∎

11institutetext: Danielski C.22institutetext: UCL Centre for Space
Exochemistry Data, Atlas Building, Fermi Avenue, Harwell Campus, Didcot, OX11
0QR (UK)
_Present address:_ Instituto de Astrofísica de Andalucía (IAA-CSIC), Glorieta
de la Astronomía s/n, 18008 Granada, Spain
22email<EMAIL_ADDRESS>33institutetext: Brucalassi A., Casali G., Magrini
L., Rainer M., Sacco G., Sanna N., Tsantaki M., Van der Swaelmen M.
44institutetext: INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5,
50125 Firenze, Italy 55institutetext: Casali G., 66institutetext: Dipartimento
di Fisica e Astronomia Augusto Righi, Universitá degli Studi di Bologna, Via
Gobetti 93/2, I-40129 Bologna, Italy 77institutetext: Benatti S., Micela G.
88institutetext: INAF - Osservatorio Astronomico di Palermo, Piazza del
Parlamento 1, 90134 Palermo, Italy 99institutetext: Campante T., Delgado-Mena
E., Adibekyan V., Bossini D., Sousa S. 1010institutetext: Instituto de
Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das
Estrelas, 4150-762 Porto, Portugal 1111institutetext: Campante T., Adibekyan
V. 1212institutetext: Departamento de Física e Astronomia, Faculdade de
Ciências da Universidade do Porto, Rua do Campo Alegre, s/n, 4169-007 Porto,
Portugal 1313institutetext: Biazzo K. 1414institutetext: INAF - Osservatorio
Astronomico di Roma Via di Frascati, 33, I-00044, Monte Porzio Catone, Italy
1515institutetext: Bruno G.1616institutetext: INAF - Osservatorio Astrofisico
di Catania, Via S. Sofia 78, 95123 Catania, Italy 1717institutetext: Kabath P.
1818institutetext: Astronomical Institute, Czech Academy of Science,
Fric̆ova 298 251 65 Ondr̆ejov C̆eská republika 1919institutetext: Morello
G.2020institutetext: AIM, CEA, CNRS, Université Paris-Saclay, Université Paris
Diderot, Sorbonne Paris Cité, F-91191 Gif-sur-Yvette, France
2121institutetext: Palladino P. 2222institutetext: Universita’ degli Studi di
Palermo, Dipartimento di Fisica e Chimica Emilio Segré, Viale delle Scienze,
Ed. 17, 90128 Palermo, Italy 2323institutetext: Sarkar S.2424institutetext:
School of Physics and Astronomy, Cardiff University, The Parade, Cardiff, CF24
3AA, UK 2525institutetext: Turrini D.2626institutetext: Institute of Space
Astrophysics and Planetology INAF-IAPS, Via Fosso del Cavaliere 100, Rome,
Italy
INAF - Osservatorio Astrofisico di Torino, Via Osservatorio 20, Pino Torinese
I-10025, Italy

# The homogeneous characterisation of Ariel host stars

Camilla Danielski  Anna Brucalassi  Serena Benatti  Tiago Campante  Elisa
Delgado-Mena  Monica Rainer  Germano Sacco  Vardan Adibekyan  Katia Biazzo
Diego Bossini  Giovanni Bruno  Giada Casali  Petr Kabath  Laura Magrini  Giusi
Micela  Giuseppe Morello  Pietro Palladino  Nicoletta Sanna  Subhajit Sarkar
Sérgio Sousa  Maria Tsantaki  Diego Turrini  Mathieu Van der Swaelmen

(Received: date / Accepted: date)

###### Abstract

The Ariel mission will characterise the chemical and thermal properties of the
atmospheres of about a thousand exoplanets transiting their host star(s). The
observation of such a large sample of planets will allow to deepen our
understanding of planetary and atmospheric formation at the early stages,
providing a truly representative picture of the chemical nature of exoplanets,
and relating this directly to the type and chemical environment of the host
star. Hence, the accurate and precise determination of the host star
fundamental properties is essential to Ariel for drawing a comprehensive
picture of the underlying essence of these planetary systems. We present here
a structured approach for the characterisation of Ariel stars that accounts
for the concepts of homogeneity and coherence among a large set of stellar
parameters. We present here the studies and benchmark analyses we have been
performing to determine robust stellar fundamental parameters, elemental
abundances, activity indices, and stellar ages. In particular, we present
results for the homogeneous estimation of the activity indices $S$ and
$\log(R^{\prime}_{\rm HK})$ , and preliminary results for elemental abundances
of Na, Al, Mg, Si, C, N. In addition, we analyse the variation of a planetary
spectrum, obtained with Ariel, as a function of the uncertainty on the stellar
effective temperature. Finally, we present our observational campaign for
precisely and homogeneously characterising all Ariel stars in order to perform
a meaningful choice of final targets before the mission launch.

###### Keywords:

Stars: abundances Stars: activity Stars: fundamental parameters Stars: general
planetary systems Planets and satellites: atmospheres

††journal: Experimental Astronomy

##  1 Introduction

The Ariel M4 space mission Tinetti2018 , recently adopted by ESA whose launch
is foreseen for 2029, has the objective to observe the atmospheres of $\sim$
1000 transiting exoplanets. By studying the chemical composition and thermal
properties of a large and diversified sample of planets, Ariel will allow us
to answer key questions such as “What are exoplanets made of?”, “How do
planets and planetary systems form?”, and “How do planets and their
atmospheres evolve over time?”. Most importantly, it will finally allow us to
place the Solar System into a broader Galactic context. The diversity in
atmospheric compositions observed today is expected to be linked to different
planetary formation and evolutionary scenarios, and our Solar System is only
one example among a vast range of possible outcomes. To achieve its goals,
Ariel will therefore need to cover a relevant range of both planetary and
stellar parameters in a statistically significant way. The relation between a
planet and its star is perpetually interweaved, so one cannot be dissected
without accounting for the other. It is therefore important to acquire an
accurate knowledge of the stellar properties well before the Ariel launch, in
order to explore the range of host-star parameters in its Reference Sample
Edwards2019 , prioritise the observations, and finally perform a meaningful
choice of Ariel targets. In fact, the Reference Sample will evolve with time
based on both the analysis of its targets’ properties, and new planetary
discoveries, to always comply the mission requirements and maximise its
science outcome.

The characterisation of planet-hosting star(s) is an important step for
understanding the nature of their planetary companion(s). On a general level,
in relation to the transiting planetary population, it is salient for the
following reasons:

##### The determination of the planetary radius, mass, and bulk composition:

the precise determination of stellar radii is crucial to retrieve an absolute
value of the radius of a transiting planet; likewise, through synergies with
the radial velocity method, the precision of the planetary mass would depend
on the stellar one. In turn, the inference of both stellar radius and mass
usually hinges on the stellar atmospheric parameters through the use of
stellar models. It is consequently important to adopt a coherent modelling
approach with well calibrated models for determining the stellar mass and
radius. The atmospheric parameters i.e. effective temperature (Teff), surface
gravity ($\log(g)$), and metallicity ([Fe/H]) can be accurately determined
through high-resolution spectroscopy.

##### The exact identification of atmospheric features:

stellar variability, caused by the interaction between magnetic fields and
turbulent plasma, is responsible for intrinsic variations of the stellar
spectrum that can be confused with planetary features (e.g. Robertson2015 ;
Ballerini2012 ) when occurring on transit (or phase-curve) timescales. It is
therefore essential to acquire an exact knowledge of the stellar spectrum to
at least the same level of the planetary signal, i.e. 10 – 50 ppm relative to
the star, for accurately determining the chemical composition and molecular
abundances in a planetary atmosphere. Furthermore, information on long-term
stellar activity is important for studying the effect of the stellar
irradiation onto the planet atmosphere and for constraining the evolution of
the atmosphere itself e.g. Locci2019 ; Johnstone2020

##### The investigation of planetary formation and migration processes:

determining the precise age of the host star and, by extension, of the
planetary system is critical as it tells us how much time was available for
the system to dynamically evolve. This, in turn, allows us to constrain the
pathways that produced its current architecture. Different dynamical pathways
(e.g. early or late migration) act on different timescales and have different
implications for the composition of planets (e.g. turrini+2015 ; Turrini2020
and references therein). Knowing the age of the system provides the temporal
dimension of the problem. In parallel, the atmospheric composition of the host
star is itself a cipher key to decode the compositional signatures on planets
left by their formation and migration histories (e.g. oberg+2011 ;
johnson+2012 ; carter-bond+2012 ; thiabaud+2014 ; marboeuf+2014a ;
marboeuf+2014b ; mordasini+2016 ; cridland+2019  and Turrini2018 ; Turrini2020
for a discussion in the context of Ariel). Stellar abundances, in fact,
provide the meter on which to measure whether planets are enriched or deprived
of a given element. Beginning with the early results of oberg+2011 , various
works point out that the comparison between the stellar metallicity and C/O
ratio, with the analogous planetary quantities (e.g. the planetary C/O ratio
being super-stellar or sub-stellar) provides information on the original
formation region of the planet with respect to the H2O, CO2 and CO snow lines,
and on the time when the planet migrated to its present orbit (e.g.
Madhusudhan2016 , and references therein, and mordasini+2016 ; cridland+2019 ;
Turrini2020 ; Turriniinprep  for recent examples). Further work shows that
similar considerations apply also to elemental ratios involving other elements
(e.g. N, S, Ti, Al), and that their comparison with the stellar abundance
ratios provides additional constraints on the planetary formation process
Turrini2018 ; oberg+2019 ; bosman+2019 ; Turrini2020 ; Turriniinprep .
Therefore, the precise knowledge of the host-star age, abundances, and
elemental ratios, is the founding stone for interpreting the planetary
composition, and the origin and evolution of planets.

##### The identification of correlations between planetary and stellar
properties:

more and more observational evidence is being reported presenting correlations
between the host-star properties and their companion properties. To cite some,
we today know correlations between planet radius versus host-star metallicity
(e.g., Buchhave2014 ; Schlaufman2015 ); eccentricity versus metallicity (e.g.,
Adibekyan2013 ; Wilson2018 ); occurrence rate of gas-giant planets versus
stellar metallicity (e.g. Santos2004 ; ValentiFischer2005 ; Sousa2008 );
correlation between hot-Jupiters surface gravity and stellar chromospheric
fluxes Hartman2010 ; Figueira2014 ; Lanza2014 ; Fossati2017 ; low-mass planets
occurrence rate versus stellar Mg/Si ratio Adibekyan2015 ; or the fact that
iron-poor planet-hosting stars are enhanced in $\alpha$-elements Adibekyan2012
; Adibekyan2012b . Such correlations are of great value in constraining both
the physics of the planet-star lifetime relation, and formation/evolution
processes. To perform this kind of statistical studies it is though essential
to work with samples of objects whose parameters have been derived in a
uniform and precise way (e.g. SWEET-Cat ; Biazzo2015 ; Andreasen2017 ;
Sousa2018 ).

For Ariel the concept of homogeneity is crucial: fundamental parameters of
host stars are usually found in the literature as the result of a case-by-case
analysis performed by different teams, resulting in an inhomogeneous census of
stars with planets. In order to achieve a comprehensive characterisation of a
statistically significant number of planetary systems, as in Ariel goals, the
accurate, precise and uniform determination of the fundamental properties of
host stars is pivotal. We present here the characterisation study we have been
performing in preparation of the Ariel mission to determine the properties of
the known host stars of the Ariel Tier 1 Reference Sample Edwards2019  with a
complete homogeneous approach. We planned and tested different types of
techniques (both model and empirical based) with the final goal to have a
catalogue of stellar properties whose measurements are homogeneous, robust and
precise.
The core of our analysis is based on atmospheric parameters retrieved from the
SWEET-Cat111https://www.astro.up.pt/resources/sweet-cat/ catalogue (Stars With
ExoplanETs Catalogue, SWEET-Cat ). At the time of writing SWEET-Cat is a
catalogue of parameters for 2872 stars with planets, 642 of which have been
analysed using the same uniform methodology. We note that the analyses we
performed throughout this manuscript have been focusing on a total of 155
Ariel stars that are in common with the homogeneously determined sample of
SWEET-Cat.

The manuscript is structured as follows: Section 2 presents the analysis
performed to robustly determine the stellar atmospheric parameters such as
Teff, $\log(g)$ and [Fe/H] for the whole Ariel parameter space. Section 3
presents a study on the accuracy of the transit depth value as a function of
the stellar fundamental parameters’ uncertainties and wavelength range.
Section 4 describes the techniques used to estimate the elemental abundances
of aluminium, carbon, nitrogen, magnesium, sodium, and silicon. Section 5
describes various techniques used to estimate useful activity indices (i.e.
$S$ and $\log(R^{\prime}_{\rm HK})$ ) from high-resolution spectra. Section 6
presents the inconsistency of the age values presented on a case-by-case study
in the literature and our approach for the determination of the age of the
Ariel stars. Finally, Section 7 presents the ground-based monitoring campaign
to obtain high-resolution spectra for those stars in the Ariel Tier 1 that
have not yet been observed with the spectral quality needed to perform a
precise characterisation. We present our conclusions in Sec. 8.

##  2 Homogeneous stellar parameters

The atmospheric parameters Teff, $\log(g)$, and [Fe/H] are the usual input
data for the determination of other stellar properties such as age, mass,
activity indices and elemental abundances. Consequently, in order to provide a
final set of homogeneous parameters which are precise, consistent and robust,
we performed a benchmark study between three different methods for measuring
such parameters. The goal of this study is to develop an overall robust and
coherent method that covers the whole Ariel stellar parameter space, and which
will be used to homogeneously determine atmospheric parameters of all Ariel
host stars.

###  2.1 Data

We analysed a total of $\sim$150 high-resolution, high S/N spectra of stars
common to both the Ariel Tier 1 and the homogeneous sample of SWEET-Cat. The
range of V magnitude spans values between $5<V<16$ mag, with spectra covering
a signal-to-noise ratio (S/N) between 50 $<$ S/N $<\sim$ 800.

###  2.2 Methods and results

We used three different spectroscopic techniques to determine the atmospheric
stellar parameters for the list of targets mentioned above. The three methods
employed for our analysis are the “Fast Automatic MOOG Analysis” (FAMA,
Magrini13 ), the “Fast Analysis of Spectra Made Automatically” (FASMA,
Tsantaki2018 ), and the method used for determining SWEET-Cat parameters
SWEET-Cat . We performed a comparison between the values of Teff, $\log(g)$,
and [Fe/H] obtained from each method, seeking possible outliers and trends
among the parameters, and we evaluated the robustness of the results by
comparing it to external benchmarks, e.g. isochrones grids, gravities derived
from both trigonometric distances (Gaia DR2), and photometric lightcurves.

Our results show a good agreement for a bulk population around the solar
values (Teff= 5000 - 6000 K, $\log(g)$=4.2 - 4.6 dex), yet at low and high
temperatures some methods tend to under/overestimate the surface gravity
$\log(g)$. specifically, within the 5000 K - 6000 K temperature range we find
no trends, however an offset is present between FAMA/FASMA and SWEET-Cat (+70
K and +34 K, respectively). For Teff$<$ 5000 K, the dispersion between the
three methods increases, while for Teff$>$ 6000 K both FAMA and FASMA yield
temperatures cooler than SWEET-Cat ones.
Concerning the surface gravity determination, we detect trends in the results
provided by both FAMA and FASMA. Specifically, the difference between their
$\log(g)$ and the SWEET-Cat estimate increases with SWEET-Cat $\log(g)$. In
the range between 4.2 - 4.6 dex the trend is almost negligible, however for
$\log(g)$$>$ 4.6 the differences become particularly high.
In relation to the metallicity [Fe/H], and considering its typical errors
$\sim$ 0.10 dex, the three methods overall converge to similar final
metallicities. We note that the three methods rely on different line lists
with different set of atomic data, which cause them to converge on slightly
different sets of Teff and $\log(g)$ values, which should satisfy both
conditions of excitation equilibrium, and ionization balance. In fact, while
the value of [Fe/H] is usually more constant, Teff and $\log(g)$ tend to vary
along a local minimum. Details specific to each method and complete set of
comparison results (including all individual stellar parameters derived by
FAMA and FASMA) are reported in a dedicated study by Brucalassi2020 .

Further studies will be carried out within the parameters’ range where the
three spectroscopic methods do not provide consistent results. Finally,
through the help of external benchmarks, we will select the method(s) that
yield(s) the most robust result, depending upon the parameters space (Teff,
$\log(g)$ and [Fe/H]) each individual Ariel star falls in. The combination of
the selected method(s) will be used to coherently build a homogeneous
catalogue of stellar atmospheric parameters for the whole Ariel Reference
Sample.

##  3 Study of the effect of stellar parameters’ uncertainties through ExoSim

In parallel to the estimation of homogeneous atmospheric parameters, we
started analysing how their uncertainties can affect the determination of the
retrieved planetary spectrum. More specifically, the uncertainties in Teff,
$\log(g)$ and [Fe/H] directly reflect onto the determination of the stellar
limb-darkening, a phenomenon that has to be taken into account when analysing
data of planets observed during their primary transit i.e. when they pass in
front of the star.

###  3.1 Stellar limb-darkening

Stellar limb-darkening is the wavelength-dependent radial decrease in specific
intensity as observed from the centre to the edge of the stellar disc.
Intensity is traditionally represented as a function $I_{\lambda}(\mu)$, where
$\lambda$ denotes the observing wavelength or passband, $\mu$ is defined as
$\mu=\cos{\theta}$, and $\theta$ is the angle between the surface normal and
the line of sight. Numerous functional forms, so-called limb-darkening laws,
have been proposed in the literature to approximate $I_{\lambda}(\mu)$. In
this study we adopt the following four-coefficient law proposed by claret00 ,
(hereinafter “claret-4”):

$\frac{I_{\lambda}(\mu)}{I_{\lambda}(1)}=1-\sum_{k=1}^{4}a_{k}(1-\mu^{k/2}).$
(1)

Previous studies indicate that the claret-4 law should be used to guarantee
the precision level required for the Ariel spectra hayek2012 ; morello17 ;
changeat2020 .

Figure 1: Left panel: Simulations of HD-209458 (V = 7.63 mag, K = 6.31 mag)
showing the standard deviation of the recovered transit depths,
$\sigma_{p}(\lambda)$, versus wavelength, for different $\sigma_{T}$ values.
The crosses give the mean value of $\sigma_{p}(\lambda)$ over 20 results (each
result is obtained from a distribution of 100 transit depths), and the error
bars give the standard deviation of these values. Also shown for comparison is
the fractional noise on the transit depth (for 1 transit observation) from
stellar photon noise for HD-209458 b (assuming no temperature variation): dots
give the mean and error bars give the standard deviation of 20 results, each
consisting of 100 realisations. Right panel: $\sigma_{p}(\lambda)$ versus
$\sigma_{T}$ for the median wavelength bin in each of the three Ariel
spectroscopic channels, and the three photometric channels.

To investigate the uncertainty in the transit depth that results from the
precision of stellar parameters, we used ExoSim Sarkar2020  to simulate the
exoplanet transit observations of HD-209458 b with all the Ariel instrument
channels. The simulations generate wavelength-dependent light curves which
applied in the generation of synthetic data. The input transit depth
($p=(R_{p}/R_{*})^{2}$) was assumed to be constant at all wavelengths.

The limb-darkening coefficients were calculated through the
ExoTETHyS222https://github.com/ucl-exoplanets/ExoTETHyS/ package
morello2020joss ; morello2020 , based on the PHOENIX_2012_13 grid of stellar
atmosphere models (claret12 , claret13 ). With this configuration the limb-
darkening coefficients depend on the stellar parameters Teff, $\log(g)$, and
[Fe/H]. The limb-darkening coefficients used for the synthetic data were fixed
to those obtained for the HD-209458 model with Teff$=6091\,K$,
$\log(g)$$=4.45$ dex, and [Fe/H]$=0$.

This data is then processed to extract spectral light curves in wavelength
bins with spectral resolution of $R=100$ (AIRS CH0), $R=30$ (AIRS CH1), and
$R=15$ (NIRSpec). No additional noise was implemented in these simulations.
The final step of this process involves the fitting of model light curves to
the simulated data curves, to extract the transit depths, $p(\lambda)$.

The light curves used for the fit however, are generated for stars with random
temperature values, obtained from a Gaussian distribution centered at
Teff$=6091\,K$, and of standard deviation, $\sigma_{T}$, which represents the
uncertainty in Teff. All other stellar parameters are kept identical to the
simulated star. The curve fitting process used a downhill simplex algorithm to
find the best-fitting curve with the transit depth being the only free
parameter. The curve fit mismatch occurs between the simulated data and the
model light curves, due to the use of the slightly wrong limb-darkening
coefficients, causing a bias in the recovered fractional transit depth. This
procedure is repeated 100 times in a Monte Carlo simulation, to obtain a
distribution of transit depths, with a standard deviation,
$\sigma_{p}(\lambda)$, an uncertainty associated with the precision of Teff,
$\sigma_{T}$. We note that dependence of the limb-darkening profile on the
$\log(g)$ and [Fe/H] is weaker than that on the Teff. The whole process is
repeated 20 times to obtain a mean and standard deviation for
$\sigma_{p}(\lambda)$.

Figure 1 (left) shows $\sigma_{p}(\lambda)$ as a function of wavelength for
different values of $\sigma_{T}$. This term should be added in quadrature with
the other sources of error in order to obtain the final error bars of the
transit depth. Figure 1 (right) shows the median spectral bin results per
spectroscopic channel, and photometric channel results plotted against
$\sigma_{T}$. We note that by determining the temperature of a solar-like star
with a precision of 80 K we can have a potential uncertainty of $\sim$ 25 ppm
in the visible channel (VisPhot). The mid-infrared channels are not
significantly affected by this source of error, given that the standard
deviation is below 10 ppm at wavelengths longer than 3 $\mu$m even if
$\sigma_{T}=$180 K.

To compare these results to the photon noise limit, we performed an ExoSim
Monte Carlo simulation where HD-209458 b was simulated using 100 realisations
with just stellar photon noise. The visible magnitude of the host star is V =
7.63 mag. Light curve fits were performed as previously, but no temperature
variations were simulated. A distribution of transit depths is again obtained
for each spectral bin. The standard deviation of this distribution gives the
fractional photon noise on the transit depth (for 1 transit) per bin. As
before we repeat this process 20 times, and obtain a mean and standard
deviation of the photon noise result. These results are shown in Figure 1
(left). Again we find that the mid-infrared channels are not significantly
affected by the stellar Teff precision, with $\sigma_{p}(\lambda)$ falling
$\sim$ an order of magnitude below the photon noise. For the FGS channels
however the fractional photon noise is much smaller and falls below the
uncertainty from stellar precision. The absolute uncertainties from stellar
precision remain overall low in these channels, but this result indicates that
the precision on Teff must be considered in the overall transit depth
uncertainty at these shorter wavelengths. We note that fainter stars have
larger photon noise error, so that the added contribution due to the
uncertainty on Teff could become negligible over the whole Ariel spectral
range.

An analogous study for other stellar types, which includes noise,
uncertainties in $\log(g)$, [Fe/H], and the possible dependence on the model
of stellar atmosphere (PHOENIX, ATLAS, MARCS, STAGGER), will be presented in a
dedicated upcoming paper.

##  4 Homogeneous stellar abundances

When it comes to transiting exoplanets, what we are observing is a close-in
population that did not form in situ but migrated inwards to their present
position from different formation regions and at different times in the life
of their respective systems. Constraining the starting position of the
planetary seeds that will either form giant planets or super-Earths is a
challenging task, but it can be confronted by comparing the chemical
composition of the planet with that of its host star oberg+2011 ;
Madhusudhan2014 ; Madhusudhan2016 . Stellar abundances reflect the chemical
composition of the initial circumstellar disc of gas and dust, hence of the
birth environment from which transiting planets and their atmospheres formed
as the results of a combination of formation, migration, disc/atmospheric
evolution and possible enrichment processes (e.g., turrini+2015 ;
Madhusudhan2016 , and references therein, and mordasini+2016 ; cridland+2019 ;
ShibataIkoma2019 ; Turrini2020 ; Turriniinprep ). Therefore, knowing the
stellar composition of planet hosts and comparing it to stars without detected
planets is essential to understand planet formation mechanisms Adibekyan2012b
; DelgadoMena2010 ; petigura2011 ; santos2015 ; Jofre2015 ; daSilva2015 ;
suarezandres2017 ; DelgadoMena2018

In the context of Ariel science we have selected here those elements which are
visible in the Ariel spectral range, and of interests for constraining both
planetary formation and stellar interior: the refractory Na, Mg, Al, Si (Sec.
4.2), and the volatiles C, N (Sec. 4.3). We present here different methods to
determine abundances from homogeneous atmospheric parameters, our preliminary
results and the need to improve such results.

###  4.1 Data

We selected a sample of stars with Teff $>$ 4500 K in common between Ariel
Tier 1 and the homogeneous sample of SWEET-Cat SWEET-Cat , for which we
already have good quality high resolution spectra obtained from different
spectrographs: HARPS, UVES, SOPHIE, FEROS, EsPaDOns, FIES, NARVAL, and SARG.
The minimum S/N of the spectra is 60 with a median value of 165. The sample is
composed of a total of 155 stars whose spectroscopic parameters (Teff,
$\log(g)$, [Fe/H], and microturbulent velocity $v_{micro}$) were derived using
the same spectra we utilise here for deriving the abundances. We note here
that the results presented in this work are preliminary and obtained with
published stellar parameters in SWEET-Cat. Once the final set of parameters is
defined (see Sec. 2) we will present a more detailed work on chemical
abundances in an upcoming paper.

###  4.2 Na, Mg, Al, Si abundances determination

In order to obtain robust results we estimated and compared the abundances of
the elements Al, Mg, Na and Si retrieved through two different approaches. The
first approach employed ARES to measure the equivalent widths (EWs) of the
selected lines for each element. The number and choice of lines with their
atomic parameters can be found in Adibekyan2012 . The radiative transfer code
to derive the abundances is MOOG 2014 sneden2014 , assuming local
thermodynamic equilibrium (LTE) and ATLAS stellar model atmospheres. The
second approach used the DOOp code, based on DAOSPEC stetson , to measure the
EWs CantatGaudin2014  and the FAMA code Magrini13 , based on MOOG 2014, to
derive the stellar abundances (which can determine also the atmospheric
parameters, as reported in Sec. 2 and fully described in Brucalassi2020 ). It
adopted MARCS stellar model atmospheres and the Gaia-ESO clean line-list
heiter15 , from which we selected only lines with the best oscillator
strengths ($\log~{}gf$).

We performed a differential analysis with respect to the Sun by measuring
stellar abundances also in a Vesta solar spectrum obtained with HARPS at very
high S/N ratio (retrieved from the ESO archive). Therefore, we provide the
[X/H] ratios, defined as the difference of absolute logarithmic abundances
between a star and the Sun:

$[\mathrm{X}/\mathrm{H}]=A(\mathrm{X})-A(\mathrm{X})_{\odot}$

where $A(\mathrm{X})$ is defined as :

$A(\mathrm{X})=\log[N({\rm X})/N({\rm H})]+12$.

For the purpose of evaluating the general behaviour of elements in the context
of the Galactic chemical evolution we make use of the [X/Fe] ratios defined
as:

$[\mathrm{X}/\mathrm{Fe}]=[\mathrm{X}/\mathrm{H}]-[\mathrm{Fe}/\mathrm{H}]$

#### Results:

Among 155 targets some of the spectra had a good enough quality (S/N
$\;\buildrel<\over{\sim}\;$ 70) for the derivation of stellar parameters but
not good enough to derive chemical abundances so neither of the methods could
analyse such stars. Moreover some stars were excluded by one or the other
technique as no reliable abundance could be derived for a given element. We
compared the results obtained for the sample of stars whose abundances were
derived by both methods. After comparing the [X/H] we considered as
preliminary abundances the average value of both methods for those elements
where the differences in [X/H] ratios between both methods was below two times
the median absolute deviation (MAD). Except for the case of Si (for which we
applied a cut of 3 times the MAD) the differences are small and within the
individual abundance errors. Moreover there are no systematic differences
caused by stellar parameters. We note that for the range of stellar parameters
in our sample the Non-local thermodynamic equilibrium (NLTE) corrections are
quite low and below the error level for Si and Mg (e.g. Osorio2015 ). For
example, Adibekyan2017  found NLTE corrections below 0.03 dex for Mg and below
0.01 dex for Si by using the database from MPIA (Max Planck Institute for
Astronomy) (e.g. Bergemann2013 ) to correct the abundances in the HARPS-GTO
sample. In a similar way the abundances of Al for solar type stars are not
significantly affected by 3D-NLTE effects (below 0.03 dex, Nordlander2017 . On
the other hand, the abundances of Na are more severely affected by NLTE
effects although they can be balanced out by considering differential
abundances with respect to the Sun Amarsi2020 .

The uncertainties are calculated by considering the error on the measurement
of the EW and the sensitivity of the abundances to the change in stellar
parameters due to their errors. Since the errors on stellar parameters are
larger as the values depart from solar, especially for cooler stars, the
errors on abundances are also larger for cooler stars. The average errors for
[X/H] ratios is 0.06 dex for Na and Si, and 0.07 dex for Mg and Al. We refer
to DelgadoMena2017  for a detailed description on the error determination. We
also examined the precision errors as a function of S/N. Meanwhile for S/N
values higher than 150 we can achieve precision errors below 0.05 dex in
elemental abundance for most of the stars, for spectra with S/N below 100 the
precision errors can go above 0.1 dex. We find small differences depending on
the Teff of the stars (where cooler stars tend to have higher errors) but the
main factor affecting the precision is the S/N of the spectra. Therefore, for
the faint stars in the Ariel target list, for which it will be difficult to
obtain spectra with S/N $>$ 100, we can expect average precision values around
0.1 dex or higher. Fig. 2 shows the preliminary [X/Fe] vs [Fe/H] of our sample
of stars (red symbols) compared to the 1111 FGK stars within the HARPS GTO
sample. In general the stars follow the expected Galactic chemical evolution
trends for these elements Adibekyan2012 ; Bensby2014  and we only can see a
small offset in the Si abundances that will be further explored in the future.

Figure 2: Final [X/Fe] ratios as a function of [Fe/H] (red circles). The black
empty circles represent the HARPS GTO 1111 FGK stars sample taken from
Adibekyan2012 .

###  4.3 C and N abundances determination

Carbon abundance is estimated with two different methods: the measurements of
the EWs of absorption lines of atomic carbon C I and the spectral synthesis of
C2 and CH molecular bands. In the wavelength range covered by our spectra,
there are two C I lines at 5052.144 Å and 6587.610 Å in the Gaia-ESO line-list
(heiter15 ) classified with high-quality flags, and one line at 5380.325 Å,
with a lower quality flag, which can be used for C abundance determination.
All three lines are discussed in amarsi19  and the effects of 3D model
atmosphere and of NLTE are negligible, as also discussed in Franchini2020 . We
used them to derive carbon abundance in about 120 spectra of our sample with
FAMA, fixing the stellar parameters to the SWEET-Cat ones, as done for the
other elements.

We tested an additional procedure to derive the abundance for C and N, based
on both the computation of a grid of synthetic spectra by varying the
abundance of the element under study, and on the comparison of the synthetic
grid to the observed spectrum. The synthesis of molecular bands might allow us
to obtain the measurement of N abundances, whose atomic lines are not
accessible in the wavelength range of our spectra. The synthesis is performed
with the radiative transfer code turbospectrum AlvarezPlez1998  using the grid
of MARCS model atmospheres Gustafsson2008 . We used an extended version of the
Gaia-ESO linelist (U. Heiter, private communication) to cover the wavelength
regions below the Gaia-ESO lowest wavelength, i.e. below
$4200\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. We include the molecular
linelists for CN, C2, CH (Masseron, private communication; see also B. Plez
linelist repository and reference therein). The synthesis are performed
assuming LTE, in 1D plane-parallel geometry (since the sample stars have
$\log(g)$ $>$ 3.5). The best-matching synthesis is chosen by a $\chi^{2}$
minimisation.

For the carbon estimation through spectral synthesis method we select three
molecular bands
$[$4208\text{\,}\mathrm{\SIUnitSymbolAngstrom}$,$4233\text{\,}\mathrm{\SIUnitSymbolAngstrom}$]$,
$[$4280\text{\,}\mathrm{\SIUnitSymbolAngstrom}$,$4330\text{\,}\mathrm{\SIUnitSymbolAngstrom}$]$
and
$[$4350\text{\,}\mathrm{\SIUnitSymbolAngstrom}$,$4400\text{\,}\mathrm{\SIUnitSymbolAngstrom}$]$,
from which the derived abundances do not show any correlation with Teff or
$\log(g)$. For nitrogen estimation we used one band:
$[$4170\text{\,}\mathrm{\SIUnitSymbolAngstrom}$,$4220\text{\,}\mathrm{\SIUnitSymbolAngstrom}$]$.
For this preliminary study, C was measured assuming
$[\mathrm{N}/\mathrm{Fe}]=0$, while N was derived assuming
$[\mathrm{C}/\mathrm{Fe}]=[\mathrm{\alpha}/\mathrm{Fe}]$. For both C and N
determinations, the synthesis was performed assuming
$[\mathrm{O}/\mathrm{Fe}]=[\mathrm{\alpha}/\mathrm{Fe}]$.

Figure 3:  Carbon abundance over Fe vs [Fe/H] from atomic C I lines. Only
stars with at least two C I lines measured in their spectra are shown. The red
lines indicate the solar abundances. Figure 4: [N/Fe] vs [Fe/H] from molecular
bands around $4200\text{\,}\mathrm{\SIUnitSymbolAngstrom}$. The red lines
indicate the solar ratios. Only upper limit on the N abundances could be
measured.

#### Results:

The [C/Fe] ratios obtained with atomic lines are shown in Fig. 3. Only stars
with at least two measured lines in their spectra are plotted. The errors are
the 1-$\sigma$ of the mean C abundance. The trend shown in Figure 3 is the
expected one for C (see e.g. Nissen2014 ; suarezandres2017 ; Franchini2020 ),
with higher [C/Fe] at lower [Fe/H], and a decreasing trend with increasing
metallicity, although we find slightly lower abundances at higher
metallicities than the cited works. This trend is typical of elements
(partially) produced by core collapse supernovae, as C (which is also produced
by low and intermediate mass stars). On the other hand, we could determine
carbon from molecular bands only for a fraction of the stars, whose [C/Fe]
ratios are mostly distributed around the solar values. However, for some of
the stars at high metallicities the abundances seem to be enhanced as compared
to the ones obtained by atomic lines.

Figure 4 shows the trend for the nitrogen from molecular bands vs [Fe/H].
Nitrogen has both a primary and secondary production, and it is expected to
increase with metallicity at high [Fe/H] (see. e.g., Ecuvillon2004a ;
suarezandres2016 ; magrini18 ). Thus, its abundance ratio [N/Fe] vs [Fe/H] is
expected to increase at high metallicity, where the secondary production
dominates. Our results indicate an almost flat behaviour, up to
[Fe/H]$\sim$0.2, and then a slightly increasing trend, but we acknowledge that
this trend might not be real since we could only measure upper limits. There
is also an offset at solar metallicity of about 0.2 dex, which can likely be
corrected with an estimate of Solar nitrogen from the same molecular band.
However, we recall that nitrogen from the molecular band [4170 Å, 4330 Å] in
warm dwarf stars is very challenging as it is very weak and blended with other
strong lines (see, e.g., sneden2014 ).

The comparison with literature results shows that the two methods, atomic and
molecular C, are in quite good agreement at sub-solar metallicity, while at
solar and super-solar metallicity the measurements of C abundance from atomic
lines have to be preferred, since C from molecular bands might be
overestimated.

Concerning nitrogen abundance, due to the difficulties encountered, it should
be preferable to analyse transitions from neutral N atoms or molecular bands
in the near-infrared or near-ultraviolet regions (sneden2014 ; Ecuvillon2004a
; suarezandres2016 , and references therein). Therefore we will apply for
observing time (see Sec. 7) to obtain new spectra covering the needed
wavelength region.

Finally, we also plan to study oxygen abundances, which unfortunately are not
measurable for many of our stars, since the optical lines covered by most of
our spectra (6158 Å, 6300 Å) are very weak (especially for cooler objects) and
a very high S/N spectrum is needed to obtain reliable abundances. For the
stars for which we collect spectra covering redder wavelengths we will explore
the use of the oxygen triplet in the NIR ($\sim$7775 Å). Nevertheless, in
order to obtain homogeneous abundances ratios (e.g. C/O) we will try to use
the same oxygen indicators for a great majority of the stars. In this regard,
the choice of the weak oxygen lines is preferred since they are not severely
affected by 3D effects or departures from LTE as does happen for the oxygen
triplet Caffau2008 .

##  5 Homogeneous stellar activity indices

Stellar activity is notably the major source of astrophysical noise in the
search and characterisation of exoplanets. Photometric modulations or the
distortion of spectral line profiles, induced by inhomogeneities on the
stellar surface (e.g. starspots, faculae, granulation), are able to hamper the
clear detection of a planet with the transit or the radial velocity method,
respectively (e.g. 1997ApJ…485..319S ; 2015PhDT…….193H ; 2018A&A…613A..50C ;
2004A&A…414.1139A ; 2013A&A…556A..19O ). Stellar activity can also affect the
planetary atmosphere characterisation, which is the main goal of Ariel (e.g.
2013MNRAS.432.2917P ; micela2015 ; 2017ApJ…844…27Z ; sarkar2018 , see also
Cracchiolo2020  for the specific case of Ariel). Knowing the activity level of
the hosts can help quantify its impact on Ariel observations and importantly
contribute to the target prioritisation process.

In the context of the characterisation of Ariel host stars, we homogeneously
analysed high-resolution spectra available for part of the Ariel Reference
Sample, aiming to derive spectroscopic activity indices. The CaII H&K lines at
393.4 and 396.8 nm are particularly sensitive to chromospheric emission (e.g.
wilson1968 ; noyes1984 ), and were used to derive the Mount Wilson $S$ and the
$\log(R^{\prime}_{\rm HK})$ indices as proxies of the stellar activity level.
From $\log(R^{\prime}_{\rm HK})$ we also obtained an independent estimate of
the stellar ages, and an indication of the stellar rotation rates. The latter
was finally compared with the rotation periods obtained from time series of
the same high-resolution spectra and photometric archival data.

###  5.1 Data

We selected 92 planet-host stars by crossmatching the Ariel Reference Sample
and the homogeneous sample of the SWEET-Cat catalogue, for which high-
resolution spectra from TNG/HARPS-N and ESO/HARPS are available. We analysed
1671 public archival spectra acquired with HARPS between 2004 and 2019 through
various programs, and 891 archival spectra obtained with HARPS-N between 2012
and 2019 in the framework of the GAPS project covino2013 . Table
LABEL:tab:sample (currently placed at the end of the manuscript for better
readability) summarises the stellar sample, the number of available spectra
for each target, the average signal-to-noise ratio (S/N) of the corresponding
spectra, and the results of our analysis. For the study of activity through
CaII H&K lines presented here, we used the one-dimensional spectra corrected
for the instrumental response and stretched to the solar barycentric reference
frame (s1d files) produced by the HARPS and the HARPS-N pipelines.

###  5.2 Activity level from Calcium lines

For all available spectra, we determined the HARPS-related $S$ index from the
Ca line cores, and converted it to the Mount Wilson $S$ following the method
lovis2011  developed specifically for HARPS spectra. In order to perform the
colour-dependent $S$-to-$R^{{}^{\prime}}_{\mathrm{HK}}$ conversion, we then
extracted the $B-V$ colours from the SIMBAD wenger2000 , the Two-Micron All-
Sky Survey (2MASS skrutskie2006 ), and NASA Exoplanet archives, which we
corrected for the effect of interstellar extinction. For all our targets we
obtained estimates of the AV extinctions (or its upper limits) using a 3D map
of Galactic interstellar dust Vergely2021 , which provides in a large number
of regions a better angular resolution than its previous version presented by
Lallement2019 . Following, we computed the $E(B-V)$ and $E(V-K)$ colour excess
assuming a standard extinction law Aλ/AV with R=3.1 Cardelli1989 . From there,
we measured the intrinsic $(B-V)_{0}$ and $(V-K)_{0}$ colours. When the
$(B-V)_{0}$ value of our objects was within the validity range of noyes1984 ’s
relationship, we used their calibration to convert the weighted-averaged $S$
value to $\log(R^{\prime}_{\rm HK})$ . Otherwise, we referred to astudillo-
defru ’s relations, derived for broader ranges of $(B-V)_{0}$ or $(V-K)_{0}$.
The error bars on $\log(R^{\prime}_{\rm HK})$ were obtained through error
propagation from the uncertainty in the measure of $S$ and the published
uncertainty of the $S$-$\log(R^{\prime}_{\rm HK})$ conversion coefficients. We
removed from our sample 29 objects, for which the S/N of the co-added spectrum
in the echelle order containing the CaII doublet was $\leq 5$. Also, we could
not calculate the $\log(R^{\prime}_{\rm HK})$ index for 16 of our targets,
whose colours, or low ($\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}0.1$) $S$-index fall off the
reported calibration ranges. This left us with 47 $\log(R^{\prime}_{\rm HK})$
index measurements, reported in Table LABEL:tab:sample.

Thanks to the derived $\log(R^{\prime}_{\rm HK})$ indices, we were then able
to estimate rotation rates (Section 5.3) and stellar ages for our sample.
These latter were calculated following the empirical relation by mamajek2008 ,
which is valid for (i) $0.5\,\mathrm{mag}<B-V<0.9\,\mathrm{mag}$; (ii) -5.1
$\;\buildrel<\over{\sim}\;$ $\log(R^{\prime}_{\rm HK})$
$\;\buildrel<\over{\sim}\;$ -4.0; and (iii) 6.7 $\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}\log({\rm age_{Gyr}})\lower
2.15277pt\hbox{$\;\buildrel<\over{\sim}\;$}$ 9.9.

Given the large number of spectra available for some of our targets, we also
inspected for variations in the $S$-index which could indicate activity cycles
(e.g. Maldonado2019 ). For this analysis, we also included the stars for which
no $S$-to-$\log(R^{\prime}_{\rm HK})$ conversion was possible. We tentatively
identified 3 objects showing $>3\sigma$ $S$-index variations around their
weighted average value. However, all such cases are impacted by the low-S/N in
the spectral order containing the CaII lines, or by possible instrumental
issues whose investigation is beyond the scope of this study. As a result,
such detected variations are likely not robust.

Figure 5: $V$ magnitude versus effective temperature for the subset of 47
Ariel stars with a valid $\log(R^{\prime}_{\rm HK})$ index. The average
$\log(R^{\prime}_{\rm HK})$ is indicated by the circle marker size, while the
targets whose spectra have an average $\mathrm{S/N}<5$ are drawn as triangles.
Colours represent the stellar age in Gyr derived from the average activity
index. Symbols with a black edge correspond to targets whose
$\log(R^{\prime}_{\rm HK})$ and colour fall within mamajek2008 ’s age
calibration range, the other targets being assigned an age of $0$ Gyr (off the
colour bar range) for representation purposes.

Figure 5 presents the $V$ magnitude of the targets with a derived
$\log(R^{\prime}_{\rm HK})$ index versus their effective temperature. The mean
activity level (obtained with a weighted average of the activity indices
measured on individual spectra) is shown by the marker size: circles indicate
targets whose average S/N $>5$, while triangles represent an average S/N $<5$,
which implies larger error bars for the $\log(R^{\prime}_{\rm HK})$ measure.

We note that Hartman2010 ; Fossati2015 ; Fossati2017  reported a correlation
between $\log(R^{\prime}_{\rm HK})$ and planetary surface gravity
$g_{\mathrm{p}}$, possibly explained by evaporated planetary material which
absorbs at the core of chromospheric resonance lines Lanza2014 . Fossati2015
identified two sub-populations, classified by their $\log(R^{\prime}_{\rm
HK})$ versus $g_{\mathrm{p}}^{-1}$ trend, among active stars hosting close-in
giant planets, and they attributed their separation to the Vaughan-Preston gap
vaughan1980 . The Vaughan-Preston Gap is in fact a low populated region with
intermediate levels of activity, which divides the high level chromospheric-
activity population, and the low level one. We looked for such correlations in
our sample: in Figure 6, the target subset with available
$\log(R^{\prime}_{\rm HK})$ is shown as a function of the inverse of the
respective close-in planet’s surface gravity.333The planetary parameters were
downloaded from the Extrasolar Planets Encyclopaedia schneider2011 , the NASA
Exoplanet Archive and the Exoplanet Orbit Database han2014 . In order to
compare our analysis with Fossati2015 ’s result, we considered only those
targets with $g_{\mathrm{p}}^{-1}<0.03$ s2 cm-1 and $\log(R^{\prime}_{\rm
HK})$ $>-6$. This allowed us to identify a higher-activity and a lower-
activity population, using the scikit-learn package scikit-learn
implementation of a Gaussian mixture model. Following the results of
Fossati2015 , we adopted two components for our models. We fitted linear
relations to the two populations and determined their intrinsic activity index
$\log R_{\mathrm{HK}}^{{}^{\prime}(0)}$ and slope $\gamma$, and the respective
uncertainties with bootstrapping. We obtained $\log
R_{\mathrm{HK}}^{{}^{\prime}(0)}=-5.05\pm 0.05,\,\gamma=-79.02\pm 49.91$ cm
s-2 and $\log R_{\mathrm{HK}}^{{}^{\prime}(0)}=-4.43\pm
0.08,\,\gamma=-14.46\pm 122.05$ cm s-2 for the two subsamples, respectively.

We tested our model on the Fossati2015 ’s dataset, and we obtained results in
agreement at the $3\sigma$ level444In our implementation, we left each
component to have its own covariance matrix, and initialised the components
through K-Means clustering.. When applying the method on our dataset, we found
results consistent with Fossati2015  within $2\sigma$ level for the intercept
of the active population, and the slope of the inactive population. The slope
of the active population is consistent within 3$\sigma$, and the intercept of
the inactive one is consistent within 5$\sigma$ with their results. These
differences can be caused by a selection effect and/or to the homoskedasticity
of the Fossati2015  data, and/or to the diversity of the clustering methods.
The investigation of such discrepancies is beyond the scope of this
manuscript, however a more thorough analysis will be presented in Claudi2020 .

Figure 6: Measured stellar $\log(R^{\prime}_{\rm HK})$ versus the inverse of
the planetary surface gravity. Two populations with high and low observed
stellar activity level are tentatively identified in red and blue,
respectively. Their linear fits are shown with dashed lines. For each
population, we report in the legend (i) the $\log
R_{\mathrm{HK}}^{{}^{\prime}(0)}$ intercept value with its $1\sigma$
uncertainty, (ii) the slope with $1\sigma$ uncertainty [cm s-2]. More details
are provided in the text.

###  5.3 Rotation periods

As a further characterisation, we used the available photometric and
spectroscopic data for a subsample of the stars we analysed in the previous
section, to search for their rotation periods. In the following, we show our
method to extract photometric periods from transit surveys data and the time
series analysis of a set of spectroscopic activity indices, aiming to detect
the activity signature. We finally compare the results of these two
approaches.

####  5.3.1 Photometry

To derive the photometric periods, we collected the available light curves of
the stars in our sample (31 targets). We downloaded the data obtained from the
transiting exoplanet surveys SuperWASP (from the NASA Exoplanets
Archive555https://exoplanetarchive.ipac.caltech.edu/docs/data.html),
HATNet666https://hatnet.org and HATS777https://hatsouth.org/. Parameters such
as the orbital periods, the transit midpoint times, and the transit duration
with corresponding uncertainties are considered as well, since we used this
information to identify all the portions in the time series where the transits
are expected to occur. Once we removed these portions from the light curves,
the resulting residuals should be only affected by the stellar contribution.

We used two different methods to measure the periodic content of the “clean”
photometric time series. The first one is the Generalized Lomb-Scargle
periodogram (GLS, Zechmeister2009 ). In general, we applied the GLS to the
whole time series, but when the gaps within the data are larger than one
observing season, we also checked the single bulk of data. This is justified
by the fact that the photometric signal described by period, amplitude and
phase, can change during the activity cycle, depending on the different
distribution of magnetic spots on the stellar disc. To evaluate the
significance of the detected peaks, we calculate the False Alarm Probability
(FAP) through a bootstrap random permutation technique. The second method is
the Auto-Correlation Function (ACF, McQuillan2013 ). As reported by
McQuillan2013 , the ACF method seems to be more robust to find the photometric
periods, as demonstrated with Kepler data. When this method is applied to the
light curve, a number of maxima can be observed in the ACF as a function of
the lag, and the position of the highest peak and the half-width at half
maximum (HWHM) of a Gaussian fit to that peak are assumed as the photometric
period with the corresponding uncertainty. An example of the application of
the two methods is shown in Figure 7, in the case of the HAT-P-6 photometric
time series. We notice that even if the main periodicity (indicated with a red
vertical dashed line) is very close to the one recovered by the GLS, the peak
height is not very different from the mean value of the adjacent areas of the
ACF. Similar behaviour is found for other targets of the sample, possibly
suggesting that the ACF method is not as suitable as in the case of space-
based or high duty-cycle observations. We compared the results of these
analyses with the estimation of the stellar rotation period as obtained from
the empirical relation by mamajek2008  between this parameter and the
$\log(R^{\prime}_{\rm HK})$ index obtained in Sect. 5.2 and reported in Table
LABEL:tab:sample. In a few cases (HAT-P-6 and WASP-14), we suspect that the
derived photometric period rather indicates the first harmonics of the real
rotation period, since its value is half the one obtained with the
spectroscopic indices (see the next section).

We reported the derived photometric periods in Table 13 (eighth column). Note
that it was not possible to derive such a parameter for all the targets in our
sample. The main reason is related to the spectral type of those stars (F or
early G). Early type stars are in fact characterised by a lack of dark
starspots, preventing us to observe and measure photometric modulations.

Figure 7: Upper panel: light curve of HAT-P-6, composed by more than 15.000
data points with the planetary transits removed. Middle panel: GLS of the
light curve. The highest periodicity is marked with a red dotted vertical line
and is equal to $4.400\pm 10^{-3}$ days. The FAP corresponding to this peak is
lower than 0.01%.

Lower panel: ACF of the same light curve, showing a similar periodicity at
$5.4\pm 1.7$ days.

Table 1: Stellar sample for which we inspected spectroscopic and photometric
data in order to evaluate the rotation period. Spectroscopic data are
collected with HARPS-N at TNG within the GAPS collaboration, while photometric
light curves are mainly provided by
SuperWASP111111https://exoplanetarchive.ipac.caltech.edu/docs/SuperWASPMission.html,
HATNet121212https://hatnet.org and HATS131313https://hatsouth.org/ surveys.
For each star, we listed: the number of the available high-resolution spectra
with the corresponding time span, the rotation period from the empirical
relations, the main spectroscopic periodicity obtained with the GLS (after the
removal of the transiting planet signature), the number of photometric data
and the corresponding timespan, and the derived photometric periodicity.

[t]  Star Nr. Timespan Empirical Spectr. Nr. Timespan Photom. Name spectra
[days] Prot [d] Period [d] data [d] Period [d] HAT-P-1 16 1875 56.8$\pm$6.4 -
4787 1029 - HAT-P-3 15 792 18.0$\pm$4.1 29.7$\pm$0.2 8131 1138 - HAT-P-4 29
2355 36.6$\pm$4.5 15.90$\pm$0.02 5717 141 - HAT-P-6 18 1860 - 9.07$\pm$0.01
19181 1232 4.4$\pm$0.1 HAT-P-8 14 1423 - - 11162 489 20.8$\pm$0.1 HAT-P-14 - -
- - 1993 37 - HAT-P-16 21 1850 6.9$\pm$2.3 4.60$\pm$0.01 12552 223 - HAT-P-17
30 2513 55.4$\pm$6.5 44.0$\pm$0.1 14552 505 - HAT-P-20 19 1137 -
16.18$\pm$0.03 2655 193 14.6$\pm$0.1 HAT-P-21 24 1495 - 54.4$\pm$0.2 27866 584
- HAT-P-22 36 2595 47.7$\pm$5.9 - 25971 3724 - HAT-P-23 - - - - 4780 103 -
HAT-P-24 17 1260 - 10.81$\pm$0.01 12323 554 11.1$\pm$1.7 HAT-P-29 32 2684 -
23.0$\pm$0.1 3603 140 - HAT-P-30 15 1386 24.4$\pm$3.5 - 12612 898 - HAT-P-31
15 1143 - 16.76$\pm$0.07 9173 117 - HATS-22 - - - - 13168 823 52.8$\pm$0.9
HATS-25 - - - - 6044 147 70$\pm$4 HATS-27 - - - - 10618 444 9.04$\pm$0.01
HATS-60 - - - - 16651 202 22.9$\pm$0.5 HD-17156 18 1860 27.7$\pm$3.7
19.00$\pm$0.04 142 1171 - WASP-1 13 1434 36.1 $\pm$4.4 11.54$\pm$0.01 12308
1294 11.1$\pm$1.8 WASP-2 - - - - 12856 1600 27.8$\pm$1.3 WASP-3 2 26 - - 5799
1543 7.6$\pm$0.5 WASP-12 23 1845 - 50.8$\pm$0.2 5435 150 67.1$\pm$5.0 WASP-13
19 918 46.5$\pm$5.1 57.0$\pm$0.1 12192 866 - WASP-14 15 1230 - 23.55$\pm$0.04
6214 1151 10.6$\pm$0.1 XO-1 15 1244 19.0$\pm$3.4 - 8665 150 - XO-2N 60 2637
42.2$\pm$5.8 - 7936 501 - XO-2S 135 2486 46.0$\pm$5.6 39.0$\pm$0.1 - - - XO-3
21 1482 - 8.28$\pm$0.01 2969 733 - XO-4 17 1165 - - 1830 63 6.8$\pm$1.8

####  5.3.2 Spectroscopy

Time series of high-resolution spectra from HARPS-N cosentino14  at TNG are
available for 25 targets analysed here, collected within the GAPS
collaboration covino2013 . Spectroscopic time series are useful to derive
information on the stellar activity, including the stellar rotation periods,
thanks to a number of activity indicators that can be obtained from the line
profiles. We exploited the HARPS-N standard reduction, performed through the
Cross Correlation Function (CCF) of the spectrum with a numerical mask
representing the spectral features of a specific spectral type (see pepe2002
). The resulting CCF is the weighted and scaled average of the lines in the
correlation mask (see Figure 8, left panel), and for this reason it can be
used as a proxy for variations of the line profiles, like the ones induced by
the activity-related phenomena. We considered the time series of the radial
velocity (RV), the bisector inverse slope (BIS, 2001A&A…379..279Q ) that is
the difference between the bisector value in the upper and lower part of the
CCF (see Figure 8, right panel), and the CCF Full Width at Half Maximum, that
are directly provided by the HARPS-N pipeline. We also analysed the asymmetry
indices of the CCF, $\Delta V$ and Vasy(mod). The asymmetry indices can be
used to define the effects of the activity on the stellar spectral lines due
to processes occurring in the photosphere (e.g., magnetoconvection, see
cegla2019 ). The $\Delta V$ 2006A&A…453..309N  is the difference between the
RV obtained with a Gaussian fit of the CCF versus the one obtained with a bi-
Gaussian fit that accounts for the asymmetry of the profile, and the $V_{\rm
asy(mod)}$ (lanza2018  and the references therein) is defined as the
difference between the RV information from the red and blue part of the CCF.
The BIS shows the impact of the passage of dark spots on the stellar disc as
the star rotates, with respect to the noise floor caused by the convective
blueshift. The information from the BIS can be different from the one provided
by the $V_{\rm asy(mod)}$ since the former is evaluated on limited ranges of
the CCF, the latter on the whole profile and thus in some cases, it can be
more sensitive to the asymmetry. To obtain these indices, we applied the
publicly available IDL procedure described in lanza2018 .

Figure 8: Left panel: plot of the Cross-Correlation Function for one of the
HARPS-N spectra we analysed for the target HAT-P-6. The CCF is depicted with a
black line while a Gaussian fit is represented with a red dashed line. Since
the CCF is not perfectly symmetric, a line bisector helps to verify the
potential distortion of the spectral lines (black vertical line). Right panel:
The actual shape of the bisector can be observed by zooming the central part
of the CCF.

Our RV periodograms show very clearly the periodicities of the transiting
planets, so we first removed the corresponding signal before searching for
signatures related to the stellar rotation/activity. The main drawback of this
analysis is the sparse data sampling of our time series (typically 20 RV data
points spread over a few years), that prevents our estimates to be robust.
This is confirmed by the large values of FAP, obtained with bootstrap
permutations. For this reason, for each target we only considered those
periodicities simultaneously detected in the GLS’ of more than one time series
(RV, BIS,…) and, just like we did with the photometry, we make use of the
empirical relations in noyes1984  and mamajek2008  as a further reference for
our investigations. In general, the highest peaks of the GLS periodograms of
the spectroscopic time series show values quite similar with respect to the
expected ones, but we stress that more data would improve their significance.
Table 13 shows a summary of the periodicities found with photometric (obtained
with ACF or GLS) and spectroscopic data (GLS). The values we reported are the
result of the Levenberg-Marquardt fit used by the GLS routine with the formal
errors or the result of a gaussian fit when ACF is used. If no value is
provided in the table, then our methods did not returned any reliable
periodicity. As a final check, we applied the pooled variance method to the
$S$ index and other spectroscopic activity indicators trying to characterise
the time-scales of the stellar activity, including the rotation periods (see
e.g. Maldonado2019 ). Unfortunately, such a technique suffers from the sparse
sampling of the time series, so the information we obtained was mainly used to
verify the results from the GLS analysis and not to make robust predictions.

In conclusion, the recovery of the stellar rotation periods of potential
targets of Ariel could be challenging. Photometry suffers when early spectral
type stars (F and G) are considered, since they show no or few star spots that
are responsible for modulations on the stellar brightness related to the
rotation. Some advantages can be obtained if we consider spectroscopic time
series of those targets, but in this case the availability of a dense
monitoring with high-resolution data is lesser than the one of the photometric
light curves. For this reason we are working to collect more data in order to
confirm such findings, as presented in section 7. A robust derivation of the
stellar rotation periods from archive data, or data obtained on purpose, would
also allow to estimate the stellar age in an independent way as derived, for
instance, from isochrones. With the homogeneous estimate of the stellar mass,
we plan to apply gyrochronology to all the stars with a derived rotation
period.

##  6 The need for homogeneous stellar ages

Figure 9: Stellar ages for a sample of 32 Ariel stars whose age has been
determined both by gyrochronology ($y$ axis) and by isochrone fitting ($x$
axis), as found in the literature. The dotted line represents the identity
line. The stellar mass ranges from 0.69 M⊙ to 1.49 M⊙. Data is reported in
Table 2.

Stellar age is extremely important as it provides the broader context
necessary to interpret the formation and evolution of the planet(s) in a
system, both in terms of composition and architecture. Age is also correlated
to stellar rotation and chromospheric activity (e.g., Skumanich1972 ;
Wilson1963 ; mamajek2008 ), important aspects to be taken into account when
analysing observations of a transiting planet (see Sec. 5).

By inspecting the literature on Ariel stars, we found large inconsistencies
between ages estimated by different teams and/or using different techniques.
To illustrate this, Fig. 9 shows literature ages estimated via gyrochronology
versus those obtained from isochrone fitting (see also Table 2). For a sample
of 32 stars hosting transiting planets and covering a mass range from 0.69 M⊙–
1.49 M⊙, gyrochronology values are systematically lower than those provided by
stellar models. Works by Brown2014 ; Maxted2015  tried to interpret such a
discrepancy as an indication of tidal interaction between the planets and
their host stars, but neither study could draw strong conclusions. Maxted2015
concluded that on a case-by-case basis it is not always clear that there is
good evidence for the tidal spin-up of the host star by the planet.

Table 2:  List of targets whose age has been plotted in Fig. 9. We report
their age estimated through isochrones fitting and gyrochronology. References
from which data was collected are reported as notes

Star Name | Isochrones Age [Gyr] | Gyrochronology Age [Gyr]
---|---|---
55Cnc | 5.10 $\pm$ 2.70 a | 8.10 $\pm$ 3.54 b
CoRoT-2 | 2.66 $\pm$ 1.62 b | 0.17 $\pm$ 0.06 b
HAT-P-11 | 5.20 $\pm$ 3.10 a | 3.89 $\pm$ 0.89b
HAT-P-19 | 8.80 $\pm$ 5.20 c | 5.50 $\begin{subarray}{c}+1.30\\\ -1.80\end{subarray}$ d
HAT-P-21 | 10.20 $\pm$ 2.50 e | 1.64 $\pm$ 0.29b
HD-219134 | 12.50 $\pm$ 0.50 f | 4.10 $\pm$ na f
K2-29 | 2.60 $\pm$ 1.20 g | 0.45 $\pm$ 0.25 g
WASP-10 | 6.00 $\pm$ 4.12 b | 0.66 $\pm$ 0.10b
WASP-106 | 7.00 $\pm$ 2.00 h | 1.40 $\begin{subarray}{c}+0.70\\\ -0.40\end{subarray}$ h
WASP-107 | 8.30 $\pm$ 4.30 i | 0.60 $\pm$ 0.20 i
WASP-113 | 5.10 $\begin{subarray}{c}+3.30\\\ -1.70\end{subarray}$ j | 1.04 $\begin{subarray}{c}+0.49\\\ -0.23\end{subarray}$ j
WASP-114 | 4.20 $\begin{subarray}{c}+1.70\\\ -1.40\end{subarray}$ j | 0.98 $\begin{subarray}{c}+0.51\\\ -0.31\end{subarray}$ j
WASP-135 | 4.40 $\pm$ 2.50 k | 0.82 $\begin{subarray}{c}+0.41\\\ -0.23\end{subarray}$k
WASP-151 | 5.13 $\pm$ 1.33 l | 1.80 $\begin{subarray}{c}+2.03\\\ -1.00\end{subarray}$ l
WASP-153 | 4.00 $\pm$ 0.77 l | 1.21 $\begin{subarray}{c}+1.19\\\ -0.60\end{subarray}$ l
WASP-156 | 6.50 $\pm$ 4.03 l | 0.58 $\begin{subarray}{c}+0.51\\\ -0.31\end{subarray}$ l
WASP-19 | 9.95 $\pm$ 2.49 b | 0.89 $\pm$ 0.12b
WASP-4 | 6.27 $\pm$ 2.34 b | 2.72 $\pm$ 0.83b
WASP-41 | 8.25 $\pm$ 3.59 b | 1.71 $\pm$ 0.21b
WASP-46 | 10.03 $\pm$ 3.51b | 1.23 $\pm$ 0.20b
WASP-5 | 5.84 $\pm$ 1.86 b | 2.13 $\pm$ 0.52b
WASP-50 | 8.57 $\pm$ 2.86 b | 1.30 $\pm$ 0.15b
WASP-57 | 2.60 $\begin{subarray}{c}+2.20\\\ -1.80\end{subarray}$ m | 1.90 $\begin{subarray}{c}+2.40\\\ -1.20\end{subarray}$ m
WASP-64 | 8.94 $\begin{subarray}{c}+3.15\\\ -2.55\end{subarray}$ n | 1.71 $\begin{subarray}{c}+1.18\\\ -0.59\end{subarray}$ n
WASP-65 | 8.92 $\begin{subarray}{c}+1.87\\\ -1.97\end{subarray}$ n | 1.51 $\begin{subarray}{c}+0.50\\\ -0.33\end{subarray}$ n
WASP-69 | 15.20 $\pm$ 1.55 b | 2.09 $\pm$ 0.12 b
WASP-70A | 4.68 $\begin{subarray}{c}+3.47\\\ -1.31\end{subarray}$ n | 8.29 $\begin{subarray}{c}+5.62\\\ -2.89\end{subarray}$ n
WASP-71 | 3.21 $\begin{subarray}{c}+0.38\\\ -0.74\end{subarray}$ n | 1.64 $\begin{subarray}{c}+0.58\\\ -0.35\end{subarray}$ n
WASP-77A | 7.57 $\pm$ 2.53 b | 1.35 $\pm$ 0.18b
WASP-84 | 1.89 $\pm$ 1.61 b | 0.99 $\pm$ 0.10b
WASP-85A | 2.09 $\pm$ 1.37 b | 1.50 $\pm$ 0.33b
WASP-89 | 12.07 $\pm$ 3.11 b | 1.88 $\pm$ 0.18 b

  * •

References: a. Bonfanti2016 ; b. Maxted2015 ; c. Bonomo2017 ; d.Mallonn2015 ;
e.Bakos2011 ; f. Johnson2016 ; g. Santerne2016 ; h. Smith2014 ; i. Mocnik2017
; j. Barros2016 ; k. Spake2016 ; l. Demangeon2018 ; m. Faedi2013 ; n.
Brown2014

For Ariel to achieve one of its main goal of shedding light on the formation
and evolution of planetary systems, a robust determination of the stellar age
is crucial, as it provides a temporal dimension of the problem. Furthermore,
this estimate needs to be homogeneous over the whole Ariel Reference sample,
to allow for both statistical studies, and chemical and orbital architecture
comparison.

Even if they applied a uniform technique for their analysis, the two studies
reported above did not use a homogeneous set of stellar parameters as input.
In order to perform a statistical analysis, we are in the process of
estimating the ages of Ariel stars via different methods, both model-based and
empirical, by using our homogeneous set of parameters as input (see Sec. 2).
Precisely, we will be using stellar models Bossini2020 , spectral analysis,
and gyrochronology (see Sec. 5). This specific study is expected to be
incremental, and unfold over the time with the continuous collection of new
data (see Sec. 7) and with the revision of the existing one, in light of an
homogeneous framework. The comparison on a relatively large sample of stars
will enable us to unveil the possible underlying causes of the methods
discrepancies, and to identify a technique that allows for consistent results.
The continuation of this work will be presented in upcoming papers.

##  7 Ground based observational campaign

Ariel Tier 1 Reference Sample consists today of 487 known planetary systems,
and it will be incremented in the upcoming years before the launch Edwards2019
. The range of Gaia $G$ magnitude, as retrieved from NASA’s Exoplanet
Archive141414https://exoplanetarchive.ipac.caltech.edu/, covers 5.2 $<G<$
16.6, with median $G$ = 12.
In such a sample not all the stars have yet been observed and/or characterised
with the level of precision needed to provide both precise stellar parameters
(Teff, $\log(g)$, and [Fe/H]) and elemental abundances. Consequently, we have
begun an observational campaign in both northern and southern hemisphere to
obtain spectra with S/N $>$ 100 in the visible spectral band, for those Ariel
candidates lacking such a precise and homogeneous characterisation, to measure
intrinsic uncertainties of the order of $\sim$ 80 K in Teff, $\sim$ 0.10 dex
in $\log(g)$, and $\sim$ 0.05 dex in elemental abundances. A higher S/N ($>$
150) would allow us to decrease even more the uncertainties: a spectrum with
S/N $\sim$ 300 would for instance allow us to measure the Teffwith intrinsic
precision of $\sigma_{T}$ $\sim$ 40 K.

The combination between high resolution, large telescope collecting area, and
accessibility made UVES@VLT and HARPS-N@TNG our best candidates for a
spectroscopic campaign. Four proposals have been accepted for this year 2020
(two proposals of 30 and 22.20 hours with UVES, in the southern hemisphere,
and two proposals of 9 hours each with HARPS-N, in the northern hemisphere).
Unfortunately, due to the world-wide closure of the observatories caused by
the Covid-19 pandemic in the first half of the year, observations of one of
our UVES proposal have been delayed to the first semester of 2021. Ariel stars
observational campaign will further continue in the future and the outcome
will be made available to the community.

##  8 Conclusions

We presented here a structured approach to the study of the transiting host-
stars belonging to the Tier 1 of the Ariel Reference Sample Edwards2019 .
Unveiling the true nature of planetary systems, their formation and evolution
is only possible if both planets and their host stars are characterised in an
homogeneous and self-consistent way.

In this manuscript we used publicly available high-resolution spectra and
photometric light curves to determine elemental abundances (C, N, Na, Mg, Al,
Si), and stellar activity indices ($S$ and $\log(R^{\prime}_{\rm HK})$ ) for a
sub sample of Ariel stars, by using for input uniform stellar parameters
reported in the SWEET-Cat catalogue SWEET-Cat .

Elemental abundances were determined via equivalent widths by two different
approaches: using ARES and MOOG or with the Fast Automatic MOOG Analysis. Our
preliminary results show average errors of 0.06 dex for Na and Si, and 0.07
dex for Al and Mg. Such abundances are found to follow the expected Galactic
chemical evolution trends. The abundances for C and N were estimated through
spectral synthesis. For carbon in particular, we compared abundances obtained
from both molecular bands and atomic lines (i.e. carbon C I measured through
EWs), to the literature, finding a good agreement at sub-solar metallicity. A
specific work on homogeneous stellar abundances for the Ariel stellar
candidates is in preparation.

We quantified CaII H&K line core emission by measuring the Mount Wilson $S$
activity index on HARPS and HARPS-N spectra, and homogeneously converted this
latter to $\log(R^{\prime}_{\rm HK})$ whenever a suitable colour index was
available. On a sample of 47 stars for which the $\log(R^{\prime}_{\rm HK})$
was measured, we report an activity index between $-6.1$ and $-4.0$, with a
median value of -5.1. This was expected, as most of our sample was selected
from radial velocity campaigns, which privilege inactive stellar hosts. We
confirmed the presence of a low- and a high-activity population, as
highlighted by Fossati2015 , and recovered the correlation between
$\log(R^{\prime}_{\rm HK})$ and planetary surface gravity reported by
Hartman2010 ; Figueira2014 ; Fossati2015 ; Fossati2017 .

The analysis of the available photometric and spectroscopic time series for a
subset of targets in the SWEET-Cat catalogue, allowed us to derive a first
estimate of their rotation periods. We performed a periodogram analysis of
both the light curves and the time series of spectroscopic activity indices
(in particular, CCF asymmetry indicators, besides radial velocities after the
removal of the Keplerian signal of the known transiting planet) and compared
the resulting periods with the empirical values obtained from the
$\log(R^{\prime}_{\rm HK})$ and the relation in mamajek2008 . Spectroscopic
indices resulted to be more suitable to derive the stellar rotation period,
being the line profiles more sensitive to the stellar activity with respect to
the available photometric data. Larger spectroscopic datasets will be useful
to improve the significance of our findings and to extend our analysis to a
larger number of targets in the Ariel stellar sample.

In parallel, in Brucalassi2020 , we performed a benchmark study between three
different spectroscopic techniques to determine stellar parameters in order to
identify the most robust method(s) to uniformly determine Teff, [Fe/H] and
$\log(g)$ all along the Ariel stellar parameter space. The uncertainty on
these parameters directly reflects on the limb-darkening estimation,
phenomenon that is important to take into account to precisely derive a
planetary spectrum. We consequently investigated the uncertainty in the
planetary transit depth as a function of the stellar temperature precision and
Ariel wavelength range, from visible to infrared. We found that a 80 K (40 K)
error can produce a maximum bias of $\sim$ 25 ppm (12 ppm) on the spectrum of
a planet like HD-209458 b transiting its star and observed by Ariel.

Finally, we highlighted the large discrepancies between literature ages
obtained with different methods and heterogeneous sets of input parameters. We
showed that, for a sub-sample of Ariel stars, the isochrone age estimate is
larger than the gyrochronology estimate, an effect already discussed in the
literature and that could be caused by tidal interaction between the planet
and the host star Brown2014 ; Maxted2015 . In upcoming works we plan on
revising such a relation with the use of ages determined through both stellar
models Bossini2020  and gyrochronology, whose input will be the homogeneous
set of Ariel atmospheric parameters.

Currently the Ariel reference sample amounts to 487 known planetary systems,
but such number is destined to increase with new planetary discoveries and
detailed observations by missions like Gaia Perryman2014 , TESS Ricker2014 ,
CHEOPS Broeg2013  and PLATO PLATO , along with ground-based surveys. The work
presented here is hence part of a long-term incremental analysis that will be
carried out over the years till the launch of the Ariel mission, which will be
of benefit for Ariel and for the whole exoplanet community.

Table 3: Stars for which the $S$ index was evaluated (typical uncertainties are $<0.01$). The $\log R^{\prime}_{\mathrm{HK}}$ is indicated for targets with magnitudes in the suitable range for the conversion (see Section 5.2). Reported colours are corrected for extinction as described in the text. We also present the stellar ages derived with mamajek2008 ’s empirical relation, when the $\log(R^{\prime}_{\rm HK})$ values are within the appropriate range of the calibration. S/N is the average signal-to-noise ratio measured among the set of spectra for each target. We then list the number of available spectra per object, and whether the $S$ index shows a $>3\sigma$ time variation. Star Name | $(B-V)_{0}$ | $(V-K)_{0}$ | $S$ | $\log(R^{\prime}_{\rm HK})$ | Age [MH08] (Gyr) | $\langle\mathrm{S/N}\rangle$ | N. spectra | $\Delta>3\sigma$
---|---|---|---|---|---|---|---|---
GJ 9827 | 1.47 | 2.90 | 0.25 $\pm$ 0.01 | -5.63$\pm$ 0.29 | (∗) | 5.47 | 7 | no
HAT-P-1 | 0.92 | 0.93 | 0.15 $\pm$ 0.00 | -5.11$\pm$ 0.07 | (∗) | 12.82 | 16 | no
HAT-P-14 | 0.40 | 1.09 | 0.16 $\pm$ 0.00 | (†) | – | 20.45 | 14 | no
HAT-P-16 | 0.45 | 1.29 | 0.17 $\pm$ 0.00 | -5.19$\pm$ 0.1 | (∗) | 9.86 | 21 | no
HAT-P-17 | 0.94 | 1.82 | 0.16 $\pm$ 0.00 | -5.08$\pm$ 0.07 | (∗) | 7.93 | 30 | no
HAT-P-20 | 1.23 | 2.74 | 1.22 $\pm$ 0.01 | -4.58$\pm$ 0.09 | (∗) | 1.60 | 19 | no
HAT-P-21 | 1.09 | 1.32 | 0.31 $\pm$ 0.00 | -4.96$\pm$ 0.07 | (∗) | 4.77 | 24 | no
HAT-P-22 | 0.86 | 1.91 | 0.16 $\pm$ 0.00 | -5.01$\pm$ 0.06 | 6.79 $\pm$ 1.19 | 13.34 | 33 | no
HAT-P-24 | 0.43 | 1.15 | 0.15 $\pm$ 0.00 | (†) | – | 6.79 | 17 | no
HAT-P-29 | 0.40 | 1.34 | 0.16 $\pm$ 0.00 | (†) | – | 3.73 | 32 | no
HAT-P-3 | 0.66 | 2.40 | 0.22 $\pm$ 0.00 | -4.73$\pm$ 0.06 | 2.31 $\pm$ 0.4 | 2.97 | 13 | no
HAT-P-30 | 0.59 | 1.18 | 0.14 $\pm$ 0.00 | -5.21$\pm$ 0.09 | (∗) | 14.90 | 15 | no
HAT-P-31 | 0.29 | 1.42 | 0.13 $\pm$ 0.00 | (†) | – | 5.66 | 14 | no
HAT-P-4 | 0.70 | 1.31 | 0.14 $\pm$ 0.00 | -5.08$\pm$ 0.07 | 8.09 $\pm$ 1.42 | 6.41 | 29 | no
HAT-P-6 | 0.32 | 0.91 | 0.19 $\pm$ 0.00 | (†) | – | 16.96 | 18 | yes
HAT-P-8 | 0.37 | 1.29 | 0.15 $\pm$ 0.00 | (†) | – | 19.64 | 14 | no
HATS-27 | 0.41 | 1.06 | 0.17 $\pm$ 0.01 | (†) | – | 2.21 | 14 | no
HATS-35 | 0.65 | 1.30 | 0.16 $\pm$ 0.00 | -4.99$\pm$ 0.06 | 6.41 $\pm$ 1.12 | 16.90 | 128 | no
HATS-39 | 0.45 | 1.15 | 0.17 $\pm$ 0.00 | -5.25$\pm$ 0.23 | (∗) | 2.86 | 16 | no
HATS-41 | 0.47 | 1.09 | 0.16 $\pm$ 0.01 | -5.35$\pm$ 0.5 | (∗) | 2.40 | 5 | no
HATS-64 | 0.38 | 0.92 | 0.07 $\pm$ 0.00 | (†) | – | 1.82 | 16 | yes
HD 106315 | 0.45 | 1.08 | 0.16 $\pm$ 0.00 | -5.35$\pm$ 0.13 | (∗) | 42.37 | 94 | no
HD 17156 | 0.62 | – | 0.14 $\pm$ 0.00 | -5.16$\pm$ 0.08 | (∗) | 35.28 | 26 | no
HD 3167 | 0.82 | 1.86 | 0.16 $\pm$ 0.00 | -5.02$\pm$ 0.06 | 6.98 $\pm$ 1.22 | 17.82 | 50 | no
HD89345 | 0.77 | 1.65 | 0.14 $\pm$ 0.00 | -5.09$\pm$ 0.07 | 8.27 $\pm$ 1.45 | 21.23 | 13 | no
HIP 41378 | 0.49 | 1.18 | 0.15 $\pm$ 0.00 | -5.39$\pm$ 0.14 | (∗) | 23.13 | 205 | no
K2-139 | 0.69 | 1.75 | 0.34 $\pm$ 0.01 | -4.46$\pm$ 0.08 | 0.46 $\pm$ 0.08 | 3.18 | 6 | no
K2-141 | 0.69 | 3.04 | 0.92 $\pm$ 0.02 | -3.95$\pm$ 0.03 | (∗) | 3.34 | 29 | no
K2-232 | 0.59 | 1.37 | 0.14 $\pm$ 0.00 | -5.28$\pm$ 0.16 | (∗) | 5.26 | 8 | no
K2-237 | 0.40 | 0.85 | 0.20 $\pm$ 0.00 | (†) | – | 6.24 | 7 | no
K2-261 | 0.91 | 1.73 | 0.13 $\pm$ 0.00 | -5.19$\pm$ 0.09 | (∗) | 8.37 | 7 | no
K2-266 | 1.19 | 2.90 | 0.28 $\pm$ 0.01 | -5.16$\pm$ 0.11 | (∗) | 3.57 | 15 | no
K2-280 | 0.66 | 1.59 | 0.12 $\pm$ 0.00 | (∙) | – | 3.66 | 20 | no
K2-287 | 0.62 | 1.91 | 0.28 $\pm$ 0.00 | -4.56$\pm$ 0.04 | 0.9 $\pm$ 0.16 | 1.16 | 421 | no
K2-3 | 1.35 | 3.60 | 0.76 $\pm$ 0.02 | -4.95$\pm$ 0.16 | (∗) | 1.06 | 138 | no
KELT-6 | 0.49 | 1.23 | 0.15 $\pm$ 0.00 | -5.38$\pm$ 0.14 | (∗) | 14.92 | 42 | no
TrES-1 | 0.92 | 1.56 | 0.22 $\pm$ 0.00 | -4.89$\pm$ 0.06 | (∗) | 3.31 | 19 | no
TrES-2 | 0.59 | 1.37 | 0.16 $\pm$ 0.00 | -5.08$\pm$ 0.09 | 8.09 $\pm$ 1.42 | 6.67 | 15 | no
TrES-4 | 0.50 | 1.19 | 0.14 $\pm$ 0.00 | -5.66$\pm$ 0.32 | (∗) | 6.52 | 19 | no
WASP-1 | 0.70 | 0.90 | 0.15 $\pm$ 0.00 | -5.07$\pm$ 0.08 | 7.91 $\pm$ 1.38 | 6.12 | 13 | no
WASP-12 | 0.51 | 1.21 | 0.10 $\pm$ 0.00 | (∙) | – | 5.77 | 23 | no
WASP-121 | 0.47 | 1.08 | 0.18 $\pm$ 0.00 | -5.05$\pm$ 0.07 | (∗) | 9.23 | 140 | no
WASP-127 | 0.63 | 1.52 | 0.14 $\pm$ 0.00 | -5.21$\pm$ 0.09 | (∗) | 7.78 | 107 | no
WASP-13 | 0.78 | 1.28 | 0.14 $\pm$ 0.00 | -5.09$\pm$ 0.07 | 8.27 $\pm$ 1.45 | 11.35 | 19 | no
WASP-14 | 0.43 | 1.10 | 0.15 $\pm$ 0.00 | (†) | – | 20.43 | 15 | no
WASP-157 | 0.03 | 2.09 | 0.19 $\pm$ 0.01 | -6.11$\pm$ 1.39 | (∗) | 2.92 | 4 | no
WASP-21 | 0.51 | 1.39 | 0.16 $\pm$ 0.00 | -5.21$\pm$ 0.14 | (∗) | 6.25 | 10 | no
WASP-24 | 0.75 | 0.99 | 0.15 $\pm$ 0.00 | -5.02$\pm$ 0.07 | 6.98 $\pm$ 1.22 | 5.64 | 14 | no
WASP-3 | 0.42 | 1.21 | 0.14 $\pm$ 0.00 | (†) | – | 21.35 | 2 | no
WASP-31 | 0.32 | 0.92 | 0.15 $\pm$ 0.00 | (†) | – | 4.26 | 17 | no
WASP-35 | 0.60 | 1.37 | 0.16 $\pm$ 0.00 | -5.08$\pm$ 0.08 | 8.09 $\pm$ 1.42 | 7.98 | 13 | no
WASP-38 | 0.46 | 1.34 | 0.15 $\pm$ 0.00 | -5.5$\pm$ 0.18 | (∗) | 25.66 | 18 | no
WASP-48 | 0.63 | 1.19 | 0.17 $\pm$ 0.00 | -4.98$\pm$ 0.07 | 6.22 $\pm$ 1.09 | 6.20 | 12 | no
WASP-49 | 0.57 | 1.58 | 0.15 $\pm$ 0.00 | -5.14$\pm$ 0.13 | (∗) | 4.92 | 9 | no
WASP-50 | 0.98 | 1.44 | 0.33 $\pm$ 0.00 | -4.77$\pm$ 0.05 | (∗) | 3.67 | 12 | no
WASP-54 | 0.59 | 1.34 | 0.14 $\pm$ 0.00 | -5.24$\pm$ 0.1 | (∗) | 12.90 | 16 | no
WASP-84 | 0.81 | 1.96 | 0.45 $\pm$ 0.01 | -4.42$\pm$ 0.04 | 0.35 $\pm$ 0.06 | 3.33 | 30 | no
WASP-85A | 0.74 | 1.66 | 0.25 $\pm$ 0.01 | -4.67$\pm$ 0.05 | 1.7 $\pm$ 0.3 | 3.74 | 13 | no
XO-1 | 0.61 | 1.68 | 0.18 $\pm$ 0.00 | -4.91$\pm$ 0.06 | 4.95 $\pm$ 0.87 | 5.33 | 15 | no
XO-2-N | 0.85 | 1.81 | 0.18 $\pm$ 0.00 | -4.93$\pm$ 0.05 | 5.31 $\pm$ 0.93 | 4.38 | 57 | no
XO-2-S | 0.83 | 1.80 | 0.16 $\pm$ 0.00 | -5.01$\pm$ 0.06 | 6.79 $\pm$ 1.19 | 4.80 | 130 | no
XO-3 | 0.35 | 0.88 | 0.23 $\pm$ 0.00 | (†) | – | 19.74 | 21 | yes
XO-4 | 0.31 | 1.33 | 0.15 $\pm$ 0.00 | (†) | – | 13.76 | 17 | no

  * (†)

Out-of-range magnitudes for the $S$-to-$\log(R^{\prime}_{\rm HK})$ conversion.

  * (∙)

While the $(B-V)_{0}$ value is within the range for the
$S$-to-$\log(R^{\prime}_{\rm HK})$ conversion, the resulting non-logarithmic
$R^{{}^{\prime}}_{\mathrm{HK}}$ is negative; following noyes1984 ’s
calibration, this happens for $S\lower
1.72221pt\hbox{$\;\buildrel<\over{\sim}\;$}0.1$ and $(B-V)_{0}\lower
1.72221pt\hbox{$\;\buildrel<\over{\sim}\;$}0.7$ mag.

  * (∗)

$\log(R^{\prime}_{\rm HK})$ out of mamajek2008 ’s calibration range for age
calculation.

###### Acknowledgements.

We thank R. Lallement for extinction estimates based on the 3D dust map of
Vergely et al., 2021, in advance of publication. We thank I. Pagano for the
useful discussions. C.D. acknowledges financial support from the State Agency
for Research of the Spanish MCIU through the “Center of Excellence Severo
Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709), and
the Group project Ref. PID2019-110689RB-I00/AEI/10.13039/501100011033; S.B.,
G.M. and D.T. acknowledge the support of the ARIEL ASI-INAF agreement n.
2018-22-HH.0; D.T. acknowledges the support of the Italian National Institute
of Astrophysics (INAF) through the INAF Main Stream project “Ariel and the
astrochemical link between circumstellar discs and planets” (CUP:
C54I19000700005); D.B. acknowledges support by FCT through the research grants
UIDB/04434/2020, UIDP/04434/2020 and PTDC/FIS-AST/30389/2017, and by FEDER -
Fundo Europeu de Desenvolvimento Regional through COMPETE2020 - Programa
Operacional Competitividade e Internacionalização (grant:
POCI-01-0145-FEDER-030389). G.B. acknowledges support from CHEOPS ASI-INAF
agreement n. 2019-29-HH.0; S.S. was supported by United Kingdom Space Agency
(UKSA) grant: ST/S002456/1.; E.D.M., V.A. and S.G.S. acknowledge the support
from Fundação para a Ciência e a Tecnologia (FCT) through national funds and
from FEDER through COMPETE2020 by the following grants: UID/FIS/04434/2019,
UIDB/04434/2020 and UIDP/04434/2020; PTDC/FIS-AST/32113/2017 and
POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/2017 and POCI-
01-0145-FEDER-028953; E.D.M., V.A., S.G.S. also acknowledge the support from
FCT through Investigador FCT contracts IF/00849/2015/CP1273/CT0003,
IF/00650/2015/CP1273/CT0001, IF/00028/2014/CP1215/CT0002; T.C. acknowledges
support from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 792848
(PULSATION). T.C. is supported by Fundação para a Ciência e a Tecnologia (FCT)
in the form of a work contract (CEECIND/00476/2018); G.M. was supported by the
LabEx P2IO, the French ANR contract 05-BLANNT09-573739; P.K. acknowledges the
support of INTER-TRANSFER grant LTT20015. The work on the stellar activity
indices was based on data from the following GAPS observation programs:
A26TAC_70 and A27TAC_52, and from observations collected with HARPS/ESO
(Chile) facilities (ESO programs IDs 0100.C-0474, 0100.C-0487, 0100.C-0750,
0100.C-0750, 0100.C-0808, 072.C-0488, 074.C-0364, 082.C-0718, 087.C-0831,
089.C-0050, 089.C-0151, 090.C-0540, 091.C-0184, 091.C-0184, 093.C-0417,
094.C-0428, 095.C-0367, 095.C-0718, 096.C-0183, 096.C-0417, 096.C-0417,
096.C-0762, 097.C-0571, 097.C-0571, 097.C-0948, 098.C-0292, 098.C-0292,
098.C-0304, 098.C-0304, 098.C-0820, 098.C-0860, 099.C-0303, 099.C-0374,
099.C-0491, 099.C-0491, 183.C-0437, 183.C-0972, 191.C-0873, 198.C-0169,
198.C-0838, 60.A-9036, 60.A-9700). This research has made use of the NASA
Exoplanet Archive, which is operated by the California Institute of
Technology, under contract with the National Aeronautics and Space
Administration under the Exoplanet Exploration Program. This publication makes
use of data products from the Two Micron All Sky Survey, which is a joint
project of the University of Massachusetts and the Infrared Processing and
Analysis Center/California Institute of Technology, funded by the National
Aeronautics and Space Administration and the National Science Foundation. This
research has made use of the SIMBAD database, operated at CDS, Strasbourg,
France.

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