11institutetext:  Observatoire de Genève, Université de Genève, 51 Chemin
Pegasi, 1290 Versoix, Switzerland 22institutetext: Department of Physics,
University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK
33institutetext: Centre for Exoplanets and Habitability, University of
Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK 44institutetext: Vanderbilt
University, Department of Physics & Astronomy, 6301 Stevenson Center Lane,
Nashville, TN 37235, USA 55institutetext: NASA Ames Research Center, Moffett
Field, CA 94035, USA 66institutetext: School of Physics and Astronomy,
University of Leicester, Leicester LE1 7RH, UK 77institutetext: Astrophysics
Science Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA
88institutetext: Institute of Planetary Research, German Aerospace Center,
Rutherfordstrasse 2, 12489 Berlin, Germany 99institutetext: Department of
Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA 1010institutetext: European
Space Agency (ESA), European Space Research and Technology Centre (ESTEC),
Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands 1111institutetext: Facultad
de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Diagonal las Torres
2640, Peñalolén, Santiago, Chile 1212institutetext: Millennium Institute for
Astrophysics, Chile 1313institutetext: Google, Cambridge, MA, USA
1414institutetext: Instituto de Astronomía, Universidad Católica del Norte,
Angamos 0610, 1270709, Antofagasta, Chile 1515institutetext: Physikalisches
Institut, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland
1616institutetext: South African Astronomical Observatory, P.O Box 9,
Observatory 7935, Cape Town, South Africa 1717institutetext: Departamento de
Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile

# An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542

Nolan Grieves , An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542
<EMAIL_ADDRESS>François Bouchy An old warm Jupiter orbiting the metal-
poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542 Solène Ulmer-Moll An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Samuel
Gill An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm
Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting
the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor
G-dwarf TOI-5542 David R. Anderson An old warm Jupiter orbiting the metal-poor
G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Angelica Psaridi An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542 Monika Lendl An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542 Keivan G. Stassun An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Jon M.
Jenkins An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Matthew R. Burleigh An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Jack S. Acton An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542 Patricia T. Boyd An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542 Sarah L. Casewell An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Philipp
Eigmüller An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Michael R. Goad An old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Robert F. Goeke An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542 Maximilian N. Günther ESA Research FellowAn old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Faith Hawthorn An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Beth A.
Henderson An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Christopher E. Henze An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Andrés Jordán An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Alicia
Kendall An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Lokesh Mishra An old
warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Dan Moldovan An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542 Maximiliano Moyano An old warm Jupiter orbiting
the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor
G-dwarf TOI-5542 Hugh Osborn An old warm Jupiter orbiting the metal-poor
G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542 Alexandre Revol An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the
metal-poor G-dwarf TOI-5542 Ramotholo R. Sefako An old warm Jupiter orbiting
the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor
G-dwarf TOI-5542 Rosanna H. Tilbrook An old warm Jupiter orbiting the metal-
poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542 Stéphane Udry An old warm Jupiter orbiting the metal-poor G-dwarf
TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Nicolas
Unger An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm
Jupiter orbiting the metal-poor G-dwarf TOI-5542 Jose I. Vines An old warm
Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting
the metal-poor G-dwarf TOI-5542 Richard G. West An old warm Jupiter orbiting
the metal-poor G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor
G-dwarf TOI-5542An old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542 Hannah L. Worters An
old warm Jupiter orbiting the metal-poor G-dwarf TOI-5542An old warm Jupiter
orbiting the metal-poor G-dwarf TOI-5542

(Received 20 May 2022; accepted 19 September 2022)

We report the discovery of a 1.32${}^{+0.10}_{-0.10}$ $\mathrm{M_{\rm Jup}}$
planet orbiting on a 75.12 day period around the G3V $10.8^{+2.1}_{-3.6}$ Gyr
old star TOI-5542 (TIC 466206508; TYC 9086-1210-1). The planet was first
detected by the Transiting Exoplanet Survey Satellite (TESS) as a single
transit event in TESS Sector 13. A second transit was observed 376 days later
in TESS Sector 27. The planetary nature of the object has been confirmed by
ground-based spectroscopic and radial velocity observations from the CORALIE
and HARPS spectrographs. A third transit event was detected by the ground-
based facilities NGTS, EulerCam, and SAAO. We find the planet has a radius of
1.009${}^{+0.036}_{-0.035}$ $\mathrm{R_{\rm Jup}}$ and an insolation of
9.6${}^{+0.9}_{-0.8}$ $S_{\oplus}$, along with a circular orbit that most
likely formed via disk migration or in situ formation, rather than high-
eccentricity migration mechanisms. Our analysis of the HARPS spectra yields a
host star metallicity of [Fe/H] = $-$0.21 $\pm$ 0.08, which does not follow
the traditional trend of high host star metallicity for giant planets and does
not bolster studies suggesting a difference among low- and high-mass giant
planet host star metallicities. Additionally, when analyzing a sample of 216
well-characterized giant planets, we find that both high masses (4
$\mathrm{M_{\rm Jup}}$ $<M_{p}<$ 13 $\mathrm{M_{\rm Jup}}$) and low masses
(0.5 $\mathrm{M_{\rm Jup}}$ $<M_{p}<$ 4 $\mathrm{M_{\rm Jup}}$), as well as
both both warm (P $>$ 10 days) and hot (P $<$ 10 days) giant planets are
preferentially located around metal-rich stars (mean [Fe/H] $>$ 0.1).
TOI-5542b is one of the oldest known warm Jupiters and it is cool enough to be
unaffected by inflation due to stellar incident flux, making it a valuable
contribution in the context of planetary composition and formation studies.

###### Key Words.:

planets and satellites: detection, dynamical evolution and stability,
formation, fundamental parameters, gaseous planets

##  1 Introduction

The first exoplanets discovered were Jupiter-sized planets with close-in
orbits (period $<$ 10 days) around their host stars, known as hot Jupiters
(e.g., Mayor & Queloz, 1995). Even with a low occurrence rate of $<$1% (e.g.,
Zhou et al., 2019), hot Jupiters remain one of the largest samples of known
exoplanets due to the observational biases of current detection methods
favoring close-in, large, and massive planets. Hot Jupiters suffer from
intense stellar irradiation that can deposit energy into their interiors and
cause these planets to have have radii larger than what would otherwise be
expected based on internal structure models (e.g., Guillot & Showman, 2002).
Hot Jupiters are also affected by powerful tidal forces that can lead to tidal
locking and dampening of orbital eccentricity and the planetary rotation
period (see Dawson & Johnson 2018 for a review), as well as intense day-night
contrasts (e.g., Knutson et al., 2007). Therefore, the original properties of
hot Jupiters have been significantly altered by their environment since their
formation, which hinders placing constraints on planet formation and evolution
models from current observations.

Warm exoplanets, which we define as exoplanets with 10-200 day orbital
periods, provide the opportunity to better understand planet formation and
evolution as their atmospheres are less altered by their host star and their
orbital arrangement reflects a less extreme migrational history, as compared
to close-in planets. Previous studies have found giant planets ($M_{p}$ $>$
100 M⊕ or 0.31 $\mathrm{M_{\rm Jup}}$) on 10-100 day periods to be relatively
less frequent than giant planets with shorter or longer orbital periods, known
as the period valley e.g., (Udry et al., 2003; Wittenmyer et al., 2010).
Transiting warm planets are particularly valuable because both the transit and
radial velocity detection methods can be used to obtain accurate masses and
radii of planets that have not been exposed to strong atmospheric escape,
which is essential for constraining the initial planet atmospheric mass
fraction (e.g., Kubyshkina et al., 2019a, b).

The space-based all-sky Transiting Exoplanet Survey Satellite (TESS; Ricker et
al., 2015) currently in operation has discovered thousands of transiting
exoplanet signals. TESS first surveyed the entire sky in 26 different sectors,
each 24 degrees by 96 degrees across, and viewed each sector for $\sim$27
days. Although some stars, such as in the ecliptic poles, are in overlapping
sectors that allow for longer baseline coverage, most stars only have
$\sim$27-day segments of continuous coverage. Planets with periods longer than
$\sim$27 days can therefore only exhibit a single transit in one sector and
their periods cannot be determined without more measurements. However, when
combined with ground-based follow-up observations, TESS single transits have
led to the discovery of new warm giant planets (e.g., Gill et al., 2020c;
Ulmer-Moll et al., 2022) as well as low-mass eclipsing binaries (e.g., Lendl
et al., 2020; Gill et al., 2020a, b, 2022). Low-mass eclipsing binaries are
crucial for testing stellar evolution models of low-mass stars (Kraus et al.,
2011; Feiden, 2015) that are need to obtain accurate calculations of the
masses and radii of single low-mass stars and of any exoplanets they may host.

Here, we report the discovery and characterization of a warm Jupiter first
detected by TESS as a single transit event. We detail our observations in
Section 2, including our radial velocity follow-up observations. In Section 3,
we describe our analysis to derive both stellar and planet properties and we
present our results. We discuss our results in Section 4 and we summarize our
conclusions in Section 5.

##  2 Observations

Figure 1: Gaia EDR3 catalog over-plotted on the TESS Target Pixel File of
TOI-5542 (TIC 466206508) for Sector 13 (top) and Sector 27 (bottom).

###  2.1 Observations and follow-up summary

Our team searched through TESS light curves for single-transit events as
described in Gill et al. (2020a, b, c). For our search and preliminary
analysis of the TESS transits, we used a custom transit model with a least
squares fit utilizing a power-2 limb-darkening law presented by Maxted & Gill
(2019) and described in Gill et al. (2020a). For our initial fit, we fixed the
orbital period to 30 days and fit only the transit epoch, $T_{0}$, the scaled
orbital separation, $R_{1}/a$, the ratio of radii, $k=R_{2}/R_{1}$, the impact
parameter, $b$, and the photometric zero-point, $zp$. We identified single
transits in the TESS data of TOI-5542 in Sectors 13 and 27 that were $T_{2-1}$
$\approx$ 375.628 days apart. After inspecting the full light curves from TESS
sectors 13 and 27, we identified the period of the planet to be greater than
that of the 27-day sectors. This left possible aliases of $\approx$ 187.8,
125.2, 93.9, 75.1, 62.6, 53.7, 47.0, 41.7, 37.6, 34.1, 31.3, and 28.9 days. We
subsequently began spectroscopic and radial velocity (RV) follow-up of the
target with the CORALIE spectrograph. We also started photometric follow-up on
NGTS to detect any possible transit events from the ground.

After 12 CORALIE observations, the highest peak in a periodogram analysis of
the RVs was at 68 days – closest to the 75.1 and 62.6 day aliases. We
continued observing with CORALIE and began observing the target with the HARPS
spectrograph. The HARPS RVs confirmed the 75.1 day alias as the most likely
period, which is evident in the periodogram in Figure 3. Finally, we
identified on the night of August 3, 2021 that all alias periods would exhibit
a transit, as this date was two times the length of time between the two TESS
transits ($T_{2-1}\times$2 $\approx$ 751.3 days after the TESS Sector 13
transit). We therefore scheduled the target on SAAO, EulerCam, and NGTS to
capture the transit on August 3, 2021. We obtained partial transits on
EulerCam and NGTS due to the target rising in the Western hemisphere and a
partial transit on SAAO due to the night ending in South Africa. We did not
catch an ingress or egress with NGTS due to scheduling constraints. We detail
the observations for each facility below.

###  2.2 Space-based TESS photometry

TOI-5542 was observed by TESS in Sector 13 (22 June 2019 to 17 July 2019 UTC)
with full-frame image (FFI) observations at a cadence of 30 minutes. We
identified a single-transit event in TOI-5542 in our search of the Sector 13
data that was clearly significant compared to the out-of-transit data; with
our preliminary transit fit, we calculated a signal-to-noise (S/N) of $\sim$
35 by dividing the transit depth by the median absolute deviation of the light
curve. For our analysis of the Sector 13 data, we used the FFI 30-minute light
curve that was processed by the Science Processing Operations Center (SPOC;
Jenkins et al., 2016) pipeline, which we obtained from the Barbara A. Mikulski
Archive for Space Telescopes (MAST) astronomical data archive hosted by the
Space Telescope Science Institute. The SPOC pipeline was first applied to TESS
2 minute data and then later applied to the 30-minute FFI data (Caldwell et
al., 2020). The SPOC pipeline produces two light curves per sector, referred
to as simple aperture photometry (SAP) and presearch data conditioning simple
aperture photometry (PDCSAP; Smith et al., 2012; Stumpe et al., 2012, 2014).
We used the PDCSAP light curves for our analysis.

We plotted the TESS target pixel file of Sector 13 in Figure 1 using
tpfplotter111https://github.com/jlillo/tpfplotter (Aller et al., 2020) to show
the possible contamination from known sources in the $Gaia$ Early Data Release
3 (EDR3) catalog (Gaia Collaboration et al., 2021), which we discuss further
in Section 3.2. To account for stellar activity as well as residual
instrumental systematics, we applied a Gaussian process (e.g., Gibson, 2014;
Haywood et al., 2014) to the TESS Sector 13 data (discussed further in Section
3.2). In Figure 2, we display the TESS Sector 13 data during the transit event
with the Gaussian process model removed . The full TESS Sector 13 light curve
with the Gaussian process model is displayed in Figure 9.

TOI-5542 was also observed by TESS in Sector 27 (5 July 2020 to 29 July 2020
UTC) with 2-minute cadence exposures222TOI-5542 obtained 2-minute data in
Sector 27 as a result of the approved TESS Guest Investigator program G03188
PI: Villanueva. We also searched TESS Sector 27 light curves for single-
transit events and identified another event around TOI-5542 with a S/N $\sim$
33, which we identified to be similar in shape and depth as the single-transit
event found in Sector 13. For our analysis, we used TESS 2-minute data that
were processed by the SPOC pipeline and again we used the PDCSAP light curves
for our analysis. As in Sector 13, we also accounted for stellar activity and
residual instrumental systematics using a Gaussian process for the TESS Sector
27 data (detailed further in Section 3.2). We display the TESS Sector 27 data
during the transit event with the Gaussian process model removed in Figure 2.
The full TESS Sector 27 light curve with the Gaussian process model is
displayed in Figure 10.

Figure 2: Light curves around each transit of TOI-5542b from the respective
facilities, as described Section 2 (top). The SAAO data is binned to 2 minutes
for visual purposes. The red lines show the best-fit transit model to each
photometry data set from our juliet analysis, as described in Section 3.2.
TESS Sectors 13 and 27 data have the Gaussian process component of their
models removed. Residuals of each transit fit and the root mean square (rms)
of the residuals for each data set (bottom). The rms values for TESS27, SAAO,
and EulerCam are calculated with the data binned to 30 minutes for comparison.

Figure 3: CORALIE and HARPS RVs, as described in Section 2. Top plot shows the
full time baseline of the RV observations, while the middle plot shows the RVs
phased to the 75.12 day period. The black lines show the best-fit Keplerian
model to the RVs from our juliet analysis, as described in Section 3.2. Lower
plot shows the Lomb-Scargle periodogram of the original data as well as the
residuals. Red dashed lines show a false alarm probability (FAP) of 0.1%.

###  2.3 NGTS photometry

After identifying the transit events in the TESS data we began monitoring
TOI-5542 with the Next Generation Transit Survey (NGTS; Wheatley et al.,
2018), a ground-based photometric survey located in Chile at the European
Southern Observatory (ESO) Paranal site. NGTS consists of twelve fully robotic
telescopes each with a 20 cm photometric aperture and a wide 8 deg2 field-of-
view. It uses a custom filter spanning 520 to 890 nm and routinely achieves
photometric precision of 150 parts per million. It has discovered a 3.18 R⊕
transiting planet (NGTS-4b; West et al., 2019), which was the shallowest
transiting system ever discovered from the ground. Wheatley et al. (2018)
gives the full details of the NGTS facility and project.

TOI-5542 was observed using between one and five cameras per night for a total
of 137 nights during the time baseline of UT 14 April 2021 to 7 April 2022
with an exposure time of 10 seconds and cadence of 13 seconds. The reduction
of raw NGTS data is detailed in Bryant et al. (2020) and uses a custom
aperture photometry pipeline that utilizes SEP (Bertin & Arnouts, 1996;
Barbary, 2016). The pipeline computes photometry for a set of circular
apertures with a range of radii and identifies the aperture size with the
minimum root mean square (rms) scatter to create the final light curve. For
TOI-5542, we used an aperture radius of four pixels. Comparison stars are
ranked to select the best non-saturated non-variable comparison stars
according to their color, brightness, and position on the image, relative to
the target star. To avoid night-to-night and camera offsets, the same
comparison stars were used for each camera and each night, and we normalized
the data for each camera separately by dividing by its median flux value.

For our analysis, we removed large outliers in flux and flux uncertainty and
binned the data to 30 minute bins. We display the full NGTS light curve as
well as a Lomb-Scargle periodogram of the data in Figure 11. We did not find a
significant signal in the periodogram around the expected rotation period from
the HARPS spectral analysis ($P_{\rm rot}$ / $\sin i_{*}$ = 17.7 $\pm$ 3.0;
see Section 3.1). We obtained NGTS data on the night beginning August 3, 2021,
when a transit on TOI-5542 occurred, but we did not observe the ingress or
egress of the transit. The offset between this night and those around it has
an amplitude expected from the planet’s transit. However, given the offsets of
the entire data set the dip in the flux on this night could originate from
telescope systematics, a variable companion star (which, however, was not
detected), or from the host star itself. Therefore, we do not include the NGTS
data in our global analysis of the planet.

###  2.4 CORALIE spectroscopy and radial velocities

After detecting two single transit events in the TESS data of TOI-5542, we
initiated spectroscopic follow-up observations and radial velocities (RVs) of
the star with the CORALIE spectrograph on the Swiss 1.2 m Euler telescope at
La Silla Observatory, Chile (Queloz et al., 2001). CORALIE has a resolution of
$R$ $\sim$ 60,000 and is fed by two fibers: a 2 arcsec on-sky science fiber
encompassing the star and another fiber that can either connect to a Fabry-
Pérot etalon for simultaneous drift correction or on-sky for background
subtraction of sky flux. We observed TOI-5542 in the simultaneous Fabry-Pérot
drift correction mode. We obtained 31 CORALIE observations between 2021 April
2 to 2021 November 23 with 2400 second exposures. We reduced the spectra with
the standard calibration reduction pipeline and computed RVs by cross-
correlating with a binary G2 mask (Pepe et al., 2002). We obtained typical RV
uncertainties of $\sim$58 m s-1 for our CORAIE RVs. The CORALIE RVs are
displayed in Figure 3 and presented in Table 3

###  2.5 HARPS spectroscopy and radial velocities

Following the initial RV observations with CORALIE, we began observing
TOI-5542 with the HARPS spectrograph (Pepe et al., 2002; Mayor et al., 2003)
to obtain a more precise mass measurement and more precise orbital properties.
HARPS is hosted by the ESO 3.6-m telescope at La Silla Observatory, Chile and
has a resolving power of $R$ $\sim$ 115,000. TOI-5542 was observed with two
HARPS programs333TOI-5542 was observed with HARPS programs Bouchy: 105.20L0
and Ulmer-Moll: 108.22L8 that both have the goal of characterizing long-period
transiting giant planets. We obtained 18 HARPS observations of TOI-5542 from
2021 July 27 to 2021 November 21 with exposure times of 1800 seconds. The RVs
were computed using the standard data reduction pipeline with a binary G2
mask. We obtained typical RV uncertainties of $\sim$7.5 m s-1 for our HARPS
RVs. We did not include the HARPS RV observation on the night of August 3,
2021 in our planetary analysis (Section 3.2) as TOI-5542b was transiting on
that night and the RV would likely be affected by the Rossiter-McLaughlin
effect as a result (Rossiter, 1924; McLaughlin, 1924). We predicted the
Rossiter-McLaughlin effect measured with the classical method is $\sim$26 m
s-1 for TOI-5542 (Eq. 40 from Winn 2010).

The HARPS spectra were also used to derive spectral parameters for TOI-5542,
as detailed in Section 3.1. The HARPS RVs are displayed in Figure 3 and
presented in Table 3. Figure 3 also displays the best-fit Keplerian model (see
Section 3.2) for both the CORALIE and HARPS RVs, the RVs phased at the best-
fit period of the planet, and the Lomb-Scargle periodogram (Lomb, 1976;
Scargle, 1982) of the combined CORALIE and HARPS RVs as well as the Lomb-
Scargle periodogram of the RV residuals after subtracting the best-fit
Keplerian model from the RVs. The original periodogram clearly shows the
strong $\sim$75 day signal of the planet, while the residuals do not have any
significant signals.

###  2.6 EulerCam photometry

We also observed TOI-5542 on the night of August 3, 2021 with EulerCam on the
1.2 m Euler telescope at La Silla Observatory, Chile. The observations were
carried out for 5.14 hours allowing for the observation of an egress of the
transit. We used a V filter and 150 second exposures for the observations. For
details on the instrument and the data analysis routines used to extract
relative aperture photometry with EulerCam, we refer to Lendl et al. (2012).
The EulerCam (ECAM) light curve is displayed in Figure 2. A full table of
reduced EulerCam photometric observations is available in a machine-readable
format at the CDS.

###  2.7 SAAO photometry

TOI-5542 was also observed the night of August 3, 2021 on the 1-m telescope at
the South African Astronomical Observatory (SAAO) in Sutherland, South Africa.
The observations were taken with one of the Sutherland High-speed Optical CCD
Cameras (specifically ”SHOCnAwe”, Plate scale = 0.167 arcsec/pixel, binned to
$4\times 4$ pixels) in the V filter with 20-second exposures for 5.39 hours
allowing us to catch a full ingress of the transit. Conditions were clear with
somewhat variable seeing from $<1.5$ to $2.5$ arcseconds. The data were
reduced and calibrated with the local SAAO SHOC pipeline (Coppejans et al.,
2013), which is driven by python scripts running iraf tasks (pyfits and
pyraf). Aperture and differential photometry was performed using the Starlink
package autophotom, utilizing a single comparison star and an aperture radius
of four pixels was selected to maximize the signal-to-noise. This telescope
and instrument setup has been used in previous studies to detect transits of
planets, brown dwarfs, and low-mass stars (e.g., Smith et al., 2021; Acton et
al., 2021; Gill et al., 2022). The SAAO photometry data binned to 2 minutes
for display purposes is shown in Figure 2. A full table of reduced SAAO
photometric observations is available in a machine-readable format at the CDS.

##  3 Analysis and results

###  3.1 Stellar parameters

Table 1:  Stellar parameters of TOI-5542.

Parameter | Value | Source
---|---|---
Identifying Information
TYC ID | TYC 9086-01210-1 | Tycho
TESS ID | TIC 466206508 | TESS
2MASS ID | 2MASS J20111163-6108076 | 2MASS
Gaia ID | 6443054270942726144 |  Gaia EDR3
Astrometric parameters
R.A. (J2000, h:m:s) | 20:11:11.62 |  Gaia EDR3
Dec (J2000, h:m:s) | -61:08:07.68 |  Gaia EDR3
Parallax (mas) | 2.827 $\pm$ 0.030 |  Gaia EDR3
Distance (pc) | 353.7 $\pm$ 3.7 |  Gaia EDR3
Photometric parameters
B | 13.063 $\pm$ 0.020 | APASS
V | 12.402 $\pm$ 0.032 | APASS
g | 12.863 $\pm$ 0.030 | APASS
r | 12.244 $\pm$ 0.030 | APASS
i | 12.087 $\pm$ 0.030 | APASS
G | 12.272 $\pm$ 0.020 |  Gaia EDR3
BP | 12.601 $\pm$ 0.020 |  Gaia EDR3
RP | 11.779 $\pm$ 0.020 |  Gaia EDR3
J | 11.266 $\pm$ 0.022 | 2MASS
H | 10.945 $\pm$ 0.023 | 2MASS
KS | 10.897 $\pm$ 0.021 | 2MASS
W1 | 10.819 $\pm$ 0.030 | WISE
W2 | 10.870 $\pm$ 0.030 | WISE
W3 | 10.738 $\pm$ 0.088 | WISE
AV | 0.046 $\pm$ 0.036 | Sec. 3.1
Bulk parameters
$T_{\rm eff}$ (K) | $5700\pm 80$ | Sect. 3.1
[Fe/H] (dex) | $-0.21\pm 0.08$ | Sect. 3.1
$\log g_{*}$ (cm s-2) | $4.2\pm 0.2$ | Sec. 3.1
Spectral type | G3V | Sect. 3.1
$v\sin i_{*}$ (km s-1) | $3.03\pm 0.50$ | Sect. 3.1
$P_{\rm rot}$ / $\sin i_{*}$ (days) | $17.7\pm 3.0$ | Sect. 3.1
Mass ($M_{\odot}$) | $0.890^{+0.056}_{-0.031}$ | Sect. 3.1
Radius ($R_{\odot}$) | $1.058\pm 0.036$ | Sect. 3.1
$\rho_{*}$ (g cm-3) | $1.07\pm 0.13$ | Sect. 3.1
Luminosity ($L_{\odot}$) | $1.057\pm 0.093$ | Sect. 3.1
Age (Gyrs) | $10.8^{+2.1}_{-3.6}$ | Sec. 3.1
log(R’HK) |  $-$5.28 $\pm$ 0.26 | Sec. 3.3

Obtaining proper and precise constraints on host star parameters is an
essential component of exoplanet studies, as many critical properties of the
planet directly depend on the estimated stellar properties, such as planet
mass, radius, and insolation. There are several methods used to constrain
various stellar properties, including spectral analysis, approximating the
spectral energy distribution (SED) by integrating fluxes from broadband
photometry in combination with model atmospheres (e.g., van Belle & von Braun,
2009; Stassun & Torres, 2016), as well as stellar isochrones and evolutionary
models (Yi et al., 2001; Dotter, 2016), which essentially constrain the
stellar mass and radius based on the stellar effective temperature, $T_{\rm
eff}$, metallicity, [Fe/H], and surface gravity, $\log g_{*}$ (see Section 2
of Eastman et al. (2019) for a detailed discussion). The $T_{\rm eff}$ and
[Fe/H] are typically best constrained by spectral analysis (e.g., Stassun et
al., 2017; Jofré et al., 2019). The $\log g_{*}$ can also be estimated by
spectral analysis, but often not as accurately (e.g., Torres et al., 2012).
The SED fit can typically best constrain the stellar radius, R∗, and stellar
luminosity, $L_{*}$, by combining the broadband photometry and parallax
information (e.g., Stassun & Torres, 2016), whereas evolutionary models are
likely best suited to constrain the stellar mass, M∗, and age (Tayar et al.,
2022).

####  3.1.1 HARPS spectra analysis

We first used the HARPS spectra of TOI-5542 to determine $T_{\rm eff}$, $\log
g_{*}$ , [Fe/H], and the rotational broadening projected into the line of
sight, $v\sin i_{*}$ . Spectra were co-added onto a common wavelength axis to
increase the signal-to-noise ratio (S/N) prior to spectral analysis. We found
the HARPS co-added spectrum to have a S/N of $\sim$54\. We used ISPEC (Blanco-
Cuaresma et al., 2014) to synthesize models using the radiative transfer code
SPECTRUM (Gray, 1999), MARCS model atmospheres (Gustafsson et al., 2008), and
version 5 of the $GAIA$ ESO survey (GES) atomic line list within ISPEC with
solar abundances from Asplund et al. (2009). The temperature was determined by
fitting the iron lines and H-$\alpha$ lines, which were well matched to find
$T_{\rm eff}$ = 5700 $\pm$ 80 K. We used the Mg triplets and Na doublet lines
to determine $\log g_{*}$ = 4.2 $\pm$ 0.2 and we found a metallicity of [Fe/H]
= $-$0.21 $\pm$ 0.08 using the individual FeI and FeII lines. There is no
evidence of lithium, which suggests that the star is on the main sequence
branch. Finally, from the HARPS spectra, we calculated a stellar rotational
velocity of $v\sin i_{*}$ = 3.03 $\pm$ 0.50 km s-1, which indicates a
moderately slow rotator. With this value, we can put an upper limit on the
stellar rotation period of $P_{\rm rot}$ / $\sin i_{*}$ = 2$\pi$R∗/$v\sin
i_{*}$ = 17.7 $\pm$ 3.0 days using the R∗ value derived in Section 3.1.2. We
use these as our final $T_{\rm eff}$, $\log g_{*}$ , and [Fe/H] values
presented in Table 1. We find the star to be a G3V spectral type from its
$T_{\rm eff}$ value using the updated table from Pecaut & Mamajek (2013)
444https://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt.

As an independent check, we also derived the stellar parameters with the co-
added HARPS spectra using SpecMatch-Emp (Yee et al., 2017), which uses a large
library of stars with well-determined parameters to match the input spectra
and derive spectral parameters. We use a spectral region that includes the Mg
I b triplet (5100 - 5400 $\AA$) to match our spectra. SpecMatch-Emp uses
$\chi^{2}$ minimization and a weighted linear combination of the five best
matching spectra in the SpecMatch-Emp library to determine stellar parameters.
With SpecMatch-Emp, we found similar stellar parameters, as compared to our
other method with $T_{\rm eff}$ = 5701 $\pm$ 110 K, $\log g_{*}$ = 4.43 $\pm$
0.12, [Fe/H] = $-$0.18 $\pm$ 0.09, M∗ $\sim$ 0.95 $\mathrm{M_{\odot}}$, R∗
$\sim$ 1.01 $\mathrm{R_{\odot}}$, and an age of $\sim$ 9.59 Gyr. However, we
used the parameters derived from the first spectral analysis method above as
our final spectral atmospheric parameters since we consider these values to be
more precise based on the fact that the estimates of the atmospheric
parameters are obtained by modeling individual spectral lines, rather than
integrated quantities of entire spectra. However, we note that both methods
are in good agreement.

####  3.1.2 Spectral energy distribution analysis

Figure 4: Spectral energy distribution (SED) for TOI-5542. Red symbols
represent the observed photometric measurements, where the horizontal bars
represent the effective width of the passband. Blue symbols are the model
fluxes from the best-fit Kurucz atmosphere model (black).

We performed a SED fit using Kurucz stellar atmosphere models (Kurucz, 2013)
with the $Gaia$ parallax following the procedures described in Stassun &
Torres (2016); Stassun et al. (2017, 2018), with the priors on $T_{\rm eff}$,
[Fe/H], and $\log g_{*}$ from the spectroscopic analysis, and the extinction
($A_{V}$) limited to the maximum line-of-sight extinction from the Galactic
dust maps of Schlegel et al. (1998). We put a Gaussian prior for parallax from
the value and uncertainty in $Gaia$ EDR3 (Gaia Collaboration et al., 2021). We
note the $Gaia$ EDR3 parallax (2.8042) was corrected by subtracting $-$0.0232
mas according to the Lindegren et al. (2021) prescription. For the SED fit we
use photometry from APASS DR9 $BVgri$ (Henden et al., 2016); $Gaia$ EDR3 G,
BP, and RP (Gaia Collaboration et al., 2021); 2MASS J, H, and KS (Skrutskie et
al., 2006); and ALL-WISE W1, W2, and W3 (Wright et al., 2010), which are
presented in Table 1. The SED fit gives our final stellar radius value of R∗ =
1.058 $\pm$ 0.036 $\mathrm{R_{\odot}}$ and is displayed in Figure 4. The SED
also gives the V-band extinction, $A_{V}$, and the stellar luminosity
presented in Table 1.

####  3.1.3 Stellar evolutionary model

We used the Modules for Experiments in Stellar Astrophysics (MESA) Isochrones
& Stellar Tracks (MIST; Choi et al., 2016; Dotter, 2016) isochrones within the
EXOFASTv2 (Eastman et al., 2013; Eastman, 2017; Eastman et al., 2019)
exoplanet and star modeling suite, which has the option of solely fitting the
star. This suite explores the parameter space through a differential evolution
Markov Chain coupled with a Metropolis-Hastings Monte Carlo sampler, and a
built-in Gelman-Rubin statistic (Gelman & Rubin, 1992; Gelman et al., 2003;
Ford, 2006) is used to check the convergence of the chains. We use the $T_{\rm
eff}$, $\log g_{*}$ , and [Fe/H] values along with their uncertainties from
the HARPS spectral analysis as priors. We did not simultaneously fit the SED
so as not to bias the stellar radius from models and we relied on the more
empirical SED-only fit above. We therefore used our SED fitted R∗ value as a
prior in the MIST model. This MIST fit gives our final stellar mass and age,
which are given in Table 1.

Table 2: TOI-5542 parameters from juliet: median and 68% confidence interval.

Parameter |  | Prior distribution* | Value
---|---|---|---
Modeled instrumental parameters: |  |
$q_{\text{1,TESS}}$ | Quadratic limb-darkening parametrization | $\mathcal{N}(0.335,0.011)$ | $0.339^{+0.010}_{-0.010}$
$q_{\text{2,TESS}}$ | Quadratic limb-darkening parametrization | $\mathcal{N}(0.261,0.030)$ | $0.277^{+0.027}_{-0.028}$
$m_{\text{flux,TESS13}}$ | Offset (relative flux) | $\mathcal{N}(0,0.01)$ | $-0.00011^{+0.00018}_{-0.00025}$
$\sigma_{\text{GP,TESS13}}$ | GP amplitude (relative flux) | $\mathcal{J}(10^{-6},1)$ | $0.00044^{+0.00033}_{-0.00012}$
$\rho_{\text{GP,TESS13}}$ | GP time-scale (days) | $\mathcal{J}(10^{-6},10^{3})$ | $2.30^{+2.51}_{-1.00}$
$m_{\text{flux,TESS27}}$ | Offset (relative flux) | $\mathcal{N}(0,0.01)$ | $-0.00009^{+0.00010}_{-0.00010}$
$\sigma_{\text{GP,TESS27}}$ | GP amplitude (relative flux) | $\mathcal{J}(10^{-6},1)$ | $0.000432^{+0.000074}_{-0.000056}$
$\rho_{\text{GP,TESS27}}$ | GP time-scale (days) | $\mathcal{J}(10^{-6},10^{3})$ | $0.54^{+0.20}_{-0.12}$
$m_{\text{flux,SAAO}}$ | Offset (relative flux) | $\mathcal{N}(0,0.01)$ | $-0.00117^{+0.00016}_{-0.00017}$
$\sigma_{\text{SAAO}}$ | Jitter (ppm) | $\mathcal{J}(0.1,10000)$ | $1585.4^{+144.7}_{-146.0}$
$m_{\text{flux,ECAM}}$ | Offset (relative flux) | $\mathcal{N}(0,0.01)$ | $-0.00819^{+0.00021}_{-0.00021}$
$\sigma_{\text{ECAM}}$ | Jitter (ppm) | $\mathcal{J}(0.1,10000)$ | $1096.7^{+162.6}_{-161.0}$
$\mu_{\text{CORALIE}}$ | Systemic RV offset (km s-1) | $\mathcal{U}(-100,100)$ | $-54.4042^{+0.0101}_{-0.0105}$
$\sigma_{\text{CORALIE}}$ | Jitter (m s-1) | $\mathcal{J}(0.01,200)$ | $0.50^{+4.66}_{-0.46}$
$\mu_{\text{HARPS}}$ | Systemic RV offset (km s-1) | $\mathcal{U}(-100,100)$ | $-54.3751^{+0.0025}_{-0.0026}$
$\sigma_{\text{HARPS}}$ | Jitter (m s-1) | $\mathcal{J}(0.01,200)$ | $5.31^{+3.10}_{-3.08}$
Modeled physical parameters: |  |
$P$ | Period (days) |  $\mathcal{U}$(75.12$\pm$0.2) | $75.12375^{+0.00019}_{-0.00018}$
$T_{0}$ | Time of transit center (BJD${}_{\text{TDB}}$) |  $\mathcal{U}$(2458679.3$\pm$0.2) | $2458679.3476^{+0.0015}_{-0.0015}$
$K$ | Radial velocity semi-amplitude (m s-1) |  $\mathcal{U}$(0,1000) | $69.17^{+4.34}_{-4.55}$
$e$ | Eccentricity of the orbit |  $\mathcal{B}$(0.867,3.03) | $0.018^{+0.026}_{-0.013}$
$\omega$ | Argument of periastron (deg) |  $\mathcal{U}$(0,360) | $125.6^{+171.4}_{-82.7}$
$r_{1}$ | Parametrization for p and b |  $\mathcal{U}$(0,1) | $0.6126^{+0.0388}_{-0.0503}$
$r_{2}$ | Parametrization for p and b |  $\mathcal{U}$(0,1) | $0.0980^{+0.0010}_{-0.0010}$
$\rho_{*}$ | Stellar density (g cm-3) |  $\mathcal{N}$(1.07,0.13) | $1.03^{+0.11}_{-0.10}$
Derived planetary parameters∗∗: |  |
$i$ | Inclination (deg) |  | $89.643^{+0.069}_{-0.061}$
$p=R_{p}/R_{\star}$ | Planet-to-star radius ratio |  | $0.0980^{+0.0010}_{-0.0010}$
$b$ | Impact parameter of the orbit |  | $0.419^{+0.058}_{-0.075}$
$a$ | Semi-major axis (AU) |  | $0.332^{+0.016}_{-0.016}$
$M_{p}$ | Planetary mass ($\mathrm{M_{\rm Jup}}$) |  | $1.32^{+0.10}_{-0.10}$
$R_{p}$ | Planetary radius ($\mathrm{R_{\rm Jup}}$) |  | $1.009^{+0.036}_{-0.035}$
$\rho_{p}$ | Planetary density (g cm-3) |  | $1.60^{+0.22}_{-0.19}$
$S$ | Insolation ($S_{\oplus}$) |  | $9.6^{+1.0}_{-0.9}$
$T_{eq}$ | Equilibrium Temperature ($K$) |  | $441^{+48}_{-74}$

*$\mathcal{U}(a,b)$ indicates a uniform distribution between $a$ and $b$; $\mathcal{J}(a,b)$ a Jeffrey or log-uniform distribution between $a$ and $b$; $\mathcal{N}(a,b)$ a normal distribution with mean $a$ and standard deviation $b$; and $\mathcal{B}(a,b)$ a Beta prior as detailed in Kipping (2014).

**We sampled from a normal distribution for the stellar mass, stellar radius,
and stellar temperature, based on the results from Section 3.1 to derive the
parameters.

###  3.2 Joint RV and transit fit

We obtained the planetary parameters by jointly modeling the photometric and
RV data with juliet (Espinoza et al., 2019), which uses Bayesian inference to
model a set number of planetary signals using batman (Kreidberg, 2015) to
model the planetary transit and radvel (Fulton et al., 2018) to model the RVs.
For the light curves stellar activity as well as instrumental systematics can
be taken into account with Gaussian processes (e.g., Gibson, 2014) or simpler
parametric functions. Several RV instruments can be taken into account with RV
offsets fit between them. For the transit model, juliet performs an efficient
parameterization by fitting for the parameters $r_{1}$ and $r_{2}$ to ensure
uniform exploration of the $p$ (planet-to-star ratio; $R_{p}/R_{\star}$) and
$b$ (impact parameter) parameter space. For our joint RV and transit global
model, we used the nested sampling method dynesty (Speagle, 2019) implemented
in juliet with 1000 live points and we ran the fit until the estimated
uncertainty on the log-evidence was smaller than 0.1.

Table 2 displays all of the modeled parameters as well as their input priors
for our joint RV and transit global model. We used a uniform prior of
75.12$\pm$0.2 days for the period of the planet from the RV-identified alias
of the two transits and a uniform prior of 0.2 days from the TESS Sector 13
transit for the time of transit center. We put broad uniform priors on the RV
semi-amplitude up to 1000 m s-1 and broad uniform priors of $\pm$100 km s-1
for the systematic RV offsets of the CORALIE and HARPS instruments. From the
near sinusoidal curve of the RV measurements, the planet is likely in a
circular orbit; however, when allowing for the eccentricity as well as
$e\cos{\omega}$ and $e\sin{\omega}$ to be freely constrained, juliet was not
converging, as it was likely stuck in a nonphysical parameter space.
Therefore, we added a Beta prior for transiting planets, as described in
Kipping (2014). We used the $\rho_{*}$ (stellar density) as a parameter
instead of the scaled semi-major axis ($\it{a}$/R∗). The normal prior on
stellar density is informed by the stellar analysis in Section 3.1, which
allowed us to derive a precise mass and radius along with their associated
errors.

For each photometric filter, we derived the quadratic stellar limb-darkening
coefficients and their uncertainties using the
LDCU555https://github.com/delinea/LDCU code, a modified version of the python
routine implemented by Espinoza & Jordán (2015). The code uses two libraries
of stellar atmosphere models, ATLAS9 (Kurucz, 1979) and PHOENIX (Husser et
al., 2013), to compute stellar intensity profiles for any given instrumental
passband. The atmosphere models are selected based on a given set of stellar
atmospheric parameters. The uncertainties on the stellar parameters are
propagated by selecting several models within the uncertainty range and
weighting them accordingly. The obtained intensity profiles are then fit with
linear, square-root, quadratic, three-parameter, non-linear, logarithmic,
exponential, and power-2 laws. The code performs three different fits for each
intensity profile and each law and provides a series of additional coefficient
values for each law by merging the outcomes from the previous fits. The
merging is done based on the assumption of normal distributions from the
estimated uncertainties, with the merging process taking place before we then
recompute the global uncertainties from quantiles. This approach allows us to
compute a precise median value while also allowing the uncertainties to
encompass the whole merged distribution and remain more conservative. For the
TESS data, we used the calculated limb-darkening coefficients of $q_{1}$ =
0.335$\pm$0.011 and $q_{2}$ = 0.261$\pm$0.030 as Gaussian priors in our global
analysis. We fixed the calculated limb darkening parameters for the SAAO and
EulerCam ground-based photometry due to the lower precision of the data. We
determined values of $q_{1}$ = 0.521$\pm$0.010 and $q_{2}$ = 0.325$\pm$0.024
for the V bandpass used for the SAAO and EulerCam photometry.

We added a white-noise jitter term in quadrature to the error bars of both the
photometry and RV data to account for underestimated uncertainties and
additional noise that was not captured by the model. The jitter terms were fit
using large log-uniform priors. For both TESS sectors 13 and 27 photometry, we
found the jitter terms to be $<$0.1 parts-per-million (ppm) and not varying
significantly from 0, so we fixed the jitter parameter to 0 for both TESS
light curves. As displayed in Figure 1, the TESS light curves have a few faint
stars (G $>$ 17) in the aperture. However, the PDCSAP light curves are
corrected for contamination from nearby stars by analyzing a synthetic scene
constructed from the pointing model, the pixel response functions (PRFs), and
the TIC catalog (Bryson et al., 2010, 2020). For sector 27 the crowding metric
(CROWDSAP) was 0.99635, indicating that the catalog predicts that 99.64% of
the flux in the photometric aperture is from TOI-5542 and for sector 13 the
CROWDSAP is 0.96673. As the PDCSAP light curves are corrected for the dilution
based on the positions of the stars over the observations, the behavior of the
focal plane electronics, and the PRFs, we thus fixed the dilution to 1 (no
dilution) for the modeling. The apertures of the ground-based photometery were
not contaminated by neighboring stars, so we fixed the dilution factor to 1.

To account for possible residual systematics and activity affecting the
transit fit of both TESS Sectors 13 and 27, we tested fitting a Gaussian
process (GP) using a Matérn-3/2 kernel via celerite (Foreman-Mackey et al.,
2017) within the juliet framework. A GP can account for correlated noise of
various origins and propagates the uncertainty. It is particularly useful when
we lack detailed knowledge on the origin of the noise and do not see any
correlations that can be modeled in an uncomplicated manner. Therefore, a GP
can correctly incorporate uncertainties introduced by red noise (e.g., Gibson
et al., 2012; Gibson, 2014). Additionally, properly fitting out of transit
data will more accurately set the baseline for in transit data. For both TESS
sectors the GP fit displayed clear modulations, as shown in Figures 9 and 10,
and thus we included it in our final analysis.

We also tested for correlated noise in the SAAO and EulerCam photometry by
fitting the data with various combinations of polynomials in airmass, detector
position, FWHM, and sky background by using a minimization of the Bayesian
Information Criterion. We determined that no combination of linear or
polynomial detrending for SAAO and EulerCam data significantly improved the
light curve fit to warrant adding additional variables to the model,
especially given the short out-of-transit baselines for both data sets. We
exemplify this approach by displaying the polynomial detrending with sky
background and airmass (the two parameters we found the most correlated with
the SAAO and EulerCam) in Figure 12. With this detrending, we found a similar
planetary radius value of $R_{p}$ = 1.00$\pm$0.04 $\mathrm{R_{\rm Jup}}$,
which is within the uncertainites of the planetary radius derived without
detrending. We also display the posterior distributions of these detrending
parameters along with $p=R_{p}/R_{\star}$, showing that the planet radius is
not correlated these parameters. We therefore did not perform any detrending
for SAAO and EulerCam in our final analysis. We additionally tested the effect
of the ground-based photometry on the planet radius by using only TESS
photometry in a global model. With TESS only photometry we obtained a radius
of $R_{p}$ = 1.02$\pm$0.04 $\mathrm{R_{\rm Jup}}$, again within the
uncertainties of the planet radius used in the final global model that
includes the ground-based photometry. We conclude that the ground-based
photometry does not bias the results.

Figures 2 and 3 display the final model fits to the photometry and RV data. In
addition to all of the modeled parameters, Table 2 also displays derived
planet parameters including the inclination, impact parameter, semi-major
axis, mass, and radius. We calculated the insolation using the equation:

$S[S_{\oplus}]=L_{*}[L_{\odot}]\left(a[\rm{AU}]\right)^{-2}.$ (1)

We calculated the equilibrium temperature assuming a Bond albedo of $A$ =
0.343 (the same as Jupiter’s) and the semi-major axis distance $a$ using the
equation:

$T_{eq}=T_{\rm eff}(1-A)^{1/4}\sqrt{\frac{\mbox{R${}_{*}$}}{2a}}.$ (2)

We set upper and lower uncertainties for the equilibrium temperature by
assuming Bond albedos of $A$ = 0 and $A$ = 0.686 (double that of Jupiter),
respectively.

###  3.3 Activity and residual analysis

We also use the HARPS spectra to estimate the activity level of TOI-5542. The
flux in the core of Ca II H & K lines is well-known to estimate magnetic
activity in solar-type stars, as demonstrated by the Mt Wilson program (e.g.,
Wilson, 1978; Duncan et al., 1991; Baliunas et al., 1995). The Mt Wilson ‘S
index’, which normalizes the measured Ca II core flux by the flux in two
continuum bandpasses on the blue and red sides of the Ca II lines, has become
a standard way of measuring chromospheric activity in stars. Here, we derive
Mt. Wilson S indexes for TOI-5442 using HARPS spectra with the method detailed
by Lovis et al. (2011). However, to be able to compare the chromospheric flux
alone (related to the energy that heats the chromosphere through the magnetic
field) to other stars, the photospheric component has to be subtracted and the
chromospheric flux normalized to the total (bolometric) luminosity of the
star. Noyes et al. (1984) introduced the well-known quantity R’HK, which can
be determined from the B and V magnitudes and the Mt. Wilson S index (e.g.,
Middelkoop, 1982; Noyes et al., 1984). With our HARPS spectra we calculate
log(R’HK) = $-$5.284 $\pm$ 0.263, which suggests that TOI-5542 is not a
chromospherically active star, since stars with log(R’HK) $<$ $-$5.1 are
generally considered very inactive (e.g., Henry et al., 1996).

To analyze the residuals, we ran a Bayesian analysis on the CORALIE and HARPS
RV residuals with the software package kima (Faria et al., 2018). The RV time
series is modeled with a sum of Keplerian signals. Different instruments are
taken into account with individual offsets and jitters. We allowed our model
to search for up to one Keplerian signal. To do so, we set the number of
planets, which is a free parameter for kima, with a uniform prior between zero
and one. The results of the search for one signal do not show any clear
detection. As presented in Standing et al. (2022), the samples from the
posterior can be used to derive detection limits. The authors also show that
this method is equivalent to the traditional test of injection and recovery of
planetary signals. Figure 13 presents the posterior samples in the RV semi-
amplitude versus orbital period space. The solid and dashed blue lines
correspond to the RV signals of Jupiter, Saturn, and Neptune mass planets. We
show that we are sensitive to sub-Saturn mass planets up to $\sim$100 days and
for longer orbital periods (up to 300 days) we can exclude the presence of
additional Jupiter mass planets.

##  4 Discussion

Figure 5: Mass as a function of orbital period for known giant planets (0.5
$\mathrm{M_{\rm Jup}}$ $<$ $M_{p}$ $<$ 13 $\mathrm{M_{\rm Jup}}$) with well
characterized masses ($\sigma_{M_{p}}$/$M_{p}$ $<$ 25%) and radii
($\sigma_{R_{p}}$/$R_{p}$ $<$ 8%) that have finite period and $T_{\rm eff}$
values and stellar metallicity errors $<$0.25, consisting of 216 giant
planets. The symbols of each planet are colored based on their eccentricity.
TOI-5542b is marked with a black circle.

We detected and characterized the warm Jupiter TOI-5542b that has a mass of
$M_{p}$ = 1.32${}^{+0.10}_{-0.10}$ $\mathrm{M_{\rm Jup}}$, radius of $R_{p}$ =
1.009${}^{+0.036}_{-0.035}$ $\mathrm{R_{\rm Jup}}$, a period of 75.12 days,
and a likely circular orbit with an eccentricity of
0.018${}^{+0.026}_{-0.013}$. TOI-5542b is warm with an insolation of $S$ =
9.6${}^{+1.0}_{-0.9}$ $S_{\oplus}$ and equilibrium temperature of $T_{eq}$ =
441${}^{+48}_{-74}$ K. To put TOI-5542b into context we obtained planet
parameters for known giant planets (0.5 $\mathrm{M_{\rm Jup}}$ $<$ $M_{p}$ $<$
13 $\mathrm{M_{\rm Jup}}$) from the NASA exoplanet
archive666https://exoplanets.nasa.gov/ on 1 September 2022 and use 25% mass
and 8% radius precision cutoffs in order to only consider well characterized
planets with robust density measurements, as has been done in previous
population studies (e.g., Otegi et al., 2020). We also required stellar
metallicity values to have errors less than 0.25 and the planet to have a
finite period and stellar $T_{\rm eff}$ values in the archive. Our final
sample of well-characterized giant planets consists of 216 planets, including
TOI-5542b. We found 28 of these planets do not have defined eccentricities,
but 25 of them have orbital periods less than 5 days, so we set the
eccentricity to 0 and for the remaining three planets, we obtained estimates
of their eccentricities from previous studies.

###  4.1 Giant planet eccentricities

We first compare TOI-5542b to our sample of well-defined giant planets by
plotting mass as a function of the orbital period in Figure 5, which shows
that TOI-5542b is one of the few well-characterized giant planets in the
sparsely populated long-period regime. From Figure 5, we can see that giant
planets exhibit a range of eccentricities and it appears that more massive
($M_{p}$ $\gtrsim$ 3-4 $\mathrm{M_{\rm Jup}}$) planets appear to have a wider
range of eccentricities than less massive giant planets, which was previously
noted by Ribas & Miralda-Escudé (2007). Both hot and warm Jupiters are thought
to have formed beyond the ice-line and then migrated inwards (e.g.,
Bodenheimer et al., 2000; Rafikov, 2006). Differences in the eccentricities of
giant planets offer insights into different formation and migration pathways.

Giant planets with lower eccentricities may have formed from disk-driven
migration (e.g., Goldreich & Tremaine, 1980; Ward, 1997; Baruteau et al.,
2014) that tend to damp eccentricities (Bitsch et al., 2013; Dunhill et al.,
2013). While giant planets with higher eccentricities may be the result of
high-eccentricity migration from dynamical instabilities due to planet–planet
gravitational interactions (e.g., Rasio & Ford, 1996; Weidenschilling &
Marzari, 1996; Lin & Ida, 1997) as well as secular perturbations due to
distant stellar (e.g., Wu & Murray, 2003; Fabrycky & Tremaine, 2007) or
planetary companions (e.g., Naoz et al., 2011; Wu & Lithwick, 2011). However,
none of these mechanisms can easily account for the observed warm Jupiter
population and it is very likely a combination of these mechanisms. Petrovich
& Tremaine (2016) found $\sim$20% of all warm Jupiters and most warm Jupiters
with eccentricity $\gtrsim$0.4 are produced by high-eccentricity migration.
The remaining population of low-eccentricity warm Jupiters ($e$ $\lesssim$
0.2) likely obtained their current orbital configurations while the gaseous
disk was still present (Petrovich & Tremaine, 2016), either by disk migration
(e.g., Goldreich & Tremaine, 1980) or in situ formation (e.g., Batygin et al.,
2016; Boley et al., 2016; Huang et al., 2016).

We found a low eccentricity of 0.018${}^{+0.026}_{-0.013}$ for TOI-5542b. We
performed the test of Lucy & Sweeney (1971), where the statistical
significance of the eccentric fit is given by:

$\rm{P}(e>0)=1-\rm{exp}\left[-\frac{\hat{e}}{2\sigma^{2}_{e}}\right],$ (3)

where $\hat{e}$ is the modal value of the eccentricity, which is well
approximated by the median for a unimode distribution. We find the statistical
significance of the eccentric fit to be P$(e>0)$ = 0.68, which is well below
the 5% significance level suggested by Lucy & Sweeney (1971), and thus
TOI-5542b likely has a circular orbit. With a circular orbit it is difficult
to predict a formation or migration pathway for TOI-5542b, but given the
absence of close planet companions based on the residuals of the RV and
photometry data, it more likely formed via disk migration or in situ
formation, compared to other mechanisms that are more likely to leave a planet
with an eccentric orbit.

Figure 6: Mass as a function of host star metallicity for known giant planets
(0.5 $\mathrm{M_{\rm Jup}}$ $<$ $M_{p}$ $<$ 13 $\mathrm{M_{\rm Jup}}$) with
well characterized masses ($\sigma_{M_{p}}$/$M_{p}$ $<$ 25%) and radii
($\sigma_{R_{p}}$/$R_{p}$ $<$ 8%) that have finite period and $T_{\rm eff}$
values and stellar metallicity errors $<$0.25, consisting of 216 giant
planets. The red symbols are planets with orbital periods $<$10 days (188
planets) and blue symbols have periods $>$10 days (28 planets). The histograms
at the top show the metallicity distribution for the two populations.
TOI-5542b is marked with a black circle.

###  4.2 Host star metallicities of giant planet

Since the early stages of exoplanet discoveries, studies have found that the
occurrence rate of close-in giant planets is enhanced around stars with higher
metallicity (e.g., Gonzalez, 1997; Santos et al., 2004; Fischer & Valenti,
2005; Johnson et al., 2010). However, several recent studies have suggested
that host star metallicity may also indicate the separation of two distinct
giant planet populations at $\sim$3-4 $\mathrm{M_{\rm Jup}}$, where more
massive giant planets appear to have host stars with lower metallicities
(e.g., Santos et al., 2017; Schlaufman, 2018; Maldonado et al., 2019; Goda &
Matsuo, 2019). These differences could serve as evidence of two different
formation mechanisms, whereby lower mass giant planets more often form from
core accretion (Pollack et al., 1996) and higher mass giant planets may more
often form via disk instability (Boss, 1997) because disk instability is
likely not to be as metallicity-dependent as core accretion (Boss, 2002; Cai
et al., 2006). However, Adibekyan (2019) did not find a transition point
between two separate formation channels and thus suggested that high mass
planets can form through different mechanisms depending on their initial
environment.

Notably, with a low metallicity of [Fe/H] = $-$0.21 $\pm$ 0.08, TOI-5542 does
not follow the traditional trend of high host-star metallicity for giant
planets and does not bolster studies suggesting a difference among low- and
high-mass giant planets. We place TOI-5542b into context in Figure 6 and plot
planet mass as a function of host star metallicity for our sample of 216 well-
defined giant planets. Although some recent studies have suggested that more
massive giant planets appear not to have an inclination toward metal-rich
stars, as compared to less massive giants, we note that in Figure 6 that there
are no massive ($M_{p}$ $>$ 4 $\mathrm{M_{\rm Jup}}$) planets with
metallicities lower than $-$0.2, in addition to there being almost no planets
more massive than $\sim$ 1 $\mathrm{M_{\rm Jup}}$. Thorngren et al. (2016)
also noted that more massive planets ($M_{p}$ $\gtrsim$ 2-3 $\mathrm{M_{\rm
Jup}}$) are found far less often around low-metallicity stars when looking at
a sample of 47 transiting warm giant planets with mass, radius, and age
measurements. Additionally, when we split our sample of 216 well-defined giant
planets at 4 $\mathrm{M_{\rm Jup}}$ we find that both samples are metal-rich
with 27 massive giant planets having a mean host star [Fe/H] = 0.11 $\pm$ 0.03
and 189 less massive giants having a mean of host star [Fe/H] = 0.11 $\pm$
0.01. We also split hot and warm giant planets at orbital periods of 10 days
to see any differences in metallicites – but, again, we found them both
preferentially around metal-rich stars with a mean metallicity of [Fe/H] =
0.11 $\pm$ 0.01 for the 188 hot Jupiters and [Fe/H] = 0.12 $\pm$ 0.03 for the
28 warm (P $>$ 10 days) Jupiters in our sample.

###  4.3 An old, warm Jupiter

Figure 7: Stellar age as a function of orbital period for known giant planets
(0.5 $\mathrm{M_{\rm Jup}}$ $<$ $M_{p}$ $<$ 13 $\mathrm{M_{\rm Jup}}$) with
well characterized masses ($\sigma_{M_{p}}$/$M_{p}$ $<$ 25%) and radii
($\sigma_{R_{p}}$/$R_{p}$ $<$ 8%) that have finite period and $T_{\rm eff}$
values and stellar metallicity errors $<$0.25, as well as relatively well
defined ages ($\sigma_{age}$/age $<$ 40%) consisting of 87 giant planets. The
symbols of each planet are colored based on their host star’s metallicity.
TOI-5542b is marked with a black circle. Figure 8: Radius as a function of
orbital period for known giant planets (0.5 $\mathrm{M_{\rm Jup}}$ $<$ $M_{p}$
$<$ 13 $\mathrm{M_{\rm Jup}}$) with well characterized masses
($\sigma_{M_{p}}$/$M_{p}$ $<$ 25%) and radii ($\sigma_{R_{p}}$/$R_{p}$ $<$ 8%)
that have finite period and $T_{\rm eff}$ values, and stellar metallicity
errors $<$0.25, consisting of 216 giant planets. The symbols of each planet
are colored based on their host star’s $T_{\rm eff}$. TOI-5542b is marked with
a black circle.

From our MIST evolutionary models (see Section 3.1.3), we find an age of
$10.8^{+2.1}_{-3.6}$ Gyr for TOI-5542, which is constrained from its low
metallicity ([Fe/H] = $-$0.21 $\pm$ 0.08), making it an old G dwarf. However,
as discussed above, given its low eccentricity, TOI-5542b likely migrated
early in the star system’s history while the gaseous disk was still present.
In Figure 7, we plot the host star age as a function of orbital period for
giant planets in our sample that have relatively well defined ages
($\sigma_{age}$/age $<$ 40%) consisting of 87 planets. Figure 7 shows that
TOI-5542b is one of the oldest known long-period warm Jupiters and one of the
few with an age estimate.

In Figure 8, we plot planet radius as a function of orbital period for our
well-defined giant planet sample. Figure 8 displays how longer period warm
Jupiters are not inflated from host star incident flux, which is known for
planets receiving an incident flux below $\sim$2$\times$108 erg s${-1}$ cm-2
or $T_{eq}$ $\lesssim$ 1000 K (Demory & Seager, 2011; Miller & Fortney, 2011).
This offers the advantage of being able to ignore inflation effects when
constraining planet compositions. With an equilibrium temperature of $T_{eq}$
= 441${}^{+48}_{-74}$ K, TOI-5542b is well below this limit, making it a
valuable data point for planet composition models and studies.

As mentioned previously, we predicted the Rossiter-McLaughlin effect to be
$\sim$26 m s-1 for TOI-5542, which is large enough that the spin-orbit angle
of the system can be measured with current high-resolution spectrographs. This
obliquity measurement can help decipher the target’s dynamical past. For
instance, in the case where a misaligned orbit were detected, the high-
eccentricity migration scenario may appear to be a more likely scenario for
its formation pathway (e.g., Bourrier et al., 2018; Attia et al., 2021) but
this may be unlikely given its circular orbit and the current lack of evidence
for other planet companions.

##  5 Conclusions

We report the discovery and characterization of the warm Jupiter TOI-5542b.
The planet was first detected by TESS as two single transit events 375.6 days
apart. We obtained radial velocities from the CORALIE and HARPS spectrographs,
which constrained the orbital period of 75.12 days from the possible aliases
of the two transits. We obtained a third transit simultaneously with the
ground-based facilities SAAO, NGTS, and EulerCam, but we do not use NGTS in
our global analysis.

Using spectral analysis, SED fitting, and evolutionary models we measure the
stellar parameters of TOI-5542 with $T_{\rm eff}$ = $5700\pm 80$ K, $\log
g_{*}$ = $4.2\pm 0.2$, [Fe/H] = $-0.21\pm 0.08$, M∗= $0.890^{+0.056}_{-0.031}$
$\mathrm{M_{\odot}}$, R∗= $1.058\pm 0.036$ $\mathrm{R_{\odot}}$, and an age of
$10.8^{+2.1}_{-3.6}$ Gyr. We found TOI-5542b to have a mass of $M_{p}$ =
1.32${}^{+0.10}_{-0.10}$ $\mathrm{M_{\rm Jup}}$, radius of $R_{p}$ =
1.009${}^{+0.036}_{-0.035}$ $\mathrm{R_{\rm Jup}}$, and a likely circular
orbit with an eccentricity of 0.018${}^{+0.026}_{-0.013}$. TOI-5542b is warm
with an insolation of $S$ = 9.6${}^{+1.0}_{-0.9}$ $S_{\oplus}$ and equilibrium
temperature of $T_{eq}$ = 441${}^{+48}_{-74}$ K. TOI-5542b likely has a
circular orbit and more likely formed via disk migration or in situ formation,
rather than high-eccentricity migration mechanisms.

We set TOI-5542b into context with a sample of well-characterized giant
planets consisting of 216 planets including TOI-5542b. TOI-5542b is one of the
few well-characterized giant planets in the sparsely populated long-period
regime. With a low metallicity of [Fe/H] = $-$0.21 $\pm$ 0.08, TOI-5542b does
not follow the traditional trend of high host star metallicity for giant
planets and does not bolster studies suggesting a difference in host star
metallicities for low- and high-mass giant planets. When looking at our sample
of well-characterized giant planets, we find both high-mass (4 $\mathrm{M_{\rm
Jup}}$ $<$ $M_{p}$ $<$ 13 $\mathrm{M_{\rm Jup}}$) and low-mass (0.5
$\mathrm{M_{\rm Jup}}$ $<$ $M_{p}$ $<$ 4 $\mathrm{M_{\rm Jup}}$) giant planets
both are preferentially located around metal-rich stars (mean [Fe/H] $>$ 0.1).
We also found that both warm (P $>$ 10 days) and hot (P $<$ 10 days) Jupiters
have mean metallicities above 0.1 dex. We determined that the Rossiter-
McLaughlin effect for TOI-5542 would have an amplitude of $\sim$26 m s-1 ,
which is high enough that the spin-orbit angle of the system can be measured
with current high-resolution spectrographs. With an age of
$10.8^{+2.1}_{-3.6}$ Gyr, TOI-5542b is one of the oldest known warm Jupiters.
With its equilibrium temperature of $T_{eq}$= 441${}^{+48}_{-74}$ K, TOI-5542b
is not affected by inflation due to stellar incident flux, making it a
valuable contribution in planetary composition and formation studies.

###### Acknowledgements.

We thank the Swiss National Science Foundation (SNSF) and the Geneva
University for their continuous support to our planet low-mass companion
search programs. This work was carried out in the frame of the Swiss National
Centre for Competence in Research (NCCR) $PlanetS$ supported by the Swiss
National Science Foundation (SNSF). This publication makes use of The Data &
Analysis Center for Exoplanets (DACE), which is a facility based at the
University of Geneva (CH) dedicated to extrasolar planet data visualization,
exchange, and analysis. DACE is a platform of NCCR $PlanetS$ and is available
at https://dace.unige.ch. This paper includes data collected by the TESS
mission. Funding for the TESS mission is provided by the NASA Explorer
Program. We acknowledge the use of public TESS data from pipelines at the TESS
Science Office and at the TESS Science Processing Operations Center. Resources
supporting this work were provided by the NASA High-End Computing (HEC)
Program through the NASA Advanced Supercomputing (NAS) Division at Ames
Research Center for the production of the SPOC data products. This paper uses
observations made at the South African Astronomical Observatory (SAAO). The
Starlink software (Currie et al., 2014) is currently supported by the East
Asian Observatory. MNG acknowledges support from the European Space Agency
(ESA) as an ESA Research Fellow. AJ acknowledges support from ANID –
Millennium Science Initiative – ICN12_009 and from FONDECYT project 1210718.
M.L. acknowledges support of the Swiss National Science Foundation under grant
number PCEFP2_194576. NG thanks Tara Grieves for her support, passion, and
kindness over the years.

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##  Appendix A Supplementary material

Figure 9: Full TESS Sector 13 data of TOI-5542 . Zoom-in on transit shown on
the right. The black circles display the 30-minute SPOC data used in the
analysis and the red line displays the full GP and transit model. Figure 10:
Left: Full TESS Sector 27 data of TOI-5542 . Zoom-in on transit shown on the
right. The black circles display the 2-minute SPOC data used in the analysis
and the red line displays the full GP and transit model. Figure 11:  NGTS data
binned to 30 minutes (top). The dashed red line displays the night TOI-5542b
transited and shows the relative offset compared to nearby nights. Due to
overall variation of the light curve and no ingress or egress of the transit,
we do not include NGTS data in our global model. Lomb-Scargle periodogram of
NGTS data (bottom). We do not see any significant peaks corresponding to a
likely stellar roation period.

Figure 12: Detrending fits for the ground-based photometry. The top plots display the fits obtained for EulerCam and SAAO when detrending with polynomials in sky and airmass. The bottom plot displays the posterior distributions of these detrending parameters along with $p=R_{p}/R_{\star}$, which shows the planet radius is not correlated these parameters. We obtained a similar planet radius of $R_{p}$ = 1.00$\pm$0.04 $\mathrm{R_{\rm Jup}}$ with this fit that was within the uncertainites of the planet radius derived without detrending and this value used for the final model. Figure 13: RV residuals analysis presenting the posterior samples in the RV semi-amplitude versus orbital period space. The results of the search for a second companion do not show any clear detection. The solid and dashed blue lines correspond to the RV signals of Jupiter-, Saturn-, and Neptune-mass planets. We show that we are sensitive to sub-Saturn-mass planets up to $\sim$100 days and for longer orbital periods (up to 300 days), we can exclude the presence of additional Jupiter-mass planets. | CORALIE |
---|---|---
Time [BJD TDB] |  RV [m s-1] |  RV error [m s-1]
2459306.87282241 | -54451.2 | 83.5
2459316.88105868 | -54461.9 | 63.2
2459322.86463654 | -54353.4 | 57.9
2459329.90496341 | -54357.1 | 60.9
2459340.88479492 | -54359.8 | 175.5
2459350.88006593 | -54445.1 | 123.6
2459358.78809994 | -54462.4 | 51.9
2459365.76126559 | -54486.7 | 39.6
2459372.72588852 | -54499.1 | 48.3
2459379.72408383 | -54444.7 | 51.8
2459408.59341530 | -54291.4 | 101.3
2459415.62714956 | -54393.7 | 69.6
2459429.68413281 | -54362.4 | 46.0
2459434.64777952 | -54318.1 | 103.0
2459438.73530854 | -54458.8 | 74.7
2459447.75931134 | -54483.5 | 35.6
2459454.60669680 | -54445.3 | 38.4
2459459.53970780 | -54457.5 | 90.1
2459464.51671181 | -54429.8 | 64.2
2459468.67790552 | -54458.3 | 88.9
2459473.60548228 | -54410.3 | 42.2
2459476.57988364 | -54355.9 | 52.2
2459480.53595794 | -54293.8 | 51.5
2459490.60161776 | -54333.8 | 44.3
2459497.53153252 | -54267.3 | 81.9
2459504.50552615 | -54390.5 | 58.2
2459509.57621809 | -54473.8 | 57.1
2459513.57881157 | -54374.4 | 52.7
2459525.53964922 | -54523.6 | 76.6
2459532.54785833 | -54474.2 | 54.4
2459541.52832420 | -54393.1 | 67.6
| HARPS |
Time [BJD TDB] |  RV [m s-1] |  RV error [m s-1]
2459422.67412022 | -54343.21 | 9.51
2459423.68107993 | -54322.18 | 7.07
2459424.65831681 | -54326.17 | 5.35
2459425.61910614 | -54359.24 | 8.40
2459428.76938868 | -54365.23 | 5.69
2459430.64989303 | -54390.56 | 10.10
2459432.61062220 | -54401.89 | 7.22
2459433.68498673 | -54399.99 | 12.35
2459449.67700834 | -54431.81 | 25.54
2459460.60745780 | -54410.36 | 6.44
2459461.64402816 | -54412.78 | 7.86
2459462.59750084 | -54409.14 | 6.85
2459463.63573612 | -54400.62 | 5.59
2459464.55511221 | -54404.66 | 11.84
2459498.60139309 | -54340.57 | 10.14
2459521.54616908 | -54440.69 | 6.02
2459529.51177399 | -54429.92 | 6.50
2459539.54222557 | -54402.57 | 7.71
Table 3: Radial velocities of TOI-5542 from the CORALIE and HARPS
spectrographs.