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\DOI{10.5802/crphys.140}
\datereceived{2022-11-18}
\dateaccepted{2023-01-17}
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\dateposted{2023-03-21}
\begin{document}

\begin{noXML}

%\TopicEF{Exoplanets}{Exoplan\`etes}

\title{Impact of stellar variability on exoplanet detectability and
characterisation}

\alttitle{Impact de la variabilit\'e stellaire sur la 
d\'etectabilit\'e et la caract\'erisation des exoplan\`etes}

\author{\firstname{Nad\`ege} \lastname{Meunier}\CDRorcid{0000-0003-0406-2754}}
\address{Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France}
\email{nadege.meunier@univ-grenoble-alpes.fr}

\def\thanksname{Note}
\thanks{Follows up on a conference-debate of the French Academy of
Sciences entitled ``Exoplanets: the new challenges'' held on 18 May 2021,
visible via
\url{https://www.academie-sciences.fr/fr/Colloques-conferences-et-debats/exoplanetes.html}}

\thanks{\textbf{Note.}
Fait suite \`a une conf\'erence-d\'ebat de l'Acad\'emie des sciences
intitul\'ee  \guillemotleft{}~Exoplan\`etes : les nouveaux 
d\'efis~\guillemotright{} tenue le 18 mai 2021, visible via
\url{https://www.academie-sciences.fr/fr/Colloques-conferences-et-debats/exoplanetes.html}}

\keywords{\kwd{Exoplanets}
\kwd{Stellar variability}
\kwd{Radial velocity}
\kwd{Photometric transits}
\kwd{Astrometry}}

\altkeywords{\kwd{Exoplan\`etes}
\kwd{Variabilit\'e stellaire}
\kwd{Vitesses radiales}
\kwd{Transits photom\'etriques}
\kwd{Astrom\'etrie}}

\begin{abstract}
Stellar variability has become a major issue to detect low mass planets
using the radial velocity technique. I present the approaches followed
to characterise the amplitude and the properties of stellar variability
in radial velocity. More specifically, the approach consisting in using
our knowledge of the Sun to understand better the different processes
which are occuring at different scales proved to be very useful. This
has been done in different ways, based on observations and models. This
is crucial because it is then possible to compare disk-integrated
radial velocities with actual structures on the solar surface, such as
spots and plages,  and with photospheric flows at different spatial
scales. Many physical processes indeed affect  the radial velocity
measurements: they are mostly due to magnetic features (spots and
plages), flows (oscillations, granulation, supergranulation, meridional
flows), and to the interactions between magnetic fields and flows
(inhibition of the convective blueshift in plages).  I present in more
detail a selection of studies aiming at characterising the impact of
stellar variability, in particular the relationship between activity
indicators and radial velocities, and then focusing on mass
characterisation and detection performance. Finally, I briefly review
the impact of stellar variability on photometric transits and
astrometry, which are also affected, but to a lesser extent. 
\end{abstract}

\begin{altabstract}
La variabilit\'e stellaire est devenue un probl\`eme majeur pour d\'etecter
les plan\`etes de faible masse en utilisant la m\'ethode des vitesses
radiales. Je pr\'esente les approches suivies pour caract\'eriser
l'amplitude et les propri\'et\'es de la variabilit\'e stellaire en vitesse
radiale. Plus pr\'ecis\'ement, l'approche consistant \`a utiliser notre
connaissance du Soleil pour mieux comprendre les diff\'erents processus
qui se produisent \`a diff\'erentes \'echelles s'est av\'er\'ee tr\`es utile. Cela
a \'et\'e fait de diff\'erentes mani\`eres, sur la base d'observations et de
mod\`eles. Ceci est crucial car il est alors possible de comparer les
vitesses radiales int\'egr\'ees au disque avec les structures r\'eelles de la
surface solaire, telles que les taches et les plages, et avec les flux
photosph\'eriques \`a diff\'erentes \'echelles spatiales. De nombreux processus
physiques affectent en effet les mesures de vitesse radiale : ils sont
principalement dus aux caract\'eristiques magn\'etiques (taches et plages),
aux \'ecoulements (oscillations, granulation, supergranulation,
circulation m\'eridienne), et aux interactions entre les champs
magn\'etiques et les \'ecoulements (inhibition du blueshift convectif dans
les plages). Je pr\'esente plus en d\'etail une s\'election d'\'etudes visant \`a
caract\'eriser l'impact de la variabilit\'e stellaire, en particulier la
relation entre les indicateurs d'activit\'e et les vitesses radiales,
puis je me concentre sur la caract\'erisation des masses et les
performances de d\'etection. Enfin, je passe bri\`evement en revue l'impact
de la variabilit\'e stellaire sur les transits photom\'etriques et
l'astrom\'etrie, qui sont \'egalement affect\'es, mais dans une 
moindre mesure.
\end{altabstract}

\maketitle

\vspace*{-6pt}

\end{noXML}

\let\rmmu\upmu

\section{Introduction: the challenge}\label{sec1}
Since the discovery of the first exoplanet around a main sequence 
star~\cite{mayor95}, 51 Peg b, over 5000 exoplanets have been detected
using a large panel of techniques. They show a very large diversity in
exoplanet properties and system architectures, as well as planets that
are very different from those of our own solar system, for example Hot
Jupiters like 51 Peg b, or very compact systems such as 
TRAPPIST-1~\cite{gillon17}. Most of the techniques to detect exoplanets
are indirect however, in the sense that they are based on the analysis
of the light coming from the star only (and not from the planet). In
the case of the radial velocity technique for example, on which I focus
in this paper, the presence of a planet orbiting the star leads to a
motion of the star around the barycenter of the system, and the
line-of-sight velocity of the star can be monitored to ascertain the
presence of the planet. However, because it is an indirect technique,
it suffers from several caveats. First of all, instruments with an
excellent long-term stability must be devised. This has been the case
for example with HARPS, and later with ESPRESSO, together with a large
panel of other instruments. This stability is however challenged by
possible modifications of the instrument during the lifetime of the
instrument, such as the fibre change on HARPS in 
2015~\cite{locurto15}, which also affect RV measurements. Furthermore,
it has been recognised  early-on~\cite{saar97} that stellar activity,
by modifying the shape of the lines, would also perturb RVs. They
therefore impact detectability, as the planetary signal can be hidden
in the stellar  ``noise'', or, even worse, the activity signal can be
mistaken for a planet. The latter case has happened several times over
these last 27 years of discoveries. The detection issue is a real
challenge for the detection of low-mass planets, because it has been 
shown~\cite{lagrange10b,meunier10,meunier10a}, based on different
approaches using the Sun as a reference, that the amplitude of the
stellar signal could be very strong, up to two orders of magnitude
larger than  the Earth signal, despite the fact that  the Sun is a
moderately active star: this is a critical challenge for the coming 
years. The lower envelope of the mass of the detected planets based on
the RV technique as a function of discovery date shows a steady
decrease after 1995, due to the improvement in instrument stability and
the availability of longer time series, but has been stagnating over
the last 10 years. Furthermore, the low-mass planets which have been
detected orbit around very low mass stars and not solar-type stars. 

This is most likely due to stellar variability, which has become
dominant compared to instrumental limitations. In this paper, I focus
on the RV techniques, which are affected by many stellar processes, due
to the presence of magnetic structures on the surface, to photospheric
flows at different spatial and temporal scales, and to the interaction
between magnetic fields and flows. Many groups have therefore addressed
this issue, to characterise the amplitude and properties of the signal
due to stellar variability, to elaborate innovative correcting
techniques. The three first sections of this paper are therefore
devoted to the impact of stellar variability on exoplanet detection. In
Section~\ref{sec2}, I describe the different approaches that have been
implemented to tackle with stellar variability. A general overview of
the different physical processes involved is given in 
Section~\ref{sec3}, as well as their main properties. Finally, in 
Section~\ref{sec4}, I present in more details several studies aiming at
characterising the impact of stellar variability, in particular in
terms of detection performance. This does not represent an exhaustive
review of all studies on the subject however, as I focus more on
certain approaches and do not describe in detail all techniques that
have been implemented to correct for the stellar contribution. Then in 
Section~\ref{sec5}, I briefly describe the impact of stellar
variability on photometric transits and astrometry, which are also
affected but to a lesser extent, because many processes affecting RVs
are directly due to flows, with no impact on those two techniques. I
conclude in Section~\ref{sec6}. 

\section{Approaches}\label{sec2}
A large panel of approaches have been implemented to understand the
impact of stellar variability on RV. Because there are many processes
involved, it is important to predict and compare the expected
amplitudes of these processes at different time scales. Their
respective properties depend on spectral type for example, or on the
average activity level of the star. Because various mitigating
techniques, based on a large panel of independent activity indicators
(i.e. observables which are not affected by the presence of the planet,
such as chromospheric indexes, photometry, or spectral line
properties), have been used, it is also crucial to understand how these
different techniques and indicators are impacted and relate to each
other in different conditions (i.e. planetary period, spectral type,
activity level of the star). This should allow to quantify the impact
of these processes on two types of studies.  First, RVs are used to
estimate the mass of planets which have been detected using photometric
transits. Transits indeed provide the radius of the planet (relatively
to the stellar radius), but not the mass. A good knowledge of this mass
is however  critical to derive the planet density and then compare with
models: it can be obtained using the RV technique during follow-up
observations (RVs provide the projected mass along the line-of-sight,
but in case of a transit, the inclination is well constrained). The
objective is to be able to reach good uncertainties on the mass to be
able to obtain low uncertainties on the planet density and
differentiate between internal structure models.  Second, blind
searches of planets in the framework of large RV surveys  have been
implemented for different types of stellar samples by many groups, and
it is important to characterise the detection performance for different
types of planets (terrestrial or giant, close to their star, in the
habitable zone or at very long period), stars (solar-type stars or M
dwarfs for example), and observational strategies. Blind tests can
therefore be implemented to answer both questions (mass estimation in
RV follow-ups and detection) and quantify the expected performance. 

These questions have been addressed using very different data sets.
First, large samples of stellar RV time series, associated to various
activity indicators, have been studied to empirically establish
correlation (or lack of correlation) between observed RVs and these
indicators depending on the type of stars, see for 
example~\cite{lovis11b,costes21}. Although most studies are usually
based on small samples, often when a planetary candidate is detected
justifying a detailed analysis of the stellar properties, it is indeed
crucial to study large samples to cover a wide range of\unskip\break 
conditions. 

Another approach has been based on our very good knowledge of solar
activity, both observationally and theoretically, to directly explore
the impact of stellar variability on RVs and activity indicators. The
proximity of the Sun, allowing a very good spatial and temporal
resolution, and guaranteeing observations of a large amount of photons
over long periods of time, is extremely favorable to tackle with this
problem. We note that the Sun is however not representative of all
stars of any masses or any evolutionary stage for example, so that
those approaches will present limitations if applied to other stars. 

This latter approach has been followed using different methods, which
are detailed here.  The observation of the Sun is naturally a good way
to obtain answers, either directly or indirectly. Historically, it has
been difficult to observe the solar RVs on long timescales with the
proper stability. Therefore, first works were based on a reconstruction
of the solar integrated RV, from observed velocity 
maps~\cite{meunier10,haywood16,milbourne19,haywood22}, usually focusing
on the contribution of spots and plages, or reconstructions based on a
model (see below). A similar reconstruction has been made from observed
meridional  circulation~\cite{meunier20c}. The solar light can also be
observed indirectly, for example with asteroids, the Moon, or Jupiter 
satellites~\cite{lanza16}. A crucial step has been achieved with the
possibility to observe the Sun as a star using stable stellar
spectrographs, first with  HARPS-N~\cite{dumusque15,phillips16,
collier19, dumusque21}. The advantage of such observations is that they
take  all physical processes into account, including possible
unidentified ones or processes which are not yet well characterised.
Furthermore, even if all processes are therefore mixed and cannot be
studied separately, it is possible to compare the observations with the
features that are actually present on the solar surface. It also has
the advantage that it is possible to study a time series for which we
are sure there is no unknown planet signal. 

Another crucial approach is based on forward modelling of the RV due to
stellar variability, starting with the Sun and then extrapolating to
other stars. The solar variability is due to complex activity (spots
and plages) pattern which can be modelled realistically by generating
random structures with well-constrained 
properties~\cite{borgniet15,meunier19,meunier19b,meunier19c}. Another
important source of variability comes from surface flows at various
spatial and temporal  scales, and in particular oscillations,
granulation and supergranulation. Granulation in particular has been
modelled based on HD or MHD simulation of the solar surface to produce
RV time  series~\cite{cegla19,sulis20}, from laws derived from HD 
simulations~\cite{meunier15}, or from solar 
observations~\cite{meunier19e,meunier20b}. The advantage of such
simulations is that it is then possible to extrapolate them to stars
other than the Sun, including various configurations (inclinations
different from edge-on) and activity levels. As for direct solar
observations, this also allows to study time series with no exoplanet
contamination. In addition, longer time-series can be analysed,
although they do not necessarily include all processes. This proved to
be very efficient to test the performance of different methods by
exploring systematically a large parameter space, both describing the
planet or the star. It also allows to study the different processes
separately to better understand their behaviour.

Finally, another possibility is to join the two approaches, by
reconstructing the solar integrated RV from observed solar features
such as spots or plages, based on a 
model~\cite{lagrange11,meunier10a,makarov10}. This allows to establish
a link between observations and models and to test those models. 

In parallel, many groups have developed different techniques to be able
to account for the stellar contribution to RVs in order to improve the
detectability of exoplanets. I give here a brief and non-exhaustive 
overview. They are based on several types of approaches: 

\begin{itemize}
\item 
Use of the information in the RV time series alone, such as the fit of
sinusoids around the rotation period and harmonics and 
pre-whitening~\cite{queloz09,boisse11,hatzes10}, spot modelling if the
temporal sampling is  sufficient~\cite{moulds13,dumusque14,herrero16},
averaging of the  signal~\cite{dumusque11b}, and periodogram 
standardisation~\cite{sulis17b}.
\item 
Use of activity indicators computed from the same spectra than the RVs,
for example correlation with the bisector  span~\cite{queloz01}, line
depth~\cite{siegel22}, or chromospheric 
emission~\cite{boisse09,dumusque12,meunier13}, gaussian processes based
on those  indicators~\cite{rajpaul15,dumusque17,malavolta18,damasso18},
PCA  analysis~\cite{davis17}, Doppler imaging
techniques~\cite{hebrard16}, CCF  shape~\cite{collier21}, or
magnitude-squared coherence  comparison~\cite{dodson22}.
\item
More complex computation of RVs, for example of subsets of spectral
lines to produce independent RV time  series~\cite{meunier17}, use of
selected lines with different sensitivity to magnetic 
field~\cite{dumusque18,cretignier20,bellotti22}, PCA analysis of the 
spectra~\cite{cretignier22},  and wavelength dependence of the 
signal~\cite{talor18}.
\item
Use of external activity indicators, mostly photometry, as in the ff'
method proposed  by~\cite{aigrain12}.
\end{itemize}

A large number of methods has been compared, to quantify detection 
performance~\cite{dumusque17,nelson20} or residuals after correction
without injecting  planets~\cite{zhao22}. In addition, efforts have
been devoted  to improve the determination of the false alarm 
level~\cite{sulis17,sulis17b,hara21,hara21b,sulis22}.

\section{Physical processes impacting radial velocity
measurements}\label{sec3}
In this section, I describe the different processes which have been
identified to impact RV measurements. They deform the lines and/or
shift them, so that they perturb the estimation of the RVs, which is
usually made assuming a symmetrical shape of the lines.
Figure~\ref{processes} presents a summary of the different categories
of processes, organised by typical temporal  scale~\cite{meunier21b}.
Some are directly due to the presence of magnetic structures, mostly
because of their contrast. The flows in the photosphere also directly
affect the RVs, at different time scales. Magnetic fields interact with
flows and therefore also produce additional contributions. These
processes are described in more detail below. Finally, the
gravitational redshift also affects radial velocities, for example if
there is a radius variability, but the effect is expected to be small
for main sequence  stars~\cite{cegla12}.

\begin{figure}
\vspace*{2pt}
\includegraphics{fig01} 
\vspace*{4pt}
\caption{\label{processes}Overview of the different processes at play,
due to magnetic regions (red), flows (blue), interaction between the
two (purple), and gravitational redshift (green). Typical time scales
indicated here correspond to the Sun. Granulation image: Pic du Midi
Observatory; Flare: H$\alpha$ image, Big Bear Solar Observatory;
Supergranulation: Dopplergram MDI/SOHO; oscillations: example of a mode
from the GONG project, NSO; differential rotation: NASA/Marshall Solar
Physics; spot drawings: Scheiner, 1625; Evershed flows: photosphere
image from Vacuum Tower Telescope, NSO/NOAO; meridional circulation
flows: Figure~1 from~\cite{makarov10b} (\copyright~AAS. Reproduced with
permission); spot number versus time from SIDC. Figure reproduced 
from~\cite{meunier21b}.}
\vspace*{6pt}
\end{figure}

\subsection{Magnetic activity: impact of spots and
plages}\label{sec3.1}
A first important contribution comes from the temperature contrast of
(dark) spots and (bright) plages, both related to strong magnetic
fields in the photosphere. As the star rotates, this deficit or excess
in flux affects different positions in the spectral lines over time,
because of the rotational broadening. This leads to an RV variability
over time, since lines are distorted and the average position of the
lines as measured by a symmetrical profile is biased in one direction
or the other (the  impact is null when on the central meridian). Simple
simulations with one spot were performed corresponding to various
configurations (such as rotation rate, inclination, 
latitude)~\cite{desort07,boisse12,dumusque14}, as well as simulations
based on complex activity  patterns~\cite{lagrange10b,meunier10a}. The
presence of spots and plages also impacts the bissector span of the
cross-correlation function of the spectrum, as well as its width, which
provides an additional diagnosis. 

Since spots and plages exhibit a strong magnetic field, from a few 100
G to a few kG on the Sun, many lines are affected by the Zeeman effect,
which could also distort lines and therefore bias the RV measurements.
Their impact has been studied  by~\cite{reiners13}, who concluded that
it was expected to be weaker than the contrast contribution in the
visible. However, with current (CARMENES, SPIRou) and future (NIRPS)
instruments in the infrared domain, this effect may have to be taken
into account in the near future, while the contrast effect is expected
to play a weaker role in this wavelength range. 

\subsection{Surface flows at different scales}\label{sec3.2}
The photosphere of stars is submitted to flows at various spatial and
temporal scales, which are also affecting RV measurements:
oscillations, granulation, supergranulation, and meridional
circulation. Oscillations are affecting the whole surface and
correspond to many modes at different frequencies. In the case of the
Sun for example, the typical frequencies are around 5~min. This
contribution is relatively easy to average out because it is composed
of periodic  components~\cite{dumusque11b,chaplin19}. It should be
noted that in addition to these modes, which are well studied in
asteroseismology, specific modes can lead to contribution at longer
timescales, for example sectoral modes at a fraction of the rotation
period, with an amplitude of a few  10~cm/s~\cite{lanza19}. 

Granulation is a small-scale convective pattern, which manifests itself
by 1000~km cells with a strong intensity contrast and strong flows
(${\sim}$1~km/s). They have a very stochastic behaviour, and the average
velocity over many granules is not exactly zero, leading to a
significant jitter, most likely around 0.4~m/s for the Sun, from 
observations~\cite{palle99} and MHD  simulations~\cite{sulis20} and
amplitude estimations  by~\cite{cegla18,cegla19} (see also the review 
by~\cite{cegla19b}). With a typical lifetime of granules of the order
of 5--10~min, the power spectrum is increasing from high frequencies
to lower frequencies, and then reaches a plateau after a turnover
frequency which depends on the lifetime of the 
structures~\cite{harvey84}. Simulations based on the properties of
granules derived from MHD simulations confirmed this behaviour,
although with a larger amplitude of 0.8~m/s,  and the difficulties to
average it by more than a factor  ${\sim}$2~\cite{meunier15}.  

At a larger scale, supergranulation is constituted of larger cells  (30
Mm) with no measurable intensity  contrast~\cite{meunier07c}, typical
horizontal flows of a few 100~m/s, and a longer lifetime (typically 
24--48~h)~\cite{rieutord10,rincon18}. 
Ref.~\cite{harvey84} proposed a law
similar to that of granulation for the power spectrum, with a turnover
corresponding to larger time  scales. 
Ref.~\cite{meunier15} showed the
importance of this contribution, with a median estimate of the jitter
of 0.7~m/s and a lower limit of 0.28~m/s.  Their impact on radial
velocities has been quantified   in~\cite{meunier19e,meunier20b}. 

Finally, meridional circulation is a global-scale flow, related to the
conservation of angular momentum and the presence of differential
rotation. On the Sun, photospheric meridional flows are poleward. When
integrated on the whole disk,  the corresponding contribution to RVs is
changing if the flows are  variable~\cite{makarov10b}. Based on a long
time series of solar meridional circulation 
measurements~\cite{ulrich10}, it was shown that the variability due to
these large scale flows could be  crucial~\cite{meunier20c}. The sign
changes for medium inclinations, and the variability for stars seen
pole-on compared to edge-on are anticorrelated. However, depending on
rotation and inclination, the amplitude can be as large as 1.7~m/s for
the edge-on configurations (and a few m/s for the pole-on
configurations), varying on cycle timescales and possibly with small
phase difference between them. 

\subsection{Interaction between surface flows and magnetic
activity}\label{sec3.3}
Due to the presence of small-scale convection (granulation), the
surface of stars appears to be shifted due to the correlation between
intensity and flows (compared to a star with no convection): for a
solar-type star, upflows correspond to the largest fraction of the
surface (granules) and are brighter than average, while downflows
correspond to a smaller fraction of the surface (intergranules) and are
darker than average: therefore, on average, there is a convective
blueshift, compared to a star with no convection. The correlation
between intensity and velocity depends on the height where the line is
forming, therefore leading to an amplitude of the effect depending on
line depth, and on line  distortion~\cite{dravins81}. Because of the
presence of strong magnetic fields in plages however, this convective
blueshift can be partially inhibited (leading to smaller granules and
weaker flows): as the plage filling factor is changing with time
(corresponding to different activity levels during the cycle, in
addition to a modulation by rotation), the amplitude of the inhibition
varies, leading to a variation of the measured  RV~\cite{saar97}. This
effect has been shown to be the dominating contribution in the solar
case, with peak-to-peak over the solar cycle up to 
8~m/s~\cite{meunier10a,meunier10}.

Other flows related to magnetic activity could also impact RVs. This is
the case of strong flares for example. Their impact is expected to be
small for solar-type stars, but outliers corresponding to flares are
observed for very active M dwarfs. Also associated to spots,  radial
flows for example  like the Evershed effect are observed for the Sun:
if they are irregular and not symmetric, they could also distort the RV
signal~\cite{haywood22}.

\subsection{Global view}\label{sec3.4}
In this last section, we present results obtained when directly
observing the Sun as as a star. There is traditionally a lack of
long-term stable RV measurements for the Sun, because solar instruments
are either focusing on spatial resolution or small field-of-view
observations, or on short timescales processes such as oscillations.
Earlier works therefore found a diversity of ranges, from a large
variability of 30~m/s (long-term) and 20~m/s (short-term) in the  K
7699~\AA~\cite{jimenez86} and at 2.3~$\rmmu$m~\cite{DP94},  to a
small variability below 4~m/s based on deep  lines~\cite{mcmillan93}.
More recently, based on GOLF data allowing only short-term 
analysis,~\cite{sulis20} found a variability due to granulation of
the order of 0.4~m/s. 

It is only recently that it was possible to observe the Sun as a star
with a long-term stability as good as stellar observations with 
HARPS-N~\cite{dumusque15,phillips16}. The last reduction of those
high-cadence  observations~\cite{dumusque21}, with an improved data
analysis, provides an extremely useful reference 3-y time-series, since
it includes all solar processes, is planet-free, and can be compared to
actual features on the solar surface for a better understanding of the
processes. These observations correspond to the end of cycle 24
however: it therefore does not include the passage by cycle maximum,
and corresponds to a low activity period. Yet, there is a strong
long-term trend in the data corresponding to the cycle variation, as
well as power in the period range corresponding to rotation and
differential rotation as expected, and some power around 200 d which
may also be due to solar variability. The day-to-day variability is
around 1~m/s, which includes a very low amount of noise (given that the
daily observations cover up to 6~h, leading to a very low SNR on the RV
daily values), a small contribution from the difference in position of
active regions from one day to the next, a small residual from
granulation, and probably mostly supergranulation.  

\section{A few applications}\label{sec4}
In this section, we describe some dedicated studies which have been
implemented on synthetic time series or on a large sample of stars, to
better  characterise  the impact of stellar variability on radial
velocities. They can be used to better understand the behaviour of the
activity indexes in relationship with RVs (two first sections), and 
allow to perform blind tests to quantify the performance (two following
sections). 

\subsection{Understanding the limitations of the linear relationship
with activity indicators}\label{sec4.1}
For some stars, the presence of a correlation between the RV time
series and the $\log R'_{HK}$ activity indicator has been widely used
to either check if the presence the presence of a peak in the
periodogram of the time series could be due to activity, or to correct
the RV time series based on a linear correlation. We focus here on the
latter use of this activity indicator. The correlation arises from the
fact the convective blueshift, producing a signal at both the
rotational timescales and on longer timescales (cycle), is strongly
correlated with the filling factor of plages, as is the $\log R'_{HK}$.
If this process is dominating, the correlation is therefore strong.
However, the other processes are degrading the correlation, and leads
to some  limitations~\cite{meunier12}. Furthermore, even when
considering only this process, the relationship is not linear, as shown
in~\cite{meunier19c} based on a large panel of simulations of realistic
RV and $\log R'_{HK}$ for solar-type stars of different activity 
levels~\cite{meunier19}. This is due to the combination of two effects.
The first one is that the activity pattern is not always in the same
latitude range over the cycle, i.e. on long timescales: Therefore, as
the average position of the plages on the disk varies with time,  it 
corresponds to different average center-to-limb distances over time.
The second effect is that both processes (inhibition of the convective
blueshift and chromospheric emission) suffer from different projection
effects. There is therefore a departure from the linear correlation,
which should be taken into  account~\cite{meunier22b}, with a
non-linear dependence of the RV on $\log R'_{HK}$ as well as a
dependence on cycle phase. 


\subsection{How do activity indicators relate to various contributions
to RV?}\label{sec4.2}
A large sample of stars observed with HARPS has been used to study the
relationship between the $\log R'_{HK}$ activity indicator and four
other indicators derived from the cross-correlation function (CCF),
i.e. the CCF bissector span, the CCF full width at half maximum (FWHM),
the CCF contrast and the CCF  area~\cite{costes21}. These 5 indicators
were also compared to the RV variability on long timescales, as a
function of spectral type. They found that long-term RV variations are
correlated with $\log R'_{HK}$, CCF bissector span and FHWM for F and G
stars, with the notable exception of the Sun which shows almost no
correlation between RV and CCF FWHM, as do a few F stars. In addition,
the CCF contrasts and areas tend to be anticorrelated with RVs. On the
other hand, K stars exhibit a larger dispersion in correlations. This
dependence on spectral type could be due to F and G stars being more
plage-dominated while K stars could be more 
spot-dominated~\cite{collier19}. The large presence of a strong
correlation between $\log R'_{HK}$ and RVs was also observed 
by~\cite{lovis11b}, with also a trend as a function of effective
temperature, which can be explained by the decrease of the convective
blueshift from F to K  stars~\cite{meunier17,meunier17b,liebing21}. The
presence of a few K stars with an anticorrelation between $\log
R'_{HK}$ and  RVs~\cite{lovis11b,costes21} has been interpreted as the
possible presence of a convective redshift. This is however not
corroborated by independent studies of the convective shift on a very
large sample of stars of similar spectral type, and importantly
including these  stars~\cite{meunier17,meunier17b,liebing21}, who found
only  positive convective blueshifts down to 4100 K. The solution to
this puzzle must lies somewhere else. A possibility for such
observations could be the presence of meridional 
circulation~\cite{meunier20c}.

\begin{figure}
\includegraphics{fig02} 
\caption{\label{ex_res}Mass uncertainties in RV follow-up (left panel),
detection rate (middle panel) and wrong planet rate (right panel) in
blind searches  versus spectral type, for 1~M$_{\mathrm{Earth}}$ (solid
line) and 2~M$_{\mathrm{Earth}}$ (dashed line) in the habitable zone,
for a a realistic amplitude of oscillation, granulation and
supergranulation alone, adpated  from~\cite{meunier20b} (in black,
sampling of 1266 nights over 10 years), and for a signal dominated by
magnetic activity, adapted  from~\cite{meunier22b}, for a sampling of
1000 nights over 10 years (in red: planet search in the whole period
range; in orange: planet search at long period only).}
\end{figure}

\subsection{Impact on performance in terms of mass
estimation}\label{sec4.3}
Exoplanet detected using the transit technique must be characterised
further using RVs. The transits indeed provide the period of the
planet, as well as its radius relatively to the stellar radius.
However, the mass cannot be estimated from the transits, which is
crucial to derive the density of the planet and therefore to compare
with internal structure models. The mass can be derived from the
amplitude of the RV planetary signal however. The objective of PLATO
mission is to detect Earth-like planet on the habitable zone around
solar type stars using photometric transits. To determine the mass of
those planets, with an objective of 10\% in precision, RV follow-ups
will be implemented to characterise the planetary candidates. Stellar
activity will however strongly degrade the achievable 
precision~\cite{meunier21,meunier22b}. A few results are illustrated in
the left panel in  Figure~\ref{ex_res}. Simulations made for RV
follow-ups of typically 1000 observations over ten years shows that for
G2 stars, the expected precision is of the order of 50--60\% for a
1~M$_{\mathrm{Earth}}$, i.e. significantly above the objective of 10\%,
when using a detection method based on a non-linear relationship
between RVs and $\log R'_{HK}$. This precision significantly improves
for larger masses (typically 15\% for a 4~M$_{\mathrm{Earth}}$ planet)
and towards K stars (typically 20\% for a 1~M$_{\mathrm{Earth}}$ in the
habitable zone around a K4 star). Mitigation of stellar activity must
therefore be significantly improved over the next 4--5 years to reach
the objective of 10\% for G2 stars, typically down to RV rms of the
residual around 0.3--0.35~m/s (for this temporal sampling). 

\subsection{Impact on performance in terms of detection rates and false
positive}\label{sec4.4}
The first blind test was organised  by~\cite{dumusque17}, with several
synthetic time series and controlled injected planets analysed by
several teams  in~\cite{dumusque18}. Several correction techniques were
tested: Those based on gaussian processes performed the best in this
blind test. A criteria was defined, showing that for K$_{\mathrm{pla}}
\sqrt{N_{\mathrm{obs}}}/\mathrm{rms}$ (where K$_{\mathrm{pla}}$ is the
amplitude of the planetary signal, and rms the root-mean-square of the
time series after a given correction) higher than  ${\sim}$7.5, the
results were globally good, while below this threshold, they were in
general corresponding to a poor performance. A smaller blind test
performed on a more limited sample of six time series 
by~\cite{nelson20} focused on comparing Bayesian approaches and their
robustness with respect to each other, but was based on gaussian noise
to model the stellar contribution.  

Blind tests have also been implemented on a very large panel of
realistic synthetic time series, covering the F6-K4 spectra type range,
and for stars of different activity levels. From these planet-free time
series, it is possible to test different sampling, to add noise of
different amplitudes, or other stellar variability contributions, and
to inject a planet which can be retrieved in a blind test. The
objective is to determine the detection rate of such planets, and to
see whether wrong planets are detected and the level of false
positives. To be able to consider a very large number of realisations,
we adopted the following simple 
protocol~\cite{meunier19e,meunier20b,meunier22b}:  After injection of a
planet (or no injection for some realisations), the time series is
corrected for stellar variability using a synthetic time series of
$\log R'_{HK}$ (when magnetic activity is present), the periodogram of
the residual is computed as well as a false alarm probability (fap)
level of 1\% based on a bootstrap approach. The highest peak in the
periodogram is identified, and if higher than the fap, it is considered
to be a detection. This detection can be compared to the injected
planet, and in particular its period, and for the detections close to
the true period (considered to be good detection), the distribution of
the fitted mass can be determined.  Granulation and supergranulation
significantly affect the performance of exoplanet detectability,
especially with the upper bound in supergranulation amplitude, leading
in this case to poor detection rates and a high level of false 
positives~\cite{meunier19e,meunier20b}. The impact is however dominated
by the presence of active regions (middle and right  panels in 
Figure~\ref{ex_res}), which leads to very poor detections rates for G2
stars (almost no detection for a 1~M$_{\mathrm{Earth}}$ in the
habitable zone of a G2 star) and very high levels of wrong planets,
which are found mostly at low periods, but they are found at long
periods at a level far above  1\%~\cite{meunier21,meunier22b}. 

\section{Impact of stellar variability on photometric transits and
astrometry?}\label{sec5}
Photometric transits and astrometry are much less affected by stellar
variability, because less processes are involved: the spot and plage
contrast is the main contribution to the variability in this case as
well as granulation. Furthermore, the transits occur only at specific
times, and usually at timescales very different from the stellar
timescales. It is therefore easier to separate the two signals compared
to RVs. Concerning astrometry, the relative amplitude between the
planetary signal and the stellar contribution is also more favorable
than for RVs. 
 
Stellar activity has not been so far a strong limitation to detect
photometric transits. However, stellar variability affects the
photometric transit properties, mostly the transit depth, due to the
presence of spots and plages, as well as granulation. In addition, it
also affects the estimation of stellar parameters (for example limb
darkening), which in turn also impact the transit 
modelling~\cite{bruno21}. Spots and plages affect the transit depth in
two ways. First, they can be non-occulted by the planet, and different
approaches to model the light curve has been proposed, 
e.g.~\cite{czesla09,haywood14}. On the other hand, they can be occulted
by the transit, distorting the profile of the 
transit~\cite{czesla09,silvavalio10,bruno16}, with some degeneracy
between spots and plages. The impact on the planet radius reaches a few
percents. The presence of granulation also affects the transit 
depth~\cite{chiavassa17} with a strong effect for Earth-like planets
around solar type stars, which can be as high as  10\%~\cite{sulis20b}.
This type of impact is critical for  PLATO~\cite {morris20} and for
future observations with JWST~\cite{bruno18} and more generally to all
transit spectroscopy studies (e.g.~\cite{rackam18,rackham19}).
In addition, spots and plages affect
transmission spectroscopy because they are wavelength-dependent. They
can create trends in the spectra or molecular spectral signal, such as
water for example. The knowledge of the host star activity level and
property (size, contrast) is therefore critical to interpret those
transmission  spectra~\cite{bruno21}. 

The impact of stellar variability on high precision astrometry
measurement has been considered early-on with very simple models. More
complex synthetic time series have then be reconstructed for the Sun 
seen  edge-on~\cite{makarov10,lagrange11}, showing that for stars like
the Sun or slightly more active, stellar variability was small, with a
jitter of typically  0.05--0.07~$\rmmu$arcsec in both directions for a
Sun at 10 pc. Such simulations have then been extended to more
configurations (inclination, activity level), and for a large array of
spectral types (F6-K4). A first series of blind tests have been made
systematically for this very large set of simulations, for a star at 
10~pc~\cite{meunier20}. The temporal sampling of the synthetic time
series was the one proposed for the THEIA 
mission~\cite{theia17,malbet21}, with 50 observations covering 3.5
years and a typical uncertainty on individual  measurements of 
0.2~$\rmmu$arcsec. The detection rates are excellent, above 50\% for
such Earth-like planet in the habitable zone, if technological
challenges can be overcome to reach such a high-precision astrometry. 
Dedicated blind tests have also been done for the most promising
targets in the solar neighbourhood, again for the THEIA 
mission~\cite{meunier22}: The detection limits were recomputed using
these realistic time series and confirmed the low impact of stellar
activity. The closest stars in the THEIA target list, $\alpha$ Cen A
and B, are more strongly affected due to their proximity, but their
detection limits remains very small (below 1~M$_{\mathrm{Earth}}$ in
the habitable zone), since the astrometric signal of planets orbiting
those stars would be large as well. The subgiants in the target list 
of~\cite{theia17} are not very promising however, due to their
habitable zone corresponding to larger periods, which cannot be well
characterised by the proposed duration of the mission. 

\section{Conclusion}\label{sec6}
In conclusion, many processes affect radial velocity measurements at
all time scales, ranging from minutes to years. Apart from the
dominating contribution of the inhibition of the convective blueshift
(in the solar case, two orders of magnitude larger than the Earth
signal) and possibly meridional circulation, which have a large
amplitude, most contributions are in the  0.3--1~m/s range, which makes
them difficult to identify and correct. In addition, stellar
variability associated to magnetic regions exhibit a complex and
stochastic pattern (number of structures, sizes, latitudinal
distribution, lifetime, stochastic variability over the cycle), and are
associated to differential rotation, which also contributes to make the
task of modelling their contribution difficult. The sum of different
contributions can also be associated to strong degeneracies (in
particular between spots and plages), leading to complex relationships
with activity indicators. Finally, the time scales of each phenomena,
although relatively well known, does not mean that they impact the
search for exoplanet only at the corresponding periods, as shown for
example for the small-scale granulation or supergranulation which may
affect the signal at long periods as well.  Among the different
approaches implemented to tackle with this issue, the use of our
knowledge of the Sun in different ways  proved to be very fruitful. It
also illustrates the strong challenge faced when searching for Earth
analogues around solar-type stars: it is very likely that very long
time series will be necessary, as well as complementary techniques to
ensure the robustness of the detections. 

\section*{Conflicts of interest}
The author has no conflict of interest to declare.

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