11institutetext: European Southern Observatory, Karl-Schwarzschild-str. 2,
85748 Garching, Germany
11email<EMAIL_ADDRESS>22institutetext: Astronomical Institute of the Czech
Academy of Sciences, Fričova 298, 25165 Ondřejov, Czech Republic
33institutetext: Faculty of Physics and Astronomy, Friedrich-Schiller-
Universität, Fürstengraben 1, 07743, Jena, Germany 44institutetext:
Dipartimento di Fisica, La Sapienza Università di Roma, Piazzale Aldo Moro 5,
Roma, 00185, Italy 55institutetext: European Southern Observatory, Casilla 13,
Vitacura, Santiago, Chile 66institutetext: European Space Agency (ESA), ESA
Office, Space Telescope Science Institute (STScI), Baltimore, MD 21218, USA.
77institutetext: Steward Observatory, The University of Arizona, Tucson, AZ
85721, USA 88institutetext: Department of Theoretical Physics and
Astrophysics, Masaryk University, Kotlářská 2, CZ-61137 Brno, Czech Republic
99institutetext: Thueringer Landessternwarte Tautenburg, Sternwarte 5, 07778
Tautenburg, Germany

# Stellar obliquity measurements of six gas giants

Orbital misalignment of WASP-101b and WASP-131b

J. Zak , 11 2 2 3 3 A. Bocchieri 44 E. Sedaghati 55 H. M. J. Boffin 11 Z.
Prudil 11 M. Skarka 22 Q. Changeat 66
E. Pascale 44 D. Itrich 11 7 7 V. D. Ivanov 11 M. Vitkova 22 8 8 P. Kabath 22
M. Roth 33 9 9 A. Hatzes 33 9 9

(Received September 15, 1996; accepted March 16, 1997)

One can infer the orbital alignment of exoplanets with respect to the spin of
their host stars using the Rossiter-McLaughlin effect, thereby giving us the
chance to test planet formation and migration theories and improve our
understanding of the currently observed population. We analyze archival HARPS
and HARPS-N spectroscopic transit time series of six gas giant exoplanets on
short orbits, namely WASP-77 Ab, WASP-101b, WASP-103b, WASP-105b, WASP-120b
and WASP-131b. We find a moderately misaligned orbit for WASP-101b
($\lambda=34\degree\ \pm$ 3) and a highly misaligned orbit for WASP-131b
($\lambda=161\degree\ \pm$ 5), while the four remaining ones appear aligned:
WASP-77 Ab ($\lambda=-8\degree\ ^{+19}_{-18}$), WASP-103b ($\lambda=2\degree\
^{+35}_{-36}$), WASP-105b ($\lambda=-14\degree\ ^{+28}_{-24}$), and WASP-120b
($\lambda=-2\degree\ \pm$ 4). For WASP-77 Ab, we were able to infer its true
orbital obliquity ($\Psi=48\degree\ ^{+22}_{-21}$). We additionally perform
transmission spectroscopy of the targets in search of strong atomic absorbers
in the exoatmospheres, but are unable to detect any features, most likely due
to the presence of high-altitude clouds or Rayleigh scattering muting the
strength of the features. Finally, we comment on future perspectives for
studying these targets with the upcoming space missions to investigate the
evolution and migration histories of these planets.

###### Key Words.:

Techniques: radial velocities – Planets and satellites: gaseous planets –
Planets and satellites: atmospheres– Planet-star interactions – Planets and
satellites: individual: WASP-77 Ab, WASP-101b, WASP-103b, WASP-105b,
WASP-120b, WASP-131b

##  1 Introduction

The formation and evolution of exoplanets and how this is linked to the
properties of their host stars and the environments in which they formed are
long-standing questions. One possible clue may come from measuring the
relative angle of the rotation axis of the star with that of the planetary
orbital angular momentum. The planets of the Solar System, for example, are
almost co-planar, as these angles – called stellar obliquities – are all very
small, leading to the idea of planet formation within a disc. The sky-
projected stellar obliquity can be inferred through the observations of the
Rossiter-McLaughlin (R-M) effect, which is a spectroscopic anomaly that occurs
when the disc of a companion passes in front of the spinning star. As usual in
astronomy, this effect is misnamed, as it was first described by Holt (1893),
and then actually detected in the binary system $\beta$ Lyrae by Rossiter
(1924). The same year, and using the methodology of Rossiter, McLaughlin
(1924) applied it to a study of Algol, while the first application of the R-M
effect to exoplanets was carried out by Queloz et al. (2000) on HD 209458. For
a more detailed review of this history, the reader is encouraged to refer to
Albrecht et al. (2011, 2022). At first, only Jupiter-mass planets were
characterized, but later development of instrumentation allowed for the
characterization of Neptunian (Bourrier et al., 2018), sub-Neptunian (Dalal et
al., 2019) and even terrestrial planets (Hirano et al., 2020; Zhao et al.,
2022). Such studies have revealed a complex architecture of exoplanetary
systems with planetary orbits varying from well-aligned, to slightly
misaligned, to planets on polar and even retrograde orbits.

Table 1: Observing logs for all six planets. The number in parenthesis represents the number of frames taken in-transit. Target | Date | No. | Exp. | Airmass | Median | Instrument
---|---|---|---|---|---|---
|  Obs |  frames | Time (s) | range | S/N |
WASP-77 A | 2018-11-05 |  21 (9) | 900 | 1.48-1.08-1.33 |  31.2-55.4 | HARPS
WASP-101 | 2015-12-20 |  54 (18) | 500 | 1.99-1.01-1.47 |  27.2-48.3 | HARPS
WASP-103 | 2016-06-01 |  33 (11) | 900 | 2.02-1.08-2.30 |  15.3-21.9 | HARPS-N
| 2016-06-14 |  29 (10) | 900 | 1.48-1.07-2.24 |  6.5-21.9 | HARPS-N
WASP-105 | 2014-09-30 |  24 (14) | 900 | 1.28-1.07-1.36 |  11.9-17.9 | HARPS
| 2014-12-10 |  20 (13) | 600-1200 | 1.09-1.07-1.82 |  8.8-18.7 | HARPS
WASP-120 | 2018-10-20 |  37 (21) | 600 | 1.73-1.04-1.14 |  17.2-31.2 | HARPS
WASP-131 | 2015-06-06 |  37 (21) | 600 | 1.13-1.00-1.87 |  36.2-53.7 | HARPS

The R-M effect is thus a valuable tool as it can provide insight into the
planetary formation and evolution (Triaud, 2018). It can be used to test
theories of planetary migration, for example to understand if the planet
formed in situ or if it has migrated to its current location. Polar and
retrograde orbits are indicative of violent history within the system, as such
orbits seem to oppose the standard formation processes for the planetary
systems where both the star and the planets form from the same rotating disc.
Several mechanisms have been proposed to explain these extreme orbits, such as
long-term interactions with a binary companion (Batygin, 2012), close fly-bys
of other stars (Bate et al., 2010), the shift of the stellar rotation axis
relative to the disc due to the effects of the stellar magnetic field (Lai et
al., 2011), gravitational scattering among the planets (Chatterjee et al.,
2008), or long term perturbations due to companion caused by Kozai-Lidov
mechanism (Fabrycky & Tremaine, 2007). Breslau & Pfalzner (2019) showed that
retrograde orbits can also be the outcome of prograde flybys.

Despite the large number (over 150) of R-M effect measurements, there are no
definitive trends in the planetary population when plotting the projected
obliquity versus other parameters. However, suggestion of some trends were
proposed; Albrecht et al. (2012) and Dawson (2014) identified two populations
of hot Jupiters, based on the effective temperature of the host star, with the
division being at the Kraft break – an abrupt decrease in the stars’ average
rotation rates at about 6200 K (Kraft, 1967). Rice et al. (2022) found
evidence that warm Jupiters in single-star systems form more quiescently
compared to their hot analogues. Hamer & Schlaufman (2022) found that hot
Jupiter host stars with larger-than-median obliquities are older than hot
Jupiter host stars with smaller-than-median obliquities.

In this study, we present the projected obliquity measurements of six gas
giants on short orbital periods around F-G-K dwarfs with previously
unpublished HARPS and HARPS-N archival data.

##  2 Data sets and their analyses

We have used datasets for five exoplanets from ESO’s HARPS instrument mounted
at the 3.6-m telescope at La Silla, Chile. Furthermore, the data for one
planet (WASP-103) were obtained with the HARPS-N instrument mounted at the
3.5-m TNG telescope at La Palma, Canary Islands. The HARPS data were
downloaded from the ESO science archive111http://archive.eso.org (program IDs
0102.C-0618, 096.C-0331, 094.C-0090, 0102.C-0319 and 095.C-0105), while the
HARPS-N data (program ID A33TAC17) were obtained from the TNG
archive222http://archives.ia2.inaf.it/tng/. Table 1 displays the properties of
the data sets that were used. The downloaded data are fully reduced products
as processed with the HARPS Data Reduction Software (DRS version 3.8). Each
spectrum is provided as a merged 1D spectrum resampled onto a 0.001 nm uniform
wavelength grid. The wavelength coverage of the spectra spans from 380 to 690
nm, with a resolving power of R $\approx$ 115 000 corresponding to 2.7 km s-1
per resolution element. The spectra are already corrected to the Solar system
barycentric frame of reference. We further summarize the properties of the
studied systems in Table 2.

Table 2: Properties of the targets (star and planet).

| Parameters | WASP-77 A | WASP-101 | WASP-103
---|---|---|---|---
Star | V mag | 11.3 | 10.3 | 12.1
| Sp. Type | G8 | F6 | F8
| Ms (M⊙) | 1.002 $\pm$ 0.045 | 1.34 $\pm$ 0.07 | 1.22 $\pm$ 0.0039
| Rs (R⊙) | 0.955 $\pm$ 0.015 | 1.29 $\pm$ 0.04 | 1.436${}^{+0.031}_{-0.052}$
| Teff (K) | 5500 $\pm$ 80 | 6380 $\pm$ 120 | 6110 $\pm$ 100
|  $v\,\rm{sin}i_{*}$ (km/s) | 4 $\pm$ 0.2 | 12.4 $\pm$ 0.5 | 8.8 $\pm$ 0.7
Planet | Mp (MJup) | 1.76 $\pm$ 0.06 | 0.50 $\pm$ 0.04 | 1.49 $\pm$ 0.088
| Rp (RJup) | 1.21 $\pm$ 0.02 | 1.41 $\pm$ 0.05 | 1.528 $\pm$ 0.03
| Period (d) | 1.3600309 $\pm$ 0.0000020 | 3.585722 $\pm$ 0.000004 | 0.925542 $\pm$ 0.000019
|  $\rm{T_{0}}$ \- 2450000 (d) | 5870.44977 $\pm$ 0.00014 | 6164.6934 $\pm$ 0.0002 | 6459.59957 $\pm$ 0.00075
| a (AU) | 0.0240 $\pm$ 0.00036 | 0.0506 $\pm$ 0.0009 | 0.01985 $\pm$ 0.00021
| e | 0. | 0. | 0.
| i (deg) | 89.4${}^{+0.4}_{-0.7}$ | 85.0 $\pm$ 0.2 | 89.7 $\pm$ 0.2
| Teq (K) | 1876 $\pm$ 80 | 1565 $\pm$ 35 | 2508${}^{+75}_{-70}$
| References | Maxted et al. (2013) | Hellier et al. (2014) | Gillon et al. (2014)

| Parameters | WASP-105 | WASP-120 | WASP-131
---|---|---|---|---
Star | V mag | 12.1 | 11 | 10.1
| Sp. Type | K3 | F5 | G0
| Ms (M⊙) | 0.89 $\pm$ 0.09 | 1.393 $\pm$ 0.057 | 1.06 $\pm$ 0.06
| Rs (R⊙) | 0.90 $\pm$ 0.03 | 1.87 $\pm$ 0.11 | 1.53 $\pm$ 0.05
| Teff (K) | 5070 $\pm$ 130 | 6450 $\pm$ 120 | 5950 $\pm$ 100
|  $v\,\rm{sin}i_{*}$ (km/s) | 1.7 $\pm$ 1.9 | 15.1 $\pm$ 1.2 | 3.0 $\pm$ 0.9
Planet | Mp (MJup) | 1.8 $\pm$ 0.1 | 4.85 $\pm$ 0.21 | 0.27 $\pm$ 0.02
| Rp (RJup) | 0.96 $\pm$ 0.03 | 1.473 $\pm$ 0.096 | 1.22 $\pm$ 0.05
| Period (d) | 7.87288 $\pm$ 0.00001 | 3.6112706 $\pm$ 0.0000043 | 5.322023 $\pm$ 0.000005
|  $\rm{T_{0}}$ \- 2450000 (d) | 6600.0765 $\pm$ 0.0002 | 6779.4352 $\pm$ 0.00044 | 6919.8236 $\pm$ 0.0004
| a (AU) | 0.075 $\pm$ 0.003 | 0.0514 $\pm$0.0007 | 0.0607 $\pm$0.0009
| e | 0. | 0.057${}^{+0.022}_{-0.018}$ | 0.
| i (deg) | 89.7 $\pm$ 0.2 | 82.54 $\pm$ 0.78 | 85.0 $\pm$ 0.3
| Teq (K) | 846 $\pm$ 20 | 1876 $\pm$ 70 | 1460 $\pm$ 30
| References | Anderson et al. (2017) | Turner et al. (2016) | Hellier et al. (2017)

###  2.1 Rossiter–McLaughlin effect

The radial velocities measured during the transit show the anomaly produced by
the R-M effect. We have retrieved the radial velocity measurements that are
obtained from the HARPS and HARPS-N DRS pipeline together with their
uncertainties. To measure the projected stellar obliquity of the system
($\lambda$) we fit the radial velocity data with a subroutine from the Radvel
package (Fulton et al., 2018) that assumes a Keplerian orbit and the R-M
effect formulation of ARoMEpy333https://github.com/esedagha/ARoMEpy (Sedaghati
et al., 2023), which is a python translation of the ARoME code (Boué et al.,
2013). We have used the R-M effect function defined for radial velocities
determined through the cross-correlation technique in our code. We fix the
radial velocity semi-amplitude $K$ to the literature value and allow the
systemic velocity $\gamma$ to be a free parameter. In the R-M effect model, we
fix the following parameters to those reported in the literature: orbital
period $P$, planet-to-star radius ratio ${R_{p}}/{R_{s}}$ and the eccentricity
$e$. The parameter $\sigma$, which is the width of the CCF (FWHM of a Gaussian
fit to the CCF), is measured on the data and fixed. Furthermore, we use the
ExoCTK444https://github.com/ExoCTK/exoctk tool to compute the quadratic limb-
darkening coefficients in the wavelength range of the HARPS and HARPS-N
instruments (380-690 nm). We allow the following parameters to be free during
the fitting procedure within the priors from photometry: central transit time
$T_{C}$, projected stellar rotational velocity $v\,\sin i_{*}$, sky-projected
angle between stellar rotation axis and normal of the orbital plane $\lambda$,
orbital inclination $i$, and the scaled semi-major axis ${a}/{R_{s}}$. To
obtain the best fitting values of the parameters we employed 3 independent
Markov Chain Monte Carlo (MCMC) simulations each with 250 000 steps, burning
the first 50 000. Using this setup we obtain our results and present them in
Sect. 3.1 and in Figs. 1 to 6.

###  2.2 Transmission spectroscopy

We performed transmission spectroscopy of our targets, following the
methodology performed by Wyttenbach et al. (2015) and Žák et al. (2019).
First, to correct for telluric emission lines we have used the fiber B which
was aimed at the adjacent sky and used the Molecfit software (Smette et al.,
2015; Kausch et al., 2015). Molecfit uses synthetic modeling of the Earth’s
atmospheric spectrum with a line-by-line approach. We carefully select nine
telluric wavelength regions in the range of 589 to 651 nm. These regions
contain unblended telluric lines produced by $\rm{H_{2}O}$ and $\rm{O_{2}}$.
The best-fit Molecfit solution was applied to the whole HARPS spectra. As the
next step, we shift all the spectra to the stellar rest frame. We have
performed a wavelength cut to isolate the region of interest and performed
flux normalization for the spectra. Normalization was done in IRAF (Tody,
1986) using the task continuum and on the regions of the spectra without
strong lines. Subsequently, we have averaged all out-of-transit spectra to
create a stellar template. We divided each spectrum during transit by this
template to obtain individual transmission spectra. Such spectra need to be
corrected for the planetary motion of the planet. These corrected residuals
were summed up and normalized to unity. Finally, unity was subtracted to
obtain the final transmission spectrum $\tilde{\mathcal{R}}(\lambda)$:

$\tilde{\mathcal{R}}(\lambda)=\sum_{\rm{in}}\left.\frac{\tilde{f}_{\rm{in}}(\lambda,t_{\rm{in}})}{\tilde{F}_{\rm{out}}(\lambda)}\right|_{\rm{Planet\
RV\ shift}}-1$ (1)

In principle, stellar activity might hinder our ability to retrieve any
planetary signal (e.g., Barnes et al., 2017). To assess the impact of stellar
activity on the transmission spectra, we have repeated our methodology on
several control lines (Mg i and Ca i). We retrieve a flat spectrum consistent
with a negligible effect of the stellar activity.

Figure 1: The Rossiter-Mclaughlin effect of WASP-77 Ab observed with HARPS.
The observed data points (black) are shown with their errorbars, which in this
case are smaller than the symbol size. The systemic velocity was removed for
better visibility. The red line shows the best fitting model to the data,
together with 1-$\sigma$ (dark grey) and 3-$\sigma$ (light grey) confidence
intervals. Figure 2: Same as Fig.1 for WASP-101b. Figure 3: Same as Fig.1 for
WASP-103b. Figure 4: Same as Fig.1 for WASP-105b. Figure 5: Same as Fig.1 for
WASP-120b. Figure 6: Same as Fig.1 for WASP-131b.

##  3 Results

###  3.1 Projected stellar obliquity measurement

We have measured the projected stellar obliquity ($\lambda$) of four targets
for the first time: WASP-77 Ab, WASP-101b, WASP-105b, and WASP-120b. WASP-103b
has been previously studied by Addison et al. (2016) using the UCLES
spectrograph. WASP-131b had its spin-orbit alignment measured by Doyle et al.
(2023) using ESPRESSO during the advanced stages of preparing this manuscript.

WASP-77 Ab is an inflated hot Jupiter orbiting a G8 host star on a short 1.4
day orbit. The host star has a fainter companion at a distance of 3 arcsec
(Maxted et al., 2013). We infer an aligned orbit of WASP-77 Ab with
$\lambda=-8^{+19}_{-18}$ deg.

WASP-101b is a highly inflated hot Jupiter orbiting a F6 host star on a 3.5
day orbit. We infer a misaligned orbit of WASP-101b with $\lambda$ =34 $\pm$ 3
deg.

WASP-103b is an ultra-hot Jupiter orbiting an F8 host star on a 0.92 day
orbit. Wöllert & Brandner (2015) discovered a nearby source that Southworth &
Evans (2016) characterized as a $0.72\pm 0.08$ M⊙ star in the WASP-103 system.
The system has been frequently observed (e.g., Maciejewski et al., 2018;
Delrez et al., 2018; Patra et al., 2020) for possible period changes. Recent
CHEOPS observations found hint of an orbital period increase due to tidal
decay (Barros et al., 2022). We infer an aligned orbit of WASP-103b with
$\lambda=2^{+35}_{-36}$ deg. The derived projected obliquity is in agreement
with the results by Addison et al. (2016) who obtained $\lambda=3\pm 33$ deg.

WASP-105b is a warm Jupiter-sized planet. It orbits its K2 host star on a 7.8
day orbit. We infer an aligned orbit with $\lambda=-14^{+28}_{-24}$ deg.

WASP-120b is a massive hot Jupiter. It orbits its F5 host star on a 3.6 day,
slightly eccentric orbit ($e=0.05$). Bohn et al. (2020) found a possible
binary companion, but further astrometric data are needed to confirm the
tertiary nature of the system. We find that the orbit of WASP-120b is well
aligned, with $\lambda$ =-2 $\pm$ 4 deg.

WASP-131b is a highly inflated hot Saturn. It orbits its G0 host star on a 5.3
day orbit. WASP-131 has a low mass stellar companion (Bohn et al., 2020;
Southworth et al., 2020). We infer a highly misaligned orbit of WASP-131b,
with $\lambda$ =161 $\pm$ 5 deg. Our results based on HARPS data are in
excellent agreement with the results from ESPRESSO,
$\lambda=162.4^{+1.3}_{-1.2}$ deg (Doyle et al., 2023).

The results of our fits are shown in Figs. 1–6, while the MCMC results are
shown in Figs. B1 to B6 of the Appendix. The derived values from the MCMC
analysis are displayed in Table 3.

The values of $v\,\sin{i_{*}}$ that we derived in our R-M effect analysis are
generally in agreement with the ones reported in the literature from spectral
synthesis. A discrepancy is, however, observed for WASP-77 A. Hence, we have
measured the $v\,\sin{i_{*}}$ from our HARPS stacked spectra, using iSpec
(Blanco-Cuaresma et al., 2014). We obtained a value of $v\,\sin{i_{*}}$ = 2.6
$\pm$ 0.4 km/s, in better agreement with the value obtained from our R-M
effect analysis in Table 3.

Table 3: MCMC analysis results. | Parameter | Prior | WASP-77 A | Prior | WASP-101 | Prior | WASP-103
---|---|---|---|---|---|---|---
|  $T_{c}$ \- 2450000 [d] | $\mathcal{N}(T_{0},0.006)$ | 8428.664${}^{+0.001}_{-0.001}$ | $\mathcal{N}(T_{0},0.003)$ | 7376.666 $\pm$ 0.002 | $\mathcal{N}(T_{0},0.006)$ | 7540.632${}^{+0.002}_{-0.001}$
|  $\lambda$ [deg] | $\mathcal{U}(-180,180)$ | -8${}^{+19}_{-18}$ | $\mathcal{U}(-180,180)$ | 34 $\pm$ 3 | $\mathcal{U}(-180,180)$ | 2${}^{+35}_{-36}$
|  $v\,\sin{i_{*}}$ [km/s] | $\mathcal{U}(0,10)$ | 2.0${}^{+0.2}_{-0.1}$ | $\mathcal{U}(0,15)$ | 8.9 $\pm$ 0.6 | $\mathcal{U}(0,10)$ | 7${}^{+2}_{-1}$
| $a/R_{s}$ | $\mathcal{N}(5.4,0.2)$ | 5.53 $\pm$ 0.05 | $\mathcal{N}(8.3,0.3)$ | 8.3 $\pm$ 0.2 | $\mathcal{N}(2.99,0.05)$ | 2.99${}^{+0.02}_{-0.02}$
| Inc. [deg] | $\mathcal{N}(89.4,0.5)$ | 89.52${}^{+0.36}_{-0.40}$ | $\mathcal{N}(85.0,0.2)$ | 84.88 ${}^{+0.39}_{-0.34}$ | $\mathcal{N}(89.7,0.2)$ | 89.43${}^{+0.4}_{-0.4}$
|  $\gamma$ [km/s] | $\mathcal{N}(1.7,0.2)$ | 1.729 $\pm 0.001$ | $\mathcal{N}(42.6,0.2)$ | 42.620 $\pm 0.002$ | $\mathcal{N}(-42.2,-0.2)$ | -41.878 $\pm 0.004$
| Parameter | Prior | WASP-105 | Prior | WASP-120 | Prior | WASP-131
|  $T_{c}$ \- 2450000 [d] | $\mathcal{N}(T_{0}\pm 0.006)$ | 6930.740${}^{+0.004}_{-0.004}$ | $\mathcal{N}(T_{0}\pm 0.006)$ | 8411.730${}^{+0.003}_{-0.003}$ | $\mathcal{N}(T_{0}\pm 0.006)$ | 7180.598$\pm 0.003$
|  $\lambda$ [deg] | $\mathcal{U}(-180,180)$ | -14 ${}^{+28}_{-24}$ | $\mathcal{U}(-180,180)$ | -2 $\pm$ 4 | $\mathcal{U}(-180,180)$ | 161 $\pm$ 5
|  $v\,\sin{i_{*}}$ [km/s] | $\mathcal{U}(0,2)$ | 0.8${}^{+0.2}_{-0.2}$ | $\mathcal{U}(0,18)$ | 14.5${}^{+2.2}_{-2.6}$ | $\mathcal{U}(0,5)$ | 2.17${}^{+0.33}_{-0.31}$
| $a/R_{s}$ | $\mathcal{N}(17.2,0.3)$ | 17.2${}^{+0.3}_{-0.3}$ | $\mathcal{N}(5.9,0.2)$ | 5.91${}^{+0.19}_{-0.19}$ | $\mathcal{N}(8.5,0.2)$ | 8.52${}^{+0.20}_{-0.20}$
| Inc. [deg] | $\mathcal{N}(89.2,0.2)$ | 89.20${}^{+0.21}_{-0.20}$ | $\mathcal{N}(82.54,0.78)$ | 82.15${}^{+0.48}_{-0.44}$ | $\mathcal{N}(85.0,0.3)$ | 85.01${}^{+0.39}_{-0.34}$
|  $\gamma$ [km/s] | $\mathcal{N}(24.6,0.2)$ | -24.684$\pm 0.001$ | $\mathcal{N}(19.8,0.2)$ | 19.827$\pm 0.004$ | $\mathcal{N}(-19.6,0.2)$ | -19.638$\pm 0.001$
Table 4: Transmission (TSM) and emission (ESM) spectroscopy metrics for our sample, as defined in Kempton et al. (2018). WASP- | 77b | 101b | 103b | 105b | 120b | 131b
---|---|---|---|---|---|---
TSM | 186 | 365 | 89 | 21 | 17 | 356
ESM | 413 | 147 | 133 | 36 | 68 | 203

###  3.2 Transmission spectroscopy

With the same data sets that were used to measure the projected stellar
obliquity we also performed transmission spectroscopy to search for strong
optical absorbers such as sodium (589 nm doublet) and hydrogen (Balmer alpha).
The most amenable targets are WASP-101b and WASP-131b, thanks to their high
transmission spectroscopy metric, which rates the suitability of the target
for atmospheric characterization (Kempton et al., 2018) – see Table 4. For all
the targets, we derive featureless spectra and show in Figs. 7 and 8 the
sodium doublet regions for WASP-101b and WASP-131b around the sodium doublet.
The results for WASP-101b are in agreement with the previous studies using the
HST in the near-infrared (NIR) and optical region (Wakeford et al., 2017a;
Rathcke et al., 2023) that found featureless spectra and attributed them to
the presence of thick clouds. While in Fig. 7 the sodium D1 appears to have
two points in the absorption, we do not claim a detection, especially as the
sodium D2 line is predicted to have a more profound line profile (Gebek & Oza,
2020) that we do not detect in our spectra. We have compared the observed
spectrum with a clear atmosphere model and a featureless spectrum using a
$\chi^{2}$ test and the featureless model is preferred.

WASP-103b is an accessible target for the investigation of Balmer-driven mass
loss due to its proximity to the host star (García Muñoz & Schneider, 2019).
We derive a featureless spectrum around the H-alpha region. We provide the
first transmission spectrum of WASP-131b which is expected to have a large
atmospheric signal. The derived spectrum shows no absorption features and
possibly hints at either, the presence of clouds, Rayleigh scattering muting
the strength of the absorption features, and/or processes depleting sodium
(Iro et al., 2005).

Figure 7: Transmission spectrum for WASP-101b showing a non-detection of any
absorbers. The blue dashed lines indicate the position of the Na D2 and D1
lines. We show in cyan a simulated spectrum corresponding to a clear
atmosphere model. In red we show a featureless spectrum. The latter model is
preferred by a $\chi^{2}$ test. Figure 8: Transmission spectrum for WASP-131b
showing a non-detection of any absorbers. The blue dashed lines indicate the
position of the Na D2 and D1 lines.

##  4 Discussion

###  4.1 Misaligned planets

We compare our results to the known sample555Retrieved from
https://exoplanetarchive.ipac.caltech.edu/ of exoplanets with measured spin-
orbit alignment (Fig. 9). WASP-131b resides in the less populated region of
highly-misaligned planets with host star temperature lower than 6250 K. This
temperature corresponds to the Kraft break, which separates stars with deep
convective envelopes and efficient magnetic dynamos from those without
(Maeder, 2009; Avallone et al., 2022). As noted in Albrecht et al. (2022),
most of the planets that are on retrograde orbits around cooler stars are
planets with Neptunian masses. WASP-131b is one of the most misaligned Saturn-
mass planets known and is an especially intriguing target for migration
theories as it is known that its host has a stellar companion on wide orbit
(Bohn et al., 2020). The Kozai-Lidov mechanism (Fabrycky & Tremaine, 2007) can
put a planet on a retrograde orbit in the presence of a wide stellar
companion. As the orbit has already been circularized through tidal
interactions with the host star, we cannot confirm this scenario. However,
future atmospheric chemistry studies may be able to provide clues about the
position in the disc where the planet formed (Madhusudhan et al., 2014).

WASP-101b with its projected obliquity of 34 degrees joins a less populated
region of misaligned planets (Fig. 9). A trend (Albrecht et al., 2021; Attia
et al., 2023) suggests that misaligned planets do not equally cover the full
range of obliquities but they rather show a preference for polar orbits
($\lambda$$\sim$90 deg). However, the mechanisms responsible for this trend
are still under debate (Lai, 2012; Petrovich et al., 2020; Siegel et al.,
2023). Furthermore, Dong & Foreman-Mackey (2023) reported that misaligned
systems have nearly isotropic stellar obliquities with no strong clustering
near 90 degrees. These contradictory findings warrant a further investigation
of the distribution of misaligned planets. The other targets join a well-
populated parameter space of aligned gas giant exoplanets.

We tried to assess whether misaligned Jupiter-mass planets around hot stars
belong to a different population of exoplanets. To this end, we performed666We
used the 2D KS test Python implementation available at
https://github.com/syrte/ndtest. a two-dimensional KS test (Peacock, 1983) to
study the parameter space Teff-Mp and compared the misaligned population
($\lambda$$\geq$20 deg) to the whole gas giant population. The test reveal
that, with a $p$-value of $1\times 10^{-11}$, we can reject the null
hypothesis that both groups originate from the same planetary population.

###  4.2 Stellar rotation and true obliquity $\Psi$

Photometric light curves can sometimes be used to derive the stellar rotation
periods (e.g., Skarka et al., 2022) due to modulations imprinted by the
presence of active regions on the spinning star – a key ingredient to derive
the stellar inclination $i_{*}$ and thus the true obliquity. We have tried to
infer the stellar rotation periods using TESS (Ricker et al., 2015) and ASAS-
SN g band (Kochanek et al., 2017) light curves, using a Lomb-Scargle
periodogram (Lomb, 1976; Scargle, 1982). We were able to detect a periodic
modulation of WASP-77 A with a period of $16.2\pm 0.25$ days in the ASAS-SN
data (FAP=$1\times 10^{-5}$, Fig. B7). This is in agreement with a literature
value for rotational modulation for WASP-77 A detected by Maxted et al. (2013)
who reported a value of $15.4\pm 0.4$ days in the WASP light curve. For other
targets, we were not able to detect any signal with high significance. Using
the values above we infer $i_{*}=42\pm 12$ deg for WASP-77 A777We used the
obtained $v\,\rm{sin}i_{*}$ from the R-M effect as the value from spectroscopy
is a combination of several broadening mechanisms (e.g., Triaud et al., 2015)
and is therefore not a good indicator of the rotation period of the star..
Combining the $\lambda$ and $i_{*}$ measurements we are able to infer the true
stellar obliquity $\Psi$ using the spherical law of cosines,
$\rm{cos}\Psi=\rm{sin}i_{*}\,\rm{sin}i\,\rm{cos}|\lambda|+\rm{cos}i_{*}\,\rm{cos}i$.
We obtain $\Psi=$48${}^{+22}_{-21}$ degrees888We note that given the errorbars
the system is still aligned within just over 2 sigmas..

Figure 9: Projected obliquity versus stellar effective temperature. Our
targets are plotted with stars. The dashed vertical black line shows the
position of the Kraft break. Figure 10: Projected obliquity versus the ratio
of the planetary to the stellar mass. Our targets are plotted with stars.

###  4.3 Future atmospheric characterization

The high-resolution transmission spectroscopy method can probe the upper
atmospheres of exoplanets by resolving the deep line cores of strong atomic
features. Optical spectra of exoplanets are valuable tools for atmospheric
retrievals using broadband infrared data. Such retrievals suffer from severe
degeneracies as multiple combinations of parameters can well fit the same data
set. These degeneracies can be lifted by constraints provided with optical
data (Welbanks & Madhusudhan, 2019). The presence of the refractory elements
is used for studying the evolution of gas planets (Lothringer et al., 2021;
Hands & Helled, 2022). Our results from section 3.2 will aid future missions
in obtaining more precise abundances of these gas giants to unravel their
history.

In the future, space and airborne missions (e.g., Ariel, Tinetti et al. 2018;
Twinkle, Edwards et al. 2019b and EXCITE, Nagler et al. 2022) will provide a
homogeneous sample of exoplanetary atmospheric spectra. ESA’s
Ariel999https://arielmission.space/ mission, scheduled for launch in 2029, is
specifically designed to conduct the first unbiased survey of a statistically
significant sample of around 1,000 transiting exoplanets across the visible
and near-infrared spectrum. With limited prior information on the targets
(mainly limited to their existence, radius, mass, and equilibrium
temperature), Ariel’s observational strategy is based on four distinct tiers
(Edwards et al., 2019a; Bocchieri et al., 2023). Tier 3 consists of repeated
observations of a select group of benchmark planets (approximately 50-100)
around bright stars to characterize their atmospheres in detail.

Knowing the spin-orbit orientation of planetary systems will complement the
information obtained by these missions especially in regard to the planetary
formation and evolution questions. In the following subsections, we summarize
atmospheric prospects for WASP-77Ab, WASP-101b, WASP-103b, and WASP-131b as
these planets are the most amenable for future atmospheric studies as
suggested by their Transmission Spectroscopy Metric (TSM) and Emission
Spectroscopy Metric (ESM), reported in Table 4.

For WASP-77Ab, WASP-101b and WASP-131b, we show the simulated atmospheric
transmission spectra as would be obtained by Ariel. These spectra were
produced by combining forward models from TauREx 3 (Al-Refaie et al., 2021)
with the Ariel radiometric simulator, ArielRad (Mugnai et al., 2020),
following the same methodology as presented in Mugnai et al. (2021). That is,
for a given planet and atmospheric model, we used TauREx 3 to generate the
high-resolution transmission spectrum. Then, we binned the raw spectrum to the
Tier-3 spectral grid (R = 20, 100, and 30, in NIRSpec, AIRS-CH0, and AIRS-CH1,
respectively) and added the associated noise predicted by ArielRad for each
spectral bin. ArielRad is a wrapper of ExoRad (Mugnai et al., 2023) (the
instrument-independent version of the radiometric simulator, available on
GitHub101010https://github.com/ExObsSim/ExoRad2-public) and ArielRad-Payloads,
the repository of configuration files for the payload maintained by the Ariel
Consortium. For reproducibility, we report the code versions in Table 5.
Finally, for WASP-103b, we show predicted JWST MIRI observations. The results
for individual planets are presented in Appendix A.

Table 5: Codes used to produce the simulated Ariel spectra. Code | Version
---|---
TauREx 3 | 3.1.1-alpha
ArielRad | 2.4.26
ExoRad | 2.1.111
ArielRad-Payloads | 0.0.17

##  5 Summary

We analyzed HARPS and HARPS-N archival data of 6 gas giants planets on short
orbits around F-G-K dwarfs. We studied the Rossiter-McLaughlin effect and
measured the spin orbit alignment for the first time for four planets. We find
that WASP-131b is on a highly misaligned orbit and joins a small number of
highly misaligned planets around host star with effective temperature below
6250 K. WASP-101b is on a misaligned orbit, while WASP-77 Ab, WASP-103b,
WASP-105b and WASP-120b are on aligned orbits. We also derived the true (3-D)
obliquity of WASP-77 Ab, $\Psi=$48${}^{+22}_{-21}$ deg. We further performed
transmission spectroscopy in order to search for strong atomic absorbers
(sodium doublet and H-alpha), but obtained featureless spectra likely due to a
cloud deck at high altitudes and/or Rayleigh scattering muting the strength of
the features. Finally, we discussed future perspectives for studying these
targets with the space missions that will be able to constrain the evolution
and migration histories of these planets via atmospheric chemistry studies.

###### Acknowledgements.

The authors would like to thank the anonymous referee for their insightful
report. We would like to also thank Prune C. August for sending us model
spectra. MV, MS would like to acknowledge the funding from MSMT LTT-20015. PK
would like to acknowledge the funding from GACR 22-30516K. The funding from
ANID-23-05 and HORIZON project number 101086149 enabled the mobility between
Czech and Chilean colleagues (MV, PK). DI acknowledges support from the
European Research Council (ERC) via the ERC Synergy Grant ECOGAL (grant
855130) and from collaborations and/or information exchange within NASA’s
Nexus for Exoplanet System Science (NExSS) research coordination network
sponsored by NASA’s Science Mission Directorate under Agreement No.
80NSSC21K0593 for the program “Alien Earths”.

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##  Appendix A Future atmospheric characterization: results for individual
planets

###  A.1 WASP-77 Ab

WASP-77 Ab is listed as a Tier-3 object in a recently proposed Ariel candidate
sample (Edwards & Tinetti 2022), with emission spectroscopy as the preferred
observing mode. Line et al. (2021) found a solar C/O ratio and sub-solar
metallicity in the planetary atmosphere using the Gemini telescope. The sub-
solar metallicity was later confirmed using the NIRSpec instrument on JWST
(August et al. 2023). Line et al. (2021) suggested that WASP-77 Ab accreted
its envelope interior to its parent protoplanetary disk’s $\rm{H_{2}O}$ ice
line from carbon-depleted gas with little subsequent planetesimal accretion or
core erosion. Such mechanisms are hard to reconcile with the non-solar
abundance ratios of WASP-77 A published by Reggiani et al. (2022). They found
that WASP-77 Ab likely formed outside of its parent protoplanetary disk’s
$\rm{H_{2}O}$ ice line ($\sim$ 4.5 AU) based on enhanced C/O ratio and then
migrated inwards. Khorshid et al. (2023), using the SimAb code, studied the
possible pathways for the formation of this planet with different initial disk
conditions. They found that the planet has likely initiated its migration
within the $\rm{CO_{2}}$ ice line ($\sim$ 15 AU) and was moved inward via
disk-free migration. Our measurement of an apparent alignment of the planet’s
orbit with the stellar rotation axis is in agreement with this. Finally,
Changeat et al. (2022) found hints of TiO in the atmosphere. Our results find
a featureless spectrum that could hint either at the presence of hazes in the
optical wavelengths or at a lower abundance of refractory materials. However,
future studies with higher S/N are needed to confirm the origin of the muted
features.

Future characterization of WASP-77 Ab with Ariel and JWST will measure several
carbon- and oxygen-bearing molecular species (such as $\rm{H_{2}O}$, $\rm{CO}$
and $\rm{CO_{2}}$) to determine its C/O ratio with unprecedented precision and
accuracy to shed more light onto its formation pathways. We show a simulated
spectrum using one eclipse in Fig. 11. We generated the spectrum assuming
equilibrium chemistry with metallicity and C/O ratio values taken from Smith
et al. (2023). A single Ariel observation will be able to unambiguously
distinguish between the two currently competing models thanks to its
continuous wavelength coverage from 0.5 to 7.8 $\mu$m observed simultaneously.

As suggested by Turrini et al. (2021), additional elemental ratios (e.g., N/O,
C/N, and S/N) may present a better opportunity to study the planetary
formation and will provide crucial information in unambiguously determining
planetary history pathways. Charnay et al. (2022) show that WASP-77 Ab would
be an excellent target for studying the redistribution of the thermal energy
via obtaining phase curves during various orbital phases of the planetary
orbit. Phase curves studies will cover the whole orbital phase; the night-side
with temperature $\approx 1\,000$ K (Keating et al. 2019) offers the best
opportunity to infer nitrogen abundances (in order to obtain C/N and N/O
ratio). Based on detailed models by Ohno & Fortney (2023), $\rm{NH_{3}}$
offers the best opportunity for detection with the JWST-MIRI instrument,
targeting its strong absorption band at 11 $\mu$m.

Figure 11: Simulated Ariel emission spectrum of WASP-77Ab’s atmosphere. In
orange and blue we show two competing models presented in August et al.
(2023). Ariel will be able to distinguish between these two models with high
confidence with a single observed eclipse due to its broad wavelength
coverage.

###  A.2 WASP-101b

Due to its high TSM, WASP-101b was initially considered as a prime candidate
for transmission spectroscopy using JWST in the Early Release Science (ERS)
program. However, Wakeford et al. (2017a) later measured a featureless
spectrum. They observed WASP-101b in the spectral region from 1.1 to 1.7$\mu$m
with HST and from the lack of spectral features inferred the possible presence
of a cloud deck or of water vapor depletion. This apparently disqualified
WASP-101b from the JWST ERS. A later study using HST in the optical region
obtained a flat spectrum and inferred the presence of clouds (Rathcke et al.
2023). In our analysis, we have obtained results consistent with the presence
of clouds yielding a featureless spectrum. Nevertheless, Kawashima et al.
(2019) have shown that, even in the presence of clouds, the redder part of the
JWST or Ariel spectrum can still provide useful information about the
atmospheric composition. WASP-101b is categorized as a Tier-3 object in
Edwards & Tinetti (2022), with transmission spectroscopy as the preferred
observing mode and we provide here a simulated transmission spectrum as would
be observed by Ariel.

Figure 12: Simulated Ariel transmission spectra of WASP-101b’s atmosphere. In
orange, we show a model with thick clouds consistent with previous HST data.
In blue, we display a model with a clear atmosphere. Colors correspond to the
different instruments/channels of the Ariel.

The simulated spectrum using 2 transits is presented in Fig. 12; in blue, the
spectrum corresponds to equilibrium chemistry with solar elemental ratios with
a clear atmosphere. In orangee, the simulated spectrum corresponds to
equilibrium chemistry and is consistent with the muted spectral features
observed with HST. This shows that, even when considering gray clouds (opaque
at all wavelengths), a worst-case assumption, this does not preclude the
possibility of atmospheric characterization. The spectral region between 2 and
4 $\mu$m still contains valuable information about the molecular composition –
in particular, features of CO and $\rm{CO_{2}}$ can still be accessible for
analysis, especially as $\rm{CO_{2}}$ is an atmospheric metallicity indicator
in giant planet atmospheres (Lodders & Fegley 2002). These observations will
improve our understanding of the environment where aerosols form, especially
as WASP-101b might belong to a sparse class of cloudy exoplanets with
equilibrium temperature above 1 500 K. Hence, future JWST observations with
the MIRI instrument might shed more light on the possible presence, origin,
and composition of the aerosols (Wakeford et al. 2017b). Furthermore, MIRI
will cover the strong $\rm{SO_{2}}$ band between 7 and 8 $\mu$m. As
$\rm{SO_{2}}$ is expected to be present in higher layers of the atmosphere, it
is less likely to be obscured, even in the presence of aerosols. $\rm{SO_{2}}$
has recently been suggested as a promising tracer of metallicity in giant
exoplanet atmospheres (Polman et al. 2023; Tsai et al. 2023).

###  A.3 WASP-103b

WASP-103b is ranked in the Ariel tier 3 for emission spectroscopy (Edwards &
Tinetti 2022). The atmosphere of WASP-103b has been studied by several teams
in the past. Lendl et al. (2017) found the presence of strong alkali metals
using the Gemini telescope. However, this result has not been confirmed by
subsequent atmospheric studies (Wilson et al. 2020; Kirk et al. 2021). Our
results are consistent with the null detection reported by the later studies.
Changeat (2022) found hints of thermal inversion and presence of
$\rm{H_{2}O}$, FeH, CO and $\rm{CH_{4}}$ features using HST data. Recent
observations with the Canada–France–Hawaii Telescope (Shi et al. 2023)
confirmed the presence of thermal inversion and also detected super-solar
metallicity composition.

Figure 13: JWST MIRI simulated spectra for day- (top) and night-side (bottom)
of WASP-103b with phase curve observations. Yellow points mark the simulated
spectra and with colored areas we show the relative contributions of various
species. SiO (in red) as a tracer of refractory elements, represents a
promising window into a characterization of thermal inversions in ultra-hot-
Jupiters as well as their origin.

Due to its high temperature (2 500 K) and reported detection of thermal
inversion, WASP-103b is an excellent candidate for the detection of ionic
species (Fe II, Ti II) and of metal oxides such as TiO and VO in the optical
and SiO in the NIR (Gandhi & Madhusudhan 2019). Lothringer et al. (2022)
reported detection of SiO for the first time in the atmosphere of an ultra-hot
Jupiter, WASP-178b, with similar equilibrium temperature ($\sim$ 2450 K) as
WASP-103b. We used TauREx3 (Al-Refaie et al. 2021) with the GGchem chemical
code (Woitke et al. 2018) and the atmospheric parameters (T-p profiles,
metallicity, and C/O ratios) inferred in Changeat (2022) to simulate day- and
night-side spectrum of WASP-103b with JWST MIRI phase-curve observations
(noise estimated via Pandexo: Batalha et al. (2017)). We have included a semi-
opaque silicate cloud layer in our simulations. Our models show that SiO can
easily be detected for 5x solar Si/O ratio Fig. 13. SiO is a refractory
material and has been proposed as one of the possible origins of thermal
inversions alongside with other refractory materials such as TiO and VO.
Detection of SiO would provide key insight into the origins of thermal
inversions as their origin is not fully understood (Parmentier et al. 2018).
For ultra-hot-Jupiters (as they are hot enough to largely avoid the
condensation of refractory species) the ratio of refractory-to-volatile
elements (e.g., Si/O) combined with other ratios provides an unique insight
into a planetary formation and migration as emphasized by Lothringer et al.
(2021).

Furthermore, MIRI observations may provide additional information on the
condensation of silicates on the night side as the temperature should be low
enough for the Si to be mostly present in the condensate form of aerosols (Gao
et al. 2020) producing a strong feature at 10 $\mu$m as found in WASP-107b
(Dyrek et al. 2023). WASP-103b hence represents an intriguing target for
future JWST observations to characterize the thermal structure and origin of
aerosols (Grant et al. 2023).

The low density of the atmosphere with the detected tidal deformation (Barros
et al. 2022) make WASP-103 b also a good target for detection of mass loss due
to Roche lobe overflow (Gillon et al. 2014) as the gravity cannot bind all the
gas that escapes to the stellar environment. Roche lobe overflow has been
detected in a few Jupiter-mass planets (e.g., Haswell et al. 2012; Yan &
Henning 2018; Czesla et al. 2022) using the strong hydrogen lines as such
indicators are well suited for detecting mass loss (Wyttenbach et al. 2020),
especially in the recombination limited regime (Lampón et al. 2023).

Our results yield no detectable feature around the H-alpha region which is
hard to reconcile with theoretical predictions (García Muñoz & Schneider
2019). In the future, high-resolution spectrographs mounted on large
telescopes (e.g., ESPRESSO and ANDES) offer the best opportunity to detect
these features in the optical while space instruments such as NIRSpec/grism
are best suited to detect Paschen lines in the NIR (Sánchez-López et al.
2022). Furthermore, the NIR Helium triplet feature has been also used as a
tracer of planetary mass loss (Spake et al. 2018), but this feature is mostly
amenable for detection in systems orbiting K and late G type stars (Oklopčić
2019). Recent detections of a Helium triplet in the upper atmosphere of an
ultra-hot Jupiter WASP-76b (Casasayas-Barris et al. 2021) and a hot Jupiter
HAT-P-32 b (Czesla et al. 2022), both orbiting F-type stars, might suggest
that this feature is also accessible for detection around planets orbiting
hotter stars. Helium triplet detection is now commonly done with ground-based
high-resolution spectrographs. Future observations can also be done with JWST
NIRISS/SOSS that has recently been shown to deliver firm He detections (Fu et
al. 2022). The atmospheric conditions needed for atmospheric mass loss and the
specific properties of the upper atmosphere are still poorly understood (Wong
et al. 2021; Lampón et al. 2023; Bourrier et al. 2023).

###  A.4 WASP-131b

WASP-131b, with its high TSM, is a suitable target for further atmospheric
follow-up with the transmission spectroscopy method (Kabáth et al. 2019). We
detect no feature in the transmission spectrum, possibly hinting at high-
altitude clouds or processes depleting sodium, but future higher S/N data are
needed to confirm this.

Fig. 14 shows the Ariel simulated spectra with the Tier 3 category, following
Edwards & Tinetti (2022), using 4 transits.

Figure 14: Simulated Ariel transmission spectra of WASP-131b’s atmosphere.
With colors, we distinguish two models with distinct C/O ratios, corresponding
to a different history of the planet.

The prime species for detection are $\rm{H_{2}O}$, CO and $\rm{CO_{2}}$
molecules. Such molecules will be crucial for constraining the C/O ratio,
which will be able to trace the formation and migration history (Brewer et al.
2017), especially as WASP-131b is on a highly misaligned orbit. We show in
blue a spectrum with a high C/O ratio, which would hint at a formation past
the ice line of the system, while in orange we show a spectrum with a low C/O
ratio, hinting at a formation interior of the ice line. These two scenarios
would have distinct histories that can be unraveled by atmospheric studies
especially as the orbit has been already circularized by tidal forces.
Furthermore, as suggested by Turrini et al. (2021) using additional abundance
ratios (e.g., N/O, C/N, and S/N) where possible, significantly improves the
gained insights into the formation pathways of giant planets. To this account,
future measurements with JWST-NIRSpec targeting $\rm{H_{2}S}$, may further
strengthen the evolution investigation. Temperatures around 1 500 K are quite
favorable for the production of $\rm{H_{2}S}$. The wavelength region around
3.78 $\mu$m has been shown to be the most favorable for $\rm{H_{2}S}$
detection (Polman et al. 2023).

##  Appendix B Additional figures

Figure B1: MCMC results of WASP-77 Ab Figure B2: MCMC results of WASP-101b
Figure B3: MCMC results of WASP-103b Figure B4: MCMC results of WASP-105b
Figure B5: MCMC results of WASP-120b Figure B6: MCMC results of WASP-131b

Figure B7: Top: Periodogram of the ASAS-SN g band data of WASP-77 A. We detect
the strongest peak with $P_{\rm{Rot}}$ =16.2 d corresponding to the stellar
rotation. Bottom: Phased ASAS-SN data with the detected stellar rotation
period