# TOI-544 b: a potential water-world inside the radius valley in a two-planet
system

H. L. M. Osborne,1,2 V. Van Eylen,1 E. Goffo,3,4 D. Gandolfi, 3 G. Nowak,5,6,7
C. M. Persson,8 J. Livingston,9,10,11 A. Weeks,1 E. Pallé,6,7 R. Luque,12 C.
Hellier,13 I. Carleo,6 S. Redfield,14 T. Hirano,9,10,11 M. Garbaccio Gili,3 J.
Alarcon,15 O. Barragán,16 N. Casasayas-Barris,6,7 M. R. Díaz,17 M. Esposito,4
J. S. Jenkins19,20 E. Knudstrup,18 F. Murgas,6,7 J. Orell-Miquel,6,7 F.
Rodler,15 L. Serrano,3 M. Stangret,6,7 S. H. Albrecht,18 A. Alqasim,1 W. D.
Cochran,22 H. J. Deeg,12,23 M. Fridlund,8,21 A. Hatzes,4 J. Korth,24 K. W. F.
Lam25
1Mullard Space Science Laboratory, University College London, Holmbury St
Mary, Dorking, Surrey RH5 6NT, UK
2European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching
bei München, Germany
3Dipartimento di Fisica, Universitá di Torino, via P. Giuria 1, 10125 Torino,
Italy
4Thüringer Landessternwarte Tautenburg, Sternwarte 5, 07778 Tautenburg,
Germany
5Institute of Astronomy, Faculty of Physics, Astronomy and Informatics,
Nicolaus Copernicus University, Grudzia̧dzka 5, 87-100 Toruń, Poland
6Instituto de Astrofísica de Canarias (IAC), c/ Via Lactea, s/n, 38205 La
Laguna, Tenerife, Spain
7Departamento de Astrofísica, Universidad de La Laguna (ULL), 38206 La Laguna,
Tenerife, Spain
8Department of Space, Earth and Environment, Chalmers University of
Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
9Astrobiology Center, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
10National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo
181-8588, Japan
11Department of Astronomy, The Graduate University for Advanced Studies
(SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo, Japan
12Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL
60637, USA
13Astrophysics Group, Keele University, Staffordshire ST5 5BG, UK
14Astronomy Department and Van Vleck Observatory, Wesleyan University,
Middletown, CT 06459, USA
15European Southern Observatory, Alonso de Cordova 3107, 7630391 Vitacura,
Santiago de Chile, Chile
16Sub-department of Astrophysics, Department of Physics, University of Oxford,
Oxford OX1 3RH, UK
17Las Campanas Observatory, Carnegie Institution of Washington, Colina el
Pino, Casilla 601 La Serena, Chile
18Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus
University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark
19Instituto de Estudios Astrofísicos, Facultad de Ingeniería y Ciencias,
Universidad Diego Portales, Av. Ejército 441, Santiago, Chile
20Centro de Astrofísica y Tecnologías Afines (CATA), Casilla 36-D, Santiago,
Chile
21Leiden Observatory, University of Leiden, PO Box 9513, 2300 RA Leiden, The
Netherlands
22McDonald Observatory and Center for Planetary Systems Habitability, The
University of Texas, Austin Texas USA
23Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta de la Astronomía
s/n, 18008 Granada, Spain
24Lund Observatory, Division of Astrophysics, Department of Physics, Lund
University, Box 43, 22100 Lund, Sweden
25Institute of Planetary Research, German Aerospace Center (DLR),
Rutherfordstrasse 2, D-12489 Berlin, Germany
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We report on the precise radial velocity follow-up of TOI-544 (HD 290498), a
bright K star (V=10.8), which hosts a small transiting planet recently
discovered by the Transiting Exoplanet Survey Satellite (TESS). We collected
122 high-resolution HARPS and HARPS-N spectra to spectroscopically confirm the
transiting planet and measure its mass. The nearly 3-year baseline of our
follow-up allowed us to unveil the presence of an additional, non-transiting,
longer-period companion planet. We derived a radius and mass for the inner
planet, TOI-544 b, of 2.018 $\pm$ 0.076 R⊕ and 2.89 $\pm$ 0.48 M⊕
respectively, which gives a bulk density of $1.93^{+0.30}_{-0.25}$g cm-3.
TOI-544 c has a minimum mass of 21.5 $\pm$ 2.0 M⊕ and orbital period of 50.1
$\pm$ 0.2 days. The low density of planet-b implies that it has either an
Earth-like rocky core with a hydrogen atmosphere, or a composition which
harbours a significant fraction of water. The composition interpretation is
degenerate depending on the specific choice of planet interior models used.
Additionally, TOI-544 b has an orbital period of 1.55 days and equilibrium
temperature of 999 $\pm$ 14 K, placing it within the predicted location of the
radius valley, where few planets are expected. TOI-544 b is a top target for
future atmospheric observations, for example with JWST, which would enable
better constraints of the planet composition.

###### keywords:

exoplanets – techniques: radial velocities – planets and satellites:
composition – planets and satellites: detection

††pubyear: 2023††pagerange: TOI-544 b: a potential water-world inside the
radius valley in a two-planet system–A

##  1 Introduction

The radius valley describes the region in the size distribution of exoplanets
where few planets exist, specifically between 1.5 and 2.0 R⊕. This feature was
first observationally identified in Fulton et al. (2017) and Van Eylen et al.
(2018) and a variety of theories have been proposed to explain this gap in
planetary radii, including photo-evaporation (Owen & Wu, 2017; Fulton et al.,
2017; Van Eylen et al., 2018) and core-powered mass loss (Collier Cameron &
Jardine, 2018; Gupta & Schlichting, 2019, 2021). Photo-evaporation models
argue that planets generally form with rocky cores and atmospheric layers
composed of hydrogen and helium (H-He) of around 1$\%$ by mass. Such planets,
with a rocky core and H-He atmosphere, are termed sub-Neptunes and located
above the radius valley in radius-period space. In some cases, the intense
X-ray flux from the nearby host star strips away these volatile gases, leaving
behind a bare rocky core, a so-called super-Earth planet, with a radius
placing it below the radius valley (Owen & Wu, 2017). Core-powered mass loss
models are similar in that they predict planets to form with atmospheric
layers and be located above the valley and subsequent atmospheric loss reduces
the radius and locates the planet below the valley. In the latter model, the
energy enabling the mass loss has come from within the planet itself; stored
heat from the formation of the planet escapes from the core and heats the
atmospheric layer from the inside, leading to gaseous escape (Gupta &
Schlichting, 2019). Despite several attempts (e.g. Lopez & Rice, 2018; Owen &
Wu, 2017; Gupta & Schlichting, 2019; Estrela et al., 2020; Gupta et al., 2022;
Ho & Van Eylen, 2023) no significant observational evidence has been found
that can differentiate between models. There is also an additional
complication in the fact that the location of the radius valley seems to
change based on other parameters, in particular on stellar mass (see e.g.
Petigura et al. (2022). Cloutier & Menou (2020) calculated the occurrence
rates of small planets orbiting low mass stars to show that the location of
the radius valley shifts to smaller sizes for decreasing stellar mass. They
also argue that for planets around lower mass stars the radius valley may have
a different formation mechanism or mechanisms, and highlight the need for
high-precision RV follow-up of a number of key targets including TOI-544 b.

Additionally, recent works have suggested that the observed distribution of
small planets (particularly those orbiting M-dwarf stars) is the result of a
distribution in core composition at formation. Specifically, Luque & Pallé
(2022) argue that the small planets around M dwarfs can be separated into
super-Earths (with rocky cores) and water worlds (with large fractions of ice
or water layers). Other recent detections have also seemed to provide evidence
towards this divergence in core compositions. Piaulet et al. (2022) presents a
detailed study of Kepler-138 d, a small planet with a bulk density which they
argue can only be explained with a water world composition (see also e.g.
Diamond-Lowe et al. (2022); Cadieux et al. (2022)). However, Rogers et al.
(2023) use models which include atmospheric boil-off shortly after planet
formation to show that the group of water-world planets presented in Luque &
Pallé (2022) are consistent with atmospheric loss models where a rocky planet
with a H-He atmosphere loses its atmospheric layers to become a stripped core.

In this context, we have performed follow-up high-resolution radial velocity
observations within the KESPRINT consortium 111https://kesprint.science of the
small planet TOI-544 b discovered by the Transiting Exoplanet Survey Satellite
(TESS, Ricker et al., 2014). The planet is particularly interesting since it
is located in the middle of the radius valley and has a short period of 1.5
days. It was recently validated by Giacalone et al. (2022), where they present
observations from the TESS follow-up programme, who argued that TOI-544 b is a
potentially interesting target for JWST.

In Section 2 we present the space-based and ground-based observations of
TOI-544, including the extensive RV measurements. In Section 3 we describe our
stellar parameter fitting method and results. In Section 4 we describe both
the transit fitting and the RV fitting and in Sections 5.1 to 5.4 we explore
the composition of the inner planet, its location in relation to the radius
valley and potential atmospheric observations of this planet. Finally, we
present conclusions in Section 6.

##  2 Observations

###  2.1 Space-based Photometry

Figure 1: TESS light curves from Sector 6 (left) and 32 (right). SPOC light
curves are shown in the upper panel, with a full transit and noise model (see
Section 4.1) shown in blue. In the middle panel, TESS light curves are shown
after subtracting the best-fit GP model, and residuals are shown in the bottom
row.

As part of its all-sky survey, TESS observed the star TIC 50618703 in Sectors
6 and 32. The cadence of observations is 120 s, the time span of Sector 6 (32)
is 2018 Dec 12 to 2019 Jan 06 (2020 Nov 19 to 2020 Dec 16), and 44/14691
(817/17977) cadences were omitted due to bad quality flags in Sector 6 (32).
After data reduction though the standard Science Processing Operations Centre
(SPOC, Jenkins et al., 2016; Twicken et al., 2019) pipeline, likely transits
were detected and the planetary candidate was promoted to a TESS object of
interest (TOI), named TOI-544, by the TESS team. TESS observations of TOI-544
are shown in Figure 1.

###  2.2 Ground-based photometry

Prior to the initial planet detection by TESS, the Wide Angle Search for
Planets (WASP) survey (Pollacco et al., 2006) observed the field of TOI-544
between 2008 and 2011, obtaining 18 000 photometric datapoints using Canon
200-mm, f/1.8 lenses with a 400–700 nm filter and CCDs with a plate scale of
$13.7\arcsec$/pixel. The data have a typical 15-min cadence and covered an
observing season of $\sim$ 100 nights in each year. TOI-544 is by far the
brightest star in the 48-arcsec extraction aperture, with a V magnitude of
10.777$\pm$0.017 . We make use of this archival data by searching the
resulting WASP lightcurves for a stellar rotational modulation, adopting the
methods described in Maxted et al. (2011a). We find a significant modulation
at a period of 20 $\pm$ 1 days and an amplitude of up to 3 mmag. In the
combined dataset the modulation is significant to a level of $>$99%
confidence. Figure 2 shows Generalised Lomb-Scargle periodograms, adapted as
described in Maxted et al. (2011b), of the WASP data for TOI-544. The 1$\%$
false-alarm probability is shown by the horizontal line and the panels to the
right show the data folded on the 20 day rotation period.

Figure 2: Generalised Lomb-Scargle Periodograms of the WASP-South data for
TOI-544. The horizontal line is the estimated 1% false-alarm probability, data
after phase 0.5 are in grey. The right-hand panels show the data folded on the
20-d rotational period.

###  2.3 High-resolution spectroscopy

We obtained 108 high-resolution spectroscopic observations of TOI-544 using
the High Accuracy Radial velocity Planet Searcher (HARPS) mounted on the
European Southern Observatory (ESO) 3.6m telescope at La Silla Observatory.
Observations took place between December 2020 and March 2022 as part of
observing programme 106.21TJ.001 (PI Gandolfi). Each observation has a typical
exposure time of between 1800 s and 2100 s, with a median RV uncertainty of
1.6 m s-1 on an individual observation. There are an additional 2 observations
taken during April 2019 as part of observing programme 0103.C-0442(A) (PI
Diaz) and 3 observations taken between December 2020 and January 2021 as part
of programme 60.A-9709(G) (Observatory Technical Time).

TOI-544 was also observed using the High Accuracy Radial velocity Planet
Searcher for the Northern hemisphere (Cosentino et al., 2012) mounted at the
3.58-m Telescopio Nazionale Galileo (TNG) of Roque de los Muchachos
Observatory in La Palma, Spain, between April 2019 and December 2020,
resulting in a total of 14 spectra from programmes CAT19A_162 and CAT19A_97
(PIs Nowak; Casasayas-Barris). Each observation had typical exposure times of
between 1230 s and 2400 s and median RV precision of 1.5 m s-1 for an
individual observation. We include these 14 observations in our RV analysis.
The total number of HARPS and HARPS-N observations is 122.

HARPS and HARPS-N spectra were extracted using versions 3.8 and 3.7 of the
Data Reduction Software (DRS) pipelines. DRS pipelines were also used to
measure absolute radial velocities (RVs) and spectral activity indicators
cross-correlation function full width half maximum (CCF_FWHM) and centre
(CCF_FWHM), the bisector span (BIS) and the S-index, by cross-correlating the
extracted spectra with a K5 mask (Baranne et al., 1996). We also used serval
code (Zechmeister et al., 2018) to measure relative RVs by the template-
matching, chromatic index (CRX), differential line width (dLW), and H$\alpha$,
and sodium Na D1 & Na D2 indexes. The standard deviation of the RV data is 7.5
m s-1 for HARPS and HARPS-N and in both cases of using the DRS and SERVAL. All
RV observational data used in this analysis is given in A.

##  3 Stellar Parameters

Table 1: Stellar parameters for TOI-544, modelled with SpecMatch-Emp and SME,
and BASTA and astroARIADNE.

Stellar Parameters |  |  |  |  |
---|---|---|---|---|---
Identifiers | TOI-544 |  |  |  |
| TIC 50618703 |  |  |  |
| HD 290498 |  |  |  |
Coordinates1 | 05:29:09.62 -00:20:34.43 |  |  |  |
Magnitudes1 | V = 10.777 $\pm$ 0.017 |  |  |  |
| TESS = 9.6504 $\pm$ 0.006 |  |  |  |
Spectroscopic Parameters |  |  |  |  |
Method | $T_{\mathrm{eff}}$ | $\log g_{\star}$ | [Fe/H] | $V\sin i$ | Luminosity
| (K) | (cgs) | (dex) | (km s-1) | (L⊙)
SpecMatch-Empa | $4169\pm 70$ | $4.68\pm 0.12$ | $-0.17\pm 0.09$ | … | …
SME | $4248\pm 130$ | $4.60\pm 0.12$ | $-0.15\pm 0.08$ | $2.3\pm 0.8$ | 0.13 $\pm$ 0.02
| RA | DEC | Parallax | G |
GAIA2 | 82.2900716 | -0.3428983 | 24.44 $\pm$ 0.02 | 10.41430 $\pm$ 0.00059 |
Derived Parameters |  |  |  |  |
Method | $M_{\star}$ | $R_{\star}$ | Distance | Age |
| ($M_{\odot}$) | ($R_{\odot}$) | (Pc) | (Gyear) |
BASTAb | $0.630\pm 0.018$ | $0.624\pm 0.013$ | 40 $\pm$ 1 | 9 $\pm 7$ |
MIST | $0.645\pm 0.021$ | $0.617\pm 0.015$ | 40.9 $\pm$ 0.03 | $5^{+5.3}_{-3.1}$ |
astroARIADNE | $0.651^{+0.015}_{-0.026}$ | $0.630^{+0.044}_{-0.017}$ | … | … |

a Adopted as priors for the stellar mass and radius modelling. b Adopted as
our final stellar parameter values to be used in analysis of the planetary
system.1 Taken from TESS Input Catalogue (TIC) version 8 (Stassun et al.,
2019). 2 Taken from Gaia DR3 (Gaia Collaboration et al., 2021).

Stellar parameters for TOI-544 were calculated using BASTA (Aguirre Børsen-
Koch et al., 2022) run on the co-added HARPS spectra, as follows. First, Gaia
magnitude $G$, RA, DEC, and Parallax $\varpi$ were taken from Gaia DR3 (Gaia
Collaboration et al., 2021). Teff and [Fe/H] were determined using the
empirical software SpecMatch-Emp (Yee et al., 2017) which compares the
observed data to a library of FGKM stars. We also compared the Spec-Match-Emp
results with SME222http://www.stsci.edu/~valenti/sme.html (Spectroscopy Made
Easy; Valenti & Piskunov, 1996; Piskunov & Valenti, 2017). SME computes
synthetic spectra with line data from VALD333http://vald.astro.uu.se
(Ryabchikova et al., 2015) and a chosen stellar atmosphere grid, in our case
Atlas12 (Kurucz, 2013), which is fitted to the observed spectra. The macro-
and micro-turbulent velocities, $V_{\rm mac}$ and $V_{\rm mic}$, were held
fixed to 1.5 km s-1 and 0.5 km s-1, respectively (Gray, 2008). A more detailed
description of the modeling procedure can be found in Fridlund et al. (2017)
and Persson et al. (2018). The results were in very good agreement with
SpecMatch-Emp within $1~{}\sigma$. Table 1 gives the spectroscopic parameters
for TOI-544 modelled with SME and SpecMatch-Emp, we select the parameters
using (SpecMatch-Emp) for our modelling of stellar mass and radius.

An age and metallicity independent prior was placed on stellar mass following
the standard Salpeter Initial Mass Function, and reddening and dust were
accounted for using the `‘Bayestar’` dustmap (Green et al., 2019). A prior was
also set for [Fe/H] allowing for the parameter space to be searched only
within an absolute tolerance range of 0.5 dex of the input value. For the
isochrones, we used the latest version of BASTI (BAg of STellar Isochrones)
(Hidalgo et al., 2018), set to the ‘Diffusion’ science case, described in
Pietrinferni et al. (2021), to account for diffusion processes in low-mass
stars.

BASTA determines model dependent parameters using a Bayesian approach,
detailed in Silva Aguirre et al. (2015) and following the formalism of
Serenelli et al. (2013).

We also used the Python isochrones (Morton, 2015) interface to the MIST
stellar evolution models (Choi et al., 2016) using the same inputs as for
BASTA, which resulted in very good agreement for the stellar mass and radius
(within $\sim$0.5$\sigma$).

We compared our results from BASTA with the software
astroARIADNE444https://github.com/jvines/astroARIADNE (Vines & Jenkins, 2022).
This python code fits the observed spectral energy distribution via broad band
photometry to atmospheric model grids to obtain the stellar radius. We fitted
the bandpasses $GG_{\rm BP}G_{\rm RP}$ (Gaia eDR3), WISE W1-W2, $JHK_{S}$
magnitudes (2MASS), the Johnson $B$ and $V$ magnitudes (APASS), and the Gaia
eDR3 parallax. We used the Phoenix v2 (Husser et al., 2013) and the BtSettl
(Allard et al., 2012) atmospheric models. The final radius was computed with
Bayesian Model Averaging and the errors with a sampling method for
conservative uncertainties as described in Vines & Jenkins (2022). In this way
we obtained a stellar radius of $0.630^{+0.044}_{-0.017}$ $R_{\odot}$. The
stellar mass was computed with ARIADNE and the MIST (Choi et al., 2016)
isochrones and was found to be $0.651^{+0.015}_{-0.026}$ $M_{\odot}$. Table 1
gives the stellar parameters derived from our analysis, as well as the
comparisons with ARIADNE, which are within 1 $\sigma$ of our results from
BASTA.

##  4 Analysis and Results

###  4.1 Transit model

We jointly fit the SPOC Pre-Search Data Conditioning Simple Aperture
Photometry (PDCSAP) light curves from TESS Sectors 6 and 32 using the PyMC3
(Salvatier et al., 2016), exoplanet555https://docs.exoplanet.codes/en/stable/
(Foreman-Mackey et al., 2019), starry (Luger et al., 2019), celerite2
(Foreman-Mackey et al., 2017a; Foreman-Mackey, 2018) software packages.

To account for stellar activity signals and instrumental Systemics we included
a Gaussian Process (GP, Rasmussen & Williams, 2005) model, using a Matérn-3/2
covariance function. We placed Gaussian priors on the stellar mass and radius
based on the results in Table 1. We also placed Gaussian priors on the limb
darkening coefficients based on interpolation of the parameters tabulated by
Claret et al. (2012) and Claret (2017), propagating the uncertainties in the
stellar parameters in Table 1 via Monte Carlo simulation.

Visual inspection of the TESS lightcurves reveals quasiperiodic variability
with a $\sim$1 ppt amplitude, and their Lomb-Scargle periodograms reveal peaks
at $\sim$8 and $\sim$10 days, which are likely the first harmonic of the
stellar rotation signal modulo instrumental noise. We thus placed loose
Gaussian priors on the GP amplitude and timescale hyperparameters of 1$\pm$0.5
ppt and 10$\pm$5 days, respectively.

We used separate white noise parameters for each TESS sector to account for
the possibility of differences in photometric precision, which could
potentially arise from different background light conditions or different
phases of the spacecraft’s operational lifetime. We used the gradient-based
BFGS algorithm (Nocedal & Wright, 2006) implemented in scipy.optimize to find
initial maximum a posteriori (MAP) parameter estimates. We used these
estimates to initialize an exploration of parameter space via “no U-turn
sampling” (NUTS, Hoffman & Gelman, 2014), an efficient gradient-based
Hamiltonian Monte Carlo (HMC) sampler implemented in PyMC3.

We sampled four chains with 4500 tuning iterations and 3000 additional draws,
for a total of 12,000 samples after burn-in; the resulting chains were well-
mixed according to a Gelman-Rubin statistic (Gelman & Rubin, 1992) value of
$<$1.01, and the sampling error was $\lesssim$1%, suggesting a sufficient
number of independent samples had been collected.

The phase-folded TESS photometry from Sector 6 and 32, along with the best-fit
transit model, is shown in Figure 3 and the results of the transit fit are
given in Table 2.

Figure 3: Phase-folded TESS photometry from Sector 6 (top) and Sector 32
(bottom), with the best-fit transit model in blue, the lower panel of each
shows the residuals to the best fit model

. The larger black points show the data binned by a factor of 30.

###  4.2 Frequency analysis of HARPS data

Figure 4: Generalised Lomb-Scargle periodograms of the DRS RV measurements and
activity indicators of TOI-544. The right and left columns cover two frequency
ranges encompassing the orbital frequency of TOI-544 c, the stellar rotation
frequency and its first two harmonics (left panels), and the orbital frequency
of TOI-544 b (right panels). The Doppler signals from the two planets are
marked as vertical red dashed lines at fc $\approx$ 0.02 d-1 (TOI-544 c) and
fb $\approx$ 0.646 d-1 (TOI-544 b). Vertical, blue dashed lines indicate the
stellar rotation frequency (frot $\approx$ 0.051 d-1) and its first two
harmonics (2 frot $\approx$ 0.102 d-1 and 3 frot $\approx$ 0.153 d-1). The
horizontal red dashed line mark the 0.1% false alarm probability. _From top to
bottom:_ the DRS RV measurements; RV residuals following the subtraction of
the Doppler reflex motion induced by TOI-544 c; RV residuals after subtracting
the signals of the star rotation, its first two harmonics, and TOI-544 c; dLW;
CCF_BIS; S-index; H$\alpha$; Na D1; Na D2.

We performed a frequency analysis of our RV time-series to search for the
Doppler reflex motion induced by the transiting planet discovered by TESS,
spectroscopically confirm its planetary nature, and possibly unveil the
presence of additional signals induced by stellar activity and/or additional
orbiting companions. In order to avoid having to account for the RV offset
between the two spectrographs, we did not include the 14 HARPS-N Doppler data
points, and used only the 108 HARPS measurements, which cover a baseline of
$\sim$1051 d (nearly 3 years), implying a frequency resolution of
$\sim$0.00095$\,d^{-1}$.

Figure 4 displays the generalised Lomb-Scargle (GLS; Zechmeister & Kürster,
2009) periodograms of the HARPS DRS radial velocity measurements and of the
activity indicators in two frequency ranges. The panels to the left show the
periodograms between 0.0 and 0.2 d-1, a range that includes the frequencies at
which we expect to detect the Doppler signals induced by active regions
corotating with the star. The panels to the right display the periodograms in
the range 0.59-0.71 d-1, which encompasses the transit frequency of TOI-544 b.
We note that the gap between these frequencies shows nothing of note and is
excluded. For each panel, the horizontal dashed line mark the false-alarm
probability (FAP) of 0.1,%, as derived using the bootstrap method (Murdoch et
al., 1993; Kuerster et al., 1997). We considered a peak to be significant if
its FAP $<$ 0.1%.

The GLS periodogram of the HARPS RVs (Fig. 4, upper left panel) displays its
most significant peak at $\sim$0.02 d-1 ($\sim$50 d). This peak does not
appear in any other periodograms of the activity indicators666We note that
there are two peaks in the periodogram for H$\alpha$ which are symmetrically
located around the peak at $\sim$0.02 d-1. However, neither these are at the
same frequency as the signal, nor they are significant (FAP $>$ 0.1 %),
providing evidence that the 50-d signal is very likely caused by an additional
companion, which we referred to as TOI-544 c throughout the paper.

We removed the Doppler reflex motion induced by TOI-544 c fixing period and
phase to the values derived from the periodogram analysis, while fitting for
the RV semi-amplitude and systemic velocity. The periodogram of the RV
residuals following the subtraction of the Doppler reflex motion induced by
TOI-544 c (Fig 4, second left panel) shows 3 equally spaced peaks at
$\sim$0.051 d-1 ($\sim$19.4 d), $\sim$0.102 d-1 ($\sim$9.8 d), and $\sim$0.153
d-1 ($\sim$6.5 d). The former is significantly detected also in the
periodograms of the dLW, CCF-BIS, S-index, H$\alpha$, Na D1, and Na D2 lines
(Fig 4, lower left panels), implying that this is very likely due to stellar
activity. We interpreted the peak at $\sim$19.4 d as the stellar rotation
period, in excellent agreement with the WASP results (Sect. 2.2). The two
peaks at $\sim$9.8 d and $\sim$6.5 d are the first and second harmonics of the
stellar rotation period, which are likely caused by the presence of spots
equally spaced in longitude and/or by the non-coherent nature of the activity-
induced signal.

We removed the stellar signal by fitting 3 Fourier components at the stellar
rotation period and its first two harmonics. The GLS periodogram of the RV
residuals (Fig. 4, third right panel) shows its strongest power at $\sim$0.646
d-1 ($\sim$1.55 d), the orbital frequency $f_{\mathrm{b}}$ of the transiting
planet TOI-544 b. Although the FAP of this feature anywhere in the frequency
range of the periodogram is higher than 0.1 %, the presence of a peak at a
known frequency, i.e., the transit frequency, provides strong evidence that
this signal is due to planet b. We estimated the FAP at the orbital frequency
of TOI-544 b using the windowing bootstrap method described in Hatzes (2019).
Briefly, we estimated the bootstrap FAP over a $\Delta\nu$ = 0.1 d-1 wide
frequency window centered on $f_{\mathrm{b}}$. We successively narrowed the
spectral window at steps of 0.01 d-1 for 10 additional bootstrap
randomizations, down to $\Delta\nu$ = 0.01 d-1. The fit of the FAP versus
window size, extrapolated to the intercept (i.e., the zero window length),
yields a FAP = 0.004 % at $f_{\mathrm{b}}$, spectroscopically confirming the
planetary nature of the transit signal discovered by TESS.

###  4.3 Radial velocity analysis

We modelled the RV data using the code pyaneti (Barragán et al., 2019, 2022)
which implements a multi-dimensional GP to help account for the impact of
stellar activity, the implementation of GPs for this purpose is described in
detail in Rajpaul et al. (2015). Essentially, this method models the RVs, and
an activity indicator of choice, assuming that the same GP,
$\mathrm{G(t_{i},t_{j})}$, can describe both of them. We use the S-index as
the activity indicator to model alongside the RVs. As TOI-544 shows a strong
stellar rotation period, we chose the quasi-periodic (QP, Equation 1) kernel
for the GP,

$G\left(t_{i},t_{j}\right)=A^{2}exp\left[\frac{\sin^{2}{\left[\pi\left(t_{i}-t_{j}\right)/P_{GP}\right]}}{2{\lambda_{p}}^{2}}-\frac{\left(t_{i}-t_{j}\right)^{2}}{{2\lambda_{e}}^{2}}\right]$
(1)

where $\mathrm{P_{GP}}$ is the GP characteristic period (which here represents
the stellar rotation period); $\mathrm{\lambda_{p}}$ is the inverse of the
harmonic complexity (related to distribution of active regions on the stellar
surface); and $\mathrm{\lambda_{e}}$ is the long-term evolution timescale (the
lifetime of active regions on the stellar disk). The two-dimensional GP used
to model the system is then given by

$RV=A_{0}G+A_{1}dG$ (2)

and

$S_{index}=A_{2}G+A_{3}dG$ (3)

where $A_{0}$, $A_{1}$ and $A_{2}$ are GP hyperparameters in the form of
amplitudes that work as a scale factor that determines the typical deviation
from the mean function, and $dG$ is the time derivative of our GP function,
$\mathrm{G(t_{i},t_{j})}$ . From first principles, $A_{3}\equiv 0$, see
Rajpaul et al. (2015) for more details. We used the stellar parameters listed
in Table 1, and priors on the orbital period and time of pericenter of planet
b based on those found in the transit fit. We use the orbital period indicated
in the GLS periodogram to place priors on planet c (see Figure 4 and Section
4.2 for description of this search). We also place a prior on $P_{GP}$
centered on the stellar rotation period found by the WASP photometry, and
wide, uniform priors on the remaining parameters. We then performed a Markov
chain Monte Carlo (MCMC) analysis. We allow for both planets to be on an
eccentric orbit in our fit. We sample the parameter space with 500 Markov
chains and use the final set of 5000 steps with a thin factor of 10 to produce
our posterior distributions, meaning a total of 250000 independent points for
each sampled parameter.

We find that TOI-544 b has an orbital period of 1.55 days and a $K_{b}$
amplitude (the radial velocity semi-amplitude) of 2.66 $\pm$ 0.44 m s-1,
equating to a planet mass of $M_{b}=$ 2.89 $\pm$ 0.48 M⊕. The eccentricity of
TOI-544 b is found to be 0.35 ${}^{+0.14}_{-0.12}$ and its argument of
periastron is 41.2°${}^{+17}_{-26}$. TOI-544 c has a period of 50.1 $\pm$ 0.2
days, $K_{c}$ amplitude of 5.21 $\pm$ 0.57 m s-1, implying a minimum mass of
$M_{c}\sin i_{c}$ = 21.5 $\pm$ 2.0 M⊕. The eccentricity of TOI-544 c is found
to be 0.30 $\pm$ 0.09 and argument of periastron is 17°${}^{+21}_{-18}$.

We assessed the significance of the eccentric solutions for the two planets by
creating 5000 sets of synthetic RV time-series that sample the best-fitting
circular solutions at the epochs of our real observations. We added Gaussian
noise at the same level of our RV measurement uncertainties and fitted the
simulated time series allowing for non-zero eccentricities. For TOI-544 b
there is a $\sim$3.5% that a best-fitting eccentric solution with e$\geq$0.35
could arise by chance if the orbit is actually circular. As for TOI-544 c, the
probability that noise can account for e$\geq$0.30 is only 0.2 %. Assuming a
significance level of 1%, the eccentric solution for TOI-544 b is likely not
real, while the eccentricity of TOI-544 c is real. Therefore, our adopted
results are for the case where the inner planet is on a circular orbit and
outer planet is on an eccentric orbit i.e. TOI-544 b has an orbital period of
1.55 days and a $K_{b}$ amplitude of 2.17 $\pm$ 0.36 m s-1, equating to a
planet mass of $M_{b}=$ 2.89 $\pm$ 0.48 M⊕, TOI-544 c has a period of 50.1
$\pm$ 0.2 days, $K_{c}$ amplitude of 5.36 $\pm$ 0.55 m s-1, implying a minimum
mass of $M_{c}\sin i_{c}$ = 21.5 $\pm$ 2.0 M⊕. The eccentricity of TOI-544 c
is found to be 0.32 $\pm$ 0.09 and argument of periastron is
12°${}^{+19}_{-17}$.

The priors used for all parameters are show in Table 8, and the results,
showing the median value and 68 $\%$ credible interval for each parameter, are
given in Table 2. The best fit model alongside the data are shown, as a
function of time, in Figure 5 and phase-folded for each planet in Figure 6.

We additionally chose to model the RV data using several other methods to
ensure the robustness of our results. Using Pyaneti, we run similar fits to
the one described above, but with: both planets on circular orbits; the inner
planet on a circular orbit and outer planet on an eccentric orbit; a fit with
Pyaneti but not multi-dimensional (i.e. fitting on only the RV data points),
and a joint model including both the transit and RV data.

We also make use of the radial velocity fitting toolkit RadVel (Fulton et al.,
2018). Using RadVel we run fits for: a two planet system with no GP to account
for stellar activity; a 1 planet system (only the transiting inner planet)
including a GP using the Celerite quasi-periodic kernel (Foreman-Mackey et
al., 2017b); a 2 planet system using the Celerite quasi-periodic kernel where
both planets are on circular orbits; and the same kernel again but where both
planets are on eccentric orbits; and a 2 planet system where we use the
square-exponential GP kernel (described in Fulton et al. (2018). As well as
this, we check for possible additional signals by fitting for a 3-planet
system, we find that the third signal is unconstrained and the BIC and AIC
increase slightly over the 2-planet case - therefore we do not believe there
are signs of additional planets in the system. We also change the choice of
priors in our models, in particular for the period of planet c to ensure we
are not biasing our results. For example, the RadVel fit for a 2-planet system
with the square exponential kernel has a uniform prior on $P_{c}$ of 0 to 100
days, and the RadVel fit for a 2-planet system with the Celerite quasi-
periodic kernel has a Gaussian prior of 50.6 $\pm$ 1.0 days, in all cases the
results are consistent. The resulting K amplitude (for TOI-544 b) found from
all models are shown in Table 7.

RadVel also allows for model comparison; we find that in models which include
more than one planet, a single-planet model is ruled out in every case -
providing greater assurance of the existence of the second planet.
Specifically, for a 1-planet system, the BIC is 1993.90 and AIC is 1965.46,
and for 2-planet system 801.24 and 765.90 respectively. We also run additional
models using only the HARPS data points to ensure the HARPS-N points (which
have a slightly higher level of scatter) are not influencing out fit, and with
RVs extracted with TERRA rather than SERVAL, in all cases the results are
consistent within 1-$\sigma$. As well as this, we run Pyaneti fits with
different activity indicators: FWHM, and contrast, and combinations of
indicators: S-index and FWHM, S-index and contrast, and FWHM and contrast. In
all cases the derived planet parameters are consistent with our other models
within 1-$\sigma$, however the GP hyperparameters are not all so well
constrained so we still use the model with the S-index as our adopted results.

Figure 5: Best-fit 2-planet Keplerian orbital model for TOI-544. HARPS data
shown by orange circles, and HARPS-N data shown by blue diamonds, both shown
as a function of time. The best-fit model for the planet signals is shown in
red, the GP model in blue, and the combined planets and GP shown in black. The
dark and light shaded areas showing the 1$\sigma$ and 2$\sigma$ credible
intervals of the corresponding GP model, respectively

.

Figure 6: The phase-folded RV data from HARPS (orange circles) and HARPS-N
(blue diamonds) alongside the best-fit planet model (with the effect of the
other planet and the GP model subtracted from each). TOI-544 b is on the left
and TOI-544 c on the right. The lower part shows the residuals from the fit.
There appears to be no trends visible in the residuals, and the augmented
sinusoid representative of an eccentric orbit is present in both phase-folded
plots

.

Table 2: Results of the transit and RV fit for TOI-544, showing the median value and 68 $\%$ credible interval for each parameter. Fitted Parameter | Median value
---|---
Planet Transit Parameters |
Stellar Mass $M_{\star}$ [$M_{\odot}$] | $0.631\pm 0.018$
Stellar Radius $R_{\star}$ [$R_{\odot}$] | $0.623\pm 0.012$
Transit Midpoint $T_{0}$ [BTJD] | $2199.031363^{+0.000614}_{-0.000703}$
Period $P$ [days] | $1.548352\pm 0.000002$
$R_{P}/R_{\star}$ | $0.0297\pm 0.0007$
Impact Parameter $b$ | $0.66^{+0.03}_{-0.04}$
$\sigma_{\mathrm{GP}}$ [ppm] | $707^{+113}_{-86}$
$\rho_{\mathrm{GP}}$ [hours] | $22.0^{+3.5}_{-2.8}$
$u_{1}$ ($T$) | $0.43\pm 0.16$
$u_{2}$ ($T$) | $0.24\pm 0.15$
$\log\sigma_{\mathrm{S6}}$ [ppt] | $-0.159094^{+0.005981}_{-0.005915}$
$\log\sigma_{\mathrm{S32}}$ [ppt] | $-0.157482^{+0.005387}_{-0.005275}$
Planet Radius $R_{\mathrm{p}}$ [$R_{\oplus}$] | $2.02\pm 0.07$
Semi-major Axis $a$ [AU] | $0.0225\pm 0.0002$
Equilibrium Temperature $T_{\mathrm{eq}}$ [K] | $999\pm 14$
Transit Duration $T_{14}$ [hours] | $1.21\pm 0.03$
Planet RV Parameters |
Period, $P_{b}$ [days] | $1.5483520\pm 0.000002$
Time of Conjunction (-2450000), $T\rm{conj}_{b}$ [JD] | 9199.0313760 $\pm$ 0.0007
Time of Periastron (-2450000), $T\rm{peri}_{b}$ [JD] | 9198.6442877 $\pm$ 0.0007
Eccentricity, $e_{b}$ | $\equiv 0$
Argument of Periastron, | $\equiv 0$
RV Amplitude, $K_{b}$ [m s-1] | $2.17\pm 0.36$
Planet Mass, $M_{b}$ [M⊕] | 2.89 $\pm$ 0.48
Period, $P_{c}$ [days] | $50.089\pm 0.24$
Time of Inf. Conjunction (-2450000), $T\rm{conj}_{c}$ [JD] | $9211.973939^{+1.8}_{-1.9}$
Time of Periastron (-2450000), $T\rm{peri}_{c}$ [JD] | $9205.3660911^{+2.2}_{-2.8}$
Eccentricity, $e_{c}$ | $0.32^{+0.08}_{-0.09}$
Argument of Periastron, $\omega_{c}$ [$\degree$] | $11^{+19}_{-17}$
RV Amplitude, $K_{c}$ [m s-1 ] | $5.36\pm 0.56$
Planet Minimum Mass, $M_{c}sini$ [M⊕] | 21.5 $\pm$ 2.0
Other Parameters |
Systemic Velocity HARPS-N [kms-1] | -0.016 $\pm$ 0.002
Systemic Velocity HARPS [kms-1] | 0.006 $\pm$ 0.001
Systemic Velocity S1 [kms-1] | 1.13 $\pm$ 0.03
Systemic Velocity S2 [kms-1] | $1.25^{+0.03}_{-0.04}$
Jitter Term, $\sigma_{\rm HARPS-N}$ [ms-1] | 3.0 $\pm$ 1.0
Jitter Term, $\sigma_{\rm HARPS}$ [ms-1] | $1.9^{+0.36}_{-0.33}$
GP Hyperparameters |
$A0$ | $0.002^{+0.001}_{-0.001}$
$A1$ | $0.025^{+0.008}_{-0.005}$
$A2$ | $0.076^{+0.025}_{-0.016}$
$A3$ | $\equiv 0$
$\lambda_{e}$ [days] | $112^{+28}_{-29}$
$\lambda_{p}$ [days] | $0.519^{+0.091}_{-0.074}$
Rotation Period, PGP [days] | $19.343^{+0.073}_{-0.076}$

##  5 Discussion

###  5.1 Composition of TOI-544 b

Figure 7: Mass-radius diagram showing confirmed planets with mass
uncertainties < 20$\%$ in grey circles, with TOI-544 b shown as the black
circle. Left: the coloured tracks show different potential planet compositions
from Zeng et al. (2019), assuming a planetary equilibrium temperature of 1000
K. The dashed lines show compositions of an Earth-like rocky core surrounded
by a layer of H-He in varying percentages by mass, the solid lines show water
world compositions with varying water mass fractions, the dotted lines show
rocky and Earth-like rocky compositions. TOI-544 b is closest to the tracks
with 100$\%$ H2O and 50$\%$ H2O with 50$\%$ rock. Right: the same as the left
panel but the the dashed lines show compositions of an Earth-like rocky core
surrounded by a layer of H-He in varying percentages by mass from Lopez &
Fortney (2014) using the models for a 10Gyr planet, with solar metalicity and
flux of 10F⊕, the solid lines show compositions from Aguichine et al. (2021)
of irradiated ocean worlds with varying water mass fractions, and the dotted
lines show the same rocky and Earth-like rocky compositions from Zeng et al.
(2019). TOI-544 b is closest to models with either 30$\%$ water mass fraction,
or a rocky core with a Hydrogen envelope of between 0.5 - 1$\%$. The data is
downloaded from the NASA Exoplanet Archive.

The calculated density of TOI-544 b is $1.93^{+0.30}_{-0.25}$g cm-3 which is
not dense enough to be composed of entirely rock and iron, where densities are
typically between 3 g cm-3 and 10 g cm-3 (Zeng et al., 2019). This implies
that a composition of a bare rocky-iron core can likely be excluded. TOI-544 b
must have some additional component to its composition, but whether it is in
the form of water/ice layers or a H-He atmosphere depends on which particular
composition models are used. Figure 7, left panel, shows the mass radius
diagram for small planets (< 4 R⊕, with mass uncertainties < 20 $\%$) with
TOI-544 b highlighted and composition tracks from Zeng et al. (2019) shown in
different colours. As noted in Rogers et al. (2023), these models are often
misinterpreted when used in mass-radius diagrams. Specifically, there are a
range of models available depending on the chosen temperature, this
temperature is often assumed to be the equilibrium temperature of the planets
but is actually the temperature at a pressure of 100 bars. In this case we
have used the incorrect temperature (equal to the planet equilibrium
temperature of $\approx$ 1000 K) in order to show a direct comparison to many
other mass-radius diagrams available in the literature. Using these models
alone, it appears that TOI-544 b does not fit the super-Earth (rocky/iron
core) scenario, and that it also does not fit the typical sub-Neptune
composition of a rocky core surrounded by atmospheric H-He. From these models
it seems likely that TOI-544 b is a water-world planet with a sizeable
fraction of H2O present. From the Zeng et al. (2019) models it seems that a
water fraction by mass of over 50$\%$ is possible for this planet. There are
few other planets detected in a similar area of parameter space, however we
note that many of the planets in this regime have multiple mass values listed
on the NASA Exoplanet Archive so their exact location on the mass-radius
diagram depends on the specific choice of literature parameters, and many have
longer orbital periods, meaning it is difficult to do a real comparison.

To further investigate the compositional nature of the planet, we use the
dimensionless parameter $\zeta$ from Zeng et al. (2021)

$\zeta\equiv\frac{(R_{c}/R_{\oplus})}{(M_{c}/M_{\oplus})^{0.25}},$ (4)

where $R_{C}$ and $M_{C}$ are the core radius and mass respectively, similar
to the approach taken in Nava et al. (2019). This parameter can be used to
distinguish between the 3 possible compositions of small exoplanets – either
rocky and earth-like ($\zeta=1$), having significant amounts of ices
($\zeta=1.4$), or icey cores with hydrogen/helium envelopes ($\zeta=2.2$). For
small planets the core radius and mass can be approximated the planet radius
and mass (in units of Earth radii and mass). The value of $\zeta$ for TOI-544
b is 1.5, which suggests an ice dominated composition.

Another approach is noting that TOI-544 b is a highly irradiated planet due to
its short semi-major axis. We make use of the Structure Model INterpolator
(SMINT)777https://github.com/cpiaulet/smint which obtains posterior
distributions of H2O mass fraction based on interpolation onto the Aguichine
et al. (2021) model grids. Using the stellar and planetary parameters listed
previously, with conservative uncertainties, we obtain an H2O fraction of 0.25
$\pm$ 0.12. This is lower than the expected H2O fraction seen in the mass-
radius diagram. We note, however, that the models from Zeng et al. (2019) do
not account for the high level of radiation such a close-in planet would
receive.

However, whilst Zeng et al. (2019) models are commonly used in mass-radius
diagrams for small planets, Rogers et al. (2023) recommend using the mass-
radius relations for sub-Neptune compositions given in Lopez & Fortney (2014),
which assume a constant planet age, rather than the Zeng et al. (2019) models
which assume a constant specific entropy. In the right panel of Figure 7, we
plot a mass-radius diagram with composition tracks from Lopez & Fortney (2014)
and Aguichine et al. (2021). The dashed lines show compositions of an Earth-
like rocky core surrounded by a layer of H-He in varying percentages by mass
from Lopez & Fortney (2014). The solid lines show compositions from Aguichine
et al. (2021) of irradiated ocean worlds with varying water mass fractions.
The dotted lines show the same rocky and Earth-like rocky compositions from
Zeng et al. (2019) which are shown in the left panel. Setting TOI-544 b on
this graph, we see that according to the Lopez & Fortney (2014) models, a
composition of an Earth-like core surrounded by a layer of H-He of between 0.5
and 1$\%$ by mass can also explain the observed mass and radius. The
composition tracks from Aguichine et al. (2021) for irradiated water-worlds
suggest an alternative composition of TOI-544 b of a rocky core with a layer
of water/ice of around 30$\%$ by mass.

As discussed in Rogers et al. (2023), for individual planets such as TOI-544
b, mass and radius alone are insufficient to uniquely constrain planet
composition. In order to break the degeneracy between the water-worlds and
sub-Neptune models, atmospheric observations of the planet are needed to rule
out (or in) the potential for H-He or H2O atmospheres. Fortunately, as
described in Section 5.4, TOI-544 b is an ideal candidate for atmospheric
studies. Future observations, with for instance JWST, should be able to help
determine more definitively whether this is a water-world or not.

From Figure 7 it can also be seen that TOI-544 b sits within an area of the
mass-radius diagram where few planets have been observed. Of the more than
5000 exoplanets confirmed to date, there are less than 200 small (< 4 R⊕)
planets which have precisely characterised masses (uncertainties < 20$\%$),
and of those, less than 30 are low mass (< 4M⊕). The majority of these small,
low mass planets with precise characterisation cluster around the composition
tracks for rocky silicates or iron composition – similar to an Earth-like
composition. The most similar planet is Kepler-307c, which is one of the only
low mass planets that has a similarly low density (seen to the top right of
TOI-544 b in Figure 7). The mass of Kepler-307c was determined through transit
timing variations rather than through RV observations. As there have been
suggestions of a potential offset between the two methods (Steffen, 2016;
Mills & Mazeh, 2017), it is possible that these two planets are not fully
comparable. In general, there are few precisely-characterised masses for small
planets, and even fewer for potential water-worlds, meaning TOI-544 b is an
important addition to this region of parameter space.

###  5.2 Location in relation to the radius valley

The orbital period and planetary radius of TOI-544 b put it within the
expected location of the small-planet radius valley for FGK stars (e.g. Ho &
Van Eylen, 2023). Figure 8 shows the period-radius diagram for confirmed
Kepler planets orbiting stars with stellar mass < 0.8 M⊙ fitted in a
homogeneous way in Ho & Van Eylen (2023). Additionally, planets with precise
mass measurements from the NASA Exoplanet Archive which orbit stars with
masses < 0.8 M⊙ are highlighted, and TOI-544 b shown. TOI-544 b sits within
the radius valley region calculated for this specific stellar mass - using
Equation 11 from (Ho & Van Eylen, 2023) and using TOI-544’s stellar mass (see
Table 1). TOI-544 b is more than $3\sigma$ away from the upper and lower
bounds of the radius valley (shown by the dashed lines). We also ran a number
of fits for stellar radius; we use the calculated stellar radii from 1, taking
the most extreme cases of the BASTA fit -1$\sigma$, and the astroARIADNE fit
+1$\sigma$ sigma (i.e.the smallest and largest possible from our results), we
find planet radii of 2.16 and 1.98 R⊕respectively. These values still put
TOI-544 within the limits of the valley given in Ho & Van Eylen (2023).The
location of TOI-544 b in the middle of the valley points towards the
possibility of the radius valley being less empty than potentially thought. In
the case of Ho & Van Eylen (2023), as well as others, the location of the
radius valley has been found based on observations and a dependence on stellar
mass has been noted. These observational results can be compared with
theoretical models such as in Owen & Wu (2017), which also predict that the
location of the valley depends on the planetary core composition. If we assume
that planets form uniformly with an icey core – rather than a rocky one – then
the theoretical models predict that the radius valley will be shifted to a
higher radius for a given orbital period. This means that, for planets with
icey cores - sometimes referred to as water world planets - the location of
TOI-544 b in the radius-period space would not put it inside the radius
valley. Instead it would sit below the valley, in a region which predicts
planets with a sizeable water/ice faction but without significant
hydrogen/helium atmospheres, potentially having undergone atmospheric loss.

Luque & Pallé (2022) argue that the radius valley distribution may in fact be
the result of two different core compositions of planets rather than purely
from atmospheric loss mechanisms, in the case of planets orbiting M dwarfs.
They state that small planets come in two distinct types: super-Earths with
rocky/iron composition, and water worlds with a combination of both rock and
water/ices. This interpretation is disputed by Rogers et al. (2023), who argue
that the properties of the sample of planets around M dwarfs studied by Luque
& Pallé (2022) can also be explained by the more traditional super-Earth sub-
Neptune classifications which arise from atmospheric loss models.

If TOI-544 b is a water world planet then its location inside the small planet
radius valley would not be so surprising as it is possible that for this
particular type of planet the radius valley is in a different location in
radius-period space. Alternatively, if TOI-544 b is confirmed to be composed
of a rocky core plus H-He then its location in the valley is more unusual,
meaning this is a particularly interesting case for future study.

We note that at this stage there is no conclusive evidence either way to
support the water worlds versus atmospheric loss explanation of the radius
valley, and further investigation is needed to fully distinguish between the
two theories. In particular, confirmation of TOI-544 b as a water world or not
(as well as other small planets) would help to understand whether the radius
valley is less empty than previously thought.

Figure 8: Period-radius diagram for a subset of confirmed planets orbiting
stars with masses < 0.8 M⊙. Purple circles are confirmed Kepler planets fitted
in a homogeneous way in Ho & Van Eylen (2023). Blue circles show planets with
precise mass measurements from the NASA Exoplanet Archive. TOI-544 b shown by
the black square. TOI-544 b sits within the expected location of the radius
valley (between the dashed lines) for this specific stellar mass - calculated
from Equation 11 in Ho & Van Eylen (2023).

###  5.3 Planet c

We searched the TESS lightcurves for signs of a transit of TOI-544 c but none
were found. If we assume that both planets are at the same orbital inclination
(which may not be the case) then planet c would not be expected to transit
given its impact parameter of 5. As a result, we can only constrain a minimum
mass for TOI-544 c of 21.5 $\pm$ 2.0 $M_{\oplus}$, for reference this is
slightly higher than the mass of Neptune. Planet c is found to have a non-zero
eccentricity, and, if it is confirmed that TOI-544 b has a large fraction of
water within its composition, then it is likely that it must have formed
exterior to the snow-line, and then migrated inwards - this migration could
have been facilitated by TOI-544 c. A full dynamical investigation of the
system architecture is beyond the scope of this paper, but could be
interesting in the future, particularly if the composition of the inner planet
is better constrained, and it is possible that if the planets do not orbit in
the same plane then plant c could in fact transit.

###  5.4 Potential atmospheric studies of TOI-544 b

We calculated the transmission spectroscopy metric (TSM, Kempton et al., 2018)
for TOI-544 b, finding a value of 163, much higher than the recommended
threshold value (90) from (Kempton et al., 2018) for planets with radii above
1.5 R⊕, placing TOI-544 b among the most appealing targets for transmission
spectroscopy characterisation with JWST (within the top 15 targets for similar
planets, see Figure 9). Moreover, the emission spectroscopic metric (ESM,
Kempton et al., 2018) is found to be 16. Considering the Kempton et al. (2018)
cutoff of 7.5, TOI-544 b lies among the top 10 most favourable targets (see
Figure 9). TOI-544 b is within the top 5 targets for both TSM and ESM for
planets with radii between 1.5 and 2.75 R⊕ and temperature between 800 and
1250K, as identified by the TESS follow-up atmospheric working group. We also
calculate the predicted S/N for atmospheric observations of TOI-544 b with
JWST (using the method in Niraula et al. (2017), finding a value of 1.000.
This puts TOI-544 b within the top dozen small planets with temperature less
than 1250K in terms of potential JWST observations. Atmospheric observations
should help to reduce the degeneracy between composition models for this
planet and determine whether a water world or a rocky and hydrogen composition
is more likely, similar to a recent study of TOI-270 d (Van Eylen et al.,
2021) for which transmission spectroscopy revealed a possible hydrogen-rich
atmosphere (Mikal-Evans et al., 2022).

Figure 9: Top panel: The transmission spectroscopy metric (TSM) against
equilibrium temperature of all small (R $<4R_{\oplus}$) confirmed planets with
a mass measurement, blue dots. The threshold given in Kempton et al. (2018) is
shown by the solid line. TOI-544 b is shown in the black circle, it is within
the top 15 planets for TSM value. Bottom Panel: Same as above but for the
emission spectroscopy metric (ESM). TOI-544 b is within the top 10 planets for
ESM value. Data from exoplanet archive.

##  6 Conclusions

We present the results of an extensive high-precision RV campaign of TOI-544.
We confirm the planet TOI-544 b and derive a mass of 2.89 $\pm$ 0.48 M⊕ which,
combined with the planetary radius of 2.018 $\pm$ 0.076 R⊕ gives a bulk
density of $1.93^{+0.30}_{-0.25}$g cm-3. The density of the planet means it
most likely has either a significant fraction of ice within its composition
(around 30$\%$ by mass) or is composed of an Earth-like rocky core surrounded
by a layer of atmospheric H-He (around 0.5 - 1 $\%$ by mass). TOI-544 b also
sits within the expected location of the small planet radius valley for FGK
stars, although improvements in the radius measurement with additional transit
observations would help confirm this further. The calculated TSM and ESM of
TOI-544 b put it within the top few planets for atmospheric observations with
similar size and temperature, meaning it is an excellent candidate for future
observations with JWST. We additionally confirm the existence of a second,
non-transiting planet within the system, TOI-544 c, with a minimum mass of
21.5 $\pm$ 2.0 M⊕. Both planets have well-characterised masses (uncertainties
of < 20$\%$) and contribute to the small but growing number of small planets
with precisely characterised masses.

## Acknowledgements

This work is done under the framework of the KESPRINT collaboration
(http://kesprint.science). KESPRINT is an international consortium devoted to
the characterization and research of exoplanets discovered with space-based
missions. Based on observations made (a) with ESO-3.6 m telescope at La Silla
Observatory (Chile) under programme IDs 106.21TJ.001, 0103.C-0442, and
60.A-9709; (b) with the Italian Telescopio Nazionale Galileo (TNG) operated on
the island of La Palma in the Spanish Observatorio del Roque de los Muchachos
(ORM) by the INAF-Fundación Galileo Galilei, under programme IDs CAT19A_162
and CAT19A_97. We are extremely grateful to the ESO and TNG staff members for
their unique and superb support during the observations. We are grateful to
Cynthia Ho for discussions on the small planet radius valley and James Owen
for discussion on use of planet composition tracks. HLMO would also like to
thank the Science and Technology Facilities Council (STFC) for funding support
through a PhD studentship. CMP gratefully acknowledge the support of the
Swedish National Space Agency (DNR 65/19). GN thanks for the research funding
from the Ministry of Education and Science programme the "Excellence
Initiative - Research University" conducted at the Centre of Excellence in
Astrophysics and Astrochemistry of the Nicolaus Copernicus University in
Toruń, Poland. RL acknowledges funding from University of La Laguna through
the Margarita Salas Fellowship from the Spanish Ministry of Universities ref.
UNI/551/2021-May 26, and under the EU Next Generation funds. APH and ME
acknowledge the support of DFG Grant HA 3279/12-1 within the DFG Schwerpunkt
SPP 1992, Exploring the Diversity of Extrasolar Planets. HJD acknowledges
support from the Spanish Research Agency of the Ministry of Science and
Innovation (AEI-MICINN) under grant PID2019-107061GB-C66, DOI:
10.13039/501100011033. KWFL was supported by Deutsche Forschungsgemeinschaft
grants RA714/14-1 within the DFG Schwerpunkt SPP 1992, Exploring the Diversity
of Extrasolar Planets. JSJ greatfully acknowledges support by FONDECYT grant
1201371 and from the ANID BASAL project FB210003.JK gratefully acknowledges
the support of the Swedish National Space Agency (SNSA; DNR 2020-00104) and of
the Swedish Research Council (VR: Etableringsbidrag 2017-04945).

## Data Availability

This paper includes raw data collected by the TESS mission, which are publicly
available from the Mikulski Archive for Space Telescopes (MAST,
https://archive.stsci.edu/tess). Some of the observations made with HARPS at
the ESO 3.6m telescope (programme 0103.C-0442(A)) are publicly available at
the ESO archive (http://archive.eso.org/), observations which are not
currently available will become open access within the next year. All
processed data underlying this article (including observations from HARPS-N)
are available in the article and in its online supplementary material.

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##  Appendix A Appendix

Table 3: Radial velocities and spectral activity indicators measured from ESO HARPS spectra with the DRS.  BJDTBD | RV | $\sigma_{\mathrm{RV}}$ | BIS | $\sigma_{\mathrm{BIS}}$ | CCF_FWHM | CCF_CTR | S-index | $\sigma_{\mathrm{S-index}}$ | SNR | $\mathrm{T_{exp}}$
---|---|---|---|---|---|---|---|---|---|---
-2450000 |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{km\,s^{-1}}$) | (%) | — | — | @550nm | (s)
8578.51514 | 8356.129 | 3.507 | 83.258 | 4.959 | 6.599 | 38.785 | 1.2868 | 0.1032 | 31.4 | 1800.0
8579.53150 | 8344.880 | 2.957 | 63.523 | 4.181 | 6.611 | 38.743 | 1.2024 | 0.1062 | 36.0 | 1500.0
9205.63053 | 8364.039 | 2.557 | 49.886 | 3.616 | 6.437 | 39.787 | 1.1723 | 0.0829 | 38.2 | 1800.0
9206.63247 | 8372.868 | 1.775 | 44.582 | 2.510 | 6.460 | 39.642 | 1.1257 | 0.0772 | 52.3 | 1800.0
9207.57568 | 8366.487 | 2.225 | 39.826 | 3.147 | 6.468 | 39.526 | 1.1505 | 0.0879 | 43.3 | 1800.0
9207.66046 | 8365.519 | 1.817 | 47.046 | 2.569 | 6.477 | 39.529 | 1.1575 | 0.0788 | 51.6 | 1800.0
9214.71815 | 8341.790 | 1.856 | 72.093 | 2.624 | 6.436 | 39.454 | 1.0980 | 0.0782 | 50.7 | 2400.0
9215.64475 | 8346.172 | 1.668 | 70.787 | 2.359 | 6.439 | 39.640 | 1.0943 | 0.0728 | 55.6 | 2400.0
9217.68640 | 8348.572 | 1.894 | 51.539 | 2.678 | 6.422 | 39.845 | 1.1191 | 0.0801 | 49.2 | 1800.0
9218.68225 | 8348.251 | 1.689 | 52.661 | 2.388 | 6.429 | 39.817 | 1.1172 | 0.0775 | 54.6 | 1800.0
9219.65704 | 8347.024 | 1.571 | 54.179 | 2.222 | 6.418 | 39.848 | 1.1777 | 0.0761 | 57.9 | 1800.0
9221.60896 | 8348.195 | 1.664 | 65.976 | 2.354 | 6.425 | 39.860 | 1.0609 | 0.0750 | 54.4 | 1800.0
9222.61015 | 8338.229 | 1.580 | 58.300 | 2.234 | 6.412 | 39.892 | 1.0784 | 0.0769 | 57.4 | 1800.0
9223.56895 | 8350.543 | 1.663 | 52.451 | 2.352 | 6.419 | 39.943 | 1.0670 | 0.0743 | 54.6 | 1800.0
9224.66129 | 8347.608 | 1.763 | 40.251 | 2.494 | 6.435 | 39.820 | 1.1253 | 0.0762 | 52.4 | 1800.0
9226.65544 | 8357.176 | 1.858 | 39.046 | 2.627 | 6.461 | 39.638 | 1.2021 | 0.0883 | 50.3 | 1800.0
9227.66789 | 8349.259 | 2.329 | 57.101 | 3.294 | 6.462 | 39.592 | 1.1583 | 0.0762 | 41.7 | 1800.0
9228.64010 | 8342.302 | 2.755 | 65.863 | 3.897 | 6.466 | 39.562 | 1.2222 | 0.0913 | 36.6 | 1800.0
9230.63045 | 8342.530 | 1.693 | 66.324 | 2.394 | 6.450 | 39.652 | 1.2046 | 0.0810 | 55.5 | 1800.0
9231.63611 | 8343.913 | 2.497 | 67.309 | 3.531 | 6.462 | 39.691 | 1.2272 | 0.0950 | 39.9 | 1800.0
9232.63467 | 8348.581 | 1.602 | 61.922 | 2.266 | 6.450 | 39.705 | 1.1484 | 0.0804 | 58.8 | 1800.0
9233.67770 | 8344.253 | 1.809 | 57.304 | 2.558 | 6.461 | 39.736 | 1.2266 | 0.0929 | 53.2 | 1800.0
9242.62501 | 8345.133 | 1.554 | 65.029 | 2.198 | 6.433 | 39.495 | 1.1102 | 0.0790 | 61.1 | 2400.0
9243.56834 | 8352.155 | 1.698 | 52.125 | 2.401 | 6.439 | 39.540 | 1.0417 | 0.0688 | 56.1 | 1800.0
9244.54494 | 8355.228 | 1.906 | 52.779 | 2.696 | 6.439 | 39.538 | 1.1671 | 0.0791 | 50.6 | 1800.0
9244.62785 | 8355.287 | 1.664 | 51.891 | 2.353 | 6.451 | 39.516 | 1.1304 | 0.0708 | 57.5 | 1800.0
9245.60955 | 8352.643 | 2.729 | 45.431 | 3.860 | 6.471 | 39.245 | 1.0851 | 0.0718 | 37.8 | 1800.0
9246.63208 | 8359.426 | 2.024 | 62.498 | 2.863 | 6.471 | 39.388 | 1.1507 | 0.0776 | 48.5 | 1800.0
9247.59527 | 8347.795 | 2.133 | 62.827 | 3.016 | 6.461 | 39.417 | 1.2665 | 0.0839 | 45.9 | 1800.0
9248.61373 | 8350.252 | 3.215 | 79.197 | 4.547 | 6.464 | 39.252 | 1.1072 | 0.0827 | 32.7 | 2700.0
9249.62657 | 8350.233 | 2.185 | 69.844 | 3.089 | 6.457 | 39.648 | 1.2247 | 0.0922 | 45.0 | 2100.0
9250.57953 | 8341.984 | 2.691 | 53.779 | 3.806 | 6.441 | 39.744 | 1.1753 | 0.0875 | 38.0 | 1860.0
9251.59236 | 8358.609 | 2.587 | 49.237 | 3.658 | 6.443 | 39.694 | 1.1218 | 0.0845 | 39.2 | 1800.0
9256.62889 | 8350.779 | 2.075 | 54.235 | 2.934 | 6.440 | 39.724 | 1.1262 | 0.0783 | 47.9 | 1800.0
9257.58116 | 8356.358 | 1.682 | 59.513 | 2.378 | 6.437 | 39.724 | 1.0802 | 0.0770 | 57.5 | 1800.0
9261.63836 | 8352.509 | 3.088 | 58.248 | 4.367 | 6.427 | 39.488 | 1.1786 | 0.0786 | 34.4 | 1800.0
9262.59334 | 8354.885 | 2.797 | 65.234 | 3.955 | 6.445 | 39.466 | 1.1362 | 0.0761 | 37.4 | 1800.0
9264.60899 | 8347.949 | 1.866 | 50.196 | 2.639 | 6.460 | 39.435 | 1.1411 | 0.0750 | 52.9 | 1800.0
9265.56638 | 8353.154 | 1.895 | 63.282 | 2.680 | 6.464 | 39.396 | 1.1437 | 0.0771 | 51.8 | 1800.0
9266.55658 | 8353.514 | 2.217 | 63.301 | 3.135 | 6.460 | 39.334 | 1.0576 | 0.0720 | 45.3 | 1800.0
9267.55362 | 8342.531 | 1.978 | 63.975 | 2.798 | 6.471 | 39.352 | 1.1276 | 0.0758 | 50.0 | 1800.0
9269.57020 | 8348.721 | 2.406 | 54.149 | 3.402 | 6.482 | 39.077 | 1.1085 | 0.0724 | 42.8 | 1800.0
9272.57672 | 8341.935 | 2.061 | 55.460 | 2.915 | 6.464 | 39.208 | 1.0226 | 0.0693 | 48.3 | 1800.0
9273.59284 | 8339.727 | 3.376 | 64.963 | 4.775 | 6.474 | 38.892 | 1.1567 | 0.0749 | 32.3 | 1800.0
9274.58962 | 8341.653 | 2.188 | 60.981 | 3.095 | 6.558 | 38.735 | 1.0481 | 0.0693 | 44.3 | 1800.0
9275.56486 | 8341.271 | 2.301 | 54.047 | 3.254 | 6.551 | 38.866 | 1.0978 | 0.0636 | 42.6 | 1800.0
9276.59246 | 8350.119 | 2.554 | 65.598 | 3.612 | 6.547 | 38.799 | 1.0985 | 0.0702 | 39.4 | 1800.0
9277.57256 | 8351.809 | 2.369 | 55.664 | 3.351 | 6.542 | 38.822 | 1.0771 | 0.0672 | 41.9 | 1800.0
9284.57306 | 8347.527 | 2.402 | 65.270 | 3.397 | 6.564 | 38.916 | 1.1223 | 0.0845 | 41.1 | 1800.0
9287.53172 | 8350.876 | 2.079 | 53.376 | 2.939 | 6.579 | 38.835 | 1.2192 | 0.0940 | 46.7 | 1800.0
9288.53857 | 8351.163 | 2.241 | 61.220 | 3.169 | 6.577 | 38.844 | 1.1957 | 0.0931 | 43.8 | 1800.0
9290.53613 | 8350.902 | 2.390 | 59.356 | 3.379 | 6.584 | 38.662 | 1.1365 | 0.0720 | 41.8 | 1800.0
9291.52201 | 8347.297 | 1.931 | 72.396 | 2.731 | 6.608 | 38.602 | 1.1060 | 0.0749 | 50.0 | 1800.0
9294.53123 | 8341.064 | 4.190 | 65.578 | 5.926 | 6.444 | 39.689 | 1.0859 | 0.0967 | 26.5 | 1800.0
9295.53344 | 8351.079 | 2.135 | 58.338 | 3.020 | 6.529 | 39.035 | 1.0850 | 0.0741 | 45.4 | 2100.0
9296.51173 | 8356.521 | 1.804 | 55.458 | 2.551 | 6.551 | 38.968 | 1.0363 | 0.0798 | 52.7 | 1800.0
9297.52848 | 8354.946 | 1.863 | 60.961 | 2.635 | 6.568 | 38.844 | 1.0801 | 0.0796 | 51.5 | 1800.0
9490.84461 | 8338.060 | 3.149 | 45.485 | 4.454 | 6.488 | 39.551 | 1.0172 | 0.0857 | 27.9 | 2100.0
9491.81716 | 8332.018 | 3.409 | 61.092 | 4.820 | 6.476 | 39.570 | 1.0940 | 0.0832 | 26.1 | 2100.0
9497.84874 | 8362.320 | 2.398 | 35.748 | 3.391 | 6.557 | 39.088 | 1.1233 | 0.0852 | 35.6 | 2100.0
9501.84420 | 8352.119 | 2.784 | 84.093 | 3.937 | 6.621 | 38.682 | 1.2121 | 0.0965 | 32.1 | 2100.0
9502.76982 | 8343.998 | 2.084 | 79.715 | 2.947 | 6.556 | 38.988 | 1.1365 | 0.0821 | 40.0 | 2100.0
9503.79777 | 8346.879 | 3.264 | 81.697 | 4.616 | 6.511 | 39.296 | 1.1667 | 0.0881 | 27.3 | 2100.0
9504.76620 | 8342.562 | 1.941 | 79.832 | 2.746 | 6.504 | 39.304 | 1.1244 | 0.0732 | 41.8 | 2100.0
9505.77836 | 8344.349 | 1.953 | 72.693 | 2.762 | 6.482 | 39.424 | 1.0848 | 0.0721 | 41.3 | 2100.0
9506.76111 | 8351.344 | 1.949 | 53.210 | 2.756 | 6.483 | 39.397 | 1.0358 | 0.0707 | 41.2 | 2100.0
9515.84526 | 8355.254 | 1.994 | 50.484 | 2.820 | 6.425 | 39.651 | 1.2000 | 0.0721 | 41.6 | 2100.0
9520.79982 | 8347.861 | 2.209 | 76.844 | 3.123 | 6.573 | 38.986 | 1.2180 | 0.0886 | 38.5 | 2100.0
9521.83149 | 8335.127 | 2.696 | 69.793 | 3.813 | 6.561 | 39.099 | 1.1404 | 0.0867 | 32.7 | 1800.0
9528.73056 | 8347.198 | 1.615 | 59.482 | 2.284 | 6.496 | 39.430 | 1.0632 | 0.0735 | 49.8 | 2100.0
9529.73908 | 8335.888 | 1.481 | 61.117 | 2.094 | 6.396 | 40.033 | 1.0866 | 0.0733 | 54.6 | 2100.0
9530.74356 | 8330.851 | 1.721 | 69.366 | 2.434 | 6.491 | 39.560 | 0.9850 | 0.0649 | 46.8 | 2100.0
9531.71638 | 8337.784 | 1.558 | 59.485 | 2.203 | 6.391 | 40.061 | 1.0512 | 0.0746 | 51.8 | 2100.0
9543.61494 | 8331.514 | 3.421 | 71.295 | 4.837 | 6.479 | 39.594 | 1.1935 | 0.0879 | 27.3 | 2100.0
9545.68951 | 8350.222 | 2.745 | 61.155 | 3.882 | 6.490 | 39.545 | 1.0379 | 0.0762 | 32.4 | 2100.0
9546.72099 | 8353.870 | 2.170 | 45.757 | 3.069 | 6.483 | 39.584 | 1.1188 | 0.0770 | 39.5 | 2100.0
9547.69656 | 8347.764 | 1.629 | 51.812 | 2.304 | 6.500 | 39.420 | 1.0565 | 0.0713 | 50.4 | 2100.0
9548.80186 | 8350.636 | 1.598 | 58.558 | 2.260 | 6.513 | 39.395 | 1.0743 | 0.0719 | 51.8 | 2100.0
9550.71766 | 8340.930 | 3.918 | 60.738 | 5.540 | 6.514 | 39.461 | 0.9871 | 0.0803 | 25.1 | 1800.0
9560.66602 | 8345.205 | 1.731 | 72.631 | 2.447 | 6.559 | 39.081 | 1.1979 | 0.0851 | 49.3 | 2100.0
9561.67646 | 8343.229 | 2.899 | 77.664 | 4.100 | 6.526 | 39.188 | 1.2474 | 0.0923 | 32.2 | 2100.0
9563.68304 | 8343.661 | 1.762 | 64.758 | 2.492 | 6.507 | 39.222 | 1.1157 | 0.0716 | 48.4 | 2100.0
9564.66694 | 8341.423 | 2.061 | 50.785 | 2.915 | 6.512 | 39.162 | 1.0863 | 0.0707 | 42.4 | 2100.0
9577.74753 | 8349.483 | 1.650 | 60.732 | 2.333 | 6.602 | 38.779 | 1.2547 | 0.0923 | 53.2 | 2100.0
9579.75033 | 8341.714 | 1.925 | 77.425 | 2.722 | 6.552 | 39.066 | 1.2268 | 0.0876 | 45.9 | 2100.0
9581.72990 | 8344.458 | 1.733 | 70.131 | 2.450 | 6.532 | 39.188 | 1.1251 | 0.0757 | 50.2 | 2100.0
9583.70601 | 8341.787 | 1.905 | 53.627 | 2.693 | 6.517 | 39.369 | 1.1079 | 0.0775 | 46.0 | 2100.0
9584.59477 | 8342.207 | 1.477 | 69.259 | 2.088 | 6.428 | 39.868 | 1.1232 | 0.0814 | 58.0 | 2100.0
9584.72285 | 8336.662 | 1.664 | 52.729 | 2.353 | 6.535 | 39.275 | 1.1191 | 0.0759 | 51.8 | 2100.0
9585.58600 | 8345.301 | 1.887 | 63.439 | 2.669 | 6.526 | 39.290 | 1.1174 | 0.0768 | 46.4 | 2100.0
9585.72824 | 8345.218 | 1.779 | 65.661 | 2.516 | 6.531 | 39.298 | 1.0603 | 0.0786 | 49.0 | 2100.0
9586.72537 | 8334.931 | 1.976 | 62.768 | 2.795 | 6.515 | 39.340 | 1.0869 | 0.0794 | 44.6 | 2100.0
9587.72124 | 8337.216 | 2.008 | 62.115 | 2.839 | 6.540 | 39.176 | 1.0358 | 0.0744 | 44.7 | 1800.0
9588.56786 | 8338.807 | 1.667 | 64.078 | 2.358 | 6.489 | 39.473 | 1.0432 | 0.0698 | 51.1 | 2100.0
9588.71681 | 8339.070 | 2.027 | 54.980 | 2.867 | 6.512 | 39.362 | 1.0236 | 0.0754 | 44.1 | 1800.0
9589.71870 | 8340.738 | 2.694 | 60.899 | 3.809 | 6.510 | 39.411 | 0.9633 | 0.0752 | 35.2 | 1808.3
9590.59269 | 8346.742 | 2.500 | 59.582 | 3.535 | 6.511 | 39.275 | 1.0094 | 0.0759 | 37.3 | 2100.0
9591.58055 | 8342.091 | 1.376 | 46.709 | 1.946 | 6.501 | 39.353 | 1.0516 | 0.0709 | 61.4 | 2100.0
9591.73732 | 8342.180 | 3.013 | 57.743 | 4.262 | 6.513 | 39.195 | 1.0267 | 0.0773 | 32.5 | 2100.0
9592.59389 | 8350.098 | 1.444 | 46.301 | 2.043 | 6.516 | 39.230 | 1.0555 | 0.0755 | 58.9 | 2100.0
9592.72732 | 8351.856 | 2.118 | 39.622 | 2.995 | 6.537 | 38.925 | 1.0912 | 0.0807 | 43.3 | 2100.0
9606.67799 | 8347.084 | 2.271 | 59.017 | 3.211 | 6.496 | 39.498 | 1.0736 | 0.0785 | 40.0 | 2100.0
9609.64815 | 8349.831 | 1.469 | 61.393 | 2.077 | 6.504 | 39.329 | 1.0997 | 0.0699 | 58.5 | 2100.0
9610.65838 | 8351.880 | 1.654 | 55.618 | 2.339 | 6.512 | 39.229 | 1.0704 | 0.0676 | 53.1 | 2100.0
9626.55046 | 8336.003 | 1.893 | 65.346 | 2.677 | 6.517 | 39.220 | 1.0483 | 0.0706 | 46.6 | 2100.0
9627.55019 | 8341.542 | 2.081 | 68.305 | 2.943 | 6.497 | 39.226 | 1.0909 | 0.0714 | 42.4 | 2100.0
9628.54583 | 8335.812 | 1.707 | 65.894 | 2.414 | 6.497 | 39.329 | 1.0654 | 0.0683 | 50.0 | 2100.0
9629.56926 | 8337.554 | 1.631 | 59.534 | 2.307 | 6.506 | 39.418 | 1.0918 | 0.0724 | 51.7 | 2100.0
Table 4: Radial velocities and spectral activity indicators measured from ESO HARPS spectra with SERVAL. BJDTBD | RV | $\sigma_{\mathrm{RV}}$ | CRX | $\sigma_{\mathrm{CRX}}$ | dlW | $\sigma_{\mathrm{dlW}}$ | $\mathrm{H_{\alpha}}$ | $\mathrm{\sigma_{H_{\alpha}}}$ | $\mathrm{NaD_{1}}$ | $\mathrm{\sigma_{NaD_{1}}}$ | $\mathrm{NaD_{2}}$ | $\mathrm{\sigma_{NaD_{2}}}$
---|---|---|---|---|---|---|---|---|---|---|---|---
-2457000 |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}\,Np^{-1}}$) |  ($\mathrm{m\,s^{-1}\,Np^{-1}}$) |  ($\mathrm{m^{2}\,s^{-2}}$) |  ($\mathrm{m^{2}\,s^{-2}}$) | — | — | — | — | — | —
8578.51514 | 3.314 | 2.646 | 7.188 | 23.403 | 35.335 | 4.281 | 0.7341 | 0.0025 | 0.2031 | 0.0028 | 0.2338 | 0.0033
8579.53150 | -3.524 | 2.107 | 5.003 | 18.756 | 31.152 | 3.291 | 0.7124 | 0.0021 | 0.2015 | 0.0024 | 0.2206 | 0.0027
9205.63053 | 19.330 | 1.633 | 0.841 | 14.072 | -5.841 | 2.940 | 0.7112 | 0.0019 | 0.1929 | 0.0022 | 0.2275 | 0.0026
9206.63247 | 30.253 | 1.401 | -2.377 | 11.990 | 2.350 | 2.235 | 0.7009 | 0.0013 | 0.1975 | 0.0015 | 0.2307 | 0.0018
9207.57568 | 21.473 | 1.886 | 8.784 | 16.222 | 10.116 | 2.465 | 0.7145 | 0.0017 | 0.1893 | 0.0019 | 0.2268 | 0.0022
9207.66046 | 22.678 | 1.325 | -8.290 | 11.317 | 16.375 | 2.089 | 0.7144 | 0.0014 | 0.1921 | 0.0015 | 0.2363 | 0.0018
9214.71815 | -2.300 | 1.388 | 3.691 | 11.913 | 12.270 | 1.901 | 0.7028 | 0.0014 | 0.1956 | 0.0015 | 0.2348 | 0.0018
9215.64475 | 0.460 | 1.236 | 5.881 | 10.548 | 1.693 | 1.970 | 0.7039 | 0.0013 | 0.1894 | 0.0014 | 0.2300 | 0.0017
9217.68640 | 2.536 | 1.266 | -2.968 | 10.861 | -14.017 | 1.893 | 0.7014 | 0.0014 | 0.1946 | 0.0016 | 0.2305 | 0.0019
9218.68225 | 5.327 | 1.601 | -14.008 | 13.511 | -7.513 | 1.984 | 0.6978 | 0.0013 | 0.1884 | 0.0014 | 0.2252 | 0.0017
9219.65704 | 1.699 | 1.062 | -7.512 | 9.024 | -9.791 | 1.484 | 0.6962 | 0.0012 | 0.1933 | 0.0013 | 0.2302 | 0.0016
9221.60896 | 0.829 | 2.125 | -12.208 | 18.042 | -18.854 | 1.895 | 0.6896 | 0.0013 | 0.1914 | 0.0014 | 0.2276 | 0.0017
9222.61015 | -2.099 | 1.196 | 1.527 | 10.197 | -19.861 | 1.644 | 0.6977 | 0.0012 | 0.1863 | 0.0013 | 0.2256 | 0.0016
9223.56895 | 6.364 | 1.582 | 4.884 | 13.466 | -22.323 | 2.034 | 0.6929 | 0.0013 | 0.1866 | 0.0014 | 0.2269 | 0.0017
9224.66129 | 7.451 | 1.449 | 6.062 | 12.381 | -15.848 | 1.723 | 0.7012 | 0.0013 | 0.1890 | 0.0015 | 0.2307 | 0.0017
9226.65544 | 17.772 | 1.779 | -6.211 | 15.210 | 11.473 | 2.019 | 0.7212 | 0.0014 | 0.1952 | 0.0016 | 0.2345 | 0.0018
9227.66789 | 7.080 | 1.710 | 3.147 | 14.675 | 12.786 | 2.815 | 0.7062 | 0.0017 | 0.1950 | 0.0020 | 0.2324 | 0.0023
9228.64010 | -3.314 | 1.806 | 18.538 | 15.425 | 18.885 | 2.760 | 0.7209 | 0.0020 | 0.1939 | 0.0023 | 0.2341 | 0.0027
9230.63045 | -2.830 | 1.543 | 4.755 | 13.288 | 7.369 | 2.212 | 0.7202 | 0.0013 | 0.1959 | 0.0014 | 0.2325 | 0.0017
9231.63611 | -1.538 | 1.815 | 6.232 | 15.706 | -0.803 | 2.833 | 0.7356 | 0.0019 | 0.1964 | 0.0021 | 0.2331 | 0.0025
9232.63467 | 5.532 | 1.425 | 5.188 | 12.322 | 1.646 | 1.757 | 0.6981 | 0.0012 | 0.1938 | 0.0014 | 0.2319 | 0.0016
9233.67770 | -1.016 | 1.175 | -6.891 | 10.166 | 0.303 | 2.145 | 0.7014 | 0.0014 | 0.1902 | 0.0015 | 0.2328 | 0.0018
9242.62501 | 3.588 | 1.087 | 2.192 | 9.439 | -4.842 | 2.241 | 0.7121 | 0.0012 | 0.1932 | 0.0013 | 0.2341 | 0.0015
9243.56834 | 8.642 | 1.606 | 26.432 | 13.497 | -4.577 | 1.923 | 0.6991 | 0.0013 | 0.1906 | 0.0014 | 0.2315 | 0.0017
9244.54494 | 13.450 | 1.409 | -17.808 | 11.972 | -0.006 | 2.332 | 0.7214 | 0.0015 | 0.2005 | 0.0016 | 0.2361 | 0.0019
9244.62785 | 10.752 | 1.301 | -14.005 | 11.248 | 1.273 | 1.847 | 0.7097 | 0.0013 | 0.1962 | 0.0014 | 0.2314 | 0.0016
9245.60955 | 10.139 | 2.186 | -9.280 | 18.994 | 13.427 | 2.948 | 0.7053 | 0.0020 | 0.1978 | 0.0023 | 0.2339 | 0.0027
9246.63208 | 17.673 | 1.137 | 16.203 | 9.661 | 14.151 | 2.489 | 0.7157 | 0.0015 | 0.1982 | 0.0017 | 0.2332 | 0.0020
9247.59527 | 6.405 | 1.482 | -1.602 | 12.801 | 9.191 | 2.329 | 0.7364 | 0.0016 | 0.2015 | 0.0018 | 0.2330 | 0.0021
9248.61373 | 5.742 | 2.048 | -0.201 | 17.859 | 12.860 | 3.295 | 0.7138 | 0.0023 | 0.1906 | 0.0027 | 0.2317 | 0.0032
9249.62657 | 6.034 | 1.378 | -0.560 | 11.921 | 0.286 | 2.392 | 0.7383 | 0.0016 | 0.2025 | 0.0018 | 0.2321 | 0.0022
9250.57953 | 3.582 | 2.060 | -23.217 | 17.728 | -4.696 | 2.810 | 0.7061 | 0.0019 | 0.1939 | 0.0023 | 0.2359 | 0.0027
9251.59236 | 17.019 | 1.832 | 30.776 | 15.390 | -0.521 | 2.707 | 0.7061 | 0.0019 | 0.1929 | 0.0022 | 0.2342 | 0.0026
9256.62889 | 11.283 | 1.565 | 14.141 | 13.478 | -7.906 | 2.410 | 0.6910 | 0.0015 | 0.1954 | 0.0017 | 0.2228 | 0.0020
9257.58116 | 10.510 | 1.192 | -6.135 | 10.332 | -8.304 | 2.014 | 0.6911 | 0.0013 | 0.1930 | 0.0014 | 0.2224 | 0.0016
9261.63836 | 11.122 | 2.025 | -1.938 | 17.657 | -7.216 | 3.008 | 0.7151 | 0.0022 | 0.1968 | 0.0026 | 0.2273 | 0.0030
9262.59334 | 8.702 | 1.855 | 2.137 | 16.168 | -0.381 | 3.071 | 0.7059 | 0.0020 | 0.1936 | 0.0023 | 0.2279 | 0.0027
9264.60899 | 8.544 | 1.535 | 24.296 | 12.972 | 7.179 | 1.991 | 0.7153 | 0.0014 | 0.1953 | 0.0015 | 0.2340 | 0.0018
9265.56638 | 10.436 | 1.436 | 13.795 | 12.338 | 12.759 | 2.045 | 0.7138 | 0.0014 | 0.1938 | 0.0015 | 0.2300 | 0.0018
9266.55658 | 6.238 | 1.619 | -13.439 | 13.935 | 18.724 | 2.392 | 0.7080 | 0.0016 | 0.1977 | 0.0018 | 0.2269 | 0.0022
9267.55362 | -2.686 | 1.776 | -27.560 | 14.919 | 15.518 | 2.293 | 0.7171 | 0.0015 | 0.1992 | 0.0016 | 0.2336 | 0.0019
9269.57020 | 3.537 | 2.133 | -16.135 | 18.425 | 25.650 | 2.512 | 0.7134 | 0.0018 | 0.1964 | 0.0020 | 0.2314 | 0.0023
9272.57672 | -3.465 | 1.668 | -22.951 | 13.976 | 18.079 | 2.304 | 0.7075 | 0.0015 | 0.1991 | 0.0016 | 0.2266 | 0.0019
9273.59284 | -6.387 | 2.303 | 24.903 | 19.605 | 20.048 | 3.875 | 0.7071 | 0.0023 | 0.1986 | 0.0026 | 0.2332 | 0.0031
9274.58962 | -3.164 | 1.817 | 0.317 | 15.364 | 9.685 | 2.157 | 0.7053 | 0.0016 | 0.1987 | 0.0017 | 0.2326 | 0.0020
9275.56486 | -1.966 | 1.875 | -9.177 | 15.842 | -0.754 | 2.498 | 0.6933 | 0.0017 | 0.1970 | 0.0018 | 0.2286 | 0.0021
9276.59246 | 4.548 | 1.946 | -35.093 | 15.930 | 4.004 | 2.586 | 0.6922 | 0.0018 | 0.1961 | 0.0020 | 0.2279 | 0.0023
9277.57256 | 10.177 | 1.750 | 9.433 | 14.785 | -2.175 | 2.527 | 0.6840 | 0.0017 | 0.1937 | 0.0018 | 0.2230 | 0.0021
9284.57306 | 1.047 | 1.642 | 16.939 | 13.749 | 0.095 | 2.474 | 0.7050 | 0.0018 | 0.1940 | 0.0018 | 0.2272 | 0.0022
9287.53172 | 4.121 | 1.584 | -8.654 | 13.383 | 1.609 | 2.558 | 0.7292 | 0.0016 | 0.2056 | 0.0016 | 0.2212 | 0.0019
9288.53857 | 5.642 | 1.954 | 18.548 | 16.385 | 1.551 | 2.570 | 0.7206 | 0.0016 | 0.2000 | 0.0017 | 0.2238 | 0.0020
9290.53613 | 4.488 | 2.091 | 5.101 | 17.695 | 9.942 | 3.013 | 0.7193 | 0.0017 | 0.1953 | 0.0018 | 0.2269 | 0.0022
9291.52201 | -0.605 | 1.661 | -9.828 | 14.060 | 11.634 | 2.126 | 0.7143 | 0.0014 | 0.1989 | 0.0015 | 0.2301 | 0.0017
9294.53123 | 1.601 | 2.727 | -40.121 | 22.837 | -3.797 | 4.585 | 0.6991 | 0.0028 | 0.1995 | 0.0033 | 0.2189 | 0.0038
9295.53344 | 8.142 | 1.649 | -20.444 | 13.710 | -12.304 | 2.553 | 0.7021 | 0.0016 | 0.1954 | 0.0017 | 0.2310 | 0.0020
9296.51173 | 11.657 | 1.445 | -22.882 | 11.932 | -13.443 | 1.922 | 0.6985 | 0.0014 | 0.1948 | 0.0014 | 0.2266 | 0.0016
9297.52848 | 9.661 | 1.454 | -10.595 | 12.253 | -6.369 | 2.075 | 0.6981 | 0.0014 | 0.1951 | 0.0014 | 0.2272 | 0.0017
9490.84461 | -2.290 | 2.154 | 33.892 | 17.457 | -21.064 | 3.368 | 0.7007 | 0.0023 | 0.1891 | 0.0025 | 0.2304 | 0.0030
9491.81716 | -4.832 | 2.421 | 4.996 | 20.181 | -19.475 | 4.313 | 0.6948 | 0.0025 | 0.1988 | 0.0028 | 0.2296 | 0.0032
9497.84874 | 22.459 | 1.752 | 13.662 | 14.434 | 13.823 | 2.668 | 0.7109 | 0.0018 | 0.1964 | 0.0019 | 0.2322 | 0.0022
9501.84420 | 8.047 | 2.028 | 24.702 | 16.635 | 37.057 | 3.449 | 0.7219 | 0.0019 | 0.1972 | 0.0020 | 0.2355 | 0.0024
9502.76982 | -3.185 | 1.796 | -32.747 | 14.310 | 23.360 | 2.633 | 0.7118 | 0.0016 | 0.1972 | 0.0017 | 0.2316 | 0.0019
9503.79777 | 4.809 | 2.138 | 11.023 | 17.806 | 10.415 | 3.027 | 0.7062 | 0.0024 | 0.2065 | 0.0027 | 0.2353 | 0.0031
9504.76620 | -3.238 | 1.503 | -10.680 | 12.362 | -5.918 | 2.392 | 0.6921 | 0.0015 | 0.1964 | 0.0016 | 0.2336 | 0.0018
9505.77836 | 0.993 | 1.285 | -5.680 | 10.560 | -17.739 | 2.390 | 0.6987 | 0.0015 | 0.1987 | 0.0016 | 0.2299 | 0.0019
9506.76111 | 12.243 | 1.535 | -6.112 | 12.684 | -16.992 | 2.887 | 0.6943 | 0.0015 | 0.2033 | 0.0016 | 0.2361 | 0.0019
9515.84526 | 16.939 | 1.208 | 16.330 | 9.739 | -2.610 | 2.311 | 0.7176 | 0.0015 | 0.1994 | 0.0016 | 0.2316 | 0.0019
9520.79982 | 5.008 | 1.826 | 12.209 | 15.052 | 25.818 | 2.849 | 0.7230 | 0.0017 | 0.2060 | 0.0018 | 0.2403 | 0.0021
9521.83149 | -10.771 | 2.322 | -37.469 | 18.682 | 17.222 | 2.716 | 0.7106 | 0.0019 | 0.2003 | 0.0021 | 0.2418 | 0.0025
9528.73056 | 3.727 | 1.479 | 8.291 | 12.139 | -28.136 | 1.918 | 0.6909 | 0.0013 | 0.1893 | 0.0013 | 0.2322 | 0.0015
9529.73908 | -4.702 | 1.331 | 11.455 | 10.808 | -26.842 | 1.738 | 0.6985 | 0.0012 | 0.1952 | 0.0012 | 0.2345 | 0.0014
9530.74356 | -12.815 | 1.664 | 10.917 | 13.606 | -31.815 | 2.029 | 0.6812 | 0.0014 | 0.1909 | 0.0014 | 0.2277 | 0.0017
9531.71638 | -4.201 | 1.377 | 3.217 | 11.237 | -36.545 | 2.072 | 0.6903 | 0.0013 | 0.1928 | 0.0013 | 0.2329 | 0.0015
9543.61494 | -6.166 | 2.422 | 59.701 | 18.646 | -21.412 | 3.220 | 0.7030 | 0.0024 | 0.2082 | 0.0028 | 0.2456 | 0.0033
9545.68951 | 5.959 | 1.777 | 6.249 | 14.656 | -32.790 | 3.281 | 0.6925 | 0.0020 | 0.2035 | 0.0023 | 0.2432 | 0.0026
9546.72099 | 11.619 | 2.060 | -2.243 | 16.991 | -27.229 | 2.270 | 0.6982 | 0.0017 | 0.1971 | 0.0018 | 0.2307 | 0.0021
9547.69656 | 4.676 | 1.303 | 16.171 | 10.514 | -23.106 | 1.724 | 0.6922 | 0.0013 | 0.1861 | 0.0013 | 0.2284 | 0.0015
9548.80186 | 7.443 | 1.230 | -3.741 | 10.154 | -24.050 | 1.842 | 0.6904 | 0.0012 | 0.1894 | 0.0013 | 0.2304 | 0.0015
9550.71766 | 1.273 | 2.193 | 42.102 | 17.505 | -28.439 | 4.311 | 0.6942 | 0.0025 | 0.1916 | 0.0030 | 0.2340 | 0.0035
9560.66602 | 2.381 | 1.500 | -10.208 | 12.287 | 12.826 | 2.204 | 0.7195 | 0.0014 | 0.1971 | 0.0014 | 0.2369 | 0.0016
9561.67646 | -1.304 | 2.013 | 22.888 | 16.418 | 6.392 | 2.986 | 0.7235 | 0.0021 | 0.2000 | 0.0023 | 0.2429 | 0.0027
9563.68304 | -0.463 | 1.711 | 6.879 | 14.044 | -9.544 | 2.068 | 0.6959 | 0.0014 | 0.1936 | 0.0014 | 0.2335 | 0.0017
9564.66694 | 0.047 | 1.430 | -13.434 | 11.712 | -12.485 | 2.830 | 0.6990 | 0.0016 | 0.1963 | 0.0016 | 0.2301 | 0.0019
9577.74753 | 3.277 | 1.201 | 6.336 | 9.945 | 26.090 | 2.350 | 0.7263 | 0.0012 | 0.1999 | 0.0013 | 0.2371 | 0.0015
9579.75033 | -3.345 | 1.610 | 12.981 | 13.271 | 6.119 | 2.132 | 0.7142 | 0.0015 | 0.1954 | 0.0015 | 0.2338 | 0.0018
9581.72990 | 1.812 | 1.490 | -0.810 | 12.353 | -13.465 | 1.732 | 0.6941 | 0.0013 | 0.1904 | 0.0014 | 0.2279 | 0.0016
9583.70601 | -1.028 | 1.692 | 11.227 | 13.968 | -15.576 | 2.268 | 0.7006 | 0.0015 | 0.1884 | 0.0015 | 0.2277 | 0.0018
9584.59477 | 0.008 | 1.033 | -3.569 | 8.486 | -15.454 | 1.444 | 0.7006 | 0.0012 | 0.1909 | 0.0012 | 0.2279 | 0.0014
9584.72285 | -4.682 | 1.361 | -3.024 | 11.281 | -17.919 | 1.783 | 0.6973 | 0.0013 | 0.1931 | 0.0013 | 0.2328 | 0.0016
9585.58600 | 1.041 | 1.754 | -27.342 | 14.008 | -20.352 | 1.977 | 0.6970 | 0.0014 | 0.1949 | 0.0015 | 0.2308 | 0.0018
9585.72824 | -0.146 | 1.393 | 20.617 | 11.233 | -17.439 | 1.921 | 0.6921 | 0.0013 | 0.1890 | 0.0014 | 0.2291 | 0.0016
9586.72537 | -6.143 | 1.475 | -10.772 | 12.176 | -19.836 | 2.562 | 0.7005 | 0.0015 | 0.1908 | 0.0016 | 0.2312 | 0.0019
9587.72124 | -4.453 | 1.865 | 18.612 | 15.302 | -27.335 | 2.209 | 0.6847 | 0.0014 | 0.1888 | 0.0015 | 0.2312 | 0.0018
9588.56786 | -2.451 | 1.148 | -12.465 | 9.291 | -25.948 | 2.003 | 0.6910 | 0.0013 | 0.1881 | 0.0014 | 0.2277 | 0.0016
9588.71681 | -3.712 | 1.334 | -10.911 | 11.008 | -31.693 | 2.344 | 0.6813 | 0.0015 | 0.1878 | 0.0016 | 0.2243 | 0.0019
9589.71870 | -2.590 | 2.044 | 8.400 | 17.089 | -36.429 | 3.760 | 0.6815 | 0.0019 | 0.1787 | 0.0020 | 0.2243 | 0.0024
9590.59269 | 4.422 | 1.798 | -20.284 | 14.754 | -29.670 | 3.155 | 0.6840 | 0.0017 | 0.1836 | 0.0019 | 0.2246 | 0.0022
9591.58055 | 0.006 | 1.174 | -9.562 | 9.629 | -29.301 | 1.762 | 0.6913 | 0.0011 | 0.1867 | 0.0011 | 0.2222 | 0.0013
9591.73732 | 4.547 | 2.133 | 22.212 | 17.608 | -30.242 | 3.604 | 0.6874 | 0.0020 | 0.1875 | 0.0022 | 0.2235 | 0.0026
9592.59389 | 9.386 | 1.463 | 7.035 | 12.076 | -18.772 | 1.752 | 0.6918 | 0.0011 | 0.1910 | 0.0012 | 0.2286 | 0.0014
9592.72732 | 10.225 | 1.678 | 10.846 | 13.937 | -9.414 | 2.372 | 0.6841 | 0.0015 | 0.1890 | 0.0016 | 0.2223 | 0.0019
9606.67799 | 6.444 | 2.122 | -10.376 | 17.547 | -32.596 | 2.702 | 0.6915 | 0.0017 | 0.1955 | 0.0018 | 0.2235 | 0.0021
9609.64815 | 4.146 | 1.054 | 5.670 | 8.725 | -33.754 | 2.017 | 0.7047 | 0.0012 | 0.1931 | 0.0012 | 0.2287 | 0.0014
9610.65838 | 7.557 | 1.513 | 0.429 | 12.590 | -31.746 | 2.437 | 0.6866 | 0.0013 | 0.1934 | 0.0013 | 0.2289 | 0.0015
9626.55046 | -5.048 | 1.397 | 7.088 | 11.554 | -14.205 | 1.934 | 0.6928 | 0.0014 | 0.1924 | 0.0015 | 0.2255 | 0.0018
9627.55019 | -1.970 | 1.779 | 35.477 | 14.004 | -10.824 | 2.848 | 0.6994 | 0.0016 | 0.1948 | 0.0017 | 0.2267 | 0.0020
9628.54583 | -6.426 | 1.388 | -25.944 | 10.957 | -22.279 | 2.089 | 0.6869 | 0.0013 | 0.1942 | 0.0014 | 0.2230 | 0.0016
9629.56926 | -4.493 | 1.544 | -19.566 | 12.608 | -29.905 | 2.234 | 0.6905 | 0.0013 | 0.1895 | 0.0013 | 0.2279 | 0.0016
Table 5: Radial velocities and spectral activity indicators measured from TNG/HARPS-N with the DRS.  BJDTBD | RV | $\sigma_{\mathrm{RV}}$ | BIS | $\sigma_{\mathrm{BIS}}$ | CCF_FWHM | CCF_CTR | S-index | $\sigma_{\mathrm{S-index}}$ | SNR | $\mathrm{T_{exp}}$
---|---|---|---|---|---|---|---|---|---|---
-2450000 |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{km\,s^{-1}}$) | (%) | — | — | @550nm | (s)
1578.35923 | 8351.931 | 1.921 | 69.592 | 2.717 | 6.510 | 39.407 | 1.271 | 0.018 | 51.6 | 2400.0
1579.35283 | 8337.606 | 4.798 | 50.801 | 6.786 | 6.495 | 39.360 | 1.099 | 0.055 | 25.1 | 1229.7
1732.71766 | 8367.753 | 5.220 | 48.690 | 7.382 | 6.491 | 39.276 | 1.342 | 0.065 | 23.1 | 1800.0
1732.74144 | 8359.114 | 6.373 | 48.581 | 9.012 | 6.514 | 39.264 | 1.285 | 0.082 | 19.8 | 1800.0
1752.68369 | 8369.174 | 1.660 | 56.420 | 2.348 | 6.483 | 39.660 | 1.151 | 0.014 | 57.7 | 1800.0
1752.70581 | 8366.539 | 1.376 | 59.965 | 1.947 | 6.483 | 39.669 | 1.167 | 0.011 | 67.4 | 1800.0
1753.70744 | 8351.294 | 2.074 | 65.679 | 2.934 | 6.484 | 39.616 | 1.189 | 0.019 | 47.3 | 1800.0
1754.71549 | 8355.059 | 1.704 | 63.221 | 2.410 | 6.486 | 39.663 | 1.221 | 0.014 | 55.7 | 1800.0
2204.51620 | 8354.052 | 2.340 | 41.932 | 3.310 | 6.427 | 39.997 | 1.083 | 0.020 | 42.4 | 1800.0
2204.65656 | 8355.979 | 1.848 | 47.025 | 2.613 | 6.422 | 40.037 | 1.108 | 0.015 | 52.0 | 1800.0
2205.54599 | 8361.889 | 1.531 | 38.587 | 2.165 | 6.431 | 40.037 | 1.107 | 0.011 | 60.1 | 1500.0
2205.63930 | 8359.041 | 1.396 | 50.983 | 1.975 | 6.437 | 40.001 | 1.122 | 0.010 | 65.9 | 1500.0
2206.47971 | 8367.418 | 1.811 | 29.132 | 2.561 | 6.457 | 39.875 | 1.079 | 0.014 | 52.3 | 1800.0
2206.65731 | 8370.507 | 1.864 | 36.226 | 2.637 | 6.449 | 39.874 | 1.090 | 0.016 | 51.4 | 2400.0
Table 6: Radial velocities and spectral activity indicators measured from TNG/HARPS-N spectra with SERVAL. BJDTBD | RV | $\sigma_{\mathrm{RV}}$ | CRX | $\sigma_{\mathrm{CRX}}$ | dlW | $\sigma_{\mathrm{dlW}}$ | $\mathrm{H_{\alpha}}$ | $\mathrm{\sigma_{H_{\alpha}}}$ | $\mathrm{NaD_{1}}$ | $\mathrm{\sigma_{NaD_{1}}}$ | $\mathrm{NaD_{2}}$ | $\mathrm{\sigma_{NaD_{2}}}$
---|---|---|---|---|---|---|---|---|---|---|---|---
-2457000 |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}}$) |  ($\mathrm{m\,s^{-1}\,Np^{-1}}$) |  ($\mathrm{m\,s^{-1}\,Np^{-1}}$) |  ($\mathrm{m^{2}\,s^{-2}}$) |  ($\mathrm{m^{2}\,s^{-2}}$) | — | — | — | — | — | —
1578.35923 | -15.286 | 1.237 | -14.213 | 10.557 | -10.331 | 3.298 | 0.7467 | 0.0016 | 0.2001 | 0.0016 | 0.2387 | 0.0018
1579.35283 | -18.902 | 2.324 | -4.860 | 20.180 | -2.017 | 4.584 | 0.7344 | 0.0032 | 0.2005 | 0.0037 | 0.2290 | 0.0042
1732.71766 | 6.165 | 2.455 | -35.894 | 20.131 | -0.417 | 5.610 | 0.7466 | 0.0032 | 0.2099 | 0.0040 | 0.2440 | 0.0044
1732.74144 | -2.947 | 3.332 | -23.484 | 28.098 | -6.190 | 5.519 | 0.7495 | 0.0037 | 0.2147 | 0.0049 | 0.2468 | 0.0053
1752.68369 | 0.429 | 1.041 | 1.003 | 8.720 | -24.896 | 2.236 | 0.7273 | 0.0014 | 0.1977 | 0.0013 | 0.2326 | 0.0015
1752.70581 | 0.065 | 0.862 | 9.871 | 7.201 | -27.621 | 2.072 | 0.7270 | 0.0012 | 0.1979 | 0.0011 | 0.2295 | 0.0013
1753.70744 | -15.327 | 1.222 | -4.919 | 10.278 | -22.886 | 2.317 | 0.7299 | 0.0017 | 0.2032 | 0.0017 | 0.2292 | 0.0019
1754.71549 | -11.854 | 1.119 | -11.948 | 9.137 | -31.619 | 2.284 | 0.7376 | 0.0014 | 0.2011 | 0.0014 | 0.2295 | 0.0015
2204.51620 | -11.496 | 1.627 | 30.076 | 13.728 | -57.931 | 2.722 | 0.7030 | 0.0020 | 0.2116 | 0.0020 | 0.2387 | 0.0023
2204.65656 | -6.948 | 1.119 | -8.303 | 9.456 | -62.660 | 2.495 | 0.7134 | 0.0015 | 0.2055 | 0.0015 | 0.2371 | 0.0017
2205.54599 | -1.871 | 1.080 | 13.321 | 9.308 | -58.627 | 2.216 | 0.7165 | 0.0015 | 0.2010 | 0.0013 | 0.2297 | 0.0015
2205.63930 | -4.398 | 0.989 | 4.622 | 8.335 | -58.836 | 1.951 | 0.7131 | 0.0012 | 0.1977 | 0.0011 | 0.2306 | 0.0013
2206.47971 | 1.664 | 1.237 | -2.439 | 11.255 | -47.854 | 2.351 | 0.7093 | 0.0019 | 0.2059 | 0.0017 | 0.2334 | 0.0019
2206.65731 | 2.199 | 1.208 | -11.085 | 9.886 | -44.826 | 2.328 | 0.7147 | 0.0014 | 0.2127 | 0.0015 | 0.2399 | 0.0017

Table 7: Comparison of all RV fitting models used, all results are within 1-sigma. Toolkit | GP Kernel | Activity Indicator | Number of planets | Eccentricity | Kb [m/s]
---|---|---|---|---|---
RadVel | No GP | - | 2 | Circular |  $2.77^{+0.81}_{-0.82}$1
RadVel | Celerite Quasi-Periodic | - | 1 | Circular | 2.61 $\pm$ 0.49
RadVel | Celerite Quasi-Periodic | - | 2 | Circular | $2.59^{+0.49}_{-0.48}$
RadVel | Celerite Quasi-Periodic | - | 2 | Both eccentric | $3.22^{+1.9}_{-0.69}$
RadVel | Celerite Quasi-Periodic | - | 3 | Circular | 2.60 $\pm$ 0.50
RadVel HARPS only | Celerite Quasi-Periodic | - | 2 | Circular | 2.83 $\pm$ 0.53
RadVel | Square Exponential | - | 2 | Circular | 2.70 $\pm$ 0.40
RadVel | Square Exponential | - | 2 | Outer planet eccentric | $2.69^{+0.37}_{-0.36}$
RadVel | Square Exponential | - | 3 | Circular | $2.67^{+0.39}_{-0.40}$
Pyaneti multi-dimensional | Quasi-Periodic | S-index | 2 | Circular | 2.07 $\pm$ 0.39
Pyaneti multi-dimensional | Quasi-Periodic | S-index | 2 | Both eccentric | $2.66^{+0.44}_{-0.41}$
Pyaneti multi-dimensional | Quasi-Periodic | S-index | 2 | Outer planet eccentric | 2.17 $\pm$ 0.36
Pyaneti multi-dimensional | Quasi-Periodic | Contrast | 2 | Both eccentric | $2.47^{+0.41}_{-0.40}$
Pyaneti multi-dimensional | Quasi-Periodic | FWHM | 2 | Both eccentric | $2.48^{+0.38}_{-0.37}$
Pyaneti multi-dimensional | Quasi-Periodic | S-index & FWHM | 2 | Both eccentric | $2.56^{+0.43}_{-0.39}$
Pyaneti multi-dimensional | Quasi-Periodic | S-index & Contrast | 2 | Both eccentric | $2.59^{+0.42}_{-0.40}$
Pyaneti multi-dimensional | Quasi-Periodic | FWHM & Contrast | 2 | Both eccentric | $2.55^{+0.46}_{-0.43}$
Pyaneti RV only | Quasi-Periodic | - | 2 | Both eccentric | $2.52^{+0.40}_{-0.38}$
Pyaneti RV only | Quasi-Periodic | - | 2 | Outer planet eccentric | 2.12 $\pm$ 0.35
Pyaneti Joint Model | Quasi-Periodic | S-index | 2 | Both eccentric | 2.58 $\pm$ 0.38
Table 8: Priors used for the RV fitting for each parameter. $\mathcal{U}$[a,b] refers to uniform priors in the range a – b, $\mathcal{N}$[a,b] refers to a Gaussian prior with mean a and width b, and $\mathcal{F}$[a,b] is a fixed parameter at value a. Fitted Parameter | Prior
---|---
Planet Parameters |
Orbital Period, $P_{b}$ [days] | $\mathcal{N}[1.5484,0.0000]$
Time of Conjunction, $T\rm{conj}_{b}$ [JD] | $\mathcal{N}[2459199.0314,0.0007]$
RV Amplitude, $K_{b}$ [km s-1] | $\mathcal{U}[0.0000,0.0500]$
$ew1_{b}$, $\sqrt{e_{b}}\sin\omega_{b}$ | $\mathcal{F}[0.0000,0.0000]$
$ew2_{b}$, $\sqrt{e_{b}}\cos\omega_{b}$ | $\mathcal{F}[0.0000,0.0000]$
Orbital Period, $P_{c}$ [days] | $\mathcal{U}[49.0000,52.0000]$
Time of Conjunction, $T\rm{conj}_{c}$ [JD] | $\mathcal{U}[2459205.0000,2459225.0000]$
RV Amplitude, $K_{c}$ [km s-1 ] | $\mathcal{U}[0.0000,0.0500]$
$ew1_{c}$, $\sqrt{e_{c}}\sin\omega_{c}$ | $\mathcal{U}[-1.0000,1.0000]$
$ew2_{c}$, $\sqrt{e_{c}}\cos\omega_{c}$ | $\mathcal{U}[-1.0000,1.0000]$
Other Parameters |
Systemic Velocity HARPS-N [kms-1] | $\mathcal{U}[-0.5189,0.5062]$
Systemic Velocity HARPS [kms-1] | $\mathcal{U}[-0.5128,0.5304]$
GP Hyperparameters |
$A0$ | $\mathcal{U}[0.0,0.05]$
$A1$ | $\mathcal{U}[0.0,0.1]$
$A2$ | $\mathcal{U}[0.,0.25]$
$A3$ | $\equiv 0$
$\lambda_{e}$ [days] | $\mathcal{U}[1,500]$
$\lambda_{p}$ [days] | $\mathcal{U}[0.1,3.0]$
Rotation Period, PGP [days] | $\mathcal{U}[15.0,25.0]$
Table 9: Priors used for the transit fitting for each parameter. $\mathcal{U}$[a,b] refers to uniform priors in the range a – b, $\mathcal{N}$[a,b] refers to a Gaussian prior with mean a and width b, and $\mathcal{F}$[a,b] is a fixed parameter at value a. Fitted Parameter | Prior
---|---
Planet Parameters |
Orbital Period, $P_{b}$ [days] | $\mathcal{U}[1.547352,1.549352]$
Time of Conjunction, $T\rm{conj}_{b}$ [JD] | $\mathcal{U}[2459199.02185,2459199.041850]$
$R_{p}/R_{\star}$ | $\mathcal{U}[0.023699,0.039530]$
$b$ | $\mathcal{U}[0,1]$
Other Parameters |
$M_{\star}$ [$M_{\odot}$] | $\mathcal{N}[0.630,0.018]$
$R_{\star}$ [$R_{\odot}$] | $\mathcal{N}[0.624,0.013]$
$u_{1}$ | $\mathcal{N}[0.436,0.202]$
$u_{2}$ | $\mathcal{N}[0.217,0.155]$
Noise Model Parameters |
$\rho_{\mathrm{GP}}$ [days] | $\mathcal{N}[10.0,5.0]$
$\sigma_{\mathrm{GP}}$ [ppt] | $\mathcal{N}[1.0,0.5]$
$\log\sigma_{\mathrm{S6}}$ [ppt] | $\mathcal{N}[-0.614,10]$
$\log\sigma_{\mathrm{S32}}$ [ppt] | $\mathcal{N}[-0.684,10]$