence for spectral modulation due to an atmosphere
(Kreidberg et al., 2014b)222We note that the spectrum recovered here has
slightly more spectral modulation than seen in (Kreidberg et al., 2014b), as
discussed in Appendix 2..

In Figure 3 we also look to see if planet radius, temperature and surface
gravity have an effect on the chances of detecting an atmosphere. We see that
large ($>$1 RJ), hotter ($>$1000 K) planets generally have a better chance of
a detection, even if the SNR is low. Meanwhile, for cooler ($<$1000 K),
smaller ($<$1 RJ), a non-detection at a high SNR is more prevalent. When
comparing the detection rate for planets with similar temperatures but with
different surface gravities, there is some indication that those with a lower
gravity more regularly have atmospheric detections. However, it is clearly
correlated with the expected SNR which is generally larger for those with a
smaller surface gravity within our sample. The effect of the differing
precision in the data with respect to the atmosphere’s size therefore makes it
difficult to distinguish if this is indeed due to this bulk parameter.

Figure 3: Top: The SNR on the expected spectral modulation due to 1 scale
height of a H/He dominated atmosphere against the significance of the
atmospheric detection from this work. While there is a positive correlation,
in some cases no atmosphere is detected despite very precise observations.
Middle: scatter plot of planet radius against planet temperature where the
colour of the points indicates the significance of the atmosphere detection
and the size shows the SNR on 1 scale height of atmosphere. Non-detections
when detections might be expected happen more often for cooler, smaller
planets while large, hot planets generally have a better chance of an
atmospheric detection, even at low SNRs. Bottom: scatter plot of planet
surface gravity against planet temperature where the colour and size again
represent the detection significance and SNR respectively. No clear trend can
be distinguished given the variance in the precision of the data will affect
the significance of the detection.

Figure 4: Retrieved abundances of H2O, CH4, HCN, NH3, TiO, VO, FeH and e-
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 lower bound of our priors. The upper bound is
shown by the dashed line. The filled regions bounded by dash-dot 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). For the lower four plots, black data points indicate planets for which
the retrieval model with these optical absorbers are preferred while grey
point represent those which the fit is preferable without them. In all cases,
abundances are only plotted if the associated models provided a $>$3 sigma
detection compared to a flat model. The thick coloured line on each plot
indicates the linear trend from the BHM while the thinner colours lines
represent the traces from the fit that were within the 1$\sigma$ errors of the
best-fit model. Only the fit to the abundance of e- gave a Bayesian evidence
which was greater than the null hypothesis.

###  4.2 Search For Trends Between Chemistry and Temperature

We sought to go beyond the work of Tsiaras et al. (2018) by also searching for
trends in the chemistry, not just the atmospheric detectability. The planets
studied in this work vary in equilibrium temperature by over 2000 K and, as
temperature and chemistry are unequivocally intertwined, we searched for
evidence of this within our data. Figure 4 shows the retrieved abundances for
a number of absorbers, each plotted against temperature. Comparing the
findings of our retrievals to chemical equilibrium models with GGchem we
notice a number of things.

Firstly, the retrieved water abundance is almost always above that which is
predicted. Indeed, many of the abundances are in fact constrained by our
priors, with the upper bound placed at a volume mixing ratio of 10%. These
high water abundances contradict the finds of Changeat et al. (2022), where
this molecule was generally found to be sub-solar. Secondly, methane is never
constrained, despite being predicted at abundances that would be detectable
with HST WFC3 at cooler temperatures. An absence of methane despite it being
predicted has also be found by previous works (e.g. Benneke et al., 2019;
Anisman et al., 2020; Carone et al., 2020; Baxter et al., 2021) and clouds,
which are found across the majority of the planet studied here, have been
suggest as a mechanism for methane depletion (Molaverdikhani et al., 2020).
Additionally, we rarely find evidence for HCN and NH3, with two of the three
“detections” of the latter species being questionable due to the large
abundance in the case of K2-24 b and the high equilibrium temperature in the
case of WASP-121 b. We do detect NH3 in the atmosphere of HD 106315 c (Teq
$\sim$ 850 K), a result which has also previously been found by Guilluy et al.
(2021), although they note that the model with NH3 is only preferred to $<$2
sigma to one without this molecule.

For the optical absorbers we considered, there are a number of planets for
which models with these species are preferred, and a couple where there
abundances are constrained in our retrievals. While no planet had a lower 1
sigma abundance limit of TiO greater than 10-9, we see evidence for VO in
WASP-103 b. As in other low-resolution studies of the planet (Skaf et al.,
2020), a large abundance of FeH was found in the atmosphere of WASP-127 b.
However, compared to Skaf et al. (2020), we do not find as high abundances of
FeH for WASP-62 b and WASP-79 b, potentially due to the inclusion of the H-
opacity, as noted for WASP-79 b in Rathcke et al. (2021). For this absorption
we followed the procedure described in Edwards et al. (2020b) and retrieved
the abundance of e-, with the strongest constraints on this species being in
the atmospheres of KELT-7 b, WASP-12 b, WASP-79 b, WASP-103 b and WASP-178 b,
all of which are planets with equilibrium temperatures higher than 1800 K. The
abundances predicted with GGchem for TiO, VO and FeH are relatively low and
potentially below the detection limit of HST WFC3 G141. Hence, any trend in
retrieved abundances is hard to draw out. However, for e-, the predicted
abundance increases strongly after 1500 K and the retrieved abundances for the
hottest planets appear to follow this trend.

In Figure 4 we also show the results of our fittings with BHM. In each case,
the best-fit linear model is shown as well as the traces that were within
1$\sigma$ of this. We computed the significance of these trends by comparing
the Bayesian evidence of this fit to one without a slope (i.e. a model of
constant abundance with temperature). Of all the species, only for e- did the
fitting with a slope provide a preferable fit to the data and, even in this
case, the significance was relatively low (2.28$\sigma$). The emergence of the
H- ion comes from the thermal dissociation of H2 at high temperatures. As H2O
can also thermally dissociate, albeit at higher temperatures than H2, we
compared our retrieved abundances of H2O and e- to explore whether a
correlation can be seen in the data. We plot these in Figure 5 and a general
trend of decreasing water abundance with increasing e- can be seen. The over-
plotted models are from GGchem, showing the expected trend in the data for
atmospheres of 1x, 10x and 100x solar metallicity. These again show that the
water abundance retrieved is generally super-solar.

Figure 5: Comparison of the retrieved abundances of H2O and e-. Black data
points indicate planets for which the retrieval model with these optical
absorbers were preferred to $>$3 sigma compared to the retrieval without
optical absorbers. Grey point represent those which are still best fit with
optical absorbers present, but at a lower significance compared to the models
without them. In all cases, abundances are only plotted if the associated
models provided a $>$3 sigma detection compared to a flat model. The blue, red
and green filled regions indicate the abundances derived from GGchem at
different metallicities at pressure of 1e2 to 1e5 Pa. The dotted lines
indicate the upper bound used as a prior for each molecule. The lower bound in
each case was log10(vmr)=-12.

###  4.3 Constraints on Formation via Elemental Ratios

The ratio of elements within the atmospheres of gaseous planets should provide
an indication of the formation and evolutionary processes that have shaped the
world into what we observe today. In particular, the metallicity and the ratio
of carbon to oxygen have been proposed as key tracers of where and how giant
planets collect gas and solids in evolving protoplanetary disks (e.g. Öberg et
al., 2011; Mordasini et al., 2016; Brewer et al., 2017; Booth et al., 2017;
Madhusudhan et al., 2017; Eistrup et al., 2018; Turrini et al., 2018; Cridland
et al., 2019; Shibata et al., 2020). Hence, in our chemical equilibrium
retrievals, we attempted to constrain both the metallicity and C/O ratio of
the planets.

In Figure 6, we show the retrieved C/O ratio against the retrieved metallicity
as well as the reduced semi-major axis of the planet. We note that the C/O
ratio is generally poorly constrained and thus a conclusive trend cannot be
extracted. Such a results is expected given that the wavelength coverage of
WFC3 G141 only offers very limited sensitivity to carbon bearing species.
While the datasets analysed here offer the possibility of detecting and
constraining CH4 and HCN, which has been proposed as an indicator of high C/O
atmospheres (Venot et al., 2015), determining the presence and abundance of CO
and CO2 is much harder as their features are weak in this band. The study of
KELT-11 b by Changeat et al. (2020b) provides a good example of the complexity
of constraining carbon-bearing species using only data from HST WFC3 G141.

Figure 6: The retrieved carbon to oxygen ratio for planets within our sample
against the retrieved metallicity (top) and planet’s semi-major axis (bottom).
We note that the C/O ratio is poorly constrained in most cases due to the
narrow wavelength coverage offered by HST WFC3 G141. In both plots, the dotted
line highlights the prior range assuming a solar metallicity. The dashed line
indicates the upper bound on the metallicity used for the planet around the
star with the highest metallicity. The dash-dot line is the lower bound for
the planet around the lowest metallicity star.

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.
However, the constraints are not precise enough to distinguish between
different formation scenarios which generally predict values between 0.5 and
0.9 (e.g. Turrini et al., 2018). Hence we can only conclude that HST WFC3 G141
data alone is not enough to accurately determine elemental ratios and thus
confidently distinguish between formation scenarios. Furthermore, we note that
work by Turrini et al. (2021) and Pacetti et al. (2022) suggests other ratios
may be more important. These definitely cannot be constrained with HST WFC3
G141 data alone but may be achievable with data where a wider spectral
coverage has been achieved with a single instrument (e.g. Gardner et al.,
2006; Edwards et al., 2019; Tinetti et al., 2018).

###  4.4 Search For A Mass-Metallicity Trend

Figure 7: Retrieved metallicity from our GGChem runs with the model from
Thorngren et al. (2016) also shown. Top: BHM results when only using
retrievals which give a $>3\sigma$ atmospheric detection. Bottom: BHM results
when using retrievals which give a $>2\sigma$ atmospheric detection. In both
cases, the BHM found a best-fit trend line which had a negative slope.
However, in both cases, the null hypothesis (metallicity is not dependent upon
mass) was preferred.

Figure 8: Ratio of H2O to H with respect to stellar metallicity values for the
planets from our study. The recovered values from Welbanks et al. (2019) are
also shown, as are their best-fit trends. Top: BHM results when only using
retrievals which give a $>3\sigma$ atmospheric detection. Bottom: BHM results
when using retrievals which give a $>2\sigma$ atmospheric detection. In the
former case, the BHM found a best-fit trend line which had a negative slope
while the latter had a positive slope. However, in both cases, the null
hypothesis (metallicity is not dependant upon mass) was preferred.
Additionally, either sign of slope, or indeed no slope, is also within the
1$\sigma$ errors of each fit.

Several previous studies of exoplanetary atmospheres have sought to find
trends between the mass of the planet and the metallicity of its atmosphere
(e.g. Wakeford et al., 2017b; Welbanks et al., 2019). Here we explore this
across our population in two ways, firstly using the GGchem chemical
equilibrium retrievals where the metallicity is a fitted parameter and,
secondly, using the methods employed in Welbanks et al. (2019). In Figure 7,
we compare our results to those of Thorngren et al. (2016), where the plotted
parameter is the ratio of the planet’s metallicity to the star’s. We find that
our retrieved planet metallicities lead to ratios which are generally far
above those found by Thorngren et al. (2016). While the best-fit model when
fitting a linear trend led to a negative slope, the BHM analysis does not find
strong evidence for a mass-metallicity trend as the null-hypothesis (i.e. a
model of constant metallicity with mass) is preferred when fitting a trend to
the retrieved metallicities. We give the preferred models, and associated
Bayesian evidence, in Table 4.

m | c | s | ln(E)
---|---|---|---
-0.71 ${}^{+0.59}_{-0.6}$ | 3.0 ${}^{+0.44}_{-0.41}$ | -0.14 ${}^{+0.13}_{-0.12}$ | -154.51
- | 2.58 ${}^{+0.34}_{-0.34}$ | -0.12 ${}^{+0.13}_{-0.11}$ | -152.86
-0.09 ${}^{+0.18}_{-0.18}$ | 2.57 ${}^{+0.32}_{-0.34}$ | -0.14 ${}^{+0.11}_{-0.1}$ | -204.46
- | 2.48 ${}^{+0.3}_{-0.29}$ | -0.17 ${}^{+0.13}_{-0.07}$ | -200.9
Table 4: Results from our BHM fittings in search of a mass-metallicity trend from our GGChem retrievals. Top: using retrievals where the GGChem model provided a $>3\sigma$ detection of an atmosphere. Bottom: using retrievals where the GGChem model provided a $>2\sigma$ detection of an atmosphere. Neither linear model, fitted in log-log space, is preferred to the null hypothesis (i.e. no trend between mass and metallicity). m | c | s | ln(E)
---|---|---|---
-0.13 ${}^{+0.48}_{-0.43}$ | 1.03 ${}^{+0.35}_{-0.34}$ | -0.31 ${}^{+0.3}_{-0.23}$ | -165.1
- | 1.11 ${}^{+0.28}_{-0.26}$ | -0.22 ${}^{+0.2}_{-0.13}$ | -161.56
0.12 ${}^{+0.41}_{-0.39}$ | 0.93 ${}^{+0.33}_{-0.36}$ | -0.14 +0.15 -0.12 | -232.99
- | 0.9 ${}^{+0.28}_{-0.29}$ | -0.19 ${}^{+0.19}_{-0.15}$ | -229.08
Table 5: Same as Table 4 except it is for the mass-metallicity fit based upon
the water-to-hydrogen ratio.

Meanwhile, in Figure 8 we show the metallicity derived from the H2O abundance,
over-plotting the data from Welbanks et al. (2019) as well as their best-fit
to the data for comparison. To maintain consistency with their study, we also
plot the results of retrievals where the detection significance is 2-3 sigma.
However, we notice their trend is evidently not reflected in our data. All
planets studied in Welbanks et al. (2019) are also included in our population
and one can also notice differences in masses, depending upon which reference
studies were used, as well as in the retrieved water to hydrogen ratios. The
latter of these could be due to a number of factors but the major cause is
likely to be a difference in the datasets used. Welbanks et al. (2019) used
data from a variety of instruments, while we used only HST WFC3 G141. Each
instrument gives access to differing absorption features and thus provides the
observer with different sensitivities. Observing the same planet but with
different instruments could provide contrasting findings on its composition.
Therefore, the same is true when observing a selection of planets with
disparate datasets and so the trend they see may be caused by these differing
sensitives to given molecules.

On the other hand, the lack of an obvious trend derived here could well imply
biases in our retrievals, with the high water abundances derived, and the
large planet-to-star metallicity ratios, potentially providing evidence for
this. Alternatively, we could conclude that HST WFC3 alone is simply not
sensitive enough to be able to accurately constrain atmospheric metallicities,
even through the form of the H2O abundance, as the uncertainty on this
parameter is generally very high. Our BHM analysis found that, as with the
GGChem metallicites, the null hypothesis is preferred over a mass-metallicity
trend, with the results given in Table 5. Hence, we find no evidence for a
mass-metallicity trend within our datasets.

###  4.5 Comparison of Free Chemistry and Chemical Equilibrium Retrievals

To assess which models may be best for fitting the population as a whole, we
compared the Bayesian evidence of our free chemistry and chemical equilibrium
retrievals. The latter has fewer free parameters and thus is penalised less
while the former is more agile as the relative abundances of molecules is
completely inhibited. By comparing the evidence for both, we find that both
provide fits of a similar quality for lower temperatures but, for planets
above 1500 K, the free chemistry model often provides a statistically
preferable fit to the data as shown in Figure 9. Such a finding could be
suggestive of disequilibrium chemistry, a claim which has also been made in
previous studies (e.g. Baxter et al., 2021; Keating & Cowan, 2022; Roudier et
al., 2021). However, this finding is in opposition to the noted dearth of
methane detected in our free chemical retrievals. Given that equilibrium
models predict significant amounts of methane at these lower temperatures, it
is strange to find they fit the data as well as models which don’t infer the
presence of this molecule. It also contrasts the results from Baxter et al.
(2021) whose analysis of Spitzer data suggested that cooler planets were not
in chemical equilibrium.

Figure 9: Comparison of the Bayesian evidence for retrievals with free
chemistry and those using the GGChem chemical equilibrium scheme.

###  4.6 Amplitude of Absorption Features

The key spectral feature within the HST WFC3 G141 band is the 1.4 $\mu$m water
feature and, instead of performing 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 (e.g.
Stevenson, 2016; Fu et al., 2017; Wakeford et al., 2019; Dymont et al., 2021).
We fitted the feature using the process described in Appendix 3.

The 1.4 $\mu$m feature size was utilised by Crossfield & Kreidberg (2017) to
imply a number of trends within the atmospheres of sub-Neptunes based off
spectra of six planets. Using the most massive planet from their sample,
HAT-P-11 b (25.7M⊕), as the upper boundary in terms of mass, and the largest
of their sample, HAT-P-26 b (6.3 R⊕), as the radii limit, we have extended
this to sixteen gas dwarf planets. The two key correlations found by
Crossfield & Kreidberg (2017) were with the planet’s H/He mass fraction and
it’s equilibrium temperature. One interpretation of the trend seen with the
former would be that planets with a low H/He mass fraction would have a high
mean molecular weight, leading to a smaller than predicted scale height which
was calculated assuming $\mu$ = 2.3. Meanwhile, a reduction in the size of the
H2O amplitude with decreasing temperature was postulated to be due to hazes
for cooler ($<$850 K) planets.

We updated these plots but find these correlations no longer hold, as shown in
Figure 10. We now find a decreasing feature size with increasing H/He mass
fraction, a result which is counter intuitive. Furthermore, we find that, at
temperatures cooler than 550 K, the feature size increase with decreasing
temperature, a result that concurs with work done by Kawashima et al. (2019).
We highlight the planets that were in the Crossfield & Kreidberg (2017) sample
and suggest the trends were seen due to a selection bias. For these trends we
find that the are driven significantly by GJ 1214 b as the feature size is
extremely well constrained but also very close to zero.

We also attempted to draw out other trends looking across two parameters
simultaneously, but found no significant correlations. From this we imply that
either a) no simplistic correlations exist or b) the sample is not large
enough, or has not been selected carefully enough, to allow for any trends to
be teased out. Such a finding highlights the importance of a structured,
hypothesis-based selection of planets when attempting population studies and
the need for dedicated exoplanet atmospheric survey missions (e.g. Twinkle,
Ariel).

Figure 10: Comparison of the 1.4 $\mu$m feature height to different bulk
parameters for the Sub-Neptunes within our study. Red data points indicated
those studied by Crossfield & Kreidberg (2017) with their trends also shown in
red. Our trends are shown in black and are linear fits, except for with
temperature where a second-order polynomial fit was used.

We extended the analysis of the feature size to all planets in our study and
Figure 11 displays the recovered 1.4 $\mu$m amplitude against temperature.
Previous studies have suggested that the surface gravity of a planet, along
with its temperature, affect the cloud coverage which in term would affect the
WFC3 feature size (e.g. Stevenson, 2016; Bruno et al., 2018). Hence, we divide
the population up by its surface gravity to search for such a trend. While
some differences in feature size are seen in planets with similar
temperatures, the surface gravity doesn’t appear to be driving this in all
cases: in some, the feature size is identical while, where there are
differences, these are not universal. In general, the distribution of feature
size is similar to those of previous studies (e.g. Fu et al., 2017), with an
increase at around 1200 K. In Figure 11, we also plot the retrieved cloud
pressure. Here we see that, in the same temperature range that the feature
size increases, the cloud pressure retrieved is deeper in the atmosphere.
Therefore, the knowledge gained by performing the spectral feature analysis is
also readily available from retrieval analyses.

Figure 11: Size of 1.4$\mu$m feature against planet temperature and sub-
divided by the planet’s surface gravity. At lower temperatures, the surface
gravity may have an impact on the cloudiness of the planet, and thus the
feature size, but, at higher temperatures, there appears to be no obvious
correlation. Grey regions highlight the expected feature size for solar
metallicity atmospheres for a given cloud pressure and a surface gravity
between 10-20m/s2. Across the entire population, the mean 1.4 $\mu$m feature
size is 0.81 scale heights in the HST/WFC3/G141 while the median was 1.37. The
feature size can be directly correlated to the retrieved cloud pressure from
our retrievals (bottom) and we note that the 1.4 $\mu$m feature size is not a
good predictor of the feature size across wider wavelength ranges due to the
stronger absorption seen at longer wavelengths. The priors for the cloud
pressure in our retrievals is shown by the dotted lines.

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 (weighted mean) feature size of 0.81 scale heights but we
noted that the median value is much higher (1.37 scale heights). We noted that
such a low value for the weighted mean is driven by the feature size of GJ
1214 b (0.12$\pm$0.04) and if one removes this from the weighted mean
calculation, an average value of 1.21 scale heights is obtained. All these
values are comparable value to previous studies: 1.4 H (Fu et al., 2017) and
0.89 H (Wakeford et al., 2019). As demonstrated in Figure 11, the amplitude of
this feature is far below what would be expect from a clear, solar metallicity
atmosphere. There would also appear to be some correlation with temperature,
with hotter planets (T$>$1500 K) generally having larger feature sizes than
cooler ones (T$<$700 K). Additionally, we see a trend at around 1200 K where
the feature size increases before decreasing again. A similar feature was
found by Fu et al. (2017) and our retrievals find these planets have a lower
cloud top pressure (see Figure 11).

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 3.68 and 2.59 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 3.74 scale heights. Finally, the expected amplitude across the
spectral coverage of Ariel (0.5-7.8 $\mu$m, Tinetti et al. (2018)) is 4.60
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: this can only be achieved by running a Bayesian retrieval
which models the passage of starlight through the atmospheric layers to
explain the spectrum via base atmospheric proprieties such as temperature,
composition and clouds.

Hence, for comparison, we also took our preferred spectral retrieval models
and computed the amplitude of features seen across these wavelength bands. For
the spectral ranges 0.6-2.8 $\mu$m, 0.5-5.3 $\mu$m and 0.5-7.8 $\mu$m, we
found a median feature size of 3.32, 3.66 and 4.38 scale heights respectively.
These are roughly 1 scale height larger than the feature amplitude fit
suggests. However, we note that these predictions may also be biased as some
species, such as CO2, are not constrained by our Hubble WFC3 observations.
Therefore, the best-fit value of these is essentially an average of the prior
range. When considering the spectrum across these longer wavelengths, this may
induce features which are not present if the molecules actually exist at
values lower than the value “retrieved”.

In any case, both models point towards features several scale heights in
amplitude being observable with future facilities, largely due to the strong
absorption that occurs at longer wavelengths. As data is collected with these
facilities, our understanding of the cloudiness of extrasolar planets will be
enhanced and therefore allow us to more confidently predict the data quality.
Nevertheless, we will never truly know until we look.

##  5 Discussion and Conclusions

The Hubble Space Telescope has been at the forefront of exoplanet atmospheric
characterisation over the last two decades. While many different instruments
on this facility have been used, WFC3 has perhaps been the mostly widely
utilised due to its sensitivity to water. In this work we have presented a
population study of atmospheres, each studied with the WFC3 G141 grism as the
planet transits its host star.

Of the 70 planets studied, we found strong evidence ($>$3 sigma) for
atmospheric features on 37 of them, with some evidence (2-3 sigma) for
spectral modulation on an additional 14 planets. We note that for several
planets (e.g. WASP-18 b), the derived spectrum has error bars that are several
scale heights in size, meaning no atmospheric constraints could be expected.
As noted by other studies, clouds are ever present and are muting the size of
the features seen. While clouds should certainly not be discounted from
observational planning, future instruments will probe longer wavelengths,
where the absorption of molecules such as H2O and CO2 are stronger, and so may
not be as affected, particularly given that the signal-to-noise ratio should
be higher for these datasets.

In this work we have largely struggled to draw out trends in the population,
despite employing BHM which exploits the full richness of the posterior
distributions from our Bayesian retrievals. Nevertheless, these null results
are not without value as they can inform us of how to approach atmospheric
studies in the future. Upon viewing our results, it may be concluded that HST
WFC3 G141 data alone is insufficient to draw out detailed trends from a
population of objects. To explore this, we created simulated datasets of the
planets for which our retrievals suggested there was evidence for spectral
modulation due to an atmosphere. For each planet, we utilised the error bars,
the retrieved cloud pressure, and retrieved 10 bar radius from the real
observations to generated fake datasets, inputting the mass-metallicity trend
suggested by Thorngren et al. (2016) and performing retrievals to see if our
simulated data would recover the trend. We added Gaussian scatter to the
datasets and the retrieved planet-to-star metallicity ratios are shown in
Figure 12. We find that our simulated data is capable of recovering the input
trend which suggests that, in our analysis of the real data, we do not recover
a trend because i) one does not exist across the whole population, ii) there
are biases in our retrieval analysis which are obscuring the true trend or
iii) both.

Figure 12: Retrieved metallicity when simulated data is created using the
model from Thorngren et al. (2016). From our fake datasets, which utilised the
error bars from the real observations as well as the retrieved 10 bar radius
and cloud pressure, we can recover the input trend, albeit it a marginal
detection due to the size of the uncertainties on the planet’s metallicity.
The finding contrasts the real data, where no obvious trend was uncovered.

In our analysis, on both the real data and the simulated, the constraints
placed on the atmospheric chemistry are poor. Such a result is not overly
surprising; all those who have worked with HST WFC3 G141 understand that its
limited wavelength coverage means the conclusions that can be drawn from the
analysis of it are similarly restricted. The inability to place tight
constraints on the planet’s metallicity or C/O ratio are a by-product of a
dataset which is only truly sensitive to a single feature of a single
molecule: the 1.4 $\mu$m water feature. As such, studies in the literature
have often combined datasets from multiple instruments to extend the
wavelength coverage and unlock additional spectral features. However, such an
approach has serious implications for the analysis, particularly when
attempting to draw trends from a population.

Firstly, the instruments experience significant systematics. While the
correction of these with different pipelines usually leads to uniform spectral
features, offsets in the transit depth are common (e.g. Guo et al., 2020;
Luque et al., 2020; Murgas et al., 2020; Yip et al., 2021; McGruder et al.,
2022). When analysing data from a single instrument, this has little effect as
the retrieved planetary radius is generally just slightly smaller or larger.
However, which combining instruments, these offsets can cause wild differences
in the retrieved atmospheric parameters (Yip et al., 2020). While an offset
can be fitted for in the retrieval, without spectral overlap between
instruments one cannot be sure of the compatibility of datasets. Currently,
only HST WFC3 G102 offers spectral overlap with HST WFC3 G141 but this filter
has rarely been used. Combining both the WFC3 IR grisms, with data from HST
STIS, can be done with some confidence due to this spectral overlap (e.g.
Wakeford et al., 2017b), although the data is not taken in the same epoch so
temporal changes may be an issue (e.g. Saba et al., 2022).

Yet, even if one can confidently combine data from multiple instruments,
another factor for consideration emerges. If one compares two planets having
utilised different instruments in each case, one cannot be sure if any
differences seen are because the planets are distinct or if the instrument’s
simply offer discrete views of these atmospheres. An example of this is
demonstrated in Pinhas et al. (2019) for HD 209458 b. If HST WFC3 G141 data is
considered alone, they retrieved water abundance of log10(H2O) =
-3.26${}^{+0.75}_{-0.75}$ which is comparable to the value obtained here of
-3.10${}^{+0.95}_{-1.17}$. With the addition of STIS data, the value retrieved
was -4.66${}^{+0.39}_{-0.30}$ which is not compatible to within 1$\sigma$ and
takes the water abundance of HD 209458 b from being solar to distinctly sub-
solar. The debate here is not about the true value; the STIS data may bring
you closer to it by avoid some degeneracies, but about the change the new data
brings about in the result. Consider another planets, for example HAT-P-38 b
or TOI-674 b, for which we retrieved a similar water abundances to HD 209458 b
(log10(H2O) = -3.07${}^{+1.12}_{-2.27}$ and -3.12${}^{+0.78}_{-1.04}$,
respectively). Comparing the retrieved abundances from the WFC3 G141 data
alone would lead us to conclude the atmospheres were similarly enriched.
Comparing the HD 209458 b abundance retrieved using the STIS data as well
would lead us to believe they had differing water abundances. As neither
HAT-P-38 b nor TOI-674 b have STIS data at the time of writing, it is
impossible to know if the retrieved water abundances would also change if such
data was also added to our retrievals. While analysing HST WFC3 G141 data
alone has its limitations, such as potentially introducing biases into the
retrievals, but these limitations are at least uniform across the population.
Therefore, when searching for trends the recovered correlations may be biased
but at least the relative trend between planets would be consistent. However,
when utilising differing instruments between planets one cannot tell if the
changes seen are due to the instruments used or due to the atmospheres
actually differing in composition. If one looks at which planets have been
studied by both STIS and WFC3, this further enforces this point: higher mass
planets have more often have both datasets whereas lower mass planets have
generally only been studied with WFC3 G141. Therefore, if one finds evidence
for a mass-metallicity trend, which is based on the H2O abundance in the
atmosphere, with inhomogeneous datasets, one cannot be sure the trend is not
caused by the addition of these datasets for the higher mass planets. As such,
if one attempts a population study where the instruments each member is
studied with varies, one must account for this bias when inferring the
presence, or lack, of trends. For example, conducting retrievals on both
datasets (e.g. with/without STIS or Spitzer) and comparing the results (e.g.
Pinhas et al., 2019; Pluriel et al., 2020; Yip et al., 2021).

The ability to seek out these correlations is further impaired by the choice
of targets, with those studied in this work essentially being a random
collection of worlds as they have been observed via a variety of proposals,
each with different aims. As such, drawing comparison becomes difficult
because, in all likelihood, more than one parameter will be affecting the
chemistry. Therefore, one may be tempted to split the targets into sub-groups
in an attempt to uncover trends but doing so after the observation is required
is risky; with the dataset available, if one tries hard enough “trends” can
uncovered due to the large uncertainties in the derived parameters and the
sparsity of the data once more than a single parameter is used to divide the
population. Such an effect can be seen in the relation suggested between
temperature and atmospheric feature sized previously proposed for sub-
Neptunes. In this case, and in all other attempts to draw conclusions, the
fact that the precision of the data with respect to the expected atmospheric
signal (i.e. the SNR) also differs across the population, makes it yet harder
to definitively draw comparisons and to imply the atmospheric conditions or
conclude on why an atmospheric detection has not occurred.

In addition to free chemistry retrievals, we fitted chemical equilibrium
models to our datasets in an attempt to draw out trends in metallicity and the
C/O ratio. However, as noted in the methodology, these retrievals are
essentially fitting two free parameters (metallicity and C/O ratio) to a
single observable (the H2O abundance). As such, the retrieved values are not
necessarily reliable. Taking again the example of HD 209458 b and HAT-P-38 b,
for which we recovered an almost identical water abundances in the free
chemistry experience, we can see the issue clearly. While we recovered a
metallicity of log10(ZP) = -0.04${}^{+0.83}_{-0.62}$ for HD 209458 b, the
value for HAT-P-38 b, 1.59${}^{+0.25}_{-0.65}$, is different to greater than
1$\sigma$ (despite the large uncertainties) as the model preferred a higher
C/O ratio for this planet. Many previous studies have fitted for these without
additional data, or with optical data which doesn’t add an additional
molecular observable, but our results suggest these findings should be taken
cautiously. Spitzer IRAC data has often been added to HST WFC3 G141 to help
further constrain the C/O ratio by given sensitivity to carbon-bearing species
(e.g. CH4, CO, CO2) but these studies are then exposed to the potential offset
risks that we have discussed previously.

Hence, our current ability to extract population-level trends in exoplanet
atmospheres are limited by a number of factors. In short, to truly perform
population studies of exoplanetary atmospheres, one must achieve a wide
spectral coverage with a single instrument and ensure that the planets are
selected in a robust manner. JWST (Gardner et al., 2006) will provide better
opportunities for this than Hubble, particularly on the spectral coverage
front, although for brighter targets multiple instruments will still need to
be combined to get the wavelength coverage necessary to accurately constrain
both refractory elements and carbon-bearing species. However, while certain
JWST proposals are designed as miniature population studies, an organised,
well-structured survey of a hundred or more worlds is unlikely to occur due to
the time required for such a survey and the proposal-based nature of time
allocation. Therefore, it is likely that the population of planets studied
will be somewhat random, with the added complexity of different instruments
being used and so some of the hurdles discussed here will still be relevant.
Additionally, the SNR achieved will vary and so comparative studies will have
to be careful when drawing conclusions, even if the same instruments are used.

To overcome these hurdles, one requires missions with dedicated exoplanet
surveys which will allow researchers to pose and, hopefully, answer specific
questions on the nature of exo-atmospheres. By allowing a large population of
targets to be selected with these questions in mind, Twinkle and Ariel will be
better placed to provide demographical insights into the atmospheres of
exoplanets, revolutionising our understanding of them in the process (e.g.
Edwards et al., 2019; Changeat et al., 2020a; Tinetti et al., 2021; Edwards &
Tinetti, 2022; Stotesbury et al., 2022). However, these missions will of
course have their own limitations in terms of data quality. For instance,
Ariel will only provide photometric data at visible wavelengths and so may
struggle to disentangle the spectral features of optical absorbers.
Furthermore, these surveys will recoup a higher science yield if they are
constructed upon robust prior knowledge instead of undertaking a blind search
for trends.

Therefore, we must strive to utilise each facility in ways which complement
their respective capabilities. It is undeniable that JWST, and the continued
use of Hubble and other facilities, will provide critical insights into the
nature of a diverse set of worlds, with JWST in particular facilitating
extraordinary sensitivity and thus offering the chance to probe for extremely
small signals (e.g. secondary atmospheres). The knowledge gained must then be
leveraged to inform us of how to use these dedicated surveys to best
understand the population at large. By striving for these meticulous chemical
surveys we will then truly begin to understand the demographics of exoplanet
atmospheres.

## Acknowledgements

BE is a Laureate of the Paris Region fellowship programme which is supported
by the Ile-de-France Region and has received funding under the Horizon 2020
innovation framework programme and the Marie Sklodowska-Curie grant agreement
no. 945298. QC is funded by the European Space Agency under the 2022 ESA
Research Fellowship Program. NS acknowledges support from the PSL Iris-OCAV
project, and from NASA (Grant #80NSSC19K0336). OV acknowledges funding from
the ANR project ‘EXACT’ (ANR-21-CE49-0008-01), from the Centre National
d’Études Spatiales (CNES), and from the CNRS/INSU Programme National de
Planétologie (PNP). This project has also received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (grant agreement No 758892, ExoAI) and from the Science
and Technology Funding Council (STFC) grant ST/S002634/1 and ST/T001836/1 and
from the UK Space Agency grant ST/W00254X/1.

We thank the referee of this manuscript for taking the time to read our work
and provide feedback. Their constructive comments guided the direction of the
paper, thereby improving the quality of the final results.

Computing: We acknowledge the availability and support from the High
Performance Computing platforms (HPC) from the Simons Foundation (Flatiron),
DIRAC and OzSTAR, which provided the computing resources necessary to perform
this work. This work utilised the Cambridge Service for Data Driven Discovery
(CSD3), part of which is operated by the University of Cambridge Research
Computing on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). The
DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital
grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1.
DiRAC is part of the National e-Infrastructure. Additionally, this work
utilised the OzSTAR national facility at Swinburne University of Technology.
The OzSTAR program receives funding in part from the Astronomy National
Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by
the Australian Government.

Software: Iraclis (Tsiaras et al., 2016b), TauREx3 (Al-Refaie et al., 2021),
ExoTETHyS (Morello et al., 2020), PyLightcurve (Tsiaras et al., 2016a),
Astropy (Astropy Collaboration et al., 2018), h5py (Collette, 2013), emcee
(Foreman-Mackey et al., 2013), Matplotlib (Hunter, 2007), Multinest (Feroz et
al., 2009; Buchner et al., 2014), Pandas (McKinney, 2011), Numpy (Oliphant,
2006), SciPy (Virtanen et al., 2020), corner (Foreman-Mackey, 2016).

Data: This work is based upon publicly-available observations taken with the
NASA/ESA Hubble Space Telescope obtained from the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5–26555. These were obtained from
the Hubble Archive which is part of the Mikulski Archive for Space Telescopes.
We are thankful to those who operate the Hubble Space Telescope and the
corresponding archive, the public nature of which increases scientific
productivity and accessibility (Peek et al., 2019).

For each observation, the associated proposal number and principal
investigator are given in Tables 1, 2 and 3. Where a NASA ADS entry could be
found for the proposal, they are given here: 11622 (Knutson, 2009), 12181
(Deming, 2010), 12449 (Deming, 2011), 12473 (Sing, 2011), 12482 (Desert,
2011), 12881 (McCullough, 2012), 12956 (Huitson, 2012), 13021 (Bean, 2012),
13431 (Huitson, 2013), 13467 (Bean, 2013), 13501 (Knutson, 2012), 13665
(Benneke et al., 2015), 14050 (Kreidberg et al., 2014a), 14218 (Berta-Thompson
et al., 2015), 14767 (Sing et al., 2016b), 14455 (Petigura et al., 2015),
14468 (Evans, 2015), 14619 (Spake et al., 2016), 14642 (Stevenson et al.,
2016a), 14664 (Beatty et al., 2016), 14682 (Benneke et al., 2016b), 14915
(Kreidberg et al., 2017), 14918 (Wakeford et al., 2017a), 15134 (Evans, 2017),
15138 (Jontof-Hutter, 2017), 15255 (Colon, 2017), 15301 (Carone, 2017), 15333
(Crossfield, 2017), 15698 (Beatty et al., 2019), 16083 (Todorov et al., 2020),
16194 (Desert et al., 2020), 16267 (Dressing et al., 2020), 16450 (Lothringer
et al., 2020), 16457 (Edwards et al., 2020a), 16462 (Panwar et al., 2020).

Planet Discovery Papers: The characterisation of exoplanetary atmospheres
cannot occur without first knowing of the planet’s existence. We are therefore
grateful to all those who have contributed to planet discovery efforts. Thus,
the works announcing the discovery of all planets studied here are now given:

CoRoT-1 b (Barge et al., 2008), GJ 436 b (Butler et al., 2004; Gillon et al.,
2007), GJ 1214 b (Charbonneau et al., 2009), GJ 3470 b (Bonfils et al., 2012),
HAT-P-1 b (Bakos et al., 2007a), HAT-P-2 b (Bakos et al., 2007b), HAT-P-3 b
(Torres et al., 2007), HAT-P-7 b (Pál et al., 2008), HAT-P-11 b (Bakos et al.,
2010), HAT-P-12 b (Hartman et al., 2009), HAT-P-17 b (Howard et al., 2012),
HAT-P-18 b (Hartman et al., 2011a), HAT-P-26 b (Hartman et al., 2011b),
HAT-P-32 b (Hartman et al., 2011c), HAT-P-38 b (Sato et al., 2012), HAT-P-41 b
(Hartman et al., 2012), HD 3167 c (Vanderburg et al., 2016a), HD 106315 c
(Rodriguez et al., 2017; Crossfield et al., 2017), HD 149026 b (Sato et al.,
2005), HD 189733 b (Bouchy et al., 2005), HD 209458 b (Charbonneau et al.,
2000; Henry et al., 2000), HD 219666 b (Esposito et al., 2019), HD 97658 b
(Howard et al., 2011), HIP 41378 b (Vanderburg et al., 2016b), HIP 41378 f
(Vanderburg et al., 2016b), K2-18 b (Montet et al., 2015; Crossfield et al.,
2016), K2-24 b (Petigura et al., 2016; Sinukoff et al., 2016), KELT-1 b
(Siverd et al., 2012), KELT-7 b (Bieryla et al., 2015), KELT-11 b (Pepper et
al., 2017), Kepler-9 b (Holman et al., 2010), Kepler-9 c (Holman et al.,
2010), Kepler-51 b (Steffen et al., 2013; Masuda, 2014), Kepler-51 d (Masuda,
2014), Kepler-79 d (Jontof-Hutter et al., 2014), LTT 9779 b (Jenkins et al.,
2020), TOI-270 c (Günther et al., 2019), TOI-270 d (Günther et al., 2019),
TOI-674 b (Murgas et al., 2021), TrES-2 b (O’Donovan et al., 2006), TrES-4 b
(Mandushev et al., 2007), V1298 Tau b, (David et al., 2019b) V1298 Tau c,
(David et al., 2019a) WASP-6 b (Gillon et al., 2009), WASP-12 b (Hebb et al.,
2009), WASP-17 b (Anderson et al., 2010a), WASP-18 b (Hellier et al., 2009),
WASP-19 b (Hellier et al., 2011a), WASP-29 b (Hellier et al., 2010), WASP-31 b
(Anderson et al., 2011), WASP-39 b (Faedi et al., 2011), WASP-43 b (Hellier et
al., 2011b), WASP-52 b (Hébrard et al., 2013), WASP-62 b (Hellier et al.,
2012), WASP-63 b (Hellier et al., 2012), WASP-67 b (Hellier et al., 2012),
WASP-69 b (Anderson et al., 2014), WASP-74 b (Hellier et al., 2015), WASP-76 b
(West et al., 2016), WASP-79 b (Smalley et al., 2012), WASP-80 b (Triaud et
al., 2013), WASP-96 b (Hellier et al., 2014), WASP-101 b (Hellier et al.,
2014), WASP-103 b (Gillon et al., 2014), WASP-107 b (Anderson et al., 2017),
WASP-117 b (Lendl et al., 2014), WASP-121 b (Delrez et al., 2016), WASP-127 b
(Lam et al., 2017), WASP-178 b (Hellier et al., 2019; Rodríguez Martínez et
al., 2020), XO-1 b (McCullough et al., 2006).

## Appendix 1: Light curve fitting with Iraclis

We carried out the analysis of the transit data using Iraclis, our highly-
specialised software for processing WFC3 spatially scanned spectroscopic
images (Tsiaras et al., 2016b, c, 2018) which has been used in a number of
studies (e.g. Libby-Roberts et al., 2021; Brande et al., 2022; Garcia et al.,
2022). The reduction process included the following steps: zero-read
subtraction, reference-pixels correction, non-linearity correction, dark
current subtraction, gain conversion, sky background subtraction, calibration,
flat-field correction and bad-pixels/cosmic-rays correction. Then we extracted
the white (1.088-1.68 $\mu$m) and the spectral light curves from the reduced
images, taking into account the geometric distortions caused by the tilted
detector of the WFC3 infrared channel.

We fitted the light curves using our transit model package PyLightcurve
(Tsiaras et al., 2016a) with the transit parameters from Table 9. The limb-
darkening coefficients were calculated using ExoTETHyS (Morello et al., 2020)
and based on the PHOENIX 2018 models from Allard et al. (2012). The stellar
parameters are also given in Table 8.

During our fitting of the white light curve, the planet-to-star radius ratio
and the mid-transit time were the only free parameters, along with a model for
the systematics (Kreidberg et al., 2014b; Tsiaras et al., 2016b). It is common
for WFC3 exoplanet observations to be affected by two kinds of time-dependent
systematics: the long-term and short-term ‘ramps’. The first affects each HST
visit and has a linear behaviour, while the second affects each HST orbit and
has an exponential behaviour. The formula we used for the white light curve
systematics (Rw) was the following:

Table 6: Stellar parameters for observations acquired from the literature. For consistency, these match those used in the original studies. Star | Fe/H | Temperature [K] | log(g) | Radius [R⊙] | Mass [M⊙] | Reference
---|---|---|---|---|---|---
GJ 436 | 0.02 | 3416 | 4.84 | 0.455 | 0.47 | Lanotte et al. (2014)
GJ 3470 | 0.17 | 3652 | 4.78 | 0.48 | 0.51 | Biddle et al. (2014)
HAT-P-1 | 0.13 | 5975 | 4.45 | 1.15 | 1.12 | Bakos et al. (2007a)
HAT-P-3 | 0.27 | 5185 | 4.56 | 0.833 | 0.936 | Torres et al. (2008)
HAT-P-11 | 0.31 | 4780 | 4.59 | 0.75 | 0.81 | Bakos et al. (2010)
HAT-P-12 | -0.29 | 4650 | 4.61 | 0.701 | 0.733 | Hartman et al. (2009)
HAT-P-17 | 0.00 | 5246 | 4.52 | 0.838 | 0.857 | Howard et al. (2012)
HAT-P-18 | 0.1 | 4870 | 4.57 | 0.749 | 0.77 | Esposito et al. (2014)
HAT-P-26 | -0.04 | 5079 | 4.56 | 0.788 | 0.816 | Hartman et al. (2011b)
HAT-P-32 | -0.04 | 6207 | 4.33 | 1.219 | 1.16 | Hartman et al. (2011c)
HAT-P-38 | 0.06 | 5330 | 4.45 | 0.923 | 0.886 | Sato et al. (2012)
HAT-P-41 | 0.21 | 6390 | 4.14 | 1.683 | 1.683 | Hartman et al. (2012)
HD 3167 | 0.03 | 5286 | 4.53 | 0.835 | 0.877 | Gandolfi et al. (2017)
HD 106315 | -0.276 | 6256 | 4.24 | 1.31 | 1.079 | Guilluy et al. (2021)
HD 149026 | 0.36 | 6160 | 4.28 | 1.368 | 1.294 | Torres et al. (2008)
HD 189733 | -0.03 | 5040 | 4.59 | 0.756 | 0.806 | Torres et al. (2008)
HD 209458 | 0.00 | 6065 | 4.36 | 1.155 | 0.806 | Torres et al. (2008)
KELT-7 | 0.139 | 6789 | 4.15 | 1.732 | 1.535 | Bieryla et al. (2015)
KELT-11 | 0.17 | 5375 | 3.70 | 2.69 | 1.44 | Beatty et al. (2017b)
K2-18 | 0.123 | 3457 | 4.77 | 0.411 | 0.359 | Benneke et al. (2017)
WASP-12 | 0.33 | 6360 | 4.16 | 1.657 | 1.434 |  Collins et al. (2017))
WASP-17 | -0.25 | 6550 | 4.149 | 1.583 | 1.286 | Southworth et al. (2012)
WASP-29 | 0.11 | 4800 | 4.54 | 0.808 | 0.825 | Hellier et al. (2010)
WASP-31 | -0.2 | 6302 | 4.31 | 1.252 | 1.163 | Anderson et al. (2011)
WASP-39 | -0.12 | 5400 | 4.50 | 0.895 | 0.93 | Faedi et al. (2011)
WASP-43 | -0.05 | 4400 | 4.65 | 0.67 | 0.58 | Hellier et al. (2011b)
WASP-52 | 0.03 | 5000 | 4.58 | 0.79 | 0.87 | Hébrard et al. (2013)
WASP-62 | 0.04 | 6230 | 4.45 | 1.29 | 1.28 | Brown et al. (2017)
WASP-63 | 0.08 | 5570 | 4.01 | 1.88 | 1.32 | Hellier et al. (2012)
WASP-67 | -0.07 | 5200 | 4.5 | 0.87 | 0.87 | Hellier et al. (2012)
WASP-69 | 0.144 | 4715 | 4.54 | 0.813 | 0.826 | Anderson et al. (2014)
WASP-74 | 0.39 | 5970 | 4.18 | 1.64 | 1.48 | Hellier et al. (2015)
WASP-76 | 0.366 | 6329 | 4.20 | 1.756 | 1.458 | Ehrenreich et al. (2020)
WASP-79 | 0.03 | 6600 | 4.06 | 1.51 | 1.39 | Brown et al. (2017)
WASP-80 | -0.13 | 4143 | 4.66 | 0.586 | 0.577 | Triaud et al. (2015)
WASP-96 | 0.14 | 5540 | 4.42 | 1.05 | 1.06 | Hellier et al. (2014)
WASP-101 | 0.2 | 6380 | 4.35 | 1.29 | 1.34 | Hellier et al. (2014)
WASP-117 | -0.11 | 6038 | 4.28 | 1.126 | 1.17 | Lendl et al. (2014)
WASP-127 | -0.18 | 5750 | 3.90 | 1.39 | 1.08 | Lam et al. (2017)
XO-1 | 0.02 | 5750 | 4.51 | 0.934 | 1.027 | Torres et al. (2008)
Table 7: Planet parameters for observations acquired from the literature. For consistency, these match those used in the original studies. Planet | Mass | Radius | Period | i | a/Rs | e | $\omega$ | Ref
---|---|---|---|---|---|---|---|---
Name | [MJ] | [$R_{J}$] | [days] | [∘] |  |  | [∘] |
GJ 436 b | 0.08 | 0.366 | 2.64389803 | 86.858 | 14.54 | 0.1616 | 327.2 | Lanotte et al. (2014)
GJ 3470 b | 0.043 | 0.346 | 3.3366487 | 88.88 | 13.94 | - | - | Biddle et al. (2014)
HAT-P-1 b | 0.53 | 1.36 | 4.46529 | 85.9 | 10.247 | - | - | Bakos et al. (2007a)
HAT-P-3 b | 0.596 | 0.899 | 2.899703 | 87.24 | 10.59 | - | - | Torres et al. (2008)
HAT-P-11 b | 0.081 | 0.422 | 4.8878162 | 88.5 | 15.58 | 0.198 | 355.2 | Bakos et al. (2010)
HAT-P-12 b | 0.211 | 0.959 | 3.2130598 | 89 | 11.77 | - | - | Hartman et al. (2009)
HAT-P-17 b | 0.534 | 1.01 | 10.338523 | 89.2 | 22.63 | 0.342 | 201 | Howard et al. (2012)
HAT-P-18 b | 0.196 | 0.947 | 5.507978 | 88.79 | 16.67 | - | - | Hartman et al. (2011a)
HAT-P-26 b | 0.057 | 0.549 | 4.234515 | 88.6 | 13.44 | - | - | Hartman et al. (2011b)
HAT-P-32 b | 0.86 | 1.789 | 2.150008 | 88.9 | 6.05 | - | - | Hartman et al. (2011c)
HAT-P-38 b | 0.267 | 0.825 | 4.640382 | 88.3 | 12.17 | - | - | Sato et al. (2012)
HAT-P-41 b | 0.8 | 1.685 | 2.694047 | 87.7 | 5.44 | - | - | Hartman et al. (2012)
HD 3167 c | 0.0262 | 0.244 | 29.84622 | 89.6 | 46.5 | 0.05 | 178 | Gandolfi et al. (2017)
HD 106315 c | 0.0459 | 0.444 | 21.05731 | 88.17 | 25.10 | 0.052 | 157 | Guilluy et al. (2021)
HD 149026 b | 0.359 | 0.654 | 2.87598 | 90 | 7.11 | - | - | Torres et al. (2008)
HD 189733 b | 1.144 | 1.138 | 2.218573 | 85.58 | 8.81 | - | - | Torres et al. (2008)
HD 209458 b | 0.685 | 1.359 | 3.524746 | 86.71 | 8.76 | - | - | Torres et al. (2008)
KELT-7 b | 1.28 | 1.533 | 2.7347749 | 83.76 | 5.49 | - | - | Bieryla et al. (2015)
KELT-11 b | 0.171 | 1.35 | 4.73613 | 85.3 | 4.98 | 0.0007 | 0 | Beatty et al. (2017b)
K2-18 b | 0.025 | 0.2033 | 32.94007 | 81.3 | 89.56 | - | - | Cloutier et al. (2017)
WASP-12 b | 1.47 | 1.9 | 1.0914203 | 83.37 | 3.039 | - | - | Collins et al. (2017)
WASP-17 b | 0.78 | 1.87 | 3.735430 | 86.63 | 8.97 | - | - | Southworth et al. (2012)
WASP-29 b | 0.244 | 0.792 | 3.922727 | 88.8 | 12.415 | - | - | Hellier et al. (2009)
WASP-31 b | 0.478 | 1.549 | 3.4059096 | 84.41 | 7.99 | - | - | Anderson et al. (2011)
WASP-39 b | 0.28 | 1.27 | 4.055259 | 87.83 | 11.647 | - | - | Faedi et al. (2011)
WASP-43 b | 1.78 | 0.93 | 0.813475 | 82.6 | 5.124 | - | - | Hellier et al. (2011b)
WASP-52 b | 0.46 | 1.27 | 1.7497798 | 85.35 | 7.401 | - | - | Hébrard et al. (2013)
WASP-62 b | 0.58 | 1.34 | 4.411953 | 88.5 | 9.5253 | - | - | Brown et al. (2017)
WASP-63 b | 0.38 | 1.43 | 4.37809 | 87.8 | 6.773 | - | - | Hellier et al. (2012)
WASP-67 b | 0.42 | 1.4 | 4.61442 | 85.8 | 12.835 | - | - | Hellier et al. (2012)
WASP-69 b | 0.26 | 1.057 | 3.8681382 | 86.71 | 11.953 | - | - | Anderson et al. (2014)
WASP-74 b | 0.95 | 1.56 | 2.13775 | 79.81 | 4.861 | - | - | Hellier et al. (2015)
WASP-76 b | 0.894 | 1.854 | 1.80988198 | 89.623 | 4.08 | - | - | Ehrenreich et al. (2020)
WASP-79 b | 0.85 | 1.53 | 3.662387 | 86.1 | 6.069 | - | - | Brown et al. (2017)
WASP-80 b | 0.538 | 0.999 | 3.06785234 | 89.02 | 12.63 | - | - | Triaud et al. (2015)
WASP-96 b | 0.48 | 1.20 | 3.4252602 | 85.14 | 8.84 | - | - | Hellier et al. (2014)
WASP-101 b | 0.5 | 1.41 | 3.585722 | 85.0 | 8.445 | - | - | Hellier et al. (2014)
WASP-117 b | 0.276 | 1.021 | 10.02 | 89.14 | 17.39 | 0.302 | 242 | Lendl et al. (2014)
WASP-127 b | 0.18 | 1.37 | 4.17807015 | 88.2 | 7.846 | - | - | Palle et al. (2017)
XO-1 b | 0.918 | 1.206 | 3.941534 | 88.81 | 11.55 | - | - | Torres et al. (2008)
Table 8: Stellar parameters utilised in this work on observations fitted here with Iraclis. Star | Fe/H | Temperature [K] | log(g) | Radius [R⊙] | Mass [M⊙] | Reference
---|---|---|---|---|---|---
CoRoT-1 | -0.3 | 5950 | 4.25 | 1.11 | 0.95 | Barge et al. (2008)
GJ 1214 | 0.29 | 3250 | 5.026 | 0.215 | 0.178 | Cloutier et al. (2021)
HAT-P-2 | 0.14 | 6290 | 4.16 | 1.64 | 1.36 | (Pál et al., 2010)
HAT-P-7 | 0.26 | 6350 | 4.07 | 1.84 | 1.47 | Esteves et al. (2015)
HD 97658 | -0.23 | 5212 | 4.64 | 0.728 | 0.85 | Ellis et al. (2021)
HD 219666 | 0.04 | 5527 | 4.40 | 1.03 | 0.92 | Esposito et al. (2019)
HIP 41378 | -0.10 | 6320 | 4.294 | 1.273 | 1.16 | Santerne et al. (2019)
KELT-1 | 0.008 | 6518 | 4.337 | 1.462 | 1.324 | Siverd et al. (2012)
Kepler-9 | 0.05 | 5774 | 4.49 | 0.958 | 1.022 | Borsato et al. (2019)
Kepler-51 | 0.05 | 5670 | 4.7 | 0.881 | 0.985 | Libby-Roberts et al. (2020)
K2-24 | 0.34 | 5625 | 4.29 | 1.16 | 1.07 | Petigura et al. (2016)
LTT 9779 | 0.27 | 5443 | 4.35 | 0.949 | 0.770 | Jenkins et al. (2020)
TOI-270 | -0.20 | 3506 | 4.872 | 0.378 | 0.386 | Van Eylen et al. (2021)
TOI-674 | 0.17 | 3514 | 5.28 | 0.42 | 0.42 | Murgas et al. (2021)
TrES-2 | -0.15 | 5850 | 4.4 | 0.952 | 0.99 | Kipping & Bakos (2011)
TrES-4 b | 0.14 | 6200 | 4.064 | 1.816 | 1.394 | Torres et al. (2008)
V1298 Tau | 0.14 | 4970 | 4.246 | 1.314 | 1.099 | David et al. (2019b)
WASP-6 | -0.20 | 5450 | 4.60 | 0.73 | 0.55 | Stassun et al. (2017)
WASP-18 | 0.11 | 6431 | 4.47 | 1.26 | 1.46 | Shporer et al. (2019)
WASP-19 | 0.15 | 5568 | 4.45 | 1.004 | 0.904 | Wong et al. (2016a)
WASP-103 | 0.06 | 6100 | 4.22 | 1.436 | 1.22 | Gillon et al. (2014)
WASP-107 | -0.02 | 4430 | 4.5 | 0.66 | 0.69 | Anderson et al. (2017)
WASP-121 | 0.13 | 6460 | 4.24 | 1.458 | 1.353 | Delrez et al. (2016)
WASP-178 | -0.06 | 8640 | 4.211 | 1.801 | 1.93 | Rodríguez Martínez et al. (2020)
Table 9: Planet parameters utilised in this work on observations fitted here with Iraclis. Planet | Mass | Radius | Period | i | a/Rs | e | $\omega$ | Ref
---|---|---|---|---|---|---|---|---
Name | [MJ] | [$R_{J}$] | [days] | [∘] |  |  | [∘] |
CoRoT-1 b | 1.03 | 1.49 | 1.5089557 | 85.1 | 4.92 | - | - | Barge et al. (2008)
GJ 1214 b | 0.0257 | 0.2446 | 1.58040433 | 88.7 | 14.85 | - | - | (Cloutier et al., 2021)
HAT-P-2 b | 9.09 | 1.157 | 5.6334729 | 86.72 | 8.99 | 0.5171 | 185.22 | (Pál et al., 2010)
HAT-P-7 b | 1.781 | 1.419 | 2.2047 | 83.143 | 4.1545 | - | - | Esteves et al. (2015)
HD 97658 b | 0.026 | 0.189 | 9.4897116 | 89.05 | 24.2 | 0.05 | 0 | Ellis et al. (2021)
HD 219666 b | 0.0522 | 0.420 | 6.03607 | 86.38 | 13.27 | - | - | Esposito et al. (2019)
HIP 41378 b | 0.0217 | 0.2315 | 15.57208 | 88.75 | 21.6721 | - | - | Santerne et al. (2019)
HIP 41378 f | 0.0378 | 0.8208 | 542.07975 | 89.97 | 231.41717 | - | - | Santerne et al. (2019)
KELT-1 b | 27.23 | 1.11 | 1.217514 | 87.8 | 3.62 | 0.0099 | 61 | Siverd et al. (2012)
Kepler-9 b | 0.137 | 0.74 | 19.23891 | 88.982 | 31.3 | 0.0609 | 357 | Borsato et al. (2019)
Kepler-9 c | 0.0941 | 0.721 | 38.9853 | 89.188 | 49.8 | 0.06691 | 167.5 | Borsato et al. (2019)
Kepler-51 b | 0.0116 | 0.615 | 45.1542 | 90 | 60.22 | 0.01 | 53.3 | Libby-Roberts et al. (2020)
Kepler-51 d | 0.0179 | 0.844 | 130.1845 | 90 | 121.98 | 0.01 | 347.4 | Libby-Roberts et al. (2020)
K2-24 b | 0.0598 | 0.48 | 20.88977 | 90 | 28.57 | 0.06 | 0 | Petigura et al. (2016)
LTT 9779 b | 0.09225 | 0.421 | 0.792052 | 76.39 | 3.877 | - | - | Jenkins et al. (2020)
TOI-270 c | 0.01932 | 0.20805 | 5.660183 | 89.35 | 25.741 | 0.031 | 34.4 | Van Eylen et al. (2021)
TOI-270 d | 0.01504 | 0.17888 | 11.38027 | 89.69 | 41.007 | 0.034 | 11.5 | Van Eylen et al. (2021)
TOI-674 b | 0.0743 | 0.468 | 1.97714 | 87.21 | 12.80 | - | - | Murgas et al. (2021)
TrES-2 b | 1.202 | 1.187 | 2.47061892 | 84.07 | 8.06 | 0.018 | 268 | Kipping & Bakos (2011)
TrES-4 b | 0.92 | 1.751 | 3.553945 | 82.81 | 6.03 | - | - | Torres et al. (2008)
V1298 Tau b | 0.64∗ | 0.911 | 24.13861 | 89.35 | 27.6 | 0.112 | 91 | David et al. (2019b)
V1298 Tau c | - | 0.499 | 8.24958 | 88.49 | 13.19 | - | - | David et al. (2019a)
WASP-6 b | 0.37 | 1.03 | 3.3610100 | 88.47 | 10.62 | 0.05 | 0 | Stassun et al. (2017)
WASP-18 b | 10.2 | 1.24 | 0.94145223 | 83.5 | 3.48 | 0.0051 | 275 | Cortés-Zuleta et al. (2020)
WASP-19 b | 1.069 | 1.392 | 0.788838989 | 78.78 | 3.46 | 0.002 | 259 | Wong et al. (2016a)
WASP-103 b | 1.49 | 1.528 | 0.925542 | 86.3 | 2.978 | - | - | Gillon et al. (2014)
WASP-107 b | 0.12 | 0.94 | 5.721490 | 89.7 | 18.2 | - | - | Anderson et al. (2017)
WASP-121 b | 1.183 | 1.865 | 1.2749255 | 87.6 | 3.754 | - | - | Delrez et al. (2016)
WASP-178 b | 1.41 | 1.66 | 3.3448412 | 84.45 | 6.49 | - | - | Rodríguez Martínez et al. (2020)
∗Mass taken from Suárez Mascareño et al. (2021).

$R_{w}(t)=n^{scan}_{w}(1-r_{a}(t-T_{0}))(1-r_{b1}e^{-r_{b2}(t-t_{)}}),$ (3)

where $t$ is time, $n^{scan}_{w}$ is a normalisation factor, $T_{0}$ is the
mid-transit time, $t_{o}$ is the time when each HST orbit starts, $r_{a}$ is
the slope of a linear systematic trend along each HST visit and
($r_{b1},r_{b2}$) are the coefficients of an exponential systematic trend
along each HST orbit. The normalisation factor we used ($n^{scan}_{w}$) was
changed to $n^{for}_{w}$ for upward scanning directions (forward scanning) and
to $n^{rev}_{w}$ for downward scanning directions (reverse scanning). The
reason for using separate normalisation factors is the slightly different
effective exposure time due to the known upstream/downstream effect
(McCullough & MacKenty, 2012).

We fitted the white light curves using the formulae above and the
uncertainties per pixel, as propagated through the data reduction process.
However, it is common in HST/WFC3 data to have additional scatter that cannot
be explained by the ramp model. For this reason, we scaled up the
uncertainties in the individual data points, for their median to match the
standard deviation of the residuals, and repeated the fitting (Tsiaras et al.,
2018). The only free parameters in our white fitting, other than the HST
systematics, were the mid-transit time and the planet-to-star radius ratio.
The full set of white light curve fits are given in Figure set A1, with an
example given in Figure 13.

Figure 13: White light-curve fit of WASP-178 b with _Iraclis_ (Top) and
residuals (Bottom). This Figure is a sample from the Figure Set A1 that
contains the same information for all the planets.

Next, we fitted the spectral light curves with a transit model (with the
planet-to-star radius ratio being the only free parameter) along with a model
for the systematics ($R_{\lambda}$) that included the white light curve
(divide-white method, Kreidberg et al., 2014b) and a wavelength-dependent,
visit-long slope (Tsiaras et al., 2016b).

$R_{\lambda}(t)=n^{scan}_{\lambda}(1-\chi_{\lambda}(t-T_{0}))\frac{LC_{w}}{M_{w}},$
(4)

where $\chi_{\lambda}$ is the slope of a wavelength-dependent linear
systematic trend along each HST visit, $LC_{w}$ is the white light curve and
$M_{w}$ is the best-fit model for the white light curve. Again, the
normalisation factor we used ($n^{scan}_{\lambda}$) was changed to
$n^{for}_{\lambda}$ or $n^{for}_{\lambda}$ for upward or downward scanning
directions respectively. Also, in the same way as for the white light curves,
we performed an initial fit using the pipeline uncertainties and then refitted
while scaling these uncertainties, for their median to match the standard
deviation of the residuals.

Table 10: White light curve depths, and transit mid times, for all observations fitted here. These will be added to the ExoClock database (Kokori et al., 2022a). Planet Name | White Depth [$\%$] | Mid Time [BJDTDB] | Planet Name | White Depth [$\%$] | Mid Time [BJDTDB]
---|---|---|---|---|---
GJ1214b | 1.3456 $\pm$ 0.0102 | 2455478.57655 $\pm$ 5.3e-05 | Kepler-9b | 0.5898 $\pm$ 0.0117 | 2456093.7579 $\pm$ 0.000918
GJ1214b | 1.3484 $\pm$ 0.0052 | 2456524.80419 $\pm$ 2.8e-05 | Kepler-9b | 0.596 $\pm$ 0.0096 | 2456151.4162 $\pm$ 0.000655
GJ1214b | 1.3491 $\pm$ 0.0064 | 2456516.90183 $\pm$ 3.1e-05 | Kepler-9c | 0.5776 $\pm$ 0.0084 | 2456098.4048 $\pm$ 0.000822
GJ1214b | 1.3652 $\pm$ 0.0058 | 2456480.552823 $\pm$ 1.9e-05 | Kepler-9c | 0.5685 $\pm$ 0.0097 | 2456293.768 $\pm$ 0.00091
GJ1214b | 1.3514 $\pm$ 0.0036 | 2456414.17563 $\pm$ 1.8e-05 | Kepler-51d | 0.9082 $\pm$ 0.0179 | 2457388.20161 $\pm$ 0.001853
GJ1214b | 1.3778 $\pm$ 0.0088 | 2456387.30978 $\pm$ 3.1e-05 | Kepler-51d | 0.9254 $\pm$ 0.0177 | 2457778.751421 $\pm$ 0.001762
GJ1214b | 1.3645 $\pm$ 0.0041 | 2456379.406717 $\pm$ 2e-05 | LTT9779b | 0.207 $\pm$ 0.0102 | 2459377.56157 $\pm$ 0.00018
GJ1214b | 1.361 $\pm$ 0.0045 | 2456366.763689 $\pm$ 1.9e-05 | TOI-270c | 0.4238 $\pm$ 0.0048 | 2458961.21466 $\pm$ 7.2e-05
GJ1214b | 1.3628 $\pm$ 0.0039 | 2456365.183036 $\pm$ 1.7e-05 | TOI-270c | 0.3341 $\pm$ 0.0086 | 2459125.371 $\pm$ 0.007551
GJ1214b | 1.3547 $\pm$ 0.0031 | 2456322.512144 $\pm$ 1.7e-05 | TOI-270c | 0.3881 $\pm$ 0.0077 | 2458904.60695 $\pm$ 0.000162
GJ1214b | 1.3577 $\pm$ 0.0048 | 2456219.786079 $\pm$ 1.9e-05 | TOI-270d | 0.2788 $\pm$ 0.0219 | 2459129.343 $\pm$ 0.009614
GJ1214b | 1.3519 $\pm$ 0.0051 | 2456211.883798 $\pm$ 2.6e-05 | TOI-674b | 1.3174 $\pm$ 0.0079 | 2459056.6099 $\pm$ 0.000775
GJ1214b | 1.3419 $\pm$ 0.0062 | 2456508.99984 $\pm$ 3.6e-05 | TOI-674b | 1.3207 $\pm$ 0.0052 | 2459042.7681 $\pm$ 0.000538
GJ1214b | 1.35 $\pm$ 0.0052 | 2456197.660221 $\pm$ 2.4e-05 | TOI-674b | 1.3064 $\pm$ 0.0067 | 2459040.79261 $\pm$ 7.8e-05
GJ1214b | 1.3414 $\pm$ 0.0039 | 2456203.981787 $\pm$ 2e-05 | TrES-2b | 1.6538 $\pm$ 0.012 | 2455479.53351 $\pm$ 0.000275
GJ1214b | 1.3853 $\pm$ 0.007 | 2455766.20993 $\pm$ 5.4e-05 | TrES-4b | 0.912 $\pm$ 0.0179 | 2455524.5351 $\pm$ 0.000372
GJ1214b | 1.3596 $\pm$ 0.0064 | 2455649.26003 $\pm$ 4.5e-05 | V1298Taub | 0.4706 $\pm$ 0.0134 | 2459119.0243 $\pm$ 0.000387
HAT-P-2b | 0.4729 $\pm$ 0.0025 | 2459204.1089 $\pm$ 0.000612 | V1298Tauc | 0.1102 $\pm$ 0.0087 | 2459505.9037 $\pm$ 0.007106
HAT-P-7b | 0.5388 $\pm$ 0.0138 | 2455761.29153 $\pm$ 0.000304 | WASP-6b | 2.0592 $\pm$ 0.0119 | 2457880.132159 $\pm$ 9.6e-05
HD97658b | 0.0906 $\pm$ 0.0058 | 2457491.0335 $\pm$ 0.001066 | WASP-18b | 0.9409 $\pm$ 0.0063 | 2456896.14839 $\pm$ 0.000278
HD97658b | 0.0846 $\pm$ 0.001 | 2457785.2052 $\pm$ 0.001584 | WASP-19b | 2.0506 $\pm$ 0.0136 | 2456820.79792 $\pm$ 8.1e-05
HD97658b | 0.0933 $\pm$ 0.001 | 2456665.462 $\pm$ 0.001538 | WASP-19b | 2.0249 $\pm$ 0.01 | 2455744.03242 $\pm$ 0.000164
HD97658b | 0.0906 $\pm$ 0.0009 | 2456646.485232 $\pm$ 7.1e-05 | WASP-103b | 1.1449 $\pm$ 0.0113 | 2457237.05754 $\pm$ 0.000155
HIP41378b | 0.0388 $\pm$ 0.0023 | 2458133.32 $\pm$ 0.00763 | WASP-103b | 1.1818 $\pm$ 0.0038 | 2457080.64093 $\pm$ 8.4e-05
HIP41378b | 0.0361 $\pm$ 0.0026 | 2458989.7623 $\pm$ 0.000532 | WASP-107b | 2.0561 $\pm$ 0.0042 | 2457910.45444 $\pm$ 5.1e-05
HIP41378b | 0.0357 $\pm$ 0.0077 | 2458242.325 $\pm$ 0.016892 | WASP-121b | 1.4518 $\pm$ 0.0027 | 2458191.11649 $\pm$ 4.1e-05
HIP41378f | 0.4709 $\pm$ 0.0015 | 2459355.10091 $\pm$ 0.000241 | WASP-121b | 1.4656 $\pm$ 0.0069 | 2457424.88673 $\pm$ 0.000115
K2-24b | 0.1971 $\pm$ 0.0017 | 2457574.4045 $\pm$ 0.000816 | WASP-121b | 1.4736 $\pm$ 0.0032 | 2458518.77202 $\pm$ 5.8e-05
KELT-1b | 0.5773 $\pm$ 0.0048 | 2457713.61848 $\pm$ 8.2e-05 | WASP-178b | 1.1462 $\pm$ 0.0052 | 2459265.1123 $\pm$ 0.000987

Figure A3: Left: Uncorrected transit spectra for each visit of HD 97658 b. The
shaded regions indicate the white light curve depth, and 1 sigma uncertainty,
for each visit. Right: Normalised transit spectra for each visit of HD 97658
b. The averaged transit spectrum, which was used in the analysis here, is
given in black. This Figure is a sample from the Figure Set A1 that contains
the same information for all the planets.

## Appendix 2: Summary of Results for Individual Planets

Here we present further information for the planets where the spectra were fit
with Iraclis for this study. We briefly summarise the data that was taken and
compare our results to any we could find in the literature for the same
dataset.

### CoRoT-1 b

The first transit of CoRoT-1 b was observed in 2008 by (Barge et al., 2008),
unveiling an inflated, 1.5 RJ planet. A ground-based transmission spectrum of
CoRoT-1 b, obtained with the InfraRed Telescope Facility (IRTF), achieved a
spectral precision which was comparable to the modulation expected from a
single scale height of atmosphere but no spectral features could be discerned
(Schlawin et al., 2014).

HST WFC3 observed the transit of CoRoT-1 b in staring mode as part of proposal
12181 (PI: Drake Deming, Deming (2010)). The GRISM128 subarray was utilised
alongside the SPARS10 sequence and 16 up-the-ramp reads leading to an exposure
time of 100.651947 s. This data was previously studied but no evidence for
molecular absorption was found due to the high uncertainties on the data
(Ranjan et al., 2014). Similar results were also recently found by Glidic et
al. (2022).

We fitted the data with Iraclis and it is worth noting that there is no post-
egress orbit, likely due to poor knowledge of the ephemeris at the time of
observing, and this leads to larger uncertainties on the transit depth. For
the transit spectrum, the decreasing absorption with wavelength is best fit
with a cloudless atmosphere and the continuous absorption from H-. The result
is consistent with the recovered temperature of around 1800 K, which should
lead to the dissociation of molecular species.

The transit spectrum is compared to literature results in Figure 15, showing a
good consistency with these results in terms of shape but with an offset
between the spectrum recovered here and that from Glidic et al. (2022).

Figure 15: Comparison of the transit spectrum of CoRoT-1 b obtained here, to
those in the literature. While the features within the spectra are similar,
there are offsets between different studies.

### GJ 1214 b

In 2011, three staring mode transits of GJ 1214 b were taken for proposal
GO-12251 (PI: Zachory Berta). The analysis of this data led to a flat spectrum
which was interpreted as suggesting GJ 1214 b had an atmosphere with a mean
molecular weight $>$ 4\. Subsequently, 15 scanning mode transits of GJ 1214 b
were taken between September 2012 and August 2013 as part of proposal GO-13021
(PI: Jacob Bean). Combining these lead to a spectrum which had uncertainties
of around 50 ppm, equivalent to around 0.15 scale heights assuming a hydrogen
dominated atmosphere. Yet, despite the high precision of the observations, not
indication of an atmosphere could be extracted (Kreidberg et al., 2014b).

We analysed all available data for GJ 1214 b. However, the scanning mode
observations provided a higher precision than the staring mode data. As
discussed in Kreidberg et al. (2014b), the observation taken on 12th April
2013 was affected by poor pointing and so was excluded from the analysis.
Kreidberg et al. (2014b) found evidence of a starspot crossing in two
observations (4th and 12th August 2013) and so they excluded these from their
analysis. We show the white light curves of these transits in Figure 16,
showing slight bumps in the residuals which could indeed be due to a starspot
crossing. We remove these data, along with the staring observations, to
compute the final spectrum analysed here. In Figure 17, we show the final
spectrum obtained in this study using different datasets as well as a
comparison to the spectrum from Kreidberg et al. (2014b). We find that the
spectrum has slightly more modulation than found by Kreidberg et al. (2014b).
Additionally, our retrievals prefer a model with spectral modulation to the
2.41$\sigma$ level for the free chemistry model and to 2.38$\sigma$ for the
chemical equilibrium run. Given the relatively low significance of these
atmospheric detections, and the large number of observations that were
combined to create the final dataset, we are cautious about inferring the
presence of atmospheric features for this planet. Given the size of the error
bars derived, the terminator of GJ 1214 b is evidently not cloud free. The
JWST MIRI phase-curve taking during Cycle 1 should shed more light on the
nature of this world.

Figure 16: White light curves for scanning mode data of GJ 1214 b on 4th (top)
and 12th (bottom) August 2013. The residuals of the in-transit orbit are non-
gaussian and this could be caused by starspot crossing.  Figure 17: Transit
spectra of GJ 1214 b using different amalgamations of datasets. All are
roughly consistent with one another and the spectrum used for atmospheric
analyses in this study is shown in black.

### HAT-P-2 b

HAT-P-2 b was discovered in 2007 by Bakos et al. (2007b). It is a massive hot
Jupiter (9.1 Mjup) that orbits its host star in an highly eccentric orbit (e =
0.52) in about 5.6 days. Due to its large density, the planet is believed to
require the presence of a large core. This large mass, combined with the
highly eccentric orbit, raises many questions regarding the physics of this
planet and its formation. For instance, along the entire orbit, the planet’s
equilibrium temperature varies from 1240K to 2150K Bakos et al. (2007b).
Studying the Rossiter-McLaughlin effect, it was found that stellar spin axis
and orbital axis of the planet should be aligned, thus implying that the
planet did not evolved through scattering or Kozai migration Winn et al.
(2007); Loeillet et al. (2008).

While being a very interesting planet, the atmosphere of HAT-P-2 b was not
studied with many instruments. A phase-curve observation with Spitzer at 3.6
$\mu$m, 4.5 $\mu$m, 5.6 $\mu$m and 8 $\mu$m was presented in Lewis et al.
(2013), highlighting a very complex atmosphere due to the particular orbital
configuration of this planet. The study also suggested the planet might
experience a temporary day side thermal inversion near periapse. In a follow-
up work, Lewis et al. (2014) performed a complementary analysis with GCM
models to evaluate the impact of the eccentricity on the chemistry and the
thermal structure of this planet, highlighting that dis-equilibrium processes
on this planet might be important.

Recently, a partial phase-curve was acquired with HST using the G141 grism
(PN: 16194, PI: Desert et al., 2020). The eclipse spectrum from this proposal
was presented in Changeat et al. (2022) and here we extract the transit
spectrum. However, due to the high mass of HAT-P-2 b, we did not recover a
spectrum that was sensitive enough to allow for atmospheric constraints to be
made.

### HAT-P-7 b

HAT-P-7 b is an inflated hot-Jupiter of 1.4 RJ (Pál et al., 2008), which was
studied during the commissioning program of Kepler when the satellite detected
the eclipse as part of an optical phase curve (Borucki et al., 2009). These
measurements indicated that HAT-P-7 b could have a day-side temperature of
around 2650 K which confirmed predictions from Pál et al. (2008); Fortney et
al. (2008). This optical eclipse measurement was combined with Spitzer
photometry over 3.5 - 8 $\mu m$ to infer the presence of a thermal inversion
(Christiansen et al., 2010), suggested by the high flux ratio in the 4.5 $\mu
m$ channel of Spitzer compared to the 3.6 $\mu m$ channel. In their paper,
chemical equilibrium models associated these emission features with CO, H2O
and CH4. A thermal inversion was also reported to provide the best fit to this
data by the atmospheric models of Spiegel & Burrows (2010); Madhusudhan &
Seager (2010) but all three studies noted that models without a thermal
inversion could also well explain the data though only with an extremely high
abundance of CH4. Further Kepler phase curves identified an offset in the day-
side hot-spot (Esteves et al., 2013, 2015) as well as changes in its location
(Armstrong et al., 2016), highlighting the complex dynamics of hot-Jupiter
atmospheres. However, while Spitzer phase curves at 3.5 & 4.5 $\mu m$ were
also best fitted with a thermal inversion on the day-side and relatively
inefficient day–night re-circulation, Wong et al. (2016b) did not find
evidence of a hot-spot offset.

We fitted the HST WFC3 data with Iraclis but it is worth noting that there is
no post-egress orbit. Combined with the fact these observations were taken in
staring mode, this led to a transit spectrum which wherein the uncertainties
on the depth were equivalent to nearly 10 scale heights, meaning no
atmospheric signal could be discerned.

### HD 97658 b

The sub-Neptune HD 97658 b was discovered as part of the NASA-UC Eta-Earth
Program (Howard et al., 2011) and four HST WFC3 transit observations have been
obtained across two proposals (GO-13501 (Knutson, 2012), GO-13665 (Benneke et
al., 2015)). These have previously been analysed in (Knutson et al., 2014; Guo
et al., 2020).

The data from GO-13501 was collected using the GRISM256 subarray, the SPARS10
sequence and 4 up-the-ramp reads leading to an exposure time of 14.970785 s.
The scan rate was 1.4 ”/s. Meanwhile, the data from GO-13665 used a different
observational setup, with an exposure time of 12.795406 s via 16 up-the-ramp
reads using the RAPID sampling sequence. The GRISM512 subarray was utilised
and a scan rate of 1.4 ”/s.

For the observations from the latter proposal, the spatial scan was not
correctly positioned within the subarray window. Therefore, the longer
wavelengths were not recovered. Hence, for consistency, we extracted the white
light curves of all data sets from 1.088-1.650 $\mu$m. The change in the white
light curve did not affect our spectral bins, which only extend to 1.643
$\mu$m. We found that the white curve depths were consistent across the first
three visits, with the fourth visit being slightly shallower. The fourth visit
also displayed a greater slope across the WFC3 bandpass.

We compared our spectrum to the literature results in Figure 18. We find that,
with the exception of a small offset between the two spectra, our fitting of
the first two visits compares well to the results of Knutson et al. (2014).
However, we find that our analysis of all four observations differs from the
spectrum of Guo et al. (2020) at shorter wavelengths, despite excellent
agreement across the 1.3-1.5 $\mu$m range. We note that Guo et al. (2020)
found that the choice of long-term detrending technique affected the white
light-curve depth for the HST WFC3 G141 observations of HD 97658 b and
suggested that a linear trend may not fully explain the systematics seen. We
only fitted a linear trend here such that the analysis was consistent across
the population. The analysis of this spectrum was complicated by the
aforementioned incorrect positioning of the spatial scan and this may have
further contributed to this discrepancy. Our retrievals showed a clear
preference for the presence of an atmosphere and the free chemistry retrieval
provided the best fit to the data.

Figure 18: Left: Comparison of the spectrum derived in this work of HD 97658
b, to that from Knutson et al. (2014) who only analysed visits 1 and 2. Other
than a slight offset, the spectra agree well after two visits but the averaged
spectrum of all four transits has a stronger slope. Right: Comparison of the
spectrum derived in this work of HD 97658 b, to that from Guo et al. (2020).
While the spectra agree over 1.3-1.5 $\mu$m, outside of this range there is a
significant disagreement in the features.

### HD 219666 b

HD 219666 b, a hot-Neptune (Teq = 1070 K, R = 4.71 R⊕), was discovered using
data from the first sector of TESS (Esposito et al., 2019) and was one of the
first discoveries by this mission to be announced. With an orbital period of
around 6 days, it lies in an under-populated region of the period-radius
diagram in an area often coined the “hot-Neptune desert”. It is one of two
planets studied in this work that lies within this region, the other being LTT
9779 b. Esposito et al. (2019) showed that the target was an excellent
candidate for atmospheric studies by simulating JWST observations.

The planet was subsequently observed as part of proposal GO-15698 (PI: Thomas
Beatty) which planned to take two transit observations of HD 219666 b. The
first set of observations were taken in June 2019 but pointing was lost and so
the target was revisited in August and November of the same year. However, for
the visit in August, the first orbit was taken during the transit of the
planet, rather than the third orbit as planned. Evidently the planning of the
observations was based on poor orbital ephemeris and this highlights the
critical importance of programmes which seek to refine the periods of
exoplanets which are good targets for atmospheric characterisation (e.g.
Edwards et al., 2021b; Kokori et al., 2021, 2022b). The extracted white light
curve of this visit is shown in Figure alongside that of the November visit,
the only one that could be utilised.

Despite these issues, the spectrum derived from this single visit led to a
confident atmospheric detection. The TauREx free chemistry retrieval recovered
a very high volume mixing ratio of water: log10(H2O) =
-1.54${}^{+0.37}_{-1.08}$. The retrieval was preferred to the flat model to
3.57$\sigma$, suggesting a strong atmospheric detection.

### HIP 41378 b

Discovered using data from the K2 mission, HIP 41378 b is a sub-Neptune (R =
2.6 R⊕) with an orbital period of 15.5712 days and an equilibrium temperature
of 960 K (Vanderburg et al., 2016b; Santerne et al., 2019). Its atmosphere has
not previously been studied and the HST transit data was taken as part of
GO-15333 (PI: Ian Crossfield). Three successful transit observations of HIP
41378 b were taken, each consisting of 7 orbits. Two other visits were
attempted with one resulting in a complete loss of data and the other having
issues due to a guide star acquisition failure which led to large shifts in
the position of the spectrum on the detector. A further two observations were
originally planned but were scrapped in favour of observing three transits of
TOI-674 b (see Section TOI-674 b). 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
0.25 ”/s.

From our free chemistry retrievals, we find the spectrum to be compatible with
a flat line. However, our chemical equilibrium retrieval provided a preferable
fit that the flat model and was preferred by 2.65$\sigma$. The 1.4$\mu$m
feature size derived was 2.25 $\pm$ 0.97.

### HIP 41378 f

The outermost cureently-know planet in the HIP 41378 system, HIP 41378 f
orbits its host star every 542 days (Vanderburg et al., 2016b; Santerne et
al., 2019). The host star is bright and, as the planet’s density is very low
(M = 12 $\pm$ 3 M⊕, R = 9.2 $\pm$ 0.1 R⊕, $\rho$=0.09 $\pm$ 0.02 Santerne et
al. (2019)), it is an excellent target for atmospheric studies. Given its
temperature (T$\sim$300 K), HIP 41378 f is also far cooler than any other
large gaseous planets studied here. The transit spectrum of HIP 41378 f
required 18 consecutive orbits of HST and was taken by proposal GO-16267 (PI:
Courtney Dressing). The data was obtained with a scan rate of 0.419 ”/s. The
SQ256 subarray was used as well as the SPARS10 reading sequence. The first
forward and reverse scans of each orbit were acquired using 7 nondestructive
reads while the rest had 9. Direct images were acquired with the F126N at
various points in the visit as a guidance check.

The transmission spectrum of HIP 41378 f was analysed in Alam et al. (2022).
However, their derived spectrum differs dramatically from ours. We performed a
number of additional fittings to check the credibility of our result. Firstly,
we fitted the data using the wavelength bins and limb-darkening coefficients
from Alam et al. (2022) but this did not yield a similar spectrum to their
work. We tried extracting the data by splitting the nondestructive reads in
case of a contamination by a background star but this did not change the
derived spectrum. We also sought an independent fit of the data, with
CASCADe333https://gitlab.com/jbouwman/CASCADe also being used to analyse the
data. The CASCADe pipeline is instrument independent, meaning the manner in
which systematic effects are removed from the data is completely different to
Iraclis, which was built purposefully for HST WFC3. The initial fit was also
done without prior knowledge of the Iraclis result but we ensured the orbital
parameters utilised were the same. The resulting CASCADe spectra has highly
similar features to the Iraclis fit. We note there is a slight offset between
the datasets, but this is common when analysing spectra with different
pipelines (e.g. Mugnai et al., 2021), as well as a slightly steeper slope in
the CASCADe data which gives lower transit depths at shorter wavelengths.

Figure 19: Comparisons of different spectra for HIP 41378 f. All spectra
derived in this work exhibit features while the result from Alam et al. (2022)
is flat. Two pipelines were used here to check the result. They give slightly
different mean depths and the Cascade spectrum has a decreasing slope at
shorter wavelengths. Utilising the wavelength bins and limb-darkening
coefficients from Alam et al. (2022) did not remedy the situation.

From comparisons between our white light curve fit and that from Alam et al.
(2022), we noted that data had been removed from their analysis (see Figure 1
from their work), including an entire orbit just after ingress. In Alam et al.
(2022) they state that the observations were affected by the SAA which is
undoubtedly true: many orbits did not acquire the full number of requested
frames. However, they do not discuss why this orbit, and data from others,
were not present in their fitting despite the data being taken and having no
obvious signs of degradation. We also attempted fits without this orbit but
still found a spectrum with the same features as before. We also noted that
the uncertainties on the spectrum derived by Alam et al. (2022) were much
higher than those from Iraclis and CASCADe. While some of this could be due to
the removal of data by Alam et al. (2022), the residuals on the white light-
curve fit are also significantly higher in their work. Here, the residuals of
the white light-curve fit had a standard deviation of around 125 ppm while the
standard deviation of the residuals from the fit of Alam et al. (2022) was
around 500 ppm. While we cannot know for sure the source of this increased
scatter on their white light-curve as their pipeline is not public, we
speculate that some part of their calibration, reduction, or extraction
process must have been sub-optimal.

Having find no way to not achieve a spectrum without significant features, we
attempted to fit the data using TauREx. Our free chemistry retrievals were
flexible enough to fit the features seen, but the credibility of the fit is
questionable. Nevertheless, we show the best fit model to the data in Figure
Y. In the case of the GGChem retrieval, while it is preferred to the flat line
fit, it is obviously unable to replicate the features in the data.

There have been suggestions that HIP 41378 f could have rings which would
inflate the measured radius of the planet, thereby explaining the very low
density (Akinsanmi et al., 2020; Belkovski et al., 2022). Based on data from
K2, their modelling suggested the true radius of HIP 41378 f could be 3.7
R$\oplus$. The effect of these rings on the transit depth is likely to be
chromatic as, at wavelengths were the rings are optically opaque, more stellar
light would be blocked. While this could be the source of the features seen,
we do not have the modelling capability to pursue this further although
frameworks have been proposed (Ohno & Fortney, 2022). If the planet’s true
radius is 3.7 R$\oplus$, the uncertainties on the transit spectrum would now
each be equivalent to around 1.5 scale heights. Therefore, any attempt to
determine the effect of rings, if present, may also need to account for the
atmospheric contribution. Over such a short spectral range, the solutions to
this are likely the be degenerate but we encourage further work into this
option as it may be useful for future data taken of this planet, and others
like it, with observatories such as JWST.

We note the the slope seen in the spectrum of HIP 41378 f is similar to that
seen for HD 97658 b and LTT 9779 b, which might suggest that all these
observations are affected by a systematic or astrophysical effect that cannot
currently be identified. The narrow wavelength range of HST WFC3 G141 makes it
difficult to determine whether strange spectra are a result of poor reduction
or are a true representation of the signal. Hopefully, future data of this
planet will allow us to uncover the truth about its nature. However, due to
the strange nature of the HST WFC3 G141 spectrum, we chose not to include in
when fitting for trends within the data using BHM.

### K2-24 b

Transits of two planets orbiting K2-24, a G3 dwarf, were detected during
Campaign 2 of the K2 mission (Petigura et al., 2016; Sinukoff et al., 2016).
K2-24 b, the inner and smaller (R = 5.68 $\pm$ 0.56 R⊕)of the two planets,
orbits the host star in 20.8851 days. With a mass of 19 ± 2 M⊕ (Petigura et
al., 2018), K2-24 b has a relatively light density which, combined with the
brightness of the host star and relatively large transit depth, makes it a
good target for atmospheric characterisation (Petigura et al., 2016).

A single transit observation was obtained with HST WFC3 G141 by proposal
GO-14455 (PI: Erik Petigura). The data was collected using the GRISM256
subarray, the SPARS10 sequence and 16 up-the-ramp reads leading to an exposure
time of 103.128586 s. The scan rate was 0.16 ”/s, leading to a peak signal of
around 20,000 counts.

Our chemical equilibrium retrieval was not capable of fitting the spectral
features seen in the K2-24 b data. However, the best-fit free chemistry model
was preferred to a flat line with a significance of 2.46$\sigma$. It suggested
the presence of NH3, in a high abundance, but did not find evidence for H2O.
Due to the shape of the spectrum, the fitting of the 1.4 $\mu$m feature
yielded a negative value (-1.04 $\pm$ 0.68).

### KELT-1 b

The first low-mass object discovered by the KELT-North survey, KELT-1 b is a
$~{}27M_{J}$, $1.12R_{J}$ planet with a very short period circular orbit of 29
hours. (Siverd et al., 2012) presented spectroscopy, photometry and radial
velocity data in order to obtain an equilibrium temperature of $T_{eq}\approx
2400$ K, assuming zero albedo, due to a significant amount of stellar
irradiation.

Its extreme temperature and significant inflation make KELT-1 b a valuable
case-study for short-period atmospheric characterisation. In several early