11institutetext:  Observatoire de l’Université de Genève, Chemin Pegasi 51,
1290 Versoix, Switzerland 22institutetext: European Southern Observatory,
Alonso de Córdova 3107, Vitacura, Región Metropolitana, Chile 33institutetext:
Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP,
Rua das Estrelas, 4150-762 Porto, Portugal 44institutetext: Departamento de
Matemática y Física Aplicadas, Universidad Católica de la Santísima
Concepción, Alonso de Rivera 2850, Concepción, Chile 55institutetext:
Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France 66institutetext:
NetGuardians SA 77institutetext: Ludwig Maximilian University, University
Observatory Munich, Scheinerstrasse 1, Munich 81679, Germany 88institutetext:
Portuguese Space Agency, Estrada das Laranjeiras, n.º 205, RC, 1649-018,
Lisboa, Portugal

# Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS)

VIII. Nondetection of sodium in the atmosphere of the aligned planet
KELT-10b††thanks: Based on observations made at the ESO 3.6m telescope (La
Silla, Chile) under ESO programme 097.C-1025

M. Steiner<EMAIL_ADDRESS>0000-0003-3036-3585 O. Attia 11
0000-0002-7971-7439 D. Ehrenreich 11 M. Lendl 11 V. Bourrier 11 C. Lovis 11 J.
V. Seidel 22 0000-0002-7990-9596 S. G. Sousa 33 D. Mounzer 11 N. Astudillo-
Defru 44 X. Bonfils 55 V. Bonvin 66 W. Dethier 55 K. Heng 77 B. Lavie 11 C.
Melo 88 G. Ottoni 11 0000-0001-9305-9631 F. Pepe 11 D. Ségransan 11 A.
Wyttenbach 11 0000-0001-9003-7699

(Received …; accepted …)

###### Abstract

Context.  The HEARTS survey aims to probe the upper layers of the atmosphere
by detecting resolved sodium doublet lines, a tracer of the temperature
gradient, and atmospheric winds. KELT-10b, one of the targets of HEARTS, is a
hot-inflated Jupiter with 1.4 $R_{\mathrm{Jup}}$ and 0.7 $M_{\mathrm{Jup}}$.
Recently, there was a report of sodium absorption in the atmosphere of
KELT-10b (0.66% ± 0.09% (D2) and 0.43% ± 0.09% (D1); VLT/UVES data from single
transit).

Aims. We searched for potential atmospheric species in KELT-10b, focusing on
sodium doublet lines (Na i; 589 nm) and the Balmer alpha line (H $\alpha$; 656
nm) in the transmission spectrum. Furthermore, we measured the planet-orbital
alignment with the spin of its host star.

Methods. We used the Rossiter-McLaughlin Revolutions technique to analyze the
local stellar lines occulted by the planet during its transit. We used the
standard transmission spectroscopy method to probe the planetary atmosphere,
including the correction for telluric lines and the Rossiter-McLaughlin effect
on the spectra. We analyzed two new light curves jointly with the public
photometry observations.

Results. We do not detect signals in the Na i and H $\alpha$ lines within the
uncertainty of our measurements. We derive the $3\sigma$ upper limit of excess
absorption due to the planetary atmosphere corresponding to equivalent height
$R_{p}$ to $1.8R_{p}$ (Na i) and $1.9R_{p}$ (H $\alpha$). The analysis of the
Rossiter-McLaughlin effect yields the sky-projected spin-orbit angle of the
system $\lambda=-5.2\pm 3.4^{\circ}$and the stellar projected equatorial
velocity $v_{\rm eq}\sin{i_{\star}}=2.58\pm 0.12$ kms-1. Photometry results
are compatible within $1\sigma$ with previous studies.

Conclusions. We found no evidence of Na i and H $\alpha$, within the precision
of our data, in the atmosphere of KELT-10b. Our detection limits allow us to
rule out the presence of neutral sodium or excited hydrogen in an escaping
extended atmosphere around KELT-10b. We cannot confirm the previous detection
of Na i at lower altitudes with VLT/UVES. We note, however, that the Rossiter-
McLaughlin effect impacts the transmission spectrum on a smaller scale than
the previous detection with UVES. Analysis of the planet-occulted stellar
lines shows the sky-projected alignment of the system, which is likely truly
aligned due to tidal interactions of the planet with its cool (Teff ¡ 6250 K)
host star.

###### Key Words.:

Planets and satellites: atmospheres – Planets and satellites: individual:
KELT-10b – Methods: data analysis – Techniques: spectroscopic

##  1 Introduction

Shortly after the discovery of the first exoplanet orbiting a solar-type star,
51 Peg b (Mayor & Queloz, 1995), we were able to observe the atmosphere around
a similar exoplanet (HD 209458b) for the first time by detecting sodium
through transmission spectroscopy using a space telescope, specifically the
Hubble Space Telescope (HST) (Charbonneau et al., 2002). This feature was
later observed using data from a ground-based facility by the Subaru
telescope/High Dispersion Spectrograph (HDS) (Snellen et al., 2008). Since
then, the field of exoplanet atmospheres has moved from the simple detection
of chemical species to the characterization of atmospheric dynamics. This
includes observations of wind patterns (e.g., Seidel et al., 2020b, 2021) or
the asymmetry between the morning and evening terminators detected by
Ehrenreich et al. (2020) and Kesseli & Snellen (2021). Furthermore, we can
observe not only the strong resonant lines such as that of the sodium doublet
(Seidel et al., 2019; Langeveld et al., 2022) but also target the cross-
correlation function of the weak lines using spectra from high-resolution
spectrographs such as High Accuracy Radial velocity Planet Searcher (HARPS)
(Mayor et al., 2003), Echelle SPectrograph for Rocky Exoplanets and Stable
Spectroscopic Observations (ESPRESSO) (Pepe et al., 2021), Ultraviolet and
Visual Echelle Spectrograph (UVES) (Dekker et al., 2000), or HDS (Noguchi et
al., 2002; Sato et al., 2002). Using the latter method allows for the creation
of a ”spectroscopic atlas,” as shown, for example, in Hoeijmakers et al.
(2019, 2020).

While the field is rapidly gaining momentum through the use of larger
telescopes, we have also started to realize the impact of stellar and telluric
effects on the results of transmission spectroscopy. The first sodium
detection (Charbonneau et al., 2002) has been recently disputed by Casasayas-
Barris et al. (2021); the reported signal seems to come from the Rossiter-
McLaughlin (RM) effect (see also Sing et al., 2008; Casasayas-Barris et al.,
2020). RM is an effect where we observe a radial velocity (RV) anomaly from
the expected Keplerian value caused by the stellar rotation and transit of the
planet. Due to the stellar rotation, the planetary disk occults regions of the
stellar surface with different velocities and spectra properties. Since the RV
is derived from the disk-integrated spectrum of the star, which is deformed by
the occulted regions, we observe the velocity anomaly. In the case of ground-
based observations, the telluric lines can also cause false positives and
negatives (e.g., Seidel et al., 2020a, c; Langeveld et al., 2021; Orell-Miquel
et al., 2022; Spake et al., 2022), and a careful correction of the Earth’s
atmosphere is necessary.

The scientific exploration of exoplanetary atmospheres, namely the detection
and characterization of chemical composition, is becoming more and more
mainstream (e.g., Borsa et al., 2021; Chen et al., 2020; Deibert et al., 2021;
Langeveld et al., 2022), such that we can start to perform population studies.
The population sample size is mainly limited by the brightness of the host
star and atmospheric scale height. There are also many potential exoplanets
for planetary characterization not observed by any sufficient observatory yet.

Recently, several teams have attempted to summarize and characterize the
detected species in exoplanetary atmospheres, including Guillot et al. (2022,
Table 1) and Stangret et al. (2021, Figure 7), for example. The former
summarize chemical species identified in exoplanetary atmospheres,
highlighting the size of the studied sample. The latter show species detected
based on planets with $T_{eq}>1000K$, mainly focusing on (ultra)hot Jupiters.
Atomic species, such as sodium or hydrogen, were observed only in several tens
of exoplanetary atmospheres, sampling mainly hot Jupiters and warm Neptunes.

We could perform a population study to understand why some chemical species
are (non)detectable in the exoplanetary atmosphere. The goal of the Hot
Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS) survey is to
characterize a sample of hot Jupiters with the high-resolution spectrograph
HARPS (Mayor et al., 2003) Figure 1, (Wyttenbach et al., 2017; Seidel et al.,
2019; Bourrier et al., 2020; Hoeijmakers et al., 2020; Seidel et al., 2020a,
c; Mounzer et al., 2022), and to serve as a pathfinder for VLT/ESPRESSO (Pepe
et al., 2021). Data from HEARTS and other surveys are now used for such
population studies, such as Langeveld et al. (2022). For the purpose of
population study, a set of planets with very similar properties, such as
planetary radius and stellar type, is interesting for atmospheric study.
However, the sample of currently known exoplanets makes it difficult for such
studies to be successful, as not many planets are similar enough and are
orbiting stars bright enough to perform such a task.

The target of this paper is KELT-10 b (Kuhn et al., 2016). This hot Jupiter
has many properties similar to the benchmark planet system HD 209458 b,
providing a valuable opportunity to compare these two planets. It notably
features a sodium detection obtained by McCloat et al. (2021) with VLT/UVES.
We obtained two transits with HARPS as part of HEARTS, which is further
discussed in Section 2, with simultaneous photometry observations discussed
and analyzed in Section 3. The RM effect analysis is discussed in Section 4,
followed by transmission spectroscopy in section 5, searching for sodium (Na
i) and hydrogen (H $\alpha$). Finally, we discuss our results with concluding
remarks in Section 6.

Figure 1: Radius-insolation flux figure of known exoplanets. The color-coding
used is as follows: yellow, KELT-10b; green, HEARTS and SPADES surveys’ sodium
detections (SPADES is a twin survey using a similar setup as HARPS-N at the
3.58m telescope at La Palma); and red, WASP-127, the only nondetection from
HEARTS. WASP-127 b has not been detected in HARPS data (Seidel et al., 2020c).
However, by using VLT/ESPRESSO, Allart et al. (2020) established a tenuous
signal below the detection limit of Seidel et al. (2020c).

##  2 Observations

We observed two transits of KELT-10b on 26 June 2016 and 21 July 2016 from La
Silla (Chile). We obtained 96 spectra111Data available from the ESO archive.
with HARPS (Mayor et al., 2003) at the 3.6 m telescope and two photometric
series with EulerCAM (ECAM) at the 1.2 m Euler
telescope222https://www.eso.org/public/teles-instr/lasilla/swiss/
simultaneously. We refer the reader to Lendl et al. (2012) for more
information about ECAM. We observed two new light curves that were analyzed
jointly with already reduced light curves introduced by Kuhn et al. (2016) to
refine the ephemeris system.

Night | # | # of spectra | Airmass | Seeing | SN56 | SN67 | Exposure time
---|---|---|---|---|---|---|---
2016-06-26 | 1 | 40 (12) | 1.05-1.35-2.17 | 1.12-1.55-2.20 | 17.2-34.5-46.1 | 17.8-34.0-45.0 | 900 s
2016-07-21 | 2 | 56 (21) | 1.05-1.31-2.24 | 0.56-0.76-1.08 |  8.3-15.8-27.7 |  8.0-14.9-26.4 | 600 s
Table 1: Observational log: The columns correspond (from left to right) to:
Date of observation; Reference number for the given night; Number of spectra
during night and number of in-transit spectra in parentheses; Airmass; Seeing
and Signal-to-Noise ratio (SNR) for a given order; Exposure time. Note that
for the Airmass, Seeing, and SNR columns, the format is min-mean-max value
during the night. We refer the reader to Figure 10 and Figure 11 for detailed
plot.

The observational conditions (Table 1) were not ideal either night, with high
seeing for the first night and partial cloud cover for the second night. Due
to the passage of clouds and exposure time (600s) used on the second night,
the observed spectra of this night suffer from a low signal-to-noise ratio
(S/N, mean $\sim$15). We ultimately rejected this night from our analysis due
to the data quality.

The ECAM light curves are shown in Figure 2. The entire transit duration is
covered, with a short gap due to a telescope software issue during the
beginning of transit on night 1. During the second night, a passage of clouds
impacted the observations, leading to significant scatter during the transit.

Figure 2: Light curves observed complementary to the HARPS dataset using the
ECAM at the 1.2 meter Euler Swiss telescope.

Finally, the CORALIE (Queloz et al., 2000) RV follow-up from Kuhn et al.
(2016) has also been used. CORALIE is a spectrograph located at the same
telescope as ECAM, with RV measurement precision up to $3$ ms-1. CORALIE has
been monitoring KELT-10 for potential companions and measuring the planetary
mass of KELT-10b. We show all RV observations for both CORALIE and HARPS in
Figure 3.

Figure 3: RV observations from CORALIE (green) and HARPS (blue and orange for
nights 1 and 2, respectively, analyzed dataset). The black line is a Keplerian
model as reported in Kuhn et al. (2016). The inset plot in the upper right
corner zooms in on the transit in detail. A strong and roughly symmetrical
velocity anomaly due to the RM effect is observed during transit.

##  3 Photometry analysis

While the overall precision of ECAM light curves is better than those used in
Kuhn et al. (2016), using only the two transits without the Kuhn et al. (2016)
set of data provides compatible yet less precise system parameters. For that
reason, we opted to analyze the entire collection of publicly available
follow-up photometry (except for the discovery light curve from the KELT-South
telescope), using the CONAN code (Lendl et al., 2017).

The first step in CONAN is to find a proper baseline model for the light
curve. We searched for different trends, including airmass, sky, $x$ and $y$
coordinate shift, Full Width Half Maximum (FWHM), and sinusoidal pattern. Both
ECAM light curves were detrended separately, and the appropriate model was
selected using the difference in Bayesian Information Criterion ($\Delta$BIC)
value and checking by eye (essential to avoid over-fitting). The 26 June 2016
light curve has been detrended for time and FWHM trends, while the 21 July
2016 light curve has been detrended for time and sky trends.

For the set of limb-darkening coefficients, we used the publicly available
code LDCU333Available at: https://github.com/delinea/LDCU (Deline et al.,
2022). The stellar parameters necessary for the limb-darkening computation
come from the UVES analysis by Sousa et al. (2018).

Once we established a proper baseline, we ran CONAN on the entire set, using
the differential evolution Markov chain Monte Carlo (DEMCMC) method described
in Lendl et al. (2017). We ran the code multiple times, and it varied whether
or not we fixed an initial parameter between the different usable jump
parameters. In the end, we fixed semi-amplitude K to the value from Kuhn et
al. (2016). We found better results with eccentricity set to 0, adopting these
values. All resulting parameters are shown in Table 2. Finally, we searched
for a wavelength dependence of the transit depth in different filters but
measured consistent broadband $R_{p}$.

Jump parameters | Parameter | Kuhn et al. (2016) | CONAN analysis |  $\sigma$– difference
---|---|---|---|---
$T_{0}$ [$BJD_{\mathrm{TBD}}$] | Mid transit time | $2457175.0439^{+0.0053}_{-0.0054}$ | $2457175.04197_{-0.00029}^{+0.00028}$ | 0.36
$\frac{R_{p}}{R_{s}}$ [1] | Planet to star radius ratio | $0.1190^{+0.0014}_{-0.0012}$ | $0.11978_{-0.0011}^{+0.00076}$ | 0.44
i [deg] | Inclination | $88.61^{+0.86}_{-0.74}$ | $87.82_{-0.45}^{+0.54}$ | 0.86
$\frac{a}{R_{s}}$ [1] | System scale | $9.34^{+0.21}_{-0.32}$ | $9.03_{-0.20}^{+0.27}$ | 0.74
P [d] | Period | $4.166285_{-0.000057}^{+0.000057}$ | $4.1662449_{-0.0000032}^{+0.0000032}$ | 0.70
Derived parameters | Parameter | Kuhn et al. (2016) | CONAN analysis |  $\sigma$– difference
$R_{p}$ [$R_{\mathrm{Jup}}$] | Planetary radius | $1.399^{+0.069}_{-0.049}$ | $1.409_{-0.051}^{+0.046}$ | 0.12
$M_{p}$ [$M_{\mathrm{Jup}}$] | Planetary mass | $0.679^{+0.039}_{-0.038}$ | $0.680_{-0.024}^{+0.024}$ | 0.02
a [au] | Semi-major axis | $0.05250^{+0.00086}_{-0.00097}$ | $0.0508_{-0.0019}^{+0.0024}$ | 0.66
b [1] | Impact parameter | $0.23^{+0.11}_{-0.14}$ | $0.344_{-0.075}^{+0.065}$ | 0.86
$T_{14}$ [day] | Transit duration | $0.1560^{+0.0016}_{-0.0012}$ | $0.1570_{-0.0013}^{+0.0010}$ | 0.49
$dF$ or $\frac{R_{p}^{2}}{R_{s}^{2}}$ [1] | Transit depth | $0.01416^{+0.00034}_{-0.00029}$ | $0.01435_{-0.00026}^{+0.00018}$ | 0.44

Table 2: Comparison of the results from the CONAN analysis and the parameters
from Kuhn et al. (2016). The top part of the table includes the parameters
that have been used as jump parameters. The bottom part provides additional
parameters we can derive from the jump parameters. From left to right, the
columns correspond to the following: parameter (and unit); Kuhn et al. (2016)
parameter set; CONAN analysis (this paper); and $\sigma$ difference between
the parameters.

The resulting ephemeris is compatible with Kuhn et al. (2016) within
$1\sigma$, which can be attributed to different analysis methods. The
precision of $T_{0}$ and $P$ values has been improved significantly (by a
factor of $\sim 18$, new precision of $T_{0}$ is ${}^{+0.00028}_{-0.00029}$
and precision of $P$ is ${}^{+0.0000032}_{-0.0000032}$) due to the more
extended baseline of observations.

##  4 Rossiter–McLaughlin effect analysis

Figure 4: Map of the CCFintr during the transit of KELT-10 b. Transit contacts
are shown as orange dashed lines. Values are colored as a function of their
normalized flux, and plotted as a function of the RV in the star rest frame
(in abscissa) and orbital phase (in ordinate). The core of the stellar line
from the planet-occulted regions is clearly visible as a bright streak. The
magenta solid line shows the stellar surface RV model from the RMR best fit.
The small gap in the first part of the transit (at phase $\sim-0.005$) is due
to a missing exposure.

###  4.1 Data reduction

We exploit one dataset obtained with HARPS during the transit of KELT-10 b on
26 June 2016. Forty exposures were acquired (with exposure times of 900 s),
among which 14 are in transit, seven are before the transit, and 19 are after
the transit. KELT-10 was observed on fiber A, while fiber B was on the sky.
The spectra were extracted from the detector images, corrected for, and
calibrated using version 3.5 of the Data Reduction Software (DRS)
pipeline444http://www.eso.org/sci/facilities/lasilla/instruments/harps/doc/DRS.pdf.
One of the DRS corrections concerns the color effect caused by the variability
of extinction induced by Earth’s atmosphere (e.g., Bourrier & Hébrard, 2014;
Wehbe et al., 2020). The flux balance of the KELT-10 spectra was reset to a G2
stellar spectrum template, before they were passed through weighted cross-
correlation (Baranne et al., 1996; Pepe et al., 2002) with a G2 numerical mask
to compute cross-correlation functions (CCFs) with a step of 0.5 kms-1. This
mask is part of a new set that was built with weights more representative of
the photonic error on the line positions, as described in Bourrier et al.
(2021).

As stated in Sect. 2, another transit was recorded with HARPS on 21 July 2016.
This visit was discarded from the analysis because of the poor S/N. In fact,
including this transit introduces spurious line variations that bias the
results and for which we could not correct. We refer to Appendix C for more
details.

Throughout the RM analysis, the posterior probability distributions (PDFs) of
free parameters describing models fitted to the data are sampled using emcee
(Foreman-Mackey et al., 2013). The number of walkers and the burn-in phase are
adjusted based on the degrees of freedom of the considered problem and the
convergence of the chains. Best-fit values for these parameters are set to the
median of their PDFs, and their 1$\sigma$ uncertainty ranges are defined using
highest density intervals (HDIs).

Figure 5: PDFs of the contrast (upper panels), FWHM (middle panels), and RVs
(lower panels) of the Gaussian line model fitted to the individual CCFintr.
Blue lines indicate the PDF median values with green dashed lines showing the
1$\sigma$ highest density interval (HDIs). In-transit exposure indices are
shown in each subplot.

###  4.2 Extraction and analysis of individual exposures

We employed a novel technique, the Rossiter–McLaughlin Revolutions (RMR,
Bourrier et al., 2021) technique, to analyze the data. This method fits the
spectral line profiles from all planet-occulted regions at once with a joint
model, which boosts the S/N by the number of in-transit exposures at first
order, allowing access to fainter RM signals. The RMR is optimal to fully
exploit a RM dataset, to assess biases due to line shape variations, and to
measure obliquities from all types of systems in a more comprehensive way than
traditional techniques. Indeed, a classical RM analysis only relies on the
anomalous RVs of the disk-integreated lines, which condense the information
contained in CCF profiles into a single measurement and limit our ability to
detect the occultation of the stellar surface by the planet. This process can
bias our interpretation of the RV anomaly if the occulted stellar line profile
is not well modeled or varies along the transit chord. The RMR technique and
its holistic analysis of the planet-occulted, rather than the disk-integrated,
starlight, has been successfully used to detect the RM signal of the super-
Earth HD 3167 b, the smallest exoplanet with a confirmed RM signal (Bourrier
et al., 2021), and to refine the orbital architecture of the warm Neptune GJ
436 b (Bourrier et al., 2022).

The disk-integrated CCFDI of each individual exposure as produced by DRS,
corresponding to the light coming from the entire star, are aligned by
correcting their velocity table for the Keplerian motion of the star. A
master-out CCF, representative of the unocculted star, was built by coadding
CCFDI outside of the transit. The master-out CCF is fitted with a Gaussian
model, and all CCFDI are shifted to the star rest frame using the derived
centroid. Aligned CCFDI are then scaled to a common flux level outside of the
transit and to the flux expected from the planetary disk absorption during
transit using a light curve computed with the batman package (Kreidberg,
2015). Cross-correlation functions from the planet-occulted regions are
retrieved by subtracting the scaled CCFDI from the master-out CCF and are then
reset to a common flux level to yield intrinsic CCFintr that allow for a more
direct comparison of the local stellar lines (Fig. 4).

Following the RMR approach, we first analyzed individual exposures to evaluate
the quality of each CCFintr and assess the possibility for line variations
along the transit chord. The various CCFintr were fitted using a Gaussian
model with uniform priors, which are broad enough to constrain the following
parameters: $\mathcal{U}(-15,15)$ kms-1 on the RV centroid (i.e., about three
times the maximum typical stellar surface RV for G-type stars);
$\mathcal{U}$$(0,20)$ kms-1 on the FWHM (i.e., about three times the width of
the master-out CCF, which is assumed to be similar to that of the CCFintr
given the slow stellar rotation); and $\mathcal{U}$$(0,1)$ on the contrast
(i.e., noninformative). A set of 100 walkers were run for 2000 steps, with a
burn-in phase of 500 steps. The model was independently fitted to each CCF
over [-150, 150] kms-1 in the star rest frame. The stellar line is detected in
all CCFintr (Fig. 4) with well-defined PDFs for their model parameters (Fig.
5), except for the first and last exposures. This is a consequence of the
darkened flux of the stellar limb and its partial occultation by the planet,
which results in a lower S/N at ingress and egress. For this reason, we
exclude these exposures from further analyses. We note that the derived
contrasts and FWHMs are consistent between the different retained exposures
(Fig. 5), as is expected from the stability of the G-type star. Surface RVs
roughly go from $-$2 to $+$2 kms-1 along the transit chord, meaning that the
planet is successively blocking just as much blueshifted as redshifted stellar
surface regions, which already suggests an aligned orbit and a moderate
stellar rotation.

Figure 6: Correlation diagrams for the PDFs of the RMR model parameters for
the KELT-10 b transit. Curved green and light blue lines show the 1 and
2$\sigma$ simultaneous 2D confidence regions that contain 39.3% and 86.5% of
the accepted steps, respectively. One-dimensional histograms correspond to the
distributions projected on the space of each line parameter, with the green
dashed lines limiting 68.3% of HDIs. The blue straight lines and squares show
the median values.

###  4.3 Derivation of the RM parameters

Parameter | Unit | Reloaded | Revolutions (adopted)
---|---|---|---
$\lambda$ | deg | $-6.4\pm 3.7$ | $-5.2\pm 3.4$
$v_{\rm eq}\sin{i_{\star}}$ | kms-1 | $2.61\pm 0.13$ | $2.58\pm 0.12$
Table 3: Derived parameters from the RM analysis, using two different methods.

The RMR technique exploits all of the information contained in the transit
time series by simultaneously fitting a model of the stellar line to all
CCFintr. The local stellar line is modeled as a Gaussian profile with a
constant FWHM and contrast, consistently with the analysis of the individual
exposures (Fig. 5). The time series of theoretical stellar lines was convolved
with a Gaussian profile of width equivalent to the HARPS resolving power
before being fitted to the CCFintr. Stellar solid-body rotation is assumed.
The MCMC jump parameters are hence the line contrast and FWHM, the projected
obliquity $\lambda$, and the projected equatorial stellar rotational velocity
$v_{\rm eq}\sin{i_{\star}}$, with the same priors for the contrast and FWHM as
in Sect. 4.2, $\mathcal{U}(-180,180)^{\circ}$ for $\lambda$ and
$\mathcal{U}(0,5)$ kms-1 for $v_{\rm eq}\sin{i_{\star}}$.

The resulting best-fit line satisfyingly reproduces the local stellar lines
along the transit chord, as can be seen in Fig. 4. The corner plot of the fit
is shown in Fig. 6. The resulting PDFs are well defined and symmetrical, in a
way that HDIs are here equivalent to quantile-based credible intervals. The
correlation diagrams show no correlation between the various parameters, such
that the system’s architecture does not depend on the line model. Consistently
with the individual exposure analysis (Sect. 4.2), we find a low obliquity and
stellar rotational velocity ($\lambda=-5.2\pm 3.4^{\circ}$, $v_{\rm
eq}\sin{i_{\star}}=2.58\pm 0.12$ kms-1), and confirm that a constant stellar
line model fits the data well.

Given the quality of the visit, we further tried to constrain finer stellar
effects. We fit for stellar differential rotation (DR) employing a law derived
from the Sun $\Omega(\theta)=\Omega_{\rm eq}(1-\alpha\sin^{2}\theta)$ (e.g.,
Cegla et al., 2016), where $\Omega_{\rm eq}$ is the equatorial rotation rate,
$\theta$ the latitude, and $\alpha\in[0,1]$ the unitless DR parameter.
Compared to the solid-body fit, two more free parameters are considered here:
$\alpha$ and $\sin{i_{\star}}$, for which we use noninformative priors. The
resulting PDFs for $\alpha$ and $\sin{i_{\star}}$ are uniform within their
definition intervals and the other parameters remain unchanged within
1$\sigma$, meaning that DR is not constrained. This is also supported by BIC
comparison, which does not justify using the DR model over the solid body one.

For completeness, and to assess the stability of our results against the
employed method, we also conducted a Reloaded Rossiter–McLaughlin (RRM, Cegla
et al., 2016) fit of the surface RVs. The RRM technique is restricted to the
interpretation of the RV centroids from the planet-occulted CCFs. It requires
that the surface RVs have a strong enough S/N to be fitted with a stellar line
model, which is the case here. We assume solid-body rotation, and the same
priors as for the RMR fit were used. The resulting parameters are consistent
within 1$\sigma$ with those derived from the RMR analysis, indicating the
robustness of our results. The various derived parameters can be found in
Table 3.

##  5 Transmission spectroscopy

This section describes the transmission spectroscopy performed on the HARPS
dataset, including all the corrections done before the calculation. We
followed the methods by Mounzer et al. (2022), which further refine methods by
Seager & Sasselov (2000), Redfield et al. (2008) and Wyttenbach et al. (2015).

We used the e2ds format of HARPS spectra (DRS version 3.5), which includes a
2D grid of 72 and 71 echelle orders (for fiber A and B, respectively), and
each order has 4098 pixels. The first step in the analysis is deblazing, using
the blaze calibration obtained for each night of observation. This study’s
primary focus is orders 56 and 67 (using the order numbering by DRS, 55 and 66
for the fiber B data). The difference in order numbering is due to a gap in
fiber B on the order of number 45 (at 5277 Å)555Table 6.1 in:
https://www.eso.org/sci/facilities/lasilla/instruments/harps/doc/DRS.pdf.
These orders include Na i and H $\alpha$.

We also excluded several additional spectra from the analysis observed at
airmass¿2. This filtering affected only the out-of-transit baseline and did
not hamper our resulting master-out spectrum (the average out-of-transit
spectrum used for stellar line correction). This filtering led to a final set
of 37 spectra used in the analysis of transmission spectroscopy.

###  5.1 Correction for Earth’s atmosphere

After correcting for the instrumental effects, we proceeded to mitigate the
impact of Earth’s atmosphere on the observed spectra. To do so, we used
several corrections. First, we used molecfit (Smette et al., 2015; Kausch et
al., 2015) to correct for the H2O and O2 lines from the atmosphere, following
the procedures described in Allart et al. (2017) and Seidel et al. (2020c). In
a few words, molecfit takes an input scientific spectrum and fits it with a
synthetic high-resolution (R$\sim$ 5 000 000) transmission spectrum in
selected wavelength regions with prominent telluric absorption. It runs a
line-by-line radiative transfer code using an extensive line list of
atmospheric lines and calculates the transmission spectrum during the given
observation. Finally, it corrects the scientific spectrum, significantly
mitigating the effect of the telluric lines. A more detailed description of
the program is in the references above.

After correcting for the H2O and O2 lines, we normalized the spectra using the
median flux of each spectrum. This normalization still leaves a color effect
in the spectrum due to the instrument that could be corrected by a better
normalization approach or by subtracting a linear fit. Since this effect is
stable for a night, it is unnecessary to rectify this trend since we will
eventually divide by the master-out spectrum.

After normalizing the spectra, we corrected for the cosmic rays. We calculated
a median spectrum and flag pixels as cosmic (and set them to the median
spectrum value) if the flux difference from the median spectrum was beyond the
5$\sigma$ level. We also manually checked the spectra for missed cosmics
during the correction, finding that no cosmic rays hampered the region of Na i
and H $\alpha$.

Finally, molecfit does not correct for sodium emission in Earth’s atmosphere.
We monitored the fiber B data (aimed at the sky background) and found
significant sodium emission. Our attempts to subtract this emission were
unsuccessful because of the fiber A/B efficiency ratio variability at night.
Due to this variation, we observed the remainder of the emission feature at
high airmass, creating a spurious signal in the transmission spectrum. As a
result, we thus opted to mask a small part (around 8 pixels) of the spectrum.

Afterward, we shifted all the spectra into the rest frame of the star, using
the BERV (approximately $2.7$ kms-1 for night 1) and systemic velocity value
calculated from the analysis of the master-out CCF (Section 4; $31.96\pm 0.02$
kms-1). The value of systemic velocity calculated from HARPS is compatible
with both the values from Kuhn et al. (2016) ($31.9\pm 0.1$ kms-1) and the one
used in McCloat et al. (2021) ($31.61\pm 1.29$ kms-1).

###  5.2 Correction for stellar effects

Once we shifted to the stellar rest frame, we could correct for the stellar
lines. At first order, we could calculate the average out-of-transit spectrum
($M_{out}$) and divide our dataset by it (Wyttenbach et al., 2015; Seidel et
al., 2019). However, doing so disregards the RM and center-to-limb variation
(CLV) effects that can affect our spectra. This approach is the one McCloat et
al. (2021) took, as the lack of precise wavelength calibration in their UVES
data disallowed the measurement of RVs from the spectra, preventing an RM
correction. HARPS, however, is designated to provide accurate RVs, hence we
could measure and correct for the RM effect and simulate its impact on the
final transmission spectrum.

To correct our spectra for the RM effect, we adapted the formula by Mounzer et
al. (2022):

$F_{\mathrm{corr,i}}=1+\left(\frac{R_{p}^{2}}{R_{s}^{2}}\right)\left(1-\frac{M_{\mathrm{out}}-F_{i}\delta_{i}}{M_{\mathrm{out,v_{i}}}\Delta_{i}}\right).$

Here, $\frac{R_{p}^{2}}{R_{s}^{2}}$ corresponds to the planet/star radius
ratio, $F_{i}$ is the spectrum we wish to correct, $M_{\mathrm{out}}$ is the
master-out spectrum, and $M_{\mathrm{out,v_{i}}}$ is master-out shifted by the
local stellar velocity. The $\delta_{i}$ and $\Delta_{i}$ correspond to the
transit depth and white-light flux received during the individual exposure.
The $v_{i}$ velocity was calculated using the $\lambda=-5.2\pm 3.4^{\circ}$and
$v_{\rm eq}\sin{i_{\star}}=2.58\pm 0.12$ kms-1 values calculated in Section 4,
using an analytical formula (for circular orbit) describing the RVs of the
stellar surface along the transit chord of the planet for each exposure:

$v_{i}(\phi)=\left(\frac{a}{R_{s}}\right)(\sin(2\pi\phi)\cos(\lambda)+\cos(2\pi\phi)\cos(i)\sin(\lambda))v_{\rm
eq}\sin{i_{\star},}$

where $\phi$ is the orbital phase at which we observed the planet. Other
parameters follow the same notation as in previous sections (cf. Table 2 and
Section 4). The shift is between $-2.6$ to $+2.6$ kms-1. This roughly
corresponds to 3-4 pixels (1 pixel $\sim 820$ms-1) in HARPS spectra from the
unshifted $M_{\mathrm{out}}$.

To estimate the impact of the RM effect on the transmission spectrum of
KELT-10 b (for comparison with the McCloat et al. (2021) detection), we used
the EVaporating Exoplanets (EVE) code (e.g., Bourrier & Lecavelier des Etangs,
2013; Allart et al., 2018). This code allows for simulations of the 3D
atmosphere of a transiting planet and calculations of synthetic transmission
spectra accounting for the geometry of the transit and the properties of the
stellar surface. First, we accounted for CLV of the local stellar spectrum by
tiling the EVE stellar grid using synthetic line profiles calculated at
different limb darkening angles with the
Turbospectrum666https://github.com/bertrandplez/Turbospectrum2019 code (Plez,
2012). Then the RM effect was naturally accounted for by shifting the local
stellar spectra according to the rotational velocity of KELT-10. Using these
settings, we simulated a transit of KELT-10b without including any atmosphere
to assess the distortion induced purely by the RM effect and CLV. We set the
code to return a time series of KELT-10 spectra as they would be observed with
HARPS and we used them to compute an average transmission spectrum comparable
to our observations.

Figure 7 shows the comparison between our EVE simulation and the best-fit
model to the UVES transmission spectrum from McCloat et al. (2021) in the
region of the sodium doublet. We are unable to explain the observed signal
with the pure RM and CLV effects. The amplitude of the effect is on the order
of $0.2\%$, and opposite to an atmospheric absorption signal, impacting the
transmission spectrum significantly. It is even possible that the RM effect is
obscuring part of the putative atmospheric signal; however, given the issues
with the wavelength calibration in the UVES data (Section 5.3 in McCloat et
al., 2021), it is difficult to draw a definite conclusion.

If the observed UVES signal is truly redshifted, we could explain the
”emission-like” shoulders apparent in the UVES transmission spectrum (Fig. 4
in McCloat et al., 2021). However, only the D1 signal there seems to be as
broad as our simulation, while the D2 signal appears to be due to a few
pixels. The amplitude of the signature would be slightly reduced, but not
enough to compromise its detection.

On the other hand, if the redshift is purely of nonastrophysical origin, the
RM effect would significantly decrease the observed signal, meaning the true
amplitude of the sodium signal is higher. In that case, KELT-10 b would have
one of the strongest sodium signals detected yet, which, considering its
location in the hot Jupiters’ population (Figure 1), seems curious, as we
would expect a stronger signal in hotter and puffier planets (as long as the
sodium itself is not ionized). It is also possible that due to the lower
resolution of UVES spectra, the RM effect is smeared out and hence weaker.

Figure 7: Modeling of the RM + CLV effect on the transmission spectrum in the
rest frame of the planet, specifically focused on the sodium detection
presented in McCloat et al. (2021) ($A_{D2}=0.66\%$, $\sigma_{D2}=0.06\r{A}$,
$\Delta\lambda_{D2}=+0.23\r{A}$; $A_{D1}=0.43\%$, and $\sigma_{D1}=0.06\r{A}$,
$\Delta\lambda_{D1}=+0.23\r{A}$). Top panel: Gaussian fit to the lines
attributed by McCloat et al. (2021) to planetary sodium (their Fig. 4, blue)
and simulated RM and CLV effects using EVE (red). We note that compared to
McCloat et al. (2021), we use a reversed y-axis (due to different units used),
that is absorption is above continuum and emission is below it. The $3\sigma$
and $5\sigma$ level reported by McCloat et al. (2021) is shown as dark blue
dashed lines. Bottom panel: O-C values (UVES - EVE simulation, blue), and
$3\sigma$ and $5\sigma$ UVES detection levels (blue).

After stellar line correction, including the RM effect (CLV is negligible
compared to RM), a visible Na i remnant is still present. This remnant results
from very low S/N in the core of the stellar Na i and should be removed, as it
can create spurious signals. We masked the core region with NaN values,
following the procedures presented in Seidel et al. (2020a, c). This way, we
could mask the sodium remnant, but we unfortunately also masked part of the
planetary signal.

To estimate how much of the planetary signal was removed, we used the value of
the mean FWHM of the Na i signal from Seidel et al. (2019) (FWHM =
0.65$\r{A}$). The area within the FWHM marked the region for the planetary
signal, and we assumed no shift of the sodium line (in the planetary rest
frame). The fraction of information lost is
$\frac{FWHM_{\mathrm{mask}}}{FWHM_{\mathrm{signal}}}=28\%$. After we shifted
the spectra to the rest frame of the planet, we calculated an average
transmission spectrum over full in-transit exposures, weighting them by S/N.

Figure 8: Transmission spectroscopy of KELT-10 b in the region of the sodium
doublet. In gray, the entire transmission spectrum is shown (corrected for RM
effect, as described in subsection 5.2), with 20x bins in dark blue. The
detection of McCloat et al. (2021) is overplotted (dark red) as a visual cue
for comparison. The black dashed line corresponds to the 3$\sigma$ and
5$\sigma$ limit above the continuum ($R_{p}^{2}/{R_{s}^{2}}\sim 1.44\%$). The
yellow area is the $\pm$1.5 $\r{A}$ region around each of the Na i lines.
Figure 9: Same as Figure 8, but in the region of H $\alpha$. The color-coding
is the same as in Fig. 8. The additional red line is a continuum of one
equivalent height. No detection is visible in this region either, with
corresponding 3$\sigma$ and 5$\sigma$ limits on the plot.

###  5.3 Transmission spectroscopy

The final transmission spectrum is shown in Figure 8 and Figure 9 for Na i and
H $\alpha$, respectively. Although we corrected our spectrum for the RM
effect, this effect is negligible within our detection limits. We also checked
the RM uncorrected spectrum, finding no significant changes in the notable
features of the spectrum.

Neither of the sodium lines were detected. As part of the comparison with
McCloat et al. (2021), a Gaussian model with their reported parameters has
been over-plotted. To calculate the upper limit, we took the mean uncertainty
in the $\pm$1.5 $\r{A}$ region around the lines, marked as a yellow area, and
used it as a $1\sigma$ estimate. We used a broader region to estimate the
uncertainty since we do not know of any potential shift of the possible
signal. These kinds of shifts can occur due to wind patterns and this is quite
common (e.g., Snellen et al., 2010; Seidel et al., 2020b, 2021; Mounzer et
al., 2022). The $3\sigma$ upper limits are $3.34\%$ for Na i and $3.97\%$ for
H $\alpha$. These upper limits are likely underestimated due to the distortion
of the putative atmospheric signal by the planet-occulted stellar lines.

In the region of Na i, we see a few bins that show absorption. However, the
location of these bins in each of the doublet lines is different, with
-30kms-1 for the D2 feature and -10kms-1 for the D1 feature. This suggests
that these features are of nonastrophysical origin. In fact, the D2 feature
can be attributed to telluric sodium. For the D1 feature, we attribute this to
a low S/N remnant (the count in the line core is below 100) and systematics in
the measurements – several features of a similar strength have been observed
(in the red part of the spectrum) as well. These features also hint at
potential correlated noise. Finally, this kind of signal, if real, would be
visible in the UVES data. Based on these arguments, we, therefore, claim
nondetection.

##  6 Conclusion

###  6.1 Bulk planetary and orbital properties

We have carried out an independent photometry analysis, which shows consistent
results with parameters from Kuhn et al. (2016) within $1\sigma$. We improved
the precision of the P and $T_{14}$ parameters by a factor of $\sim 18$.

We were able to study the RM effect with great precision using the RMR method
(Bourrier et al., 2021), finding the orbit of KELT-10 b to be aligned with the
stellar rotation plane, in projection onto the plane of the sky
$\lambda=-5.2\pm 3.4^{\circ}$. The system is likely truly aligned, as previous
results show that hot Jupiters around late-type stars ($T_{\rm eff}<6250$ K)
tend to live on aligned orbits (Winn et al., 2010; Albrecht et al., 2022).
Indeed, late-type stars are expected to have substantial convective envelopes,
which trigger stronger tidal interactions, thus realigning their systems more
efficiently. This argument is supported by the proximity of KELT-10 b to its
host star ($a/R_{\star}<10$, Table 2), and by the relatively old age of the
system ($4.5\pm 0.7$ Gyr, Kuhn et al., 2016).

###  6.2 Transmission spectroscopy

The nondetection of $3\sigma_{lim}=1.8R_{p}$ (Na i) and
$3\sigma_{lim}=1.9R_{p}$ (H $\alpha$) corresponds to no extreme extension of
upper atmospheric layers, as expected from such a ”well-behaved” system. The
RM + CLV effects create a spurious signal, very similar to the one detected by
Casasayas-Barris et al. (2021) on the example of HD 209458 b. In future
studies of this system, these effects should be corrected for in the
transmission spectra or included in EVE-like simulations to derive (a)
confident atmospheric detection(s).

###  6.3 Comparison with previous sodium detection

Recently, McCloat et al. (2021) have claimed sodium detection from a VLT/UVES
single transit dataset. However, these data could not allow these authors to
obtain RV measurements precise enough to correct for the RM effect (which was
attributed to molecfit being unable to fine-tune the wavelength grid – see
section 4.6 in McCloat et al. (2021)).

Since the authors could not measure the RVs during the transit, a potential RM
effect could have created a significant signal, as in the case of Casasayas-
Barris et al. (2021). Furthermore, the tentative sodium detection had a
significant redshift, likely due to the wavelength calibration issues
mentioned above.

We modeled the effect of RM and CLV on the transmission spectrum, finding that
the distortion by planet-occulted stellar lines cannot explain the measured
sodium detection. This discrepancy with the detection of McCloat et al. (2021)
is surprising, especially if the observed redshift is instrumental, as the RM
effect would significantly strengthen the sodium detection, making it one of
the strongest detections of the Na i doublet to date.

Our transmission spectrum cannot confirm the UVES sodium detection (McCloat et
al., 2021), but we also cannot rule it out, as the lower quality of the final
transmission spectrum does not allow us to probe to such detection limits.
There are several potential reasons why our results do not fully match.

First, our RM correction method might introduce several biases. In this work,
we did not thoroughly investigate different stellar models to use in the
RM+CLV modeling. Incorrect RM correction can then introduce spurious effects
that blur the signal (under-correction) or create a fake one (over-
correction).

Furthermore, molecfit struggles with the correction of low S/N spectra, which
is the case locally in the core region of the sodium doublet. In addition to
that, due to low counts on the detector in the stellar core (¡100), we are no
longer photon-noise dominated but red-noise dominated (Seidel et al. (2022);
Pepe et al. (2021), see section 5 and Appendix D). This is the case for all
observations when the observed planetary signal is on the order of (or less
than) a single photon on the detector and needs to be treated carefully.

Finally, it is possible that either this work or McCloat et al. (2021) is
further affected by some unaccounted effect (e.g., stellar variability,
instrument issue), which could cause a discrepancy between the observations.
In fact, the peaks in our transmission spectrum further in the red hint at the
possibility of correlated noise and systematic errors, which are also on the
same order as the expected signal based on UVES (McCloat et al., 2021). On the
other hand, atmospheric variability can significantly affect the dataset,
especially for slit-based spectrographs such as UVES.

We conclude that to properly address the question on the presence of chemical
species in the atmosphere of KELT-10b (and confirmation of the previous Na i
detection), we need additional data from larger telescopes than the 3.6 m
telescope at La Silla to obtain a good S/N and temporal sampling and to
correct for the stellar effects such as RM that cause a significant impact
($\sim 0.2\%$) on the transmission spectrum.

###### Acknowledgements.

We would like to thank the anonymous reviewer for the insightful comments. We
would like to thank Sean McCloat, who was kind enough to provide reduced UVES
data for comparison purposes with the analysis presented in this paper. This
project has received funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 research and innovation programme (project
Four Aces; grant agreement No 724427). It has also been carried out in the
frame of the National Centre for Competence in Research PlanetS supported by
the Swiss National Science Foundation (SNSF). DE and MS acknowledges financial
support from the SNSF for project 200021_200726. OA and VB’s work has been
carried out in the frame of the National Centre for Competence in Research
PlanetS supported by the Swiss National Science Foundation (SNSF). OA and VB
acknowledge funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (project Spice
Dune; grant agreement No 947634). This project has also been carried out in
the frame of the National Centre for Competence in Research PlanetS supported
by the SNSF. M.L. acknowledges support of the Swiss National Science
Foundation under grant number PCEFP2_194576. This project has received funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation program (grant agreement No 742095 ; SPIDI :
Star-Planets-Inner Disk-Interactions; http://www.spidi-eu.org). S.G.S
acknowledges the support from FCT through the contract nr.CEECIND/00826/2018
and POPH/FSE (EC)
Python packages used: numpy, scipy, matplotlib, astropy777Astropy
Collaboration et al. (2022), specutils, batman

## References

  * Albrecht et al. (2022) Albrecht, S. H., Dawson, R. I., & Winn, J. N. 2022, Tech. rep.
  * Allart et al. (2018) Allart, R., Bourrier, V., Lovis, C., et al. 2018, Science, 362, 1384
  * Allart et al. (2017) Allart, R., Lovis, C., Pino, L., et al. 2017, Astronomy & Astrophysics, 606, A144
  * Allart et al. (2020) Allart, R., Pino, L., Lovis, C., et al. 2020, Astronomy & Astrophysics, 644, A155
  * Astropy Collaboration et al. (2022) Astropy Collaboration, Price-Whelan, A. M., Lim, P. L., et al. 2022, The Astrophysical Journal, 935, 167
  * Baranne et al. (1996) Baranne, A., Queloz, D., Mayor, M., et al. 1996, Astronomy and Astrophysics Supplement Series, 119, 373
  * Borsa et al. (2021) Borsa, F., Allart, R., Casasayas-Barris, N., et al. 2021, Astronomy & Astrophysics, Volume 645, id.A24, 14 pp., 645, A24
  * Bourrier et al. (2020) Bourrier, V., Ehrenreich, D., Lendl, M., et al. 2020, Astronomy & Astrophysics, 635, A205
  * Bourrier & Hébrard (2014) Bourrier, V. & Hébrard, G. 2014, Astronomy and Astrophysics, 569, A65
  * Bourrier & Lecavelier des Etangs (2013) Bourrier, V. & Lecavelier des Etangs, A. 2013, Astronomy & Astrophysics, Volume 557, id.A124, 18 pp., 557, A124
  * Bourrier et al. (2021) Bourrier, V., Lovis, C., Cretignier, M., et al. 2021, Astronomy and Astrophysics, 654, A152
  * Bourrier et al. (2022) Bourrier, V., Zapatero Osorio, M. R., Allart, R., et al. 2022, Tech. rep.
  * Casasayas-Barris et al. (2021) Casasayas-Barris, N., Palle, E., Stangret, M., et al. 2021, Astronomy and Astrophysics, 647, A26
  * Casasayas-Barris et al. (2020) Casasayas-Barris, N., Pallé, E., Yan, F., et al. 2020, Astronomy & Astrophysics, Volume 635, id.A206, 18 pp., 635, A206
  * Cegla et al. (2016) Cegla, H. M., Lovis, C., Bourrier, V., et al. 2016, Astronomy and Astrophysics, 588, A127
  * Charbonneau et al. (2002) Charbonneau, D., Brown, T. M., Noyes, R. W., & Gilliland, R. L. 2002, The Astrophysical Journal, 568, 377
  * Chen et al. (2020) Chen, G., Casasayas-Barris, N., Palle, E., et al. 2020, Astronomy & Astrophysics, 635, A171
  * Deibert et al. (2021) Deibert, E. K., de Mooij, E. J. W., Jayawardhana, R., et al. 2021, arXiv:2109.04373 [astro-ph]
  * Dekker et al. (2000) Dekker, H., D’Odorico, S., Kaufer, A., Delabre, B., & Kotzlowski, H. 2000, 4008, 534
  * Deline et al. (2022) Deline, A., Hooton, M. J., Lendl, M., et al. 2022, Astronomy & Astrophysics, 659, A74
  * Ehrenreich et al. (2020) Ehrenreich, D., Lovis, C., Allart, R., et al. 2020, Nature, 580, 597
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, Publications of the Astronomical Society of the Pacific, 125, 306
  * Guillot et al. (2022) Guillot, T., Fletcher, L. N., Helled, R., et al. 2022, Tech. rep.
  * Hoeijmakers et al. (2019) Hoeijmakers, H. J., Ehrenreich, D., Kitzmann, D., et al. 2019, Astronomy and Astrophysics, 627, A165
  * Hoeijmakers et al. (2020) Hoeijmakers, H. J., Seidel, J. V., Pino, L., et al. 2020, Astronomy and Astrophysics, 641, A123
  * Kausch et al. (2015) Kausch, W., Noll, S., Smette, A., et al. 2015, Astronomy & Astrophysics, 576, A78
  * Kesseli & Snellen (2021) Kesseli, A. Y. & Snellen, I. A. G. 2021, The Astrophysical Journal, 908, L17
  * Kreidberg (2015) Kreidberg, L. 2015, Publications of the Astronomical Society of the Pacific, 127, 1161
  * Kuhn et al. (2016) Kuhn, R. B., Rodriguez, J. E., Collins, K. A., et al. 2016, Monthly Notices of the Royal Astronomical Society, 459, 4281
  * Langeveld et al. (2022) Langeveld, A. B., Madhusudhan, N., & Cabot, S. H. C. 2022, Tech. rep.
  * Langeveld et al. (2021) Langeveld, A. B., Madhusudhan, N., Cabot, S. H. C., & Hodgkin, S. T. 2021, Monthly Notices of the Royal Astronomical Society, 502, 4392
  * Lendl et al. (2012) Lendl, M., Anderson, D. R., Collier-Cameron, A., et al. 2012, Astronomy & Astrophysics, 544, A72
  * Lendl et al. (2017) Lendl, M., Cubillos, P. E., Hagelberg, J., et al. 2017, Astronomy & Astrophysics, 606, A18
  * Mayor et al. (2003) Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20
  * Mayor & Queloz (1995) Mayor, M. & Queloz, D. 1995, Nature, 378, 355
  * McCloat et al. (2021) McCloat, S., von Essen, C., & Fieber-Beyer, S. 2021, The Astronomical Journal, 162, 132
  * Mounzer et al. (2022) Mounzer, D., Lovis, C., Seidel, J. V., et al. 2022, Tech. rep.
  * Noguchi et al. (2002) Noguchi, K., Aoki, W., Kawanomoto, S., et al. 2002, Publications of the Astronomical Society of Japan, 54, 855
  * Orell-Miquel et al. (2022) Orell-Miquel, J., Murgas, F., Pallé, E., et al. 2022, Astronomy & Astrophysics, Volume 659, id.A55, 12 pp., 659, A55
  * Pepe et al. (2021) Pepe, F., Cristiani, S., Rebolo, R., et al. 2021, Astronomy and Astrophysics, 645, A96
  * Pepe et al. (2002) Pepe, F., Mayor, M., Galland, F., et al. 2002, Astronomy and Astrophysics, 388, 632
  * Plez (2012) Plez, B. 2012, Astrophysics Source Code Library, ascl:1205.004
  * Queloz et al. (2000) Queloz, D., Mayor, M., Weber, L., et al. 2000, Astronomy and Astrophysics, v.354, p.99-102 (2000), 354, 99
  * Redfield et al. (2008) Redfield, S., Endl, M., Cochran, W. D., & Koesterke, L. 2008, The Astrophysical Journal, 673, L87
  * Sato et al. (2002) Sato, B., Kambe, E., Takeda, Y., Izumiura, H., & Ando, H. 2002, Publications of the Astronomical Society of Japan, 54, 873
  * Seager & Sasselov (2000) Seager, S. & Sasselov, D. D. 2000, The Astrophysical Journal, 537, 916
  * Seidel et al. (2022) Seidel, J. V., Cegla, H. M., Doyle, L., et al. 2022, Monthly Notices of the Royal Astronomical Society, 513, L15
  * Seidel et al. (2021) Seidel, J. V., Ehrenreich, D., Allart, R., et al. 2021, Astronomy & Astrophysics, 653, A73
  * Seidel et al. (2020a) Seidel, J. V., Ehrenreich, D., Bourrier, V., et al. 2020a, Astronomy and Astrophysics, 641, L7
  * Seidel et al. (2020b) Seidel, J. V., Ehrenreich, D., Pino, L., et al. 2020b, Astronomy & Astrophysics, Volume 633, id.A86, <NUMPAGES>24</NUMPAGES> pp., 633, A86
  * Seidel et al. (2019) Seidel, J. V., Ehrenreich, D., Wyttenbach, A., et al. 2019, Astronomy and Astrophysics, 623, A166
  * Seidel et al. (2020c) Seidel, J. V., Lendl, M., Bourrier, V., et al. 2020c, Astronomy and Astrophysics, 643, A45
  * Sing et al. (2008) Sing, D. K., Vidal-Madjar, A., Désert, J. M., Lecavelier des Etangs, A., & Ballester, G. 2008, The Astrophysical Journal, 686, 658
  * Smette et al. (2015) Smette, A., Sana, H., Noll, S., et al. 2015, Astronomy & Astrophysics, 576, A77
  * Snellen et al. (2008) Snellen, I. a. G., Albrecht, S., de Mooij, E. J. W., & Le Poole, R. S. 2008, Astronomy and Astrophysics, 487, 357
  * Snellen et al. (2010) Snellen, I. A. G., de Kok, R. J., de Mooij, E. J. W., & Albrecht, S. 2010, Nature, 465, 1049
  * Sousa et al. (2018) Sousa, S. G., Adibekyan, V., Delgado-Mena, E., et al. 2018, Astronomy & Astrophysics, 620, A58
  * Spake et al. (2022) Spake, J. J., Oklopčić, A., Hillenbrand, L. A., et al. 2022, The Astrophysical Journal, 939, L11
  * Stangret et al. (2021) Stangret, M., Casasayas-Barris, N., Pallé, E., et al. 2021, Tech. rep.
  * Wehbe et al. (2020) Wehbe, B., Cabral, A., Martins, J. H. C., et al. 2020, Monthly Notices of the Royal Astronomical Society, 491, 3515
  * Winn et al. (2010) Winn, J. N., Fabrycky, D., Albrecht, S., & Johnson, J. A. 2010, The Astrophysical Journal, 718, L145
  * Wyttenbach et al. (2015) Wyttenbach, A., Ehrenreich, D., Lovis, C., Udry, S., & Pepe, F. 2015, Astronomy & Astrophysics, 577, A62
  * Wyttenbach et al. (2017) Wyttenbach, A., Lovis, C., Ehrenreich, D., et al. 2017, Astronomy & Astrophysics, 602, A36

##  Appendix A Observational log

Detailed observational log for both nights of HARPS. The first night (Figure
10) suffered from high seeing, which varied during the night. The second night
(Figure 11) shows a low S/N, leading to removal from the dataset.

Figure 10: Observational log for the first night (26 June 2016). Top panel:
Airmass (blue) and seeing (red). Bottom panel: S/N for order number 56 (blue)
and 67 (red). Figure 11: Same as Figure 10, but for the second night (21 July
2016).

##  Appendix B Fiber B sodium emission

As discussed in Section 5.1, we detected a significant telluric emission
feature from sodium. This is shown in Figure 12, on a total master spectrum of
the first night of fiber B.

Figure 12: Sodium emission observed on fiber B during the first night of
observation. Not correcting for it causes a significant absorption feature. No
features were found on fiber B for the wavelength region of H $\alpha$. The
red dashed line signifies the masked part of the emission.

##  Appendix C RM analysis of the discarded visit

Figure 13: Contrast of the disk-integrated CCFs as a function of orbital phase
(top) and S/N (bottom) for the 26 June 2016 visit (blue points) and the 21
July 2016 visit (red points). The horizontal dashed lines indicate the mean
value for each visit. The vertical dashed lines represent the transit
contacts. Out-of-transit (in-transit, resp.) exposures are shown as squares
(circles, resp.). The full-line curve in the lower plot represents the best
polynomial fit.

An additional transit was recorded with HARPS on 21 July 2016. The S/N of this
visit is substantially lower than the 26 June 2016 one (16 on average for the
former versus 31 for the latter, see Fig. Figure 10 and Figure 11).
Furthermore, the 21 July 2016 spectra were Moon-contaminated shortly after the
end of the transit, resulting in spurious features in the affected CCFs. This
is visible in the disk-integrated contrast fluctuations starting after the
transit (Fig. 13, upper panel). We show the contrasts of the 26 June 2016 CCFs
for a visual comparison of the stability of the two nights.

Figure 14: Intrinsic RVs as a function of orbital phase before (top) and after
(bottom) the correction for the contrast–S/N correlation, for the 26 June 2016
visit (blue points) and the 21 July 2016 visit (red points). The horizontal
dashed line indicates the zero RV level. The vertical dashed lines represent
the transit contacts. The solid black line is the analytical RV curve for the
adopted values of Table 3.

The 21 July 2016 fluctuations correlate with the S/N, as seen in Fig. 13
(lower panel). We have captured this correlation by fitting a third order
polynomial to the affected visit, based on BIC comparison. We then corrected
the disk-integrated (DI) CCFs of this visit according to the fit result, which
reduced the dispersion around the mean contrast value by a factor of $\sim$
3\. Ultimately, this correction turned out to be detrimental to the intrinsic
CCFs. Indeed, Fig. 14 shows a large dispersion of the derived intrinsic RVs
after correction, which results in very large error bars for the derived RM
parameters. We have thus discarded the correction.

We further tried to circumvent the Moon contamination by excluding the post-
transit baseline from the construction of the master out. Expectedly, the
systemic velocity derived from the master out now coincides 26 times better
between the two nights. Yet, the RMR analysis after this correction yields a
very large difference in the derived parameters between the two nights. The
same settings for the MCMC exploration as in Sect. 4 were used. The best-fit
results for the affected visit are $v_{\rm eq}\sin{i_{\star}}=1.88\pm 0.21$
kms-1 and $\lambda=23.0^{+8.7}_{-9.0}{{}^{\circ}}$. Due to the 2.9-$\sigma$
discrepancy between the two nights for the obliquity value, we have also
discarded the correction.

As a last attempt, we excluded the Moon-affected regions from the DI CCFs
(roughly [-20 , 0] kms-1), which should represent a smoother correction than
excluding the full post-transit baseline. Still, a significant discrepancy in
the RMR results between the two nights persists, even if it is lower than with
the last correction: $v_{\rm eq}\sin{i_{\star}}=2.43^{+0.21}_{-0.22}$ kms-1
and $\lambda=9.1^{+8.8}_{-9.1}{{}^{\circ}}$. Even if the stellar equatorial
velocities are now compatible, the obliquities have a 1.5-$\sigma$ discrepancy
between the two nights. In the absence of agreement between the two visits and
despite our tentative corrections, we have discarded the Moon-contaminated
night.

##  Appendix D Masking stellar sodium remnant

After correcting for master out, we observed a low S/N remnant in the sodium
doublet due to line saturation. To remove this effect, we masked the region,
as shown in Figure 15

Figure 15: Used mask in the steps as described in Section 5. Top panel:
Colormap of all spectra during the first night in the rest frame of the star.
The red dashed lines correspond to transit contact points. The white mask is
the mask used for telluric sodium, located at roughly $-30$kms-1. Middle
panel: Master-out spectrum, with the following colored lines: white dash-dot
line, masked region; and green, sodium line $\pm\frac{FWHM}{2}$ region as
reported in Seidel et al. (2019). Bottom panel: Masked stellar signal based on
the mask shown in the middle panel (white lines), which is still in the rest
frame of the star. The black line corresponds to the sodium line in the
planetary rest frame, considering no additional shifts (e.g., due to winds).
Green lines are offset by $\pm\frac{FWHM}{2}$ as used in the middle panel, and
they correspond to the area from which we estimated our lost signal. The noisy
spectra at ingress and egress (around red dashed line) are due to RM
correction and light-curve weighting. These two spectra were not used in the
final transmission spectrum.