# A Comparative Simulation Study of Hot and Ultra-hot Jupiter Atmospheres
using Different Ground-based High-resolution Spectrographs with Cross-
correlation Spectroscopy

Dwaipayan Dubey School of Earth and Planetary Sciences, National Institute of
Science Education and Research, Jatni 752050, Odisha, India  Homi Bhabha
National Institute, Training School Complex, Anushaktinagar, Mumbai 400094,
India  Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians-
Universität München, Scheinerstr. 1, D-81679 München, Germany
Exzellenzcluster ‘Origins’, Boltzmannstr. 2, D-85748 Garching, Germany  Liton
Majumdar School of Earth and Planetary Sciences, National Institute of Science
Education and Research, Jatni 752050, Odisha, India  Homi Bhabha National
Institute, Training School Complex, Anushaktinagar, Mumbai 400094, India

###### Abstract

In the era of state-of-the-art space-borne telescopes, high-resolution ground-
based observation has emerged as a crucial method for characterizing
exoplanets, providing essential insights into their atmospheric compositions.
In the optical and NIR regions, high-resolution spectroscopy has been powerful
for hot Jupiters (HJ) and ultra-hot Jupiters (UHJ) during their primary
transits, as it can probe molecules with better sensitivity. Here, we focus on
a comparative simulation study of WASP-76 b (UHJ) and WASP-77 A b (HJ) for
different number of transits, utilizing three ground-based spectrographs
(GIANO-B (TNG), CARMENES (CAHA), and ANDES (E-ELT)) with varying instrumental
parameters, spectral coverages, and resolutions. We aim to evaluate the
feasibility of the upcoming ground-based European Extremely Large Telescope
(E-ELT) in probing molecules from planet atmospheres and how it surpasses
other ground-based observatories in terms of detectability. With the 1-D
model, petitCODE, we have self-consistently simulated the atmospheric
pressure-temperature profiles, which are subsequently integrated into the 1-D
chemical kinetics model, VULCAN, to evolve the atmospheric chemistry. High-
resolution spectra are obtained by performing line-by-line radiative transfer
using petitRADTRANS. Finally, we use the resulting spectra to assess the
detectability ($\mathrm{\sigma_{det}}$) of molecular bands, employing the
ground-based noise simulator SPECTR. Utilizing cross-correlation spectroscopy,
we have successfully demonstrated the robust consistency between our
simulation study and real-time observations for both planets. ANDES excels
overall in molecular detection due to its enhanced instrumental architecture,
reinforcing E-ELT’s importance for studying exoplanet atmospheres.
Additionally, our theoretical simulations predict the detection of
$\mathrm{CO}$, $\mathrm{NH_{3}}$, and $\mathrm{H_{2}S}$ on WASP-76 b
atmosphere with a $\mathrm{\sigma_{det}}$ $>$ 3.

Extrasolar gaseous planets (2172); Hot Jupiters (753); Exoplanet atmospheres
(487); Exoplanet atmospheric composition (2021); Spectroscopy (1558); High
resolution spectroscopy (2096)

##  1 Introduction

Exoplanetary science has made remarkable advancements in recent years, driven
by numerous discoveries that have significantly changed our understanding of
planetary systems and their complex characteristics. In recent decades,
spectroscopic measurements have become an essential window for understanding
atmospheric compositions, its dynamics, and temperature profiles of exoplanets
(Crossfield, 2015). While space-based observations have historically been
crucial in providing initial characterizations of atmospheres for transiting
exoplanets, ground-based observations have increasingly taken on a significant
role in undertaking in-depth investigations of their atmospheric chemistry
(Snellen et al., 2010; Wyttenbach et al., 2015; Brogi et al., 2016, 2018;
Alonso-Floriano et al., 2019; Sánchez-López et al., 2019; Giacobbe et al.,
2021). In contrast to low-resolution spectroscopy, high-resolution
spectroscopy offers the clear differentiation of molecular fingerprints
originating from various species, hence facilitating more accurate detection.
The initial breakthrough in ground-based observations occurred with the
detection of Na in the atmospheres of HD 189733 b (Redfield et al., 2008) and
HD 209458 b (Snellen et al., 2008). Since then, a large number of molecules
have been identified in $\mathrm{H_{2}}$-dominated atmospheres of gas giants,
primarily in the near-infrared spectral range, leveraging high-resolution
spectroscopy: $\mathrm{H_{2}O}$ (Birkby et al., 2013a; Alonso-Floriano et al.,
2019), CO (Snellen et al., 2010; Brogi et al., 2012), $\mathrm{CH_{4}}$
(Guilluy et al., 2019), $\mathrm{C_{2}H_{2}}$, $\mathrm{NH_{3}}$ (Giacobbe et
al., 2021; Carleo et al., 2022), HCN (Hawker et al., 2018; Cabot et al.,
2019), etc.

Ground-based observatories, particularly the inbuilt high-resolution
spectrographs, can resolve the molecular features into an ensemble of
distinctive lines. In spectroscopy, the signal-to-noise ratio improves as the
square root of the number of lines observed ($\mathrm{N_{lines}}$) in a
planetary spectrum, hence making high-resolution spectroscopy more suitable
for broadband absorbers of comparable line strengths (Birkby, 2018). For high-
resolution spectroscopy, this can be understood from the simplified first-
order signal-to-noise ratio equation from Birkby (2018) in the photon-limited
region:

$\mathrm{SNR_{planet}=\Big{(}\frac{S_{p}}{S_{*}}\Big{)}SNR_{star}\sqrt{N_{lines}}}$

Here, $\mathrm{\frac{S_{p}}{S_{*}}}$ is the planet-to-star signal ratio and
$\mathrm{SNR_{star}}$ is the square root of the photon-limited, total signal-
to-noise of the host star. However, this method encounters the inherent
challenge of disentangling the planetary signals from strong stellar and
telluric backgrounds (Sánchez-López et al., 2019). This challenge can be
effectively addressed through the detrending process. It incorporates Doppler
shifts into the planet spectra over an extended observation period during the
transit and, consequently, separates the planet signal successfully from the
complex backgrounds of stellar and telluric lines. The detrended spectra are
then subjected to cross-correlation with molecular templates, thereby
quantifying the detection significance associated with different molecules
(Snellen et al., 2010; Brogi et al., 2012; Birkby et al., 2013b).

The increased spectral resolution is particularly significant when studying
the expanded absorption and emission characteristics observed in hot Jupiters
(HJs) and ultra-hot Jupiters (UHJs), as they often display pronounced thermal
inversions and exhibit unique chemical compositions (Fortney et al., 2008;
Madhusudhan & Seager, 2010; Line et al., 2016; Parmentier et al., 2018;
Arcangeli et al., 2018; Bell & Cowan, 2018). These gas giants are of great
importance in the realm of exoplanetary science since they can challenge our
current understanding of the planetary formation, migration, and atmospheric
evolution (Wright et al., 2012; Dash et al., 2022). While HJs are recognized
for their elevated temperatures, UHJs, positioned in even closer proximity to
their host stars, experience substantial irradiation, which causes them to
have a day-side temperature $\gtrsim$ 2200 K (Parmentier et al., 2018). These
extreme climatic conditions facilitate the development of unique and often
exotic atmospheric chemical processes such as the thermal dissociation of
molecules followed by recombination of them on the cooler night side
(Parmentier et al., 2018; Arcangeli et al., 2018; Bell & Cowan, 2018).
Furthermore, they represent the most extensively observed category of
exoplanets to date and, consequently, the most preferred targets for ground-
based observations.

WASP-77 A b and WASP-76 b, our targeted HJ and UHJ, are crucial in this regard
as they show distinct non-inverted and inverted behaviors, respectively, in
the pressure-temperature profile (PT profile) (Edwards et al., 2020; Line et
al., 2021; Changeat et al., 2022; Edwards & Changeat, 2024) and thus have
different implications on their atmospheres. While several atomic and ionic
species have been detected in the atmospheres of UHJs (Hoeijmakers et al.,
2019, 2020; Casasayas-Barris et al., 2019; Tabernero et al., 2021), it is
equally expected to have diatomic and triatomic molecular species as a crucial
part of their atmospheric compositions (Landman et al., 2021). The recent
detections of OH, $\mathrm{H_{2}O}$, and HCN in the atmosphere of WASP-76 b
using CAREMENS spectrograph serve as compelling evidence supporting this fact
(Sánchez-López et al., 2022; Landman et al., 2021). Conversely, CO and
$\mathrm{H_{2}O}$ line detections on WASP-77 A b using IGRINS spectrometer
paves the way for conducting a simultaneous comprehensive analysis to study
HJs too using ground-based observation (Line et al., 2021).

Figure 1: Flowchart representing our methodical pipeline: The big boxes
represent the four different pillars (radiative-convective equilibrium
calculation, disequilibrium chemistry, high-resolution spectra, and synthetic
observations), which are connected with each other, of our analysis. The cyan
rectangles represent the outputs from each model, while the white shapes are
the user-specified inputs for the respective models. Gray rectangles are the
outcomes of the whole pipeline, which lead to the calculation of the detection
significance of molecular bands.

In this work, we present a complementary analysis of WASP-77 A b and WASP-76 b
atmospheres using three high-resolution ground-based spectrographs: GIANO-B
(Telescopio Nazionale Galileo:
TNG)111https://www.tng.iac.es/instruments/giano-b/ (Oliva et al., 2012),
CARMENES (Centro Astronomico Hispano Alemán:
CAHA)222https://www.caha.es/telescope-3-5m/carmenes (Quirrenbach et al., 2014,
2018), and ANDES (European Extremely Large Telescope: E-ELT; From this point
forward, throughout this paper, the E-ELT will be referred to as the
ELT.)333https://elt.eso.org/instrument/ANDES/ (Di Marcantonio et al., 2022).
Our main motivation lies in understanding the spectrographs’ ability to probe
different molecular bands using cross-correlation spectroscopy. In section 2,
we have outlined our assumptions and methods for simulating the planet’s
atmosphere using the 1-D radiative-convective equilibrium model, petitCODE
(Mollière et al., 2015; Mollière, 2017), and 1-D chemical kinetics model,
VULCAN (Tsai et al., 2017, 2021). In addition, we have briefed our method of
calculating synthetic observation using the 1-D radiative transfer model,
petitRADTRANS (Mollière et al., 2019, 2020), and the ground-based noise
simulator, Spectral Planetary ELT Calculator (SPECTR) (Currie et al., 2023).
The next section, i.e., Section 3, presents our results from the atmospheric
models and the detection significance of molecular bands. Finally, we end up
with our findings in Section 4.

Table 1: Relevant parameters of the WASP-77 A b and WASP-76 b systems

|  Star Parameters |  |
---|---|---|---
| WASP-77 A |  WASP-76 |
3.5 Parameters | Values |  References |  | Values |  References
$M_{*}$/$M_{\odot}$ | 1.002 |  Maxted et al. (2012) |  | 1.460 |  West et al. (2016) |
$R_{*}$/$R_{\odot}$ | 1.12 |  Maxted et al. (2012) |  | 1.730 |  West et al. (2016) |
$[$Fe/H$]$ | 0 |  Maxted et al. (2012) |  | 0.23 |  West et al. (2016) |
$T_{*}$ (K) | 5500 |  Maxted et al. (2012) |  | 6250 |  West et al. (2016) |
|  Planet Parameters |  |
| WASP-77 A b |  WASP-76 b |
3.5 $M\mathrm{{}_{p}}$/$M\mathrm{{}_{Jup}}$ | 1.759 |  Maxted et al. (2012) |  | 0.922 |  West et al. (2016)
$R\mathrm{{}_{p}}$/$R\mathrm{{}_{Jup}}$ | 1.210 |  Maxted et al. (2012) |  | 1.877 |  West et al. (2016) |
log(g) | 3.477 |  Southworth et al. (2007) |  | 2.8 |  Southworth et al. (2007) |
$T\mathrm{{}_{eq}}$ (K) | 1715 |  Cortés-Zuleta et al. (2020) |  | 2160 |  West et al. (2016) |
C/O | 0.8 |  Hoch et al. (2023) |  | 1.2 |  Hoch et al. (2023) |
$a$ (AU) | 0.023 |  Cortés-Zuleta et al. (2020) |  | 0.033 |  West et al. (2016) |
Period (days) | 1.36 |  Ivshina & Winn (2022) |  | 1.81 |  Ivshina & Winn (2022) |
Distance (parsec) | 93 |  Maxted et al. (2012) |  | 120 |  West et al. (2016) |

##  2 Methods

Our methodical pipeline for assessing the detectability of molecular spectral
features using the cross-correlation analysis is outlined in Figure 1. In this
current section, we discuss a detailed description of the methods followed.

###  2.1 Atmospheric structures of WASP-76 b and WASP-77 A b

The physical characteristics of a planet’s atmosphere exert a direct influence
on its spectral properties and molecular abundance profiles. We self-
consistently construct the PT profiles for these two planets using 1-D forward
model petitCODE (see Figure 2). petitCODE employs a radiative-convective and
thermochemical equilibrium assumption to simulate planetary atmospheres
numerically. Based on the input parameters (star and planet parameters for
both systems are listed in Table LABEL:tab:system), petitCODE iterates the
atmospheric structure of the planet till it achieves an equilibrium between
the chemical abundances, their opacities and radiation fields with the PT
profile of the atmosphere. It solves the radiative transfer using the
Feautrier method and implements the Accelerated Lambda Iteration (Olson et
al., 1986) and Ng acceleration (Ng, 1974) methods to expedite convergence.

Figure 2: Self-consistent PT profile for both planets, simulated with the 1-D
radiative-convective equilibrium model, petitCODE, using the system parameters
and elemental abundances listed in Table LABEL:tab:system. The orange line
shows the inverted PT profile for WASP-76 b, whereas the violet one represents
the non-inverted PT profile for WASP-77 A b.

We have used petitCODE’s default chemical parameters for the calculation and
considered $\mathrm{CH_{4}}$, $\mathrm{H_{2}O}$, $\mathrm{CO_{2}}$,
$\mathrm{HCN}$, $\mathrm{CO}$, $\mathrm{H_{2}S}$, $\mathrm{NH_{3}}$,
$\mathrm{C_{2}H_{2}}$, $\mathrm{Na}$, $\mathrm{K}$, $\mathrm{TiO}$, and
$\mathrm{VO}$ as opacity sources in the atmosphere. Additionally,
$\mathrm{H_{2}}$-$\mathrm{H_{2}}$ and $\mathrm{H_{2}}$-$\mathrm{He}$ opacities
were used as collision induced absorption (CIA) species. For defining the
carbon-to-oxygen ratio (C/O), we followed the same prescription as Madhusudhan
(2012), Mollière et al. (2015), Woitke et al. (2018), and Molaverdikhani et
al. (2019), where the oxygen elemental abundance was altered, but the carbon
elemental abundance was maintained at a constant value.

We considered globally averaged insolation treatment for radiative transfer
calculation. For cloud treatment, we opted for Ackerman & Marley (Ackerman &
Marley, 2001) prescription: providing the settling factor
($f\mathrm{{}_{sed}}$) = 2 and lognormal particle distribution width
($\sigma\mathrm{{}_{g}}$) = 1.05.

###  2.2 Chemical evolution: vertical mixing and photochemistry in action

In our study, we have taken the PT profiles from petitCODE as input for the
1-D chemical kinetics model VULCAN444https://github.com/exoclime/VULCAN and
then evolved the atmospheric chemistry for both planets. We utilize the
original ‘SNCHO photo network’ from the repository, which consists of 1150
reactions connecting 96 different species. Disequilibrium chemistry is
effectively incorporated into planet atmospheres by implementing eddy
diffusion, molecular diffusion, and photochemical processes. While chemical
reactions govern molecular diffusion and photochemistry, eddy diffusion is
regulated by the Eddy diffusion coefficient ($K_{\mathrm{zz}}$), which is kept
constant = $\mathrm{10^{10}}$ $\mathrm{cm^{2}/s}$ (following the most common
value from Tsai et al. (2017)) for both planets. Apart from the star-planet
parameters, planet-specific elemental abundances (O/H, N/H, C/H, S/H, and
He/H) are also necessary for VULCAN to initiate the equilibrium chemistry
calculation using its coupled equilibrium chemistry solver,
Fastchem555https://github.com/exoclime/FastChem (Stock et al., 2018). We keep
the He/H abundance ratio constant at 0.085 and change the remaining abundance
values accordingly, following the C/O ratio and metallicity of planets (see
Table LABEL:tab:system). The C/O ratio influences the elemental abundances of
carbon and oxygen specifically (refer to Section 2.1). In contrast,
metallicity affects the elemental abundances of all elements. The notation
[Fe/H] is used to represent metallicity on a logarithmic scale. Here, [Fe/H] =
0 denotes solar metallicity, [Fe/H] = 1 indicates an elemental abundance ten
times greater than solar, and [Fe/H] = -1 signifies an elemental abundance ten
times lower than solar.

Table 2: Instrumental configuration for three ground-based observatories

Telescope/ | Wavelength | Resolution | Diameter (m) | Read Noise | Dark Current | $\mathrm{T_{opt}}$
---|---|---|---|---|---|---
Instrument | ($\mu$m) |  | (m) | ($\mathrm{e^{-}}$) | ($\mathrm{e^{-}}$/pixel/s) | (K)
3.5 TNG (GIANO-B) | 0.95-2.45 | 50000 | 3.58 | 5 | 0.05 | 50
CAHA (CARMENES) | 0.52-1.71 | 80000 | 3.5 | 13.52 | 0.002 | 140
ELT (ANDES) | 0.4-1.8 | 100000 | 39.3 | 3 | 0.00056 (optical) | 143
|  |  |  |  | 0.0011 (NIR) |

  * a

Note: The instrumental parameters are taken from the respective websites of
the high-resolution spectrographs. GIANO-B:
https://www.tng.iac.es/instruments/giano-b/. CARMENES:
https://www.caha.es/telescope-3-5m/carmenes. ANDES:
https://elt.eso.org/instrument/ANDES/.

###  2.3 Transmission spectra simulation from planet atmospheres

We couple the time-evolved chemistry from VULCAN to the 1-D radiative transfer
model, petitRADTRANS666https://petitradtrans.readthedocs.io/en/latest/, to
simulate high-resolution line-by-line synthetic transmission spectra for both
planets at a reference pressure level of $P_{0}$ = 0.01 bar. We utilize a
customized Python3 wrapper for this purpose. We have considered OH,
$\mathrm{H_{2}O}$, CO, $\mathrm{CO_{2}}$ (Rothman et al., 2010),
$\mathrm{CH_{4}}$, $\mathrm{HCN}$, $\mathrm{NH_{3}}$, $\mathrm{H_{2}S}$ (Chubb
et al., 2021) (for WASP-76 b) and OH, $\mathrm{H_{2}O}$, CO,
$\mathrm{CO_{2}}$, $\mathrm{NH_{3}}$, $\mathrm{H_{2}S}$ (for WASP-77 A b) as
opacity sources. The selection of chemical species is determined by their
average molecular volume mixing ratios (VMRs) $>$ $\mathrm{10^{-8}}$ at the
photospheric level. Molecules with a lower VMR than $\mathrm{10^{-8}}$ would
not have a significant impact on the planet’s spectra. Hence, considering
other molecules does not add any additional change to the planet’s spectra and
hence, to the analysis. The photosphere is the region in the atmosphere that
contributes more to the planet’s spectra and lies in the nexus of 1 bar-0.1
mbar region in the atmosphere. In addition, we use CIA opacities for
$\mathrm{H_{2}}$-$\mathrm{H_{2}}$ and $\mathrm{H_{2}}$-$\mathrm{He}$ and
$\mathrm{H_{2}}$ and He as Rayleigh scattering species. The wavelength range
and resolution for different spectra are instrument-specific (see Table
LABEL:tab:instruments). The default resolution for line-by-line opacities is R
= $\mathrm{10^{6}}$ in petitRADTRANS. To avoid numerical inefficiency, we
downsample the high-resolution molecular opacity files to the spectrograph
resolutions before the radiative transfer calculation. For different
instrumental resolutions, the rebinning of the opacity files is done using the
inbuilt opacity sampling method (by providing the resolution downsampling
factor) of petitRADTRANS.

###  2.4 Noise calculation and observation simulation

Ground-based observations pose significant challenges, primarily due to the
presence of Earth’s atmosphere. The prominent challenge stems from the
interference of telluric lines in the observed spectra, which introduces a
caveat when attempting to estimate the molecular fingerprints within the
planetary spectrum. To address this issue, we have employed a cutting-edge,
coronagraph-free, ground-based noise simulator pipeline,
SPECTR777https://github.com/curriem/spectr, to simulate the observations for
both planets using different ground-based instruments. It quantifies the
planetary photon count as the signal while considering starlight, zodiacal
light, exo-zodiacal light, moonlight, airglow, instrumental thermal emission,
and Earth’s atmosphere (telluric) photon counts as noise sources.

Figure 3: Telluric transmission from SkyCalc for the total wavelength coverage
of all the instruments: blue band is for TNG (0.95-2.45 $\mu$m), orange band
for CAHA (0.52-1.71 $\mu$m), and green band for ELT (0.4-1.8 $\mu$m). The
telluric lines were calculated for the resolution R = 80000. It shows the
differential effect of telluric lines on the instrumental wavelength
coverages. While similar telluric lines impact CARMENES and ANDES
observations, GIANO-B has some influence at the longer wavelengths.

SPECTR is integrated with the state-of-the-art atmospheric telluric model,
Cerro Paranal Advanced Sky Model
(SkyCalc)888https://www.eso.org/observing/etc/doc/skycalc/helpskycalccli.html
(Noll et al., 2012), from the European Southern Observatory for simulating
wavelength-dependent background and telluric lines at the resolution specific
to the instrument. In line with the approach outlined in the (Currie et al.,
2023), we have selected Paranal as the observatory location and assumed a
precipitable water vapor level of 3.5 mm for calculating Earth’s atmospheric
telluric lines. Observed telluric transmission at the site of observation is
shown in Figure 3. The read noise and dark current values for different
instruments are listed in Table LABEL:tab:instruments. We have set the
exposure duration equal to 488 seconds for each target, following the WASP-76
b observations by Landman et al. (2021) and Sánchez-López et al. (2022) using
CARMENES spectrograph. We have kept the same exposure time for all the
spectrographs to estimate a comparative understanding of the instrumental
capability of molecular detection.

It is important to note that we have assumed a consistent throughput of 21%
for GIANO-B (Oliva et al., 2006), 7.9% for CARMENES (Seifert et al., 2016),
and 10% for ANDES (Currie et al., 2023). Throughputs are usually wavelength-
dependent. However, the measurements of instrumental throughputs are limited
to certain wavelength points. To overcome this issue, we have considered the
best throughput value for the spectrographs. Hence, our assumption serves as
an upper limit for molecular detection from the perspective of the
instrumental throughput parameter. For telescope mirror temperature, we have
followed (Currie et al., 2023) and maintained a consistent temperature of 273
K across all observatories. But the detector temperatures ($\mathrm{T_{opt}}$)
are set according to the specifications outlined in Table
LABEL:tab:instruments. Different sources of noise components are shown in
Figure 4. Furthermore, for uniformity, we have designated 100 detector pixels
per resolution for all the detectors and carried out the observation for 1 and
3 transits for both planets (following the observations on hot gas giant
planets by Sánchez-López et al. (2020), Landman et al. (2021), Sánchez-López
et al. (2022), Carleo et al. (2022), Borsato et al. (2024), and Prinoth et al.
(2024)).

Figure 4: Different noise sources in the visible and NIR region for different
instruments: 1. Background noise (telluric emission + thermal emission of
instrument + zodiacal light + airglow) (bluish-green) 2. Readout noise (red),
and 3. Dark current noise (blue). The noises are measured for an exposure
duration of 488 seconds at native resolutions specific to instruments (see
Table LABEL:tab:instruments). It shows the variability of background noise
over a wide wavelength span, the different instrumental read-out noise, and
the dark current values. Overall, it presents the differential influence of
noise profiles on different telescopic observations. The step function
observed in the Dark current noise for the ELT arises from the distinct dark
current counts in the optical and NIR regions. For TNG, the values for readout
noise and dark current noise are the same.

The pipeline Doppler shifts the planet’s spectrum and multiplies the telluric
lines at each exposure to it. The systematic radial velocity shifts relative
to Earth are taken to be -1.07 km $\mathrm{s^{-1}}$ for WASP-76 b (West et
al., 2016) and 1.68 km $\mathrm{s^{-1}}$ for WASP-77 A b (Maxted et al.,
2012). The pipeline systematically includes out-of-transit observations
alongside each in-transit observation to facilitate the precise isolation of
the planet signal and noise within observed transmission spectra. To enhance
data quality, the pipeline employs an outlier mask and high-pass filters to
eliminate data points with exceptionally low signal-to-noise ratios and
mitigate low-frequency variations.

Figure 5: Mixing ratio profiles from VULCAN for specific molecules in the
atmosphere of both planets. WASP-77 A b (left): OH, $\mathrm{H_{2}O}$, CO,
$\mathrm{CO_{2}}$, $\mathrm{NH_{3}}$, $\mathrm{H_{2}S}$, and WASP-76 b
(right): OH, $\mathrm{H_{2}O}$, CO, $\mathrm{CO_{2}}$, $\mathrm{NH_{3}}$,
$\mathrm{H_{2}S}$, $\mathrm{CH_{4}}$, HCN. Molecules are selected considering
the average mixing ratios $>$ $\mathrm{10^{-8}}$ between the 1 bar-0.1 mbar
pressure layers (photosphere).

It computes the detection significance ($\mathrm{\sigma_{det}}$) of molecular
bands using the cross-correlation spectroscopy technique as outlined in (Brogi
et al., 2016). This method exhibits a high degree of sensitivity to line
features and demonstrates robustness even in the presence of minimal
perturbations in radial velocity. Our approach involves cross-correlating the
simulated spectra ($\mathrm{f(\lambda)}$) for both planets with Doppler-
shifted template spectra ($\mathrm{f(\lambda-\lambda^{\prime})}$) representing
various molecular bands and, thus, calculating the detectability of these
molecules across a range of ground-based facilities operating at different
resolutions and different wavelength regimes. Here, $\mathrm{\lambda}$ denotes
the bin number, while $\mathrm{\lambda^{\prime}}$ signifies the bin shift
attributable to relative velocity. To generate velocity-shifted template
spectra, we opt for an extensive grid of Doppler velocities, spanning from
-150 km $\mathrm{s^{-1}}$ to +150 km $\mathrm{s^{-1}}$, with 101 intervals.
Here, we will brief the numerical recipe to compute the
$\mathrm{\sigma_{det}}$ following (Currie et al., 2023) (for more details see
Brogi & Line (2019)):

$\ \mathrm{s_{f}^{2}=\frac{1}{N}\sum_{\lambda}f^{2}(\lambda),}\text{
$\mathrm{s_{f}^{2}}$ = variance of the observed spectrum}$ (1)

$\mathrm{s_{g}^{2}=\frac{1}{N}\sum_{\lambda}f^{2}(\lambda-\lambda^{\prime}),}\text{
$\mathrm{s_{g}^{2}}$ = variance of the template spectrum}$ (2)

where N is the total number of pixels. Hence, the cross-covariance can be
defined as

$\mathrm{R(\lambda)=\frac{1}{N}\sum_{\lambda}f(\lambda)f(\lambda-\lambda^{\prime})}$
(3)

Now, Eqs. 1,2, and 3 can be coupled together to estimate the cross-correlation
function (CCF) ($\mathrm{C(\lambda)}$), which peaks at the relative velocity
of zero for a detectable planetary signal

$\mathrm{C(\lambda)=\frac{R(\lambda)}{\sqrt{\mathrm{s_{f}^{2}s_{g}^{2}}}}}$
(4)

Thereafter, a $\mathrm{\chi^{2}}$ analysis is followed between estimated CCF
and a flat line to test for a signal (Brogi et al., 2016)

$\mathrm{\chi^{2}_{CCF}=\sum_{\lambda}\frac{[C(|\lambda|<\lambda_{0})-0]^{2}}{\sigma^{2}_{C(|\lambda|>\lambda_{0})}}}$
(5)

In Eq. 5, the $\mathrm{\chi^{2}_{CCF}}$ is summed over the velocity shifts
($\mathrm{|\lambda|}$) less than $\mathrm{\lambda_{0}}$ = 5 km
$\mathrm{s^{-1}}$. These values only represent the planet signal in the
calculation and the typical width of the CCF peak. The denominator, on the
other hand, signifies the variance, excluding any potential planetary signals.
Utilizing the cumulative $\mathrm{\chi^{2}}$ distribution function and inverse
survival function of a normal distribution, $\mathrm{\chi^{2}_{CCF}}$ is
converted to p-value and later on, to a sigma interval. Finally,
$\mathrm{\sigma_{det}}$ is estimated as a measure of the deviation of the CCF
from a Gaussian distribution.

Figure 6: Illustration of the principal chemical pathways and their conversion
rates at a pressure level of 0.01 bar (consistent with the photosphere) for
specific molecules. Left panel: WASP-76 b. Right panel: WASP-77 A b. The “tan”
shaded areas represent molecules with an average VMR $>$ $\mathrm{10^{-8}}$
between 1 bar-0.1 mbar (photosphere). Molecules outside these ‘tan’ regions,
indicated by ‘magenta’ circles, are non-significant in terms of VMR, but they
serve as crucial sources and sinks for some molecules. For detailed model-
specific analyses of reaction pathways, including the incorporation of all
secondary reactants, see Figures 11, 12 in the Appendix A.

##  3 Results

###  3.1 High-resolution transmission spectra: linking molecular VMRs to their
spectral signatures

As discussed in Section 2.3, the determination of molecules for simulating
synthetic high-resolution spectra depends on their average VMRs $>$
$\mathrm{10^{-8}}$ in the planetary photosphere. The criterion leads us to the
inclusion of OH, $\mathrm{H_{2}O}$, $\mathrm{CH_{4}}$, CO, $\mathrm{CO_{2}}$,
$\mathrm{HCN}$, $\mathrm{NH_{3}}$, $\mathrm{H_{2}S}$ in the atmosphere of
WASP-76 b and OH, $\mathrm{H_{2}O}$, CO, $\mathrm{CO_{2}}$, $\mathrm{NH_{3}}$,
$\mathrm{H_{2}S}$ in the atmosphere of WASP-77 A b. The molecular VMRs for
both planets have been showcased in Figure 5. The atmospheric compositions of
the planets are significantly influenced by CO and $\mathrm{H_{2}O}$, with
$\mathrm{H_{2}S}$ also showing a considerable presence in both of them. It is
worth mentioning that at a pressure level of $\sim$ 0.01 bar, the VMR of OH
starts rising for both planets, and this can be attributed to the reduction in
levels of $\mathrm{H_{2}O}$ and, in particular, $\mathrm{NH_{3}}$ (see Figure
6). They both contribute $\sim$ 74% (for WASP-76 b) and $\sim$ 99% (for
WASP-77 A b) to the net OH formation at the specific pressure level. While
$\mathrm{H_{2}O}$ undergoes a single reaction: $\mathrm{H_{2}O}$ \+ H
$\rightarrow$ OH + $\mathrm{H_{2}}$ for the conversion, $\mathrm{NH_{3}}$ has
different routes to form OH. For WASP-76 b, the fastest interconversion
follows the path

$\mathrm{NH_{3}}$ \+ H $\rightarrow$ $\mathrm{NH_{2}}$ \+ $\mathrm{H_{2}}$
---
$\mathrm{NH_{2}}$ \+ H $\rightarrow$ $\mathrm{H_{2}}$ \+ $\mathrm{NH}$
$\mathrm{NH}$ \+ S $\rightarrow$ $\mathrm{H}$ \+ $\mathrm{NS}$
$\mathrm{NS}$ \+ H $\rightarrow$ $\mathrm{SH}$ \+ $\mathrm{N}$
$\mathrm{H_{2}O}$ \+ SH $\rightarrow$ $\mathrm{H_{2}S}$ \+ $\mathrm{OH}$
net: $\mathbf{NH_{3}}$ \+ $\mathrm{H_{2}O}$ \+ 2H + S $\rightarrow$ OH +
$\mathrm{H_{2}S}$ \+ N + $\mathrm{2H_{2}}$

whereas, for WASP-77 A b it undergoes

$\mathrm{NH_{3}}$ \+ SH $\rightarrow$ $\mathrm{NH_{2}}$ \+ $\mathrm{H_{2}}S$
---
$\mathrm{H_{2}S}$ \+ H $\rightarrow$ $\mathrm{H_{2}}$ \+ $\mathrm{SH}$
$\mathrm{SH}$ \+ $\mathrm{H_{2}O}$ $\rightarrow$ $\mathrm{H_{2}S}$ \+
$\mathrm{OH}$
net: $\mathbf{NH_{3}}$ \+ $\mathrm{H_{2}O}$ \+ SH + H $\rightarrow$ OH +
$\mathrm{H_{2}S}$ \+ $\mathrm{NH_{2}}$ \+ $\mathrm{H_{2}}$

Figure 7: High-resolution transmission spectra of WASP-77 A b for different
instruments (see instrumental parameters from Table LABEL:tab:instruments.
Blue: GIANO-B (TNG). Orange: CARMENES (CAHA). Green: ANDES (ELT). The figure
illustrates the contributions from different molecular bands to the net planet
spectra for all cases. Despite having a significant average photospheric VMR,
discernible $\mathrm{CO_{2}}$ and $\mathrm{NH_{3}}$ features are not present
in any of the synthetic spectra.

Figure 8: High-resolution transmission spectra of WASP-76 b for different
instruments (see instrumental parameters from Table LABEL:tab:instruments.
Blue: GIANO-B (TNG). Orange: CARMENES (CAHA). Green: ANDES (ELT). The figure
illustrates the contributions from different molecular bands to the net planet
spectra for all cases. Despite having significant average photospheric VMRs,
discernible $\mathrm{CH_{4}}$ and $\mathrm{CO_{2}}$ features are not present
in any of the synthetic spectra.

The reactions in red colors indicate the rate-limiting steps for the whole
reaction pathways. On the other hand, a large amount of $\mathrm{NH_{3}}$ gets
converted to $\mathrm{H_{2}S}$ and $\mathrm{H_{2}O}$, leading to a further
reduction in $\mathrm{NH_{3}}$ concentration on both planets. A similar story
for HCN has been observed too on WASP-76 b, producing $\mathrm{H_{2}O}$ and
$\mathrm{H_{2}CN}$ significantly. Figure 6, which provides a robust visual
representation of chemical networks for both planets, emphasizes this fact
further. The figure highlights the molecular interconversions, with their net
percentage contribution to the formation and destruction of other molecules.
Types of reaction intermediates that participate in the fastest molecular
conversion pathway are shown in Figures 11 and 12. The shortest route for
molecular interconversions is built upon the principle of Dijkstra’s algorithm
(the principle of finding the least distance between two nodes in a complex
network with other nodes present in between) (Dijkstra, 2022) and is adopted
from Tsai et al. (2018). While not being present significantly in the
atmospheres, NH, SH, NS, and $\mathrm{NH_{2}}$ play very crucial roles in the
interconversions (see Appendix A).

Figures 7 and 8 present synthetic spectra for WASP-77 A b and WASP-76 b,
respectively, showcasing their spectral characteristics. These models are
generated at the resolutions and wavelength ranges corresponding to the TNG
(GIANO-B), CAHA (CARMENES), and ELT (ANDES) instruments. The figures also
illustrate the molecular contributors responsible for various spectral
features. It is noteworthy that WASP-77 A b lacks discernible
$\mathrm{NH_{3}}$ and $\mathrm{CO_{2}}$ features, while WASP-76 b exhibits an
absence of $\mathrm{CH_{4}}$ and $\mathrm{CO_{2}}$ features in their
respective spectra. This is due to the prominent features of other molecules,
coupled with the lower abundance of the respective molecules.

Figure 9: Correlation coefficient vs. velocity shift map for different
molecular bands for 3 transits of WASP-76 b. Blue: GIANO-B (TNG). Orange:
CARMENES (CAHA). Green: ANDES (ELT). Each row corresponds to a specific
molecule (from top to bottom: OH, $\mathrm{H_{2}O}$, $\mathrm{CH_{4}}$, CO,
$\mathrm{CO_{2}}$, $\mathrm{HCN}$, $\mathrm{NH_{3}}$, $\mathrm{H_{2}S}$).
Molecular bands are listed explicitly in Table LABEL:tab:detetcion_Wasp76b.
Table 3: Table summarizing the $\mathrm{\sigma_{det}}$ achieved for different
molecular bands for different number of transits of WASP-76 b from different
ground-based instruments (bands with $\mathrm{\sigma_{det}}$ $>$ 3 are shown
in bold)

|  |  |  | No. of transit = 1 |  |  | No. of transit = 3 |
---|---|---|---|---|---|---|---|---
3.5 Molecules | Bands | Wavelength range | TNG | CAHA | E-ELT | TNG | CAHA | E-ELT
| ($\mu$m) | ($\mu$m) | (GIANO-B) | (CARMENES) | (ANDES) | (GIANO-B) | (CARMENES) | (ANDES)
3.5 OH | 0.68 | 0.66 - 0.70 | – | No detection | No detection | – | No detection | No detection
| 0.85 | 0.77 - 0.93 | – | No detection | No detection | – | No detection | No detection
| 1.15 | 1.0 - 1.3 | No detection | No detection | 2.36 | No detection | 3.06 | 3.31
| 1.60 | 1.5 - 1.7 | 3.98 | 3.23 | 12.87 | 4.66 | 4.41 | 14.75
$\mathrm{H_{2}O}$ | 0.90 | 0.89 - 0.99 | 6.35 | 5.10 | 19 | 6.68 | 5.64 | 19.12
| 0.94 | 0.93 - 0.95 | – | 1.96 | 13.17 | – | 3.27 | 14.45
| 1.00 | 0.95 - 1.05 | 3.58 | 1.21 | 18.57 | 8.64 | 4.54 | 19.94
| 1.10 | 1.1 - 1.2 | 3.01 | No detection | 15.87 | 3.34 | No detection | 17.63
| 1.30 | 1.3 - 1.55 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.90 | 1.8 - 2.1 | No detection | – | – | No detection | – | –
CO | 1.55 | 1.555 - 1.60 | 2.36 | 1.24 | 9.38 | 3.15 | 2.10 | 10.34
| 2.30 | 2.319 - 2.3315 | No detection | – | – | No detection | – | –
$\mathrm{CO_{2}}$ | 1.30 | 1.2 - 1.4 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.59 | 1.45 - 1.66 | No detection | No detection | No detection | No detection | No detection | No detection
$\mathrm{NH_{3}}$ | 1.00 | 1.0 - 1.1 | No detection | No detection | 3.83 | 1.97 | 1.71 | 4.29
| 1.50 | 1.45 - 1.65 | No detection | No detection | No detection | No detection | No detection | No detection
| 2.00 | 2.0 - 2.1 | No detection | – | – | No detection | – | –
| 2.30 | 2.2 - 2.4 | No detection | – | – | No detection | – | –
$\mathrm{H_{2}S}$ | 1.00 | 1.0 - 1.03 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.30 | 1.27 - 1.37 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.60 | 1.55 - 1.66 | 1.85 | No detection | 3.46 | 3.18 | No detection | 4.35
| 2.00 | 1.9 - 2.1 | No detection | – | – | No detection | – | –
$\mathrm{CH_{4}}$ | 0.89 | 0.875 - 0.91 | – | No detection | No detection | – | No detection | No detection
| 1.00 | 0.98 - 1.05 | No detection | No detection | 1.41 | 1.78 | No detection | 2.26
| 1.10 | 1.1 - 1.2 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.30 | 1.3 - 1.55 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.60 | 1.6 - 1.8 | No detection | No detection | 1.16 | No detection | No detection | 2.70
| 2.40 | 2.2 - 2.5 | No detection | – | – | No detection | – | –
HCN | 0.80 | 0.8 - 0.9 | – | No detection | 1.07 | – | 2.42 | 2.65
| 1.10 | 1.0 - 1.2 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.50 | 1.47 - 1.56 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.90 | 1.85 - 1.95 | No detection | – | – | No detection | – | –

###  3.2 Cross-correlation spectroscopy: estimation of $\mathrm{\sigma_{det}}$
for molecular bands

In our analysis, assessing the detectability of molecular signatures presents
a unique challenge, primarily arising from the complex spectral profiles
characterized by more spectral lines present in the spectrum. Unlike the
conventional signal-to-noise ratio (S/N) estimation, where a non-detection
typically results in an S/N of zero, our approach yields a non-detection
consistent with a significance level of $\mathrm{\sigma_{det}}$ $\sim$ 1
(Currie et al., 2023). This deviation from the traditional methodology is
driven by the intricacies of our detection scheme, which accounts for the
complex nature of the spectral lines and their interactions, making our scheme
a more appropriate means of determining detectability in this context.

Therefore, our approach involves a more detailed analysis rather than
employing the conventional S/N estimator, which provides a detectability
estimate for the entire wavelength range. We have defined specific molecular
bands corresponding to each molecule of interest (see Table
LABEL:tab:detetcion_Wasp76b and LABEL:tab:detetcion_Wasp77ab) and provided an
overview in terms of $\mathrm{\sigma_{det}}$ for each of the molecular bands
using three different spectrographs for 1 and 3 transits, respectively. This
approach allows us to assess the detectability of individual molecular
features within the broader spectrum, providing a more detailed and accurate
characterization of their presence in a better way. In the subsequent
sections, we have discussed a comprehensive analysis of detecting various
molecular bands on both planets using all the instruments. Transit depths for
all bands are shown in Figures 13, 14, 15 (for WASP-76 b) and Figures 16, 17,
18 (for WASP-77 A b). The cross-correlation spectroscopy for molecular bands
has been depicted in Figures 9 and 10, where a clear detection is indicated by
a pronounced peak at zero velocity shift in the correlation coefficient vs.
velocity shift map.

Figure 10: Correlation coefficient vs. velocity shift map for different
molecular bands for 3 transits of WASP-77 A b. Blue: GIANO-B (TNG). Orange:
CARMENES (CAHA). Green: ANDES (ELT). Each row corresponds to a specific
molecule (from top to bottom: OH, $\mathrm{H_{2}O}$, CO, $\mathrm{CO_{2}}$,
$\mathrm{NH_{3}}$, $\mathrm{H_{2}S}$). Molecular bands are listed explicitly
in Table LABEL:tab:detetcion_Wasp77ab. Table 4: Table summarizing the
$\mathrm{\sigma_{det}}$ achieved for different molecular bands for different
number of transits of WASP-77 A b from different ground-based instruments
(bands with $\mathrm{\sigma_{det}}$ $>$ 3 are shown in bold)

|  |  |  | No. of transit = 1 |  |  | No. of transit = 3 |
---|---|---|---|---|---|---|---|---
3.5 Molecules | Bands | Wavelength range | TNG | CAHA | E-ELT | TNG | CAHA | E-ELT
| ($\mu$m) | ($\mu$m) | (GIANO-B) | (CARMENES) | (ANDES) | (GIANO-B) | (CARMENES) | (ANDES)
3.5 OH | 0.68 | 0.66 - 0.70 | – | No detection | No detection | – | No detection | No detection
| 0.85 | 0.77 - 0.93 | – | No detection | No detection | – | No detection | No detection
| 1.15 | 1.0 - 1.3 | No detection | No detection | No detection | No detection | No detection | 2.02
| 1.60 | 1.5 - 1.7 | No detection | No detection | No detection | No detection | No detection | 2.76
$\mathrm{H_{2}O}$ | 0.90 | 0.89 - 0.99 | 2.49 | 2.10 | 13.04 | 3.44 | 3.30 | 18.77
| 0.94 | 0.93 - 0.95 | – | 1.74 | 5.76 | – | 4.53 | 10.52
| 1.00 | 0.95 - 1.05 | 1.56 | 1.50 | 12.85 | 4.56 | 3.70 | 15.52
| 1.10 | 1.1 - 1.2 | 2.56 | No detection | 5.45 | 4.87 | No detection | 7.89
| 1.30 | 1.3 - 1.55 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.90 | 1.8 - 2.1 | 1.63 | – | – | 2.98 | – | –
CO | 1.55 | 1.555 - 1.60 | 1.55 | 1.16 | 1.92 | 2.75 | 1.93 | 3.49
| 2.30 | 2.319 - 2.3315 | No detection | – | – | No detection | – | –
$\mathrm{CO_{2}}$ | 1.30 | 1.2 - 1.4 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.59 | 1.45 - 1.66 | No detection | No detection | No detection | No detection | No detection | No detection
$\mathrm{NH_{3}}$ | 1.00 | 1.0 - 1.1 | No detection | No detection | No detection | No detection | No detection | 2.61
| 1.50 | 1.45 - 1.65 | No detection | No detection | No detection | No detection | No detection | No detection
| 2.00 | 2.0 - 2.1 | No detection | – | – | No detection | – | –
| 2.30 | 2.2 - 2.4 | No detection | – | – | No detection | – | –
$\mathrm{H_{2}S}$ | 1.00 | 1.0 - 1.03 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.30 | 1.27 - 1.37 | No detection | No detection | No detection | No detection | No detection | No detection
| 1.60 | 1.55 - 1.66 | No detection | No detection | 1.72 | No detection | No detection | 2.11
| 2.00 | 1.9 - 2.1 | No detection | – | – | No detection | – | –

####  3.2.1 $\mathrm{OH}$

OH is one of the major byproducts that have formed during the atmospheric
dissociation of $\mathrm{H_{2}O}$ (Landman et al., 2021). For HJs and UHJs,
the enrichment of OH at the top of the atmosphere can be attributed to the
photolysis of water molecules. It was proven during the detection of OH (with
a 5.5$\sigma$ significance) on Wasp-33 b, where the insignificant detection of
$\mathrm{H_{2}O}$ lends support to the hypothesis that OH formation is
facilitated by the thermal dissociation of $\mathrm{H_{2}O}$ molecules
(Nugroho et al., 2021). However, from Figure 6, it is evident that
$\mathrm{H_{2}O}$ does play a substantial role in the generation of OH
radicals through the following reaction: $\mathrm{H_{2}O}$ \+ H $\rightarrow$
OH + $\mathrm{H_{2}}$ (see Figure 11 and 12), but not with direct photolysis.
A more detailed understanding of this necessitates further exploration, which
can be achieved through the utilization of more intricate chemical networks.

For WASP-76 b, all spectrographs demonstrate superior sensitivity in probing
the 1.60 $\mu$m band. While achieving a better $\mathrm{\sigma_{det}}$
requires more transits for GIANO-B and CARMENES, ANDES is capable of reaching
a commendable $\mathrm{\sigma_{det}}$ within 1 transit. Additionally, CARMENES
and ANDES exhibit significant precision in detecting the 1.15 $\mu$m band with
a higher number of transits. Similarly, in the case of WASP-77 A b, ANDES
exhibits reasonable precision in detecting the 1.15 $\mu$m and 1.60 $\mu$m
features with an increased number of transits. However, it’s worth noting that
ANDES exhibits a lower level of confidence for detecting the 1.60 $\mu$m band
compared to the observations of WASP-76 b.

####  3.2.2 $\mathrm{H_{2}O}$

From the planet spectra, it is clear that both planets are water-dominated.
Among all six bands, the 0.90, 1.00, and 1.10 $\mu$m bands in the optical and
NIR spectral regions exhibit notably higher precision across three instruments
for a higher number of transits. It is important to note that ANDES
demonstrates superior capability in containing these features even with a
single transit. Both CARMENES and ANDES exhibit favorable detectability for
the 0.94 $\mu$m band too. All over, CARMENES shows a lower level of
sensitivity towards detecting different bands. This is attributed to the
higher read noise value of the spectrograph and the lower collecting area of
the mirror.

In our analysis, the 0.90, 0.94, 1.00, and 1.10 $\mu$m bands have proven to be
more dependable in terms of detection. Although the 1.30 $\mu$m band exhibits
pronounced features, they are susceptible to overlap with the prominent
telluric transmission features, resulting in reduced significance during
detection. A similar effect is also observed for the 1.10 $\mu$m band, albeit
to a lesser extent.

####  3.2.3 $\mathrm{CO}$

CO emerges as the predominant molecule in terms of VMR on both planets (see
Figure 5). It is produced mainly by the direct reduction $\mathrm{CO_{2}}$
molecule in the atmospheres: $\mathrm{CO_{2}}$ \+ H $\rightarrow$ CO + OH (see
Figure 6 and Appendix A). GIANO-B and ANDES exhibit potential in detecting the
1.55 $\mu$m band with $\mathrm{\sigma_{det}}$ $>$ 3 in the atmosphere of
WASP-76 b (GIANO-B: with 3 transits and ANDES: with a single transit).
Moreover, the detection of CO on WASP-77 A b is insignificant with GIANO-B and
CARMENES with a $\mathrm{\sigma_{det}}$ $<$ 3 even with 3 transits. ANDES can
achieve a significance level of $\mathrm{\sigma_{det}}$ $>$ 3 for the 1.55
$\mu$m CO band when observing for 3 transits. The detectability increases in
the sequence from CARMENES to GIANO-B to ANDES.

####  3.2.4 $\mathrm{CO_{2}}$

With a threshold of average photospheric VMR $>$ $\mathrm{10^{-8}}$, it is
apparent that $\mathrm{CO_{2}}$ is the least abundant species on both planets.
Unfortunately, neither of its bands is detectable for all instruments.

####  3.2.5 $\mathrm{NH_{3}}$

As previously discussed in Section 3.1, the contribution of $\mathrm{NH_{3}}$
to the planetary spectra is not visually distinguishable for WASP-77 A b,
indicating a minimal likelihood of detection. ANDES exhibits reasonable
detection significance for WASP-77 A b for the 1.00 $\mu$m band. Nevertheless,
it demands more transits to achieve a significant detection. In contrast, for
WASP-76 b, the ANDES instrument is capable of resolving the 1.00 $\mu$m band
with higher precision ($\mathrm{\sigma_{det}}$ $>$ 3) even with a single
transit.

####  3.2.6 $\mathrm{H_{2}S}$

On both studied planets, sulfur is exclusively found in the form of
$\mathrm{H_{2}S}$. Despite being the third most prevalent compound in their
atmospheres, no prior detection has been recorded for this molecule. Our
analysis, however, indicates a substantial detection of the 1.60 $\mu$m band
on WASP-76 b and a moderate level of detection on WASP-77 A b, using the ANDES
instrument. With additional transits, GIANO-B too shows prominence in
detecting the 1.60 $\mu$m band on WASP-76 b. The significant formation of this
molecule in the atmosphere can be attributed to the destruction
$\mathrm{NH_{3}}$ and SH radical (see Figure 6 and Appendix A).

####  3.2.7 $\mathrm{CH_{4}}$

Detecting $\mathrm{CH_{4}}$ is particularly challenging across all three
instruments due to its extremely low atmospheric abundance on WASP-76 b.
Nevertheless, ANDES displays a little promising capability in detecting the
1.00 and 1.60 $\mu$m bands with 3 transits, each with a
$\mathrm{\sigma_{det}}$ $>$ 2\. However, none of these instruments exhibits a
distinct, sharp feature in the correlation coefficient vs. velocity shift map.

####  3.2.8 $\mathrm{HCN}$

Despite having a prominent detection on WASP-76 b, our model falls short of
establishing a sufficient detection of HCN in the atmosphere, leading to the
following conclusion: it is anticipated that HCN will originate in the lower
temperature region of the planetary nightside and subsequently migrate to the
dayside via atmospheric circulation. Given the higher detection significance
of $\mathrm{H_{2}O}$, the presence of HCN is intriguing, as $\mathrm{H_{2}O}$
and HCN are not typically expected to coexist (Sánchez-López et al., 2022).
However, HCN can be detected to some extent with an increased number of
transits on WASP-76 b. Notably, the CARMENES and ANDES instruments demonstrate
a reasonable capability to resolve the 0.80 $\mu$m band with a detection
significance $\mathrm{\sigma_{det}}$ $>$ 2.

###  3.3 Present observations and the future with ELT

Recent advancements in ground-based observatories have opened up new horizons
in the field of exoplanetary science, particularly exploring planet
atmospheres and comprehending the underlying atmospheric chemistry. By
comparing present observations with simulation studies, we can anticipate
future observations using more advanced instruments like ELT and gain insights
into how ELT will excel the existing instruments in detecting molecular
signatures in planetary atmospheres. Our model exhibits good coherence with
the present observations for both planets. On WASP-76 b, Landman et al. (2021)
detect OH with a significance of 6.1, while Sánchez-López et al. (2022) report
the detection of $\mathrm{H_{2}O}$ (with a significance of 5.5) and HCN (with
a significance of 5.2) using the CARMENES spectrograph during a single transit
observation. We successfully retrieve $\mathrm{H_{2}O}$ signature from the
0.90 $\mu$m band with a $\mathrm{\sigma_{det}}$ of 5.10 and OH from the 1.60
$\mu$m band with a little lower $\mathrm{\sigma_{det}}$ of 3.23 for single
transit. As discussed in Section 3.2.8, the production of HCN is more
favorable in the cooler regions of the planet. Due to the limitations imposed
by 1D models, we are unable to attain a significant VMR of HCN on the planet
and detect it solely through single transit observations. However, with 3
transits, CARMENES can detect the 0.80 $\mu$m band of HCN with a
$\mathrm{\sigma_{det}}$ of 2.42.

On the other hand, observations conducted during pre and post-eclipse of
WASP-77 A b using the IGRINS spectrograph indicate the presence of CO (with a
significance $\sim$ 3.5) and $\mathrm{H_{2}O}$ (with a significance $\sim$ 9)
in the atmosphere (Smith et al., 2024). Our analysis utilizing GIANO-B and
CARMENES also detects CO and $\mathrm{H_{2}O}$, albeit with slightly lower
significance levels for three transits. This is due to the differential
spectrograph architectures between GIANO-B, CARMENES, and IGRINS.
Specifically, the IGRINS spectrograph has a larger mirror diameter of 8.1
meters compared to 3.58 meters for GIANO-B and 3.5 meters for CARMENES. This
larger diameter translates to a doubling in collecting area, leading to a
greater influx of photons and consequently enhancing detectability. Thus, the
observed differences in detection significance values across the instruments
are justified by these architectural distinctions. Given the accordance
between our simulations and real-time observations, it is anticipated that the
ELT will surpass other ground-based observatories, paving the way for a new
era in atmospheric studies with heightened sensitivity for detecting molecular
signatures in exoplanet atmospheres. With a larger diameter of 39.3 meters and
a resolution of 100000, ELT can probe molecules that are hard to observe using
other instruments and disentangle molecular features with better precision.

##  4 Conclusions

HJs and UHJs present us with a unique opportunity to characterize their
atmospheres and determine the molecular abundances of O- and C-bearing species
(Guillot et al., 2022), offering insights into the exotic chemical processes
taking place within their atmospheres. The primary objective of this work was
to investigate the atmospheres of WASP-77 A b (HJ) and WASP-76 b (UHJ) using
three high-resolution ground-based spectrographs (GIANO-B, CARMENES, ANDES)
and conduct a complementary analysis to assess the detectability of different
molecular bands. Among all instruments, ANDES demonstrated significantly
better precision in detecting molecular bands, thanks to its larger collecting
area and higher instrumental resolution. The alignment between our simulation
analyses and actual observations for both planets underscores the significance
of utilizing the ELT. With its advanced capabilities, ELT holds the promise of
significantly enhancing the ability to probe molecules within exoplanet
atmospheres with better sensitivity, further advancing our understanding of
these distant worlds.

Based on the diverse wavelength coverage and distinct instrumental parameters,
spectrographs possess a sweet spot where they excel in detecting particular
molecules with enhanced significance. Employing the cross-correlation
spectroscopy method, we anticipate the detection of various molecules,
including OH (1.15 $\mu$m: CARMENES, ANDES; 1.60 $\mu$m: GIANO-B, CARMENES,
ANDES), $\mathrm{H_{2}O}$ (0.90, 1.00 $\mu$m: GIANO-B, CARMENES, ANDES; 0.94
$\mu$m: CARMENES, ANDES; 1.10 $\mu$m: GIANO-B, ANDES), $\mathrm{CH_{4}}$
(1.00, 1.60 $\mu$m: ANDES), $\mathrm{CO}$ (1.55 $\mu$m: GIANO-B, ANDES), HCN
(0.80 $\mu$m: CARMENES, ANDES), $\mathrm{NH_{3}}$ (1.00 $\mu$m: ANDES), and
$\mathrm{H_{2}S}$ (1.60 $\mu$m: GIANO-B, ANDES) for WASP-76 b. This indeed
encompasses molecular detection from single transit to a maximum of 3 transits
for the planet (see Table LABEL:tab:detetcion_Wasp76b). ANDES surpasses
CARMENES and GIANO-B in terms of the instrumental capability for detecting
most of the molecular bands with a single transit. More transits are usually
favorable for detecting the molecules (e.g. OH, CO, and $\mathrm{H_{2}S}$)
using GIANO-B and CARMENES spectrographs.

For WASP-77 A b, we have identified the presence of OH (1.15, 1.60 $\mu$m:
ANDES), $\mathrm{H_{2}O}$ (0.90, 1.00 $\mu$m: GIANO-B, CARMENES, ANDES; 0.94
$\mu$m: CARMENES, ANDES; 1.10 $\mu$m: GIANO-B, ANDES), $\mathrm{CO}$
(1.55$\mu$m: ANDES), $\mathrm{NH_{3}}$ (1.00 $\mu$m: ANDES) and
$\mathrm{H_{2}S}$ (1.60 $\mu$m: ANDES). For both planets, we have reached a
$\mathrm{\sigma_{det}}$ $>$ 2 for above mentioned molecular bands for
different numbers of transits (see Tables LABEL:tab:detetcion_Wasp76b and
LABEL:tab:detetcion_Wasp77ab). The spectral bands of $\mathrm{H_{2}O}$, CO,
OH, $\mathrm{NH_{3}}$, and $\mathrm{H_{2}S}$ are sufficiently robust for
WASP-76 b, enabling their detection with a $\mathrm{\sigma_{det}}$ $>$ 3
within 3 transits. Conversely, the signals are a little fainter for WASP-77 A
b except $\mathrm{H_{2}O}$. This prioritizes the need for more transits to
significantly detect CO, OH, $\mathrm{NH_{3}}$, and $\mathrm{H_{2}S}$ in the
atmosphere of WASP-77 A b.

By examining the interlinked chemical network and molecular conversion
pathways, we have developed a detailed understanding of the atmospheric
chemistry on both planets. It is noteworthy that, aside from photolysis, OH
can be formed through alternative reaction mechanisms from water.
Additionally, within the photosphere, the rise in the OH mixing ratio is
related to the depletion of $\mathrm{H_{2}O}$ and $\mathrm{NH_{3}}$. Our
efforts to identify HCN signatures in the atmosphere of WASP-76 b were
inconclusive due to the extremely low VMR in our 1-D models. Nevertheless, we
highlight the significance of nitrogen chemistry, particularly in the cooler
night side of the planet (Sánchez-López et al., 2022). The non-detection of
$\mathrm{CO_{2}}$ in the atmosphere of WASP-77 A b is consistent with recent
JWST observations (August et al., 2023). The detection of $\mathrm{H_{2}S}$,
particularly on WASP-76 b, as the only sulfur-bearing molecular entity, serves
as motivation for emphasizing the significance of sulfur chemistry within the
atmospheres of irradiated gas giants.

## acknowledgements

L.M. acknowledges financial support from DAE and DST-SERB research grants
(SRG/2021/002116 and MTR/2021/000864) of the Government of India. D.D. also
acknowledges financial support from the DST-SERB research grant
SRG/2021/002116, which supported this work. L.M. thanks Dr. Paul Mollière of
MPIA Heidelberg, Germany, for providing access to petitCODE and for actively
participating in discussions regarding its use and applications. We would like
to thank the anonymous referee for constructive comments that helped improve
the manuscript.

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##  Appendix A Reaction profile diagrams for molecular interconversions

Figure 11: Shortest pathway analysis for molecular conversion using Dijkstra’s
algorithm at 0.01 bar. The conversion networks are shown based on Figure 6 for
the atmosphere of WASP-77 A b. The texts besides the arrows explain the
reactions involved (First row: reaction rates in $\mathrm{cm^{-1}s^{-1}}$,
Second row: reaction number from the VULCAN network. The odd number is for the
forward reaction and the even number is for the backward reaction. The
contribution of that particular reaction to the interconversion has also been
provided in brackets. Third row: reaction involved in the interconversion.)
Thicker black lines represent faster reactions, while the red lines represent
the slowest reaction, i.e. the rate-limiting step for the molecular conversion
pathway.

Figure 12: Same as Figure 11, but for the WASP-76 b molecular network in
Figure 6.

##  Appendix B Molecular bands of WASP-76 b

Figure 13: Continuum subtracted WASP-76 b molecular bands using high pass
filters, calculated for 3 transits for TNG.

Figure 14: Same as Figure 13, but for CAHA.

Figure 15: Same as Figure 13, but for ELT.

##  Appendix C Molecular bands of WASP-77 A b

Figure 16: Continuum subtracted WASP-77 A b molecular bands using high pass
filters, calculated for 3 transits for TNG.

Figure 17: Same as Figure 16, but for CAHA.

Figure 18: Same as Figure 16, but for ELT.