# Measuring Tracers of Planet Formation in the Atmosphere of WASP-77A b: Sub-
stellar O/H and C/H ratios, with a stellar C/O ratio and a potentially Super-
stellar Ti/H ratio

Billy Edwards SRON, Netherlands Institute for Space Research, Niels Bohrweg 4,
NL-2333 CA, Leiden, The Netherlands  Department of Physics and Astronomy,
University College London, Gower Street, WC1E 6BT London, United Kingdom
Quentin Changeat European Space Agency (ESA), ESA Office, Space Telescope
Science Institute (STScI), Baltimore MD 21218, USA  Department of Physics and
Astronomy, University College London, Gower Street, WC1E 6BT London, United
Kingdom

(Received September 1, 2023; Revised December 18, 2023; Accepted December 19,
2023)

###### Abstract

We present a comprehensive atmospheric retrieval study of the hot Jupiter
WASP-77A b using eclipse observations from the Hubble Space Telescope (HST)
and JWST. Using atmospheric retrievals, the spectral features of H2O, CO, and
TiO are identified, with volume mixing ratios estimated at log10(VMR) =
-4.40${}^{+0.14}_{-0.11}$, -4.44${}^{+0.34}_{-0.28}$, and
-6.40${}^{+0.22}_{-0.23}$, respectively. We derive the atmospheric carbon-to-
oxygen ratio – a key planetary formation tracer – to be C/O = 0.54$\pm$0.12,
which is consistent with both the stellar host value and previous studies of
the planet’s atmosphere, suggesting a relatively close-in formation. Computing
other elemental ratios (i.e., C/H, O/H, and Ti/H), we conclude that the
general enrichment of the atmosphere (i.e., metallicity) is sub-stellar, is
depleted in C and O, but that Ti appears slightly super-stellar. A low C and O
content could be obtained, in combination with a stellar C/O ratio, if the
planet formed outside of the CO2 snow line before migrating inwards.
Meanwhile, a super-stellar Ti/H could be obtained by late contamination from
refractory rich planetesimals. While broadly in agreement with previous works,
we do find some differences and discuss these while also highlighting the need
for homogeneous analyses when comparative exoplanetology is conducted.

Exoplanet atmospheres (487); Hot Jupiters (753); Hubble Space Telescope (761);
JWST (2291)

††journal: ApJ Letters††facilities: Hubble Space Telescope (WFC3), JWST
(NIRSpec).††software: TauREx3 (Al-Refaie et al., 2021), TauREx GGChem (Woitke
et al., 2018; Al-Refaie et al., 2022), Multinest (Feroz et al., 2009; Buchner
et al., 2014), Iraclis (Tsiaras et al., 2016b), PyLightcurve (Tsiaras et al.,
2016a), Astropy (Astropy Collaboration et al., 2013, 2018, 2022), h5py
(Collette, 2013), emcee (Foreman-Mackey et al., 2013), Matplotlib (Hunter,
2007), Pandas (McKinney, 2011), Numpy (Oliphant, 2006), SciPy (Virtanen et
al., 2020), corner (Foreman-Mackey, 2016).

##  1 Introduction

Despite being a rare outcome of planetary formation, numerous hot Jupiters
have been detected due to the transit technique being biased toward large
planets on short orbits. As their size and temperature are favourable for
atmospheric characterisation, most atmospheric observational studies using
space-based instruments have focused on this class of objects. With the advent
of the spatial scanning technique (McCullough & MacKenty, 2012), the Wide
Field Camera 3 (WFC3) on board the Hubble Space Telescope (HST) has enabled
around one hundred of those planets to be characterised via transit (e.g.,
Tsiaras et al., 2018; Pinhas et al., 2019; Cubillos & Blecic, 2021; Kawashima
& Min, 2021; Edwards et al., 2023) and eclipse (e.g., Mansfield et al., 2021;
Changeat et al., 2022) spectroscopy, enabling the search for trends in their
atmospheric composition.

More recently, JWST has become the premier facility for space-based exoplanet
spectroscopy. The four instruments on board JWST offer a wider simultaneous
wavelength coverage than was previously available as well as access to
previously uncharted spectral regions. Early studies of giant exoplanets have
successfully used each of these JWST instruments for transit (e.g., Dyrek et
al., 2023; Feinstein et al., 2023), eclipse (e.g., Bean et al., 2023; Coulombe
et al., 2023) and phase-curve observations (e.g., Bell et al., 2023).

Here, we conduct a comprehensive retrieval study on WASP-77A b, an inflated
hot Jupiter in a wide binary system (Maxted et al., 2013), using data from HST
and JWST. The planet orbits WASP-77A, a G8V star. WASP-77 B, a fainter K-dwarf
companion to WASP-77A, is separated by 3”. WASP-77A b has been previously
observed in emission with the ground-based high-resolution Immersion GRating
INfrared Spectrometer (IGRINS) on Gemini-South (covering wavelengths from
$\lambda\in[1.45,2.55]\,\mu$m). Those observations led to tight constraints on
the atmospheric metallicity (log10(M/H) = -0.48${}^{+0.15}_{-0.13}$) and the
carbon-to-oxygen ratio (C/O = 0.59$\pm$0.08) through the measurement of the
atmospheric H2O and CO abundances (Line et al., 2021). Hence, the data
suggested a metal-poor atmosphere and a solar C/O ratio.

Low-resolution eclipse observations from the HST Wide Field Camera 3 (WFC3)
G141 grism complemented this picture, showing a clear water absorption feature
at $\lambda=1.4\,\mu$m (Changeat et al., 2022; Mansfield et al., 2022) and
indicating a dayside positive lapse rate (i.e., a decreasing with altitude
thermal structure). The data, however, did not precisely constrain the H2O
abundance, nor was it possible to clearly infer the amount of CO in the
atmosphere, even when combining it with photometric data from Spitzer
(Mansfield et al., 2022).

As part of the GTO-1274 programme, an eclipse of WASP-77A b was captured using
the Near-InfraRed Spectrometer (NIRSpec) on JWST. August et al. (2023)
analysed this data using chemical equilibrium retrievals, concluding that the
data was best-fit by a sub-solar metallicity (log10(M/H) =
-0.91${}^{+0.24}_{-0.16}$) and a low C/O ratio (0.36${}^{+0.10}_{-0.09}$)
atmospheres. These results roughly agreed with the conclusions from the Gemini
data, but the preferred models were not able to fit the HST WFC3 spectrum from
Mansfield et al. (2022). However, the spectrum from Mansfield et al. (2022) is
visually at odds with one obtained by Changeat et al. (2022), despite being
derived from the same HST data.

In this work we explore the atmospheric properties of WASP-77A b, focusing on
the recovery of key planetary formation tracers. We use information from the
novel eclipse observations by JWST-NIRSpec (August et al., 2023), attempting
to reconcile the tension between the different HST reductions (Changeat et
al., 2022; Mansfield et al., 2022) to provide a comprehensive interpretation
of WASP-77A b’s atmosphere. In Section 2 we describe the data used in this
study and our retrieval setup. We present our results in Section 3 and discuss
their implications in Section 4.

##  2 Methodology

The emission spectrum of WASP-77A b has been captured at low-resolution (i.e.,
R $<$ 5000) by both HST and JWST. The HST data were taken with the WFC3 G141
grism, giving a spectral coverage of $\lambda\in[1.1,1.6]\,\mu$m. In the main
text, we focus on the reduction from Changeat et al. (2022) but discuss its
robustness in Appendix A, comparing their methodology against that of
Mansfield et al. (2022). The JWST data was acquired with the NIRSpec
instrument using the Bright Object Time-Series (BOTS) mode, with the G395H
grating and F290LP filter combination. The spectrum analysed in our study is
from August et al. (2023) and covers $\lambda\in[2.674,3.716]\,\mu$m (NRS1)
and $\lambda\in[3.827,5.173\,\mu$m (NRS2). More details on the observational
setups and data reduction procedure can be found in each of these studies.

We invert the atmospheric properties of WASP-77A b from the observed spectra
using the publicly available Bayesian retrieval suite TauREx 3.1 (Al-Refaie et
al., 2021, 2022)111https://github.com/ucl-exoplanets/TauREx3_public. We assume
WASP-77A b possesses a primary atmosphere with a solar helium-to-hydrogen
ratio (He/H2 = 0.17). The atmosphere is modelled between
$p\in[10^{-4},10^{6}]$ Pa using 100 plane-parallel layers uniformly
partitioned in log-space. The radiative contributions of the relevant
molecules, Collision Induced Absorption (CIA) from H2-H2 (Abel et al., 2011;
Fletcher et al., 2018) and H2-He (Abel et al., 2012), and Rayleigh scattering
(Cox, 2015) are included in the model. Stellar and planetary parameters are
taken from Maxted et al. (2013), with the host-star emission being modeled by
a PHOENIX spectrum (Allard et al., 2012).

We perform two types of retrievals: 1) retrievals where each molecular species
is independently fitted for (referred to as free retrievals), and 2)
retrievals that assume a gas mixture at chemical equilibrium via Gibbs free
energy minimisation (referred to as equilibrium retrievals).

1) Free retrievals: We include the molecular opacities from the ExoMol
(Tennyson et al., 2016; Chubb et al., 2021), HITRAN (Gordon et al., 2016) and
HITEMP (Rothman & Gordon, 2014) databases. Considered species are H2O
(Polyansky et al., 2018), CH4 (Yurchenko & Tennyson, 2014), CO (Li et al.,
2015), CO2 (Rothman et al., 2010), TiO (McKemmish et al., 2019), VO (McKemmish
et al., 2016), FeH (Wende et al., 2010) and H-. To include H-, we use the
description in Edwards et al. (2020) with the coefficients of Table 1 from
John (1988). For the molecular abundances, uniform priors of log10(VMR)
$\in[-15,-1]$ are used.

2) Equilibrium retrievals: We use the code GGchem (Woitke et al., 2018) via
the TauREx 3 plugin system (Al-Refaie et al., 2022) to model the atmospheric
chemistry of WASP-77A b. The free chemical parameters are: atmospheric
metallicity (M/H), the C/O ratio, and the Ti/O ratio. The Ti/O ratio is
included following Changeat et al. (2022), who noted an apparent population-
wide refractory enrichment for hot Jupiter planets, leading to poor fits of
HST WFC3 spectra when assuming solar Ti/O ratio. For those retrievals, the
priors are also uniform with log10(M/H) $\in[-2,2]$, C/O $\in[0.05,2]$, and
log10(Ti/O) $\in[-10,5]$.

For all our retrievals, we employed a parametric N-point temperature-pressure
($T-p$) profile. Following Changeat et al. (2021), we retrieve the temperature
value of height nodes at fixed pressures
($p\in\\{10^{1},10^{0},10^{-1},10^{-2},10^{-3},10^{-4},10^{-6},10^{-8}\\}$
Bar). Such a $T-p$ profile allows the temperature structure of the planet to
be determined wholly from the data without any a priori assumptions.

For HST, recovering absolute transit or eclipse depths is difficult due to its
strong instrument systematics (e.g., Guo et al., 2020; Changeat et al., 2022;
Edwards et al., 2023). To mitigate for this in retrievals that combine
spectral from different instruments, one can fit for an additional mean offset
(e.g., Yip et al., 2021) to attempt to alleviate any biases. In our
retrievals, we always allow the HST WFC3 G141 spectrum to be shifted relative
to the JWST NIRSpec spectrum due to its stronger systematics and the potential
residual contamination from WASP-77B when deriving the spectrum (Changeat et
al., 2022; Mansfield et al., 2022). In the high-resolution mode, the NIRSpec
data are split across two detectors (NRS1 and NRS2). As there could be offsets
between these spectra, we also allow for the NRS2 spectrum to be offset with
respect to the NRS1 spectrum222We also performed retrievals where the NRS1
spectrum was offset and this did not change our results or conclusions.. For
both offsets, the bounds for the offset ($\Delta$) are set to be extremely
broad with $\Delta\in[-500,+500]$ ppm.

We explore 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.

The free chemical retrievals serve to derive elemental ratios for WASP-77A b,
which are then compared with the host-star values. With respect to solar
values, Polanski et al. (2022) measured C/H = -0.02, O/H = 0.06, and Ti/H =
0.01. Using the solar abundance for these elements (Asplund et al., 2009),
these yield C/O = 0.46 and Ti/O = 1.6$\times$10-4. We compare those values to
the derived/fitted ratios from our retrievals. In Section 4.3, we discuss the
implication of comparing to the stellar abundances derived in other studies.

##  3 Results

The joint WFC3+NIRSpec fit shows evidence for three molecules: H2O, CO, and
TiO. The preferred abundances for these species are log10(H2O) =
-4.58${}^{+0.16}_{-0.13}$, log10(CO) = -4.51${}^{+0.28}_{-0.26}$, and
log10(TiO) = -6.52${}^{+0.22}_{-0.23}$. The molecular features are seen in
absorption, indicating a positive lapse rate (see Figure 1) with no evidence
for a stratosphere. The free retrieval prefers the application of a small
offset ($\Delta$ = -39${}^{+22}_{-20}$ ppm and -56${}^{+36}_{-33}$ ppm) to the
WFC3 and NRS2 spectra but, as shown by the posterior distributions in Figure
2, these parameters do not have a strong correlation with the molecular
abundances.

Using the retrieved abundances of H2O, CO, and TiO, we compute the following
ratios to 1$\sigma$: C/O = 0.54$\pm$0.12 and log10(Ti/O) =
-2.30${}^{+0.20}_{-0.23}$. Therefore, the planetary C/O ratio is compatible
both with that of WASP-77A (C/O = 0.46, Polanski et al., 2022), and the solar
value (0.55, Asplund et al., 2009). However, we find the Ti/O ratio to be much
higher for the planet than for the host star (log10(Ti/O) = -3.79, Polanski et
al., 2022).

We also determine the elemental ratios with respect to hydrogen. For C/H and
Ti/H, only the CO abundance and the TiO abundance are used, respectively. For
O/H, all three molecules are used. These ratios were normalised to the solar
values from Asplund et al. (2009) and the stellar values from Polanski et al.
(2022).

Figure 1: Best-fit free retrieval of the JWST NIRSpec and HST WFC3 data for
WASP-77A b. The coloured regions show the individual contribution of three
species (H2O, CO, and TiO) and Collision Induced Absorption (CIA), while the
inset shows the 1, 2, and 3$\sigma$ confidence intervals for the retrieved
temperature-pressure ($T-p$) profile. These three species are detected in the
HST and JWST data, allowing us to place constraints on elemental ratios for
this atmosphere. The best-fit $T-p$ profile has a positive lapse rate (i.e, no
evidence for a thermal inversion) in the pressure region probed by our
observations ($p\in[10^{5},100]$ Pa). Figure 2: Posterior distributions for
the dayside of WASP-77A b. For the free chemistry retrievals, the C/O and Ti/O
ratios are derived parameters. Where there are two reported values, they are
given as those from the combined JWST NIRSpec and HST WFC3 fit (left) and the
JWST NIRSpec only (right). Both free and equilibrium chemistry models, as well
as fits to both datasets or just JWST NIRSpec, prefer a roughly stellar C/O
ratio. The free and equilibrium retrievals to the combined datasets also
prefer a distinctly super-stellar Ti/O ratio. All elemental-to-hydrogen
abundances are given with respect to solar values. Again, C/H and O/H are sub-
stellar whereas Ti/H is super-stellar. All ratios and abundances are computed
in terms of the volume mixing ratio.

We find that C/H and O/H are both clearly sub-stellar, with C/H =
0.06${}^{+0.06}_{-0.03}\,\times$stellar and O/H =
0.06${}^{+0.04}_{-0.02}\,\times$stellar. However, we find a slightly super-
stellar Ti/H ratio: Ti/H = 1.77${}^{+1.15}_{-0.72}\,\times$stellar. The
apparent enrichment in titanium compared to the stellar value is far smaller
when considering Ti/H than Ti/O, due to the simultaneous sub-stellar
prevalence of oxygen. All these ratios are given in Table 1, which can be
found in Appendix B.

As our retrievals indicate a depletion in carbon and oxygen for WASP-77A b’s
atmosphere, the metallicity when calculated from these elements is also sub-
stellar with (C+O)/H = 0.06${}^{+0.04}_{-0.02}\,\times$stellar. However, this
contrasts with the retrieved abundance of Ti that is suggestive of a super-
stellar Ti/H ratio. Nevertheless, accounting for Ti in the metallicity by
using (C+O+Ti)/H makes little difference due to the low abundance of Ti
compared to the other elements (see Table 1).

While the free retrieval to both datasets is our preferred approach due to its
unassuming nature, we use additional retrievals to explore the robustness of
our results.

Firstly, we conduct an equilibrium retrieval on the joint dataset, finding
similar, though slightly lower, C/O and Ti/O ratios to the free retrieval: C/O
= 0.49${}^{+0.11}_{-0.10}$ and log10(Ti/O) = -2.12${}^{+0.21}_{-0.23}$.
Comparing the metallicity (M/H) again shows excellent agreement, with
log10(M/H) = -1.08${}^{+0.19}_{-0.17}$ (M/H = 0.09$\pm$0.03$\,\times$stellar).
Hence, free and equilibrium retrievals on the WFC3+NIRSpec data show a
consistent picture, strongly suggesting that WASP-77A b hosts a low
metallicity atmosphere, a conclusion which is in line with previous studies.
They also both suggest a slight enrichment of Ti.

Secondly, both free and equilibrium retrievals are performed on the NIRSpec
spectrum alone. As the spectral features of CO and H2O are prominent in the
NIRSpec spectrum, the free retrieval infers similar abundances for those
molecules to the combined fit. Hence, the derived C/O ratio remains similar,
suggesting that the NIRSpec data drive our conclusions for these species. The
equilibrium retrieval finds a similar metallicity but a lower C/O ratio.
However, as TiO does not have broadband spectral features in the NIRSpec G395
spectral range, both free and equilibrium retrievals could not place
constraints on TiO. Therefore, the Ti/O ratio remains unconstrained in the
NIRSpec-only retrievals.

Comparisons of all these retrievals are shown in Figure 2, including the
derived elemental ratios. Each model led to a C/O ratio that was consistent to
1$\sigma$ with the stellar value (Polanski et al., 2022) and to a definitively
sub-stellar metallicity. The retrievals that included both NIRSpec and WFC3
data were consistent with an atmosphere enriched in titanium when compared to
the host star.

##  4 Discussion

###  4.1 Potential implications for planet formation

Elemental ratios – such as those derived in this study – have long been
proposed as potential tracers of planetary formation and evolution. The most
widely considered tracers are the bulk metallicity (i.e., M/H) and the C/O
ratio (e.g., Öberg et al., 2011; Mordasini et al., 2016; Madhusudhan et al.,
2017; Eistrup et al., 2018; Cridland et al., 2019), although more recently,
other tracers – such as S/O, N/O (e.g., Turrini et al., 2021; Pacetti et al.,
2022; Ohno & Fortney, 2023a, b), or refractory-to-O (labelled R/O: Lothringer
et al., 2021) – have also been suggested to break the degeneracy in current
formation models.

Suggestions of super-stellar metallicities for close-in giant planets from
observational studies (e.g., Thorngren et al., 2016; Fortney et al., 2020;
Bean et al., 2023; Feinstein et al., 2023) have motivated a growing body of
works to explain their formation by forming far out in the protoplanetary disk
before undergoing extensive disk migration, which is coupled with the
efficient accretion of planetesimals and gas-enriched materials at the disk
snow-lines (Booth et al., 2017; Hasegawa et al., 2018; Shibata et al., 2020;
Turrini et al., 2021; Pacetti et al., 2022; Khorshid et al., 2022; Schneider &
Bitsch, 2021). However, this picture does not fully explain the diversity of
hot Jupiter compositions, with evidence for sub-stellar O/H exoplanets and
trends for high refractory content also being found (Changeat et al., 2022).
Clearly, WASP-77A b does not appear to be enriched in volatiles (O and C)
relative to its host star but could possess a high R/O ratio (here probed by
Ti/O), thus suggesting an alternative pathway to its formation.

The roughly stellar C/O suggested by our retrievals implies that WASP-77A b
might have formed around the H2O/CO2 ice lines (i.e, relatively close-in
formation), as one would expect an enriched C/O ratio ($>$0.8, Öberg et al.,
2011; Madhusudhan et al., 2017) if significant accretion had occurred beyond
the snow lines. However, for these lower C/O ratios, models also usually
predict super-stellar C and O abundances (e.g. Schneider & Bitsch, 2021),
which we do not find here: our estimate of the C/H ratio, for instance, is far
below the stellar ratio as well as that of the Solar System gas giants (Atreya
et al., 2016). A low C and O content could be obtained if the planet formed
mainly from gas (e.g., from gravitational instabilities rather than core
accretion), but this is believed to only occur far out in the protoplanetary
disk. One formation pathway that could explain a low C and O content, combined
with a stellar C/O ratio, is if WASP-77A b planet formed exterior to the CO2
evaporation front and only crossed the CO2 snow line, which is located at
around 15 AU, very late in its evolution (Bitsch et al., 2022).

A high R/O ratio (e.g., here Ti/O) also implies a close-in formation rather
than extensive migration after the disk dispersal and could indicate complex
interactions at the snow lines involving evaporating pebbles (Schneider &
Bitsch, 2021; Bitsch et al., 2022). As our retrievals suggest a low prevalence
of oxygen and carbon with a potentially super-stellar abundance of titanium
(i.e., a high R/H ratio), WASP-77A b could be well explained by a formation
around the CO2 ice line with late enrichment of its atmosphere by rock-rich
planetesimals (Lothringer et al., 2021; Bitsch et al., 2022). Data that allow
us to constrain other R/O ratios (e.g., Si/O via SiO) may yield further
insights into the formation pathway for this planet by independently measuring
the enrichment of those elements as well as adding sensitivity to additional
oxygen reservoirs, reducing the chance of an oxygen deficit in our
calculations (Fonte et al., 2023).

###  4.2 Strength of the TiO Detection

Evidence for TiO has been found in the HST WFC3 emission spectra of several
other planets (e.g., Haynes et al., 2015; Edwards et al., 2020; Changeat &
Edwards, 2021). However, these claims have sometimes been disputed by
independent analyses (e.g., Jacobs et al., 2022) or by non-detections via
high-resolution spectroscopy (e.g., Merritt et al., 2020; Kasper et al.,
2021). For WASP-77A b, the high-resolution study by Line et al. (2021) did not
consider TiO, likely due to the lack of sensitivity of their data to this
molecule due to the observed wavelengths ($\lambda\in[1.43,2.42]\,\mu$m).

Often, the “detection” of optical absorbers with WFC3 G141 stems from only one
or two data points. However, for WASP-77A b, the detection is supported by two
features: one below $\lambda=1.15\,\mu$m (i.e., at the edge of the WFC3 G141
bandpass) and a second at $\lambda\in[1.23,1.28]\,\mu$m (see Figure 3).
Performing an equilibrium retrieval which assumes a solar Ti/O ratio smooths
the TiO absorption features in those regions and leads to a poorer fit of the
WFC3 data, with $\Delta$ln(E) = 6.8 in favour of the model with super-solar
Ti/O (i.e., a 4.2$\sigma$ preference). Note that, since the data strongly
favours a sub-stellar O/H ratio that is driven by the more precise NIRSpec
data, a solar Ti/O ratio enforces a distinctly sub-stellar Ti/H ratio, when
our preferred enhanced Ti model is only slightly super-solar. Therefore, this
suggests Ti/H may be a more relevant marker of planetary formation processes
than Ti/O.

While the Bayesian evidence points toward the presence of TiO, the combination
of this molecule and a lack of a stratosphere is unexpected for highly-
irradiated atmospheres. TiO, and other oxides and hydrides, are strong
absorbers of visible light and are therefore expected to cause thermal
inversion (e.g., Hubeny et al., 2003) by the deposition of stellar energy at
high altitudes. Cold traps, where the temperature profile dips below the
condensation curve of a molecule, have been suggested as a way of sequestering
TiO from the atmosphere (e.g., Spiegel et al., 2009; Beatty et al., 2017).
Usually, these models predict the cold-trap to lie between a deeper, warmer
atmospheric layer where TiO is present and the stratosphere where again
temperatures are hot enough for TiO to avoid condensation. While we do not
detect evidence for a thermal inversion, the large uncertainty in the $T-p$
profile at high altitudes (i.e., p $<$ 100 Pa) does not strongly rule out the
presence of one either.

Figure 3: Comparison of the chemical equilibrium retrieval results when we
allow the Ti/O ratio to vary (purple) and when we fix it to solar (yellow).
The latter does not provide a good fit to the two highlighted regions, and our
retrievals suggest the features in these regions are due to TiO.

###  4.3 Comparisons to other works and implications for comparative
planetology

Multiple studies have made independent inferences for the dayside chemistry
and thermal structure of WASP-77A b using several instruments. Prior studies
of the high-resolution Gemini observations (Line et al., 2021) and the JWST
NIRSpec data (August et al., 2023) both suggested an atmosphere depleted in
carbon and oxygen. However, they slightly disagreed on the value of the C/O
ratio. These studies, as well as those of the HST WFC3 spectrum (Changeat et
al., 2022; Mansfield et al., 2022), find a $T-p$ profile with a positive lapse
rate. Our joint fit to the HST and JWST data leads to the same general
conclusions though with some differences that are worth discussing.

In Figure 4, we compare the molecular abundances and elemental ratios inferred
from the WFC3+NIRSpec joint free fit to those from these previous works. Our
retrieved abundances of H2O and CO are significantly lower than those reported
in Line et al. (2021). Hence, while both works support the conclusion that the
atmosphere of WASP-77A b is depleted in C and O, the level of depletion is
somewhat different.

Figure 4: Comparison between the molecular abundances and elemental ratios
found here for WASP-77A b and those found by literature works. No work has
previously tried to constrain the Ti/H ratio, so it is not plotted here. We
note that M/H refers to (C+O)/H for Line et al. (2021), M/H for August et al.
(2023), and (C+O+Ti)/H for the atmospheric constraints from this work as well
as the measurements of the enrichment of the host star, WASP-77A.

Additionally, the preferred C/O ratio from our retrievals lies between those
derived by Line et al. (2021) and August et al. (2023), agreeing with both to
within 1$\sigma$. The difference with August et al. (2023) comes from the
addition of the WFC3 data. When performing the chemical equilibrium retrieval
on only the NIRSpec data, we also obtain a lower C/O ratio (0.40$\pm$0.1)
though it is still within 1$\sigma$ of the stellar value from Polanski et al.
(2022). August et al. (2023) noted that a reasonable joint fit with the WFC3
data from Mansfield et al. (2022) could not be achieved. As we find no such
issue with the spectrum from Changeat et al. (2022), we explore the cause of
this in Appendix A.

Furthermore, it is worth noting that Line et al. (2021) analysed the IGRINS
data with two different retrieval codes: CHIMERA (Line et al., 2013) and
HyDRA-H (Gandhi et al., 2019). The C/O ratio using their CO and H2O abundances
(ED Fig. 6) from these fits are 0.59 and 0.38, respectively. Hence, while
their main result claims that WASP-77A b has a solar C/O ratio, their
secondary result finds a sub-solar C/O ratio that agrees with the JWST
NIRSpec-only analyses from this work and August et al. (2023).

Using the main results of Line et al. (2021), studies have implied that
WASP-77A b must have formed far out in the disk beyond the H2O ice line
(Reggiani et al., 2022; Khorshid et al., 2023). Such a formation was inferred
based upon sub-stellar carbon and oxygen abundances and a super-stellar C/O
ratio, a condition which Öberg et al. (2011) suggested as a unique signature
of this formation process. However, in our work, and in that of August et al.
(2023), the C/O is not found to be definitively super-stellar and is instead
consistent with, or below, the stellar value. If such findings are confirmed
(i.e, stellar C/O but depletion in C and O), different planetary formation and
evolution mechanisms are required to explain the existence of WASP-77A b.

Furthermore, disagreement can occur depending upon the study from which the
stellar abundances are taken. Several works have analysed the host star
(Kolecki & Wang, 2022; Polanski et al., 2022; Reggiani et al., 2022) and their
conclusions also do not always agree. As shown in Figure 4, the C/O ratios for
WASP-77A differ between studies,333We note that Reggiani et al. (2022)
suggested that the higher C/O ratio derived in Kolecki & Wang (2022) was due
to the latter study neglecting extinction in their analysis and that the
values from Polanski et al. (2022) and Reggiani et al. (2022) are in good
agreement for this elemental ratio., as do the C/H and O/H ratios. Hence, the
inferences made about the planet’s formation will clearly change depending
upon the study from which the stellar proprieties are derived as well as the
atmospheric study of WASP-77A b. As such, it becomes extremely difficult to
exactly pinpoint the formation scenario for WASP-77A b. These differences, and
thus issues, are highlighted in Figure 5 which shows the deviation from the
stellar C/O ratio depending on different datasets and analyses for WASP-77A
and WASP-77A b.

Clearly, studying a single planet alone will not be sufficient to place strict
constraints on the dominant formation and evolutionary pathway for hot
Jupiters. Instead, by observing many objects, correlations can be sought
between their bulk parameters and the atmospheric chemistry, thereby perhaps
shedding light on the processes that dominate their formation at a population
level. Such comparative planetology has been a long-held desire within the
field of exoplanetary atmospheres (e.g., Cowan & Agol, 2011; Tessenyi et al.,
2012). Population studies of exoplanet atmospheres have been conducted with
HST and Spitzer (e.g., Pinhas et al., 2019; Baxter et al., 2020; Kawashima &
Min, 2021; Changeat et al., 2022; Edwards et al., 2023), comparisons are
already being made between the inferences of JWST data for different planets
(e.g., August et al., 2023; Bean et al., 2023), and future missions are being
constructed specifically for this task (e.g., Tinetti et al., 2018; Stotesbury
et al., 2022).

Figure 5: The deviation from stellar C/O ratio for each atmospheric study of
WASP-77 A b when considering different stellar abundances. While it is no
longer applicable in this case, we also show the comparison to solar
abundances as these are the reference values if no stellar measurements have
been made. Most studies prefer a sub-stellar (blue squares) or stellar (whiter
squares) C/O ratio. The exception is the CHIMERA retrievals from Line et al.
(2021) although we note that they are all consistent with all of the stellar
values to 1$\sigma$ due to the large uncertainties on the planetary C/O ratio.

Thus far, most population studies have utilised heterogeneous datasets,
comparing the implied chemistry from a variety of studies and instruments.
However, without homogeneity, one may invoke a correlation that exists purely
because of the sensitivity of the datasets used: it is clear from this study,
as well as those from the literature (e.g., Pinhas et al., 2019; Pluriel et
al., 2020), that different datasets can lead to different atmospheric
compositions for the same planet. While it is clear that homogeneity will be
the key to comparative planetology, we note that homogeneity is by no means a
guarantee of success: biases will no doubt still be present, and the data will
never be sensitive to all species.

##  5 Conclusions

A joint fit to JWST NIRSpec and HST WFC3 spectra of WASP-77A b’s atmosphere
suggests a depletion in carbon and oxygen with respect to stellar values,
albeit with a C/O ratio that remains consistent with the stellar value as well
as evidence for a slightly super-stellar Ti/H ratio. From a formation
perspective, these results suggest that WASP-77A b may have formed outside of
the CO2 snow line, before migrating inwards and accreting significant rock-
rich planetesimals in its atmosphere. Further constraining Ti – as well as
other refractory species: Fe, V, Al, etc. – will allow us to more confidently
assess the claim for super-solar refractory abundance in WASP-77A b. In this
new era, the unprecedented constraints on elemental ratios offered by JWST
data should help us narrow down the diversity of formation pathways for hot
Jupiter exoplanets.

## Acknowledgements

The authors wish to thank Dr. Kazumasa Ohno and Dr. Tadahiro Kimura for their
insightful comments and discussion on the potential formation pathways for
WASP-77A b.

Funding: Q.C. is funded by the European Space Agency (ESA) under the 2022 ESA
Research Fellowship Program. B.E. received travel support for this work under
the ESA Science Faculty Funds, funding reference ESA-SCI-SC-LE117. The project
also received funding from the Science and Technology Funding Council (STFC)
grants ST/S002634/1 and ST/T001836/1.

Computing: The FI, DIRAC, and OzSTAR national facility at Swinburne University
of Technology provided the computing resources; this work utilized 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.
The OzSTAR program receives funding in part from the Astronomy National
Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by
the Australian Government.

Data: This work is based upon publicly available observations taken with the
NASA/ESA Hubble Space Telescope (GO-16168, PI: Megan Mansfield; Mansfield et
al., 2020) and the NASA/ESA/CSA JWST (GTO-1274, PI: Jonathan Lunine; Lunine &
Bean, 2017). These observations were facilitated by the Space Telescope
Science Institute, which is operated by the Association of Universities for
Research in Astronomy, Inc., under NASA contract NAS 5–26555. The HST and JWST
data presented in this paper were obtained from the Mikulski Archive for Space
Telescopes (MAST) at the Space Telescope Science Institute and can be accessed
via DOI: 10.17909/bsnh-fz53. We took the NIRSpec spectrum from Table 1 of
August et al. (2023) and the WFC3 spectrum from Changeat et al.
(2022)444https://github.com/QuentChangeat/HST_WFC3_Population/tree/main/Eclipse/Spectra/Eclipses.

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##  Appendix A Contamination Correction for the HST WFC3 Data of WASP-77A b

Here we discuss the reduction of the HST WFC3 spatial scanning data of the
eclipse of WASP-77A b and the complexities caused by WASP-77B, a fainter (by
$\sim$2 magnitudes; Maxted et al., 2013) K-dwarf companion to WASP-77A with a
3” separation. On the detector, the spectra from WASP-77A and WASP-77B
overlap, which would adversely affect the recovered emission spectrum for the
planet if the contamination is not corrected for.555Note that the JWST NIRSpec
data are not affected by similar issues because the slit (1.6” x 1.6”) and the
diffraction-limited point spread function (0.17”) are both smaller than the
separation between the two stars ($\sim$3”, Maxted et al., 2013; August et
al., 2023). Two HST visits were taken under programme GO-16168 (PI: Megan
Mansfield; Mansfield et al., 2020), each covering an eclipse. The separation
of the stars on the detector was different in each case. Two independent
studies using a different methodology to handle the contamination from
WASP-77B have previously reduced the emission spectrum of WASP-77A b: Changeat
et al. (2022) and Mansfield et al. (2022).

Changeat et al. (2022) used Wayne, a specialised WFC3 simulator (Varley et
al., 2017; Tsiaras & Ozden, 2019), to model the contribution of the secondary
star. First, they extracted the high-resolution spectra of each star using
Iraclis (Tsiaras et al., 2016b). These spectra, and the observational setup of
the real data, were then used as inputs to Wayne, which simulated high-
resolution, spatially scanned WFC3 images for each star individually. By
determining the flux from each star falling in each spectral bin, they
determined the flux ratio between the two stars and applied this as a
correction to the eclipse spectrum of WASP-77A b for each visit.

Meanwhile, Mansfield et al. (2022) utilised a different methodology. At the
beginning of each visit, a 0.556 s staring mode spectrum was taken with the
G141 grism. In this data, the spectra from the stars were not overlapping, so
the flux of each star could be independently extracted. They then used these
spectra to determine the fluxes of the WASP-77A and WASP-77B in each bandpass
and corrected the extracted flux using these. Next, they fitted the corrected
light curves to obtain the emission spectrum. In their work, Mansfield et al.
(2022) noted that their atmospheric models struggled to explain the spectrum
and attempted fits in which they deleted several of the data points in an
attempt to improve the fit.

Figure 6: Example extraction apertures when splitting the WFC3 data by the
non-destructive reads from the reverse (top) and forward (bottom) scans. The
extraction is clearly still contaminated by the fainter secondary star. When
the light curve from this extraction is fitted, the spectrum (see Figure 7)
closely matches that from Mansfield et al. (2022), suggesting that their
spectrum is still suffering from contamination. Figure 7: Comparison between
different HST WFC3 G141 reductions. The contaminated fit from the extraction
shown in Figure 6 matches the spectrum from Mansfield et al. (2022). The
spectrum from Changeat et al. (2022), which used Wayne to model the
contamination, has similar features but a different slope, being significantly
deeper at longer wavelengths. Left: absolute eclipse depth. Right: relative
eclipse depth having subtracted the mean depth.

In their work, August et al. (2023) noted a disagreement between the HST WFC3
spectrum from Mansfield et al. (2022) and their atmospheric models derived
from the JWST NIRSpec data only. When attempting a joint fit, they found their
models poorly fitted the HST data. The issue seemed to stem from the spectral
shape of the WFC3 data rather than the absolute eclipse depth. An absolute
offset is commonly found when using different models for the systematics seen
in HST data, but the spectral shape is generally conserved (Mugnai et al.,
2021; Edwards et al., 2023). Therefore, they suggested that perhaps the HST
WFC3 data could not be trusted but did not investigate the causes of this
discrepancy.

Here, we compare the spectra from Mansfield et al. (2022) and Changeat et al.
(2022), finding differences in their spectral shape. Given the robustness of
the spectral shape to pipeline assumptions when reducing and analysing most
HST data, the treatment of the contamination by WASP-77B seems the mostly
likely cause of this discrepancy.

Both studies extracted the spectrum using the non-destructive reads rather
than the full scan. Extracting WFC3 spatial scan data using the non-
destructive reads can be a good way of avoiding contamination from other
sources in the field of view. However, given the scan rate used, the
separation is not large enough in this case to allow for the spectra to be
disentangled in this way. To demonstrate this, Figure 6 shows example
extraction apertures from the second visit using this splitting extraction
mode for both forward and reverse scans. WASP-77B clearly contaminates the
extraction apertures, and so the resulting light curve contains flux from both
stars, demonstrating the need for a corrective factor to be applied.

Figure 8: Best-fit model when jointly fitting the JWST NIRSpec data and HST
WFC3 data from Mansfield et al. (2022). The residuals show a clear
correlation, indicating a poor fit which is likely due to the contamination
present in the spectrum.

In Figure 7, we show the contaminated eclipse spectrum that is obtained by
fitting the light curves of this extraction, as well as the corrected spectrum
from Changeat et al. (2022) (i.e, after the contamination factor is applied).
We note that the same pipeline, Iraclis, is used to extract and fit the light
curves in both cases. A clear difference in the two spectra is seen, both in
absolute depth and in spectral shape. Both differences are expected: WASP-77B
contributes flux to the aperture, thereby reducing the eclipse depth, and this
contribution is wavelength dependent.

In the same plot, we also compare the Iraclis spectra to the one reported by
Mansfield et al. (2022), which appears to closely match the contaminated
spectrum from Iraclis. The corrected spectrum from Changeat et al. (2022), on
the other hand, strongly disagrees with the one from Mansfield et al. (2022).
Looking more closely at methodology utilised by Mansfield et al. (2022), one
finds that they corrected for the contamination by applying a multiplicative
factor to the observed flux (see Equation 1). However, this is incorrect as
multiplying both the in- and out-of-eclipse data by the same factor does not
change the eclipse depth. Instead, one should subtract the flux from the
contaminating star.

The analysis of HST WFC3 data is complex. For instance, due to the geometry of
the instrument, the spectrum does not scan perfectly vertically, the scan rate
changes with position on the detector, and the forward and reverse scans have
different lengths (e.g., McCullough & MacKenty, 2012; Tsiaras et al., 2016b,
c). Hence, removing the flux contribution of a resolvable background star is
also difficult and requires specialised software (e.g., Varley et al., 2017).
It remains, of course, impossible to perfectly correct for such contamination.
However, the agreement between findings from the HST WFC3 data of Changeat et
al. (2022) and the JWST NIRSpec data from August et al. (2023), as well as the
ability to jointly fit both datasets, suggest that the methodology employed by
Changeat et al. (2022), which accounted for these instrumental complexities,
has led to a more trustworthy spectrum.

To further support this statement, we reproduce the joint retrievals presented
in the main text using the HST spectrum from Mansfield et al. (2022). In this
case, the models cannot explain the spectral shape of the WFC3 data, echoing
the results of August et al. (2023). Figure 8 shows the best-fit free
retrieval for this spectrum and highlights the strong remaining correlations
in the residuals. The retrieval also prefers an unphysically large abundance
of FeH (i.e, log10(FeH) = -3.26${}^{+0.39}_{-0.33}$). The CO and H2O
abundances, however, remained consistent with those stated in the main text
with log10(CO) = -4.58${}^{+0.36}_{-0.29}$, and log10(H2O) =
-4.47${}^{+0.18}_{-0.10}$. The result suggests, again, that the NIRSpec data
drive the robust constraints on CO and H2O, while the abundance of TiO, which
is mainly determined from the HST data, should be interpreted with caution.

Overall, our investigations for the HST WFC3 data of WASP-77A b reiterate the
conclusions from August et al. (2023): the HST spectrum from Mansfield et al.
(2022) cannot be reconciled with the JWST NIRSpec data. We suggest that the
main reason for this is that their reduction did not properly account for the
contamination of the companion star, WASP-77B.

##  Appendix B Table of Results

Here we present Table 1, which contains the elemental ratios derived in this
work.

Table 1: Elemental ratios derived from our joint fit to the HST WFC3 and JWST NIRSpec data using free chemistry. Stellar values (i.e., those for WASP-77A) are taken from Polanski et al. (2022) while the solar abundances are from Asplund et al. (2009). Ratio | Value | w.r.t Stellar | w.r.t Solar
---|---|---|---
C/O | 0.54${}^{+0.12}_{-0.12}$ | 0.91-1.43 | 0.76-1.2
log10(Ti/O) | -2.30${}^{+0.20}_{-0.23}$ | 18.00-49.58 | 16.05-44.19
log10(C/H) | -1.21${}^{+0.28}_{-0.26}$ | 0.03-0.12 | 0.03-0.12
log10(O/H) | -1.08${}^{+0.24}_{-0.17}$ | 0.04-0.10 | 0.04-0.10
log10(Ti/H) | 0.38${}^{+0.22}_{-0.23}$ | 1.05-2.92 | 1.07-2.99
log10(C+O/H) | -1.10${}^{+0.28}_{-0.20}$ | 0.04-0.10 | 0.04-0.10
log10(C+O+Ti/H) | -1.10${}^{+0.28}_{-0.20}$ | 0.04-0.10 | 0.04-0.10