E Ects of Stellar Activity on the Measurement of Precise Radial

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Joao˜ Gomes da Silva

E↵ects of stellar activity on the measurement of precise radial velocity

Departamento de F´ısica e Astronomia Faculdade de Cienciasˆ da Universidade do Porto Maio de 2014 Joao˜ Gomes da Silva

E↵ects of stellar activity on the measurement of precise radial velocity

Tese submetida àFaculdade de Ciênciasda Universidade do Porto para obten¸cãodo grau de Doutor em Astronomia

Departamento de F´ısica e Astronomia Faculdade de Cienciasˆ da Universidade do Porto Maio de 2014 Acknowledgments

I would like to thank my supervisor, Nuno, the motivation, patience, guidance, and scientiﬁc expertise he shared with me, and for all the work he had to make this thesis a reality. I would also like to thank all my co-workers and staff at CAUP for helping me with the scientiﬁc and bureaucratic aspects of the PhD, but also for the fun we had in innumerable occasions during these last four years. And of course to all my friends and family.

This research was funded by Fundac¸ao˜ para a Cienciaˆ e Tecnologia, Portugal (grant reference SFRH/BD/64722/2009) as well as by the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953.

3 Abstract

The radial velocity (RV) method is one of the most prolific techniques in detecting and confirming extrasolar planets. However, due to its indirect nature, it is also sensitive to other sources of RV signals. One of the most important limiting factors of using the RV method to discover low-mass or long-period extrasolar planets is stellar activity. The phenomena that comprises activity is capable of inducing ”artificial” RV variations that will interfere with planetary detections, by adding noise to the data or producing periodic modulations that might be confused with the ones originating from the pull of planetary companions. These phenomena have a large range of timescales, from stellar oscillations and flares that can last for minutes, to magnetic cycles that last for decades. When searching for planets with various orbital periods, all these timescales need to be taken into account. Therefore, it is very important to understand the activity diagnostic tools and how activity interferes with the measured RV.

In this thesis my focus is on the long-term interference of activity on the measured RV signals and how to diagnose them. A large part of the work involved studying activity cycles of M dwarfs, due to their increasing importance in planetary searches, mainly because of their low-mass, which maximises the detection of planets by using methods such as RV or transits. I compared various activity indicators measured over timescales of years to try to understand how they relate to each other and select the most appropriate for these kind of stars. The ﬂux in the Na i D lines was found to follow very well the activity measured by the Ca ii H & K lines. Furthermore their use is most appropriate for M dwarfs due to the higher signal-to-noise at the Na i D wavelengths. I also found that the ﬂux in the Ca ii and H↵ lines is correlated for the highest activity stars but uncorrelated or anti-correlated for he most quiet M dwarfs. Indications that activity cycles are present in early-M dwarfs were also detected.

In a following study with one more year of extended data, the ﬂux on the Na i lines was used to detect activity cycles and compare those variations with the simultaneous RV signals. This was done with the aim of ﬁnding correlations between activity and RV and

4 to understand to which order those cycles could be One of the results of this work was that around 2/3 of early-M dwarfs present long-term variability. This fraction of stars with long-term variability is comparable to that of FGK stars. However, only 19% of early-M dwarfs show the presence of activity cycles (cf. 60% for FGKs). This might be a signal ⇠ of departure from an ↵⌦-dynamo to an ↵2-dynamo were no activity cycles are expected. I also found that long term activity variations are capable of producing RV signals with 1 amplitudes that can reach the 5ms level. This is enough to hide the signal of a ⇠ low-mass planet or to simulate that of a long-period planet.

In the last part of this thesis I studied the long-term correlation between two of the most widely used optical activity indicators, the Ca ii H & K and the H↵ lines, for a sample of FGK stars. These two indices are known to have a wide range of correlations but this behaviour is not well studied. The correlations between these indices was found to be depend on the activity level of the stars (as was found also for M dwarfs) and the stellar metal content might be also having an effect on the correlations between these two activity indices.

5 Contents

Acknowledgments 3

Abstract 4

List of Tables 8

List of Figures 9

1 Introduction 10

1.1 Detecting exoplanets using radial velocity ...... 12

1.1.1 General properties of exoplanets ...... 13

1.1.2 The radial velocity method ...... 16

1.1.3 Limitations of the radial velocity method ...... 18

1.2 Stellar activity ...... 19

1.2.1 Stellar chromospheric activity ...... 20

1.2.2 Activity proxies ...... 25

1.2.3 Mean activity level of stars ...... 30

1.3 Stellar activity at different time scales and its inﬂuence on RV ...... 32

1.3.1 Oscillations and Granulation ...... 32

1.3.2 Rotationally modulated active regions ...... 36

1.3.3 Long-term activity: magnetic cycles ...... 38

6 1.4 Motivation ...... 43

2 Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program I. Comparison of activity indices 45

3 Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program II. Activity and radial velocity 63

4 On the long-term correlation between the ﬂux in the Ca ii H & K and Halpha lines of FGK stars 89

5 Conclusions 108

5.1 Activity indices for M dwarfs ...... 108

5.2 Long-term activity variability and cycles of M dwarfs ...... 110

5.3 Inﬂuence of long-term activity on the RV of M dwarfs ...... 111

5.4 The long-term correlation between Ca II and Halpha for FGK stars . . . 112

5.5 Future prospects and things to be done ...... 113

5.5.1 Activity cycles in M dwarfs ...... 114

5.5.2 Activity indices ...... 115

References 116

7 List of Tables

1.1 Stellar activity at different timescales and correction of RV...... 33

8 List of Figures

1.1 Mass distribution of close-in, low-mass planets ...... 14

1.2 Radius distribution of low-mass planets ...... 15

1.3 Solar ﬂare ...... 21

1.4 Temperature structure of the solar chromosphere ...... 23

1.5 RV induced by stellar oscillations ...... 34

1.6 Effect of granulation on line bisector ...... 35

1.7 Effect of spots on line proﬁle and RV ...... 37

1.8 The Sun’s butterﬂy diagram and average sunspot area ...... 39

1.9 MWO long-term activity classiﬁcation ...... 40

1.10 Long-term correlations between RV and activity proxies ...... 42

9 Chapter 1

Introduction

During the last 15 years, astronomers have been discovering dozens of planets orbiting other stars. This quest is, however, not an easy task. The difﬁculty of detecting extrasolar planets arises from the fact that most of the optical radiation coming from a planet is simply reﬂected starlight. Because of this, exoplanets will be billions of times fainter than their host stars. And since they generally orbit at extremely small angular separations, their direct detection is incredibly hard. One way to circumvent this problem is to use indirect methods such as detecting the dynamical perturbations provoked in the host star by a planetary companion.

Several indirect methods exists now that are able to detect these small bodies in other stellar systems. The most successful to date are the radial velocity (RV) method, one of the focus of this thesis, which measures the line-of-sight velocity of star as it moves around of the star-planet centre of mass (e.g. Mayor & Queloz 1995), and transit photometry which detects the shallow brightness decrease of a star as a planet passes in front of its disk (e.g. Henry et al. 1999; Charbonneau et al. 2000). Other indirect methods currently in use include astrometry, which measures the apparent movements of the parent star by measuring it’s position with time (e.g. Benedict et al. 2006), gravitational microlensing events, which detects the huge jump in the brightness of a planet as a lens star passes in front of its host star (this method is however not easily repeatable) (e.g. Bond et al. 2004). Transit timing variations, which measure the variations in the transit time of a planet produced by another perturbing body (e.g. Ballard et al. 2011), is recent new method for conﬁrming or detecting exoplanets. Another example of an indirect planet search technique is pulsar timing, which measures the tiny anomalies in the timing of its observed radio pulses and can be used to track the pulsar’s motion, and therefore to detect a perturbing companion (e.g. Wolszczan & Frail 1992). This last

10 CHAPTER 1. INTRODUCTION 11 one was the technique that ﬁrst detected planet mass objects outside the solar system Wolszczan & Frail (1992).

Due to the indirect nature of these methods, they will become sensitive to other sources of signals, similar to the ones they are supposed to detect, which can be produced by the parent star. In this thesis I am more concerned with the RV method. Activity perturbations in the stellar atmosphere, stellar oscillations, surface granulation, and magnetic activity cycles, can all perturb the observed RV to different scales in terms of time and amplitude. These effects might make the detection of exoplanets extremely difﬁcult, by hiding their signal in the stellar noise or by producing periodic signals that can be confused with the ones of real orbiting planets (e.g. Queloz et al. 2001).

The study of these stellar activity sources of noise is the main aim of this thesis, in particular the long-term activity variations of solar-type stars and M dwarfs and the way they influence a star’s RV. A first step in the understanding of how activity affects RV is to first know how to interpret the activity diagnostics. Different activity indicators will trace different activity phenomena, which will affect the RV in different ways. And by understanding precisely which are the effects of each activity phenomena and how to correct them, a higher RV precision might be attained. If the true RV signals of real planets can be effectively disentangled from stellar RV noise, then the path is open for first detection of an Earth twin.

The organisation of this thesis is the following. I start by introducing the topic of extrasolar planet search using the radial velocity method in section 1.1 where I give a brief summary of the occurrence and main properties of the exoplanets detected so far (sect. 1.1.1), then describe the fundamentals of the method (sect. 1.1.2) and its main limitations (sect. 1.1.3). I then move to the subject of stellar activity in section 1.2. Here I discuss what is stellar activity, a chromosphere, and what produces them, what stars have activity and chromospheres and why stellar activity is important for exoplanet research (sect. 1.2.1). I also describe the distribution of the activity levels of stars, the connection between mean activity level and other stellar parameters and the inﬂuence of activity on RV in general terms (sect. 1.2.3). Then I move to the ﬁeld of activity detection, where I give a small description of the most common activity diagnostics in use (sect. 1.2.2). Finally, I go through all the timescales of the different activity phenomena, how they affect RV and describe some ways to correct or minimise their effects (sect. 1.3). The motivation of this thesis is presented in the end of this chapter (sect. 1.4). In chapters 2, 3, and 4, I present the results of this work in the form of three peer-reviewed papers. Finally, in chapter 5 I conclude by discussing the results of this thesis and giving some future prospects. CHAPTER 1. INTRODUCTION 12

1.1 Detecting exoplanets using radial velocity

The first confirmed planet orbiting another solar-type1 star was the famous 51 Peg b discovered by Mayor & Queloz (1995). It is a giant planet with a mass of 0.47 MJ and orbiting extremely close to its parent star, with an orbital period of just 4.2 days. Other two massive planets were rapidly announced in the same year following this first discovery (Marcy & Butler 1996; Butler & Marcy 1996). This realisation that planets orbiting other stars existed accelerated this new field in astronomy and the discovery of planets in other stellar systems has now become routine.

To date, 531 planets were confirmed via the radial velocity method (also known as Doppler spectroscopy). This includes 399 planetary systems where 93 are multiple- planet systems2. The first discovered planets were very massive and orbiting their parent stars on short period orbits. Jupiter mass planets in close orbits or very eccentric planets were not expected configurations from theories of giant-planet formation based on the only stellar system that we had known for millennia (Pollack et al. 1996). Differ- ent theories have appeared which explained these new configurations, as for example that massive exoplanets are formed far from the star and then migrate to their current positions (e.g. Lin et al. 1996; Trilling et al. 2002). However, more recently, giant planets much more similar to the solar system giants (e.g. Wright et al. 2008; Boisse et al. 2012) along with smaller mass planets with sizes closer to that of rocky planets have been detected (e.g. Udry et al. 2007; Mayor et al. 2009; Dumusque et al. 2012). This was a result of improved spectrograph precision (for example, HARPS3 can now reach 1 below 1 m s precision, Pepe et al. 2005), observational strategies capable of removing RV noise caused by stellar oscillations (Santos et al. 2004; Dumusque et al. 2011b), and increased timespan of observations which will enable the easier detection of lower- amplitude signals immersed in noise or add enough data to detect the long-period planets.

1 The ﬁrst extrasolar planet detected by the radial velocity method was a 1.7 MJ mass planet with a period of 2.7 yr around Cep announced by Campbell et al. (1988). However, this planet would need to wait almost two decades before being conﬁrmed (Hatzes et al. 2003). 2From http://exoplanet.eu/, (Schneider et al. 2011). 3HARPS (High Accuracy Radial velocity Planet Searcher, Mayor et al. 2003) is a high-resolution spectrograph mounted on the 3.6-m ESO telescope at La Silla Observatory in Chile. CHAPTER 1. INTRODUCTION 13

1.1.1 General properties of exoplanets

Since the focus of this thesis is on planet detection (by studying the limiting factors), I will describe very brieﬂy some of the basic properties and planet occurrence rates obtained from some important planet search surveys.

Close-in, low-mass planets Contrarily to what can be found in our solar system, planets of intermediate sizes between Earth and Neptune are very common in other stellar systems. They also appear to outnumber the larger sized planets at close-in orbits (Howard et al. 2010; Mayor et al. 2011).

The results from the Eta-Earth RV Survey (166 G and K-type stars) shown that 15% of Sun-like stars host at least one low mass planet with M sin i = 3-30 MEarth in orbits closer than 0.25 AU (P < 50 days) and that, by extrapolation of the power law ﬁtted to their data, another 14% of stars host planets with M sin i = 1-3 MEarth (Howard et al. 2010).

On it’s hand, the HARPS RV survey of 376 FGK stars shown that more than 50% of the solar-type stars harbour at least one planet of any mass at short orbital distances with P < 100 days (Mayor et al. 2011). For the case of low-mass planets, this survey found that the mass distribution of super-Earths and Neptune-mass planets (with P < 50 days) strongly increases between 30 and 15 MEarth. The orbital eccentricities of these type of planets are generally low, with e values lower than 0.45. No correlation between the occurrence rate and host star metallicity was detected. In this survey, it was also demonstrated that low-mass planets are normally found in multi-planet systems with 2-4 small planets with orbital periods of weeks or months.

These two surveys showed that the occurrence of low-mass and close-in planets increases with decreasing mass (see e.g. Fig. 1.1).

The Kepler transit survey increased the number of detected low-mass candidate planets to the thousands. As can be observed in Fig. 1.2, the distribution of planetary sizes follows a similar pattern as the mass distribution where the frequency o planets rises with decreasing planetary radii (Howard et al. 2012; Petigura et al. 2013; Fressin et al. 2013). However, the increase in occurrence with decreasing radii stagnates at 2.8 ⇠ REarth and becomes roughly constant for smaller radii (Petigura et al. 2013). This means that it is as common to ﬁnd an Earth-sized planet within 0.25 AU as to ﬁnd a Super- Earth with twice the Earth’s size. As was found for the mass distribution, the smaller- size planets detected by Kepler appear to have less eccentricity than larger planets CHAPTER 1. INTRODUCTION 14

Figure 1.1: Mass distribution of close-in, low-mass planets with periods P < 50 days. Black line is the observed histogram and red line the equivalent histogram after correction for the detection bias. From Mayor et al. (2011).

(Plavchan et al. 2012). An interpretation of this can be that these planets suffer reduced dynamical interactions (Howard 2013). Twenty three percent of the Kepler stars host two or more transiting planets (Burke et al. 2013).

Regarding low-mass planets orbiting M-dwarfs, the HARPS M-dwarf survey found that super-Earths (M sin i = 1–10 MEarth) are relatively common around these stars (Bonﬁls et al. 2013). Around 36% of M-dwarfs host a super-Earth with an orbital period between 1 and 10 days, while 52% host a super-Earth with a period between 10 and 100 days.

Gas giant planets These planets are the easiest to detect, both by the radial velocity method and the transit technique. Observations taken at the Keck Observatory have shown that 10.5% of G and K-type stars host at least one giant planet with masses between 0.3 and 10 M in orbital periods in the range 2-2000 days ( 0.03-3 AU) and Jupiter ⇠ that the occurrence rate of giant planets increases with increasing orbital distance and decreasing mass (Cumming et al. 2008). By extrapolation of the giant planet distribution, 17-20% of the solar-type stars harbour giant planets orbiting within 20 AU (P 90 yrs, ⇠ CHAPTER 1. INTRODUCTION 15

Figure 1.2: Radius distribution of low-mass planets. The red line is the power law ﬁtted to the histogram. From Howard et al. (2012).

Cumming et al. 2008). This is consistent with the detection of giant planets at longer distances than 2 AU by microlensing surveys (Gould et al. 2010). ⇠ The HARPS survey found similar results. About 18% of solar-type stars have a planetary companion more massive than 50 MEarth on an orbit with a period shorter than 10 years and the occurrence rate of giant planets grows with the logarithm of the period. They also found cases of orbital eccentricities of gas giants higher than e = 0.9 (Mayor et al. 2011).

There is a tendency for orbital distances of giant planets to be larger than 1 AU however ⇠ there is also a small pile-up at very short distances from the stars, near 0.05 AU, the so ⇠ called ”hot Jupiters” (see e.g. Udry et al. 2003; Howard 2013). These two populations of giant planets are thought to be the result of different migration scenarios acting during the planet’s evolution (see e.g. Udry et al. 2003). For the case of multi-planet systems, the orbital distribution is more homogeneous: there is no pile-up of hot Jupiters and now increase of occurrence with increasing distance after 1AU. ⇠ The giant planet eccentricity is different between single-planet and multi-planet systems: single planets show higher eccentricity rates than the planets in multi-planet systems (e.g. Howard 2013). This can be a result of planet-planet scattering processes in action as shown by Chatterjee et al. (2008). CHAPTER 1. INTRODUCTION 16

The frequency of hot Jupiters (giant planets with P 10 days) is not as high as for other  types of planets. The California Planet Survey from the Lick and Keck planet searches estimated that only 1.2% 0.38% of Sun-like stars host such a planet (Wright et al. ± 2012). A similar occurrence rate of 0.9% for hot Jupiters with M 50 M and P 11 Earth  days was also found by the HARPS survey (Mayor et al. 2011). Contrarily to close- in low-mass planets, hot Jupiters are not commonly found in multiple-systems (Steffen et al. 2012). There is also a tendency for low eccentricity among these planets due to tidal circularization (Marcy et al. 2005).

The HARPS M-dwarf survey also found low occurrence rates for giant planets orbiting these small stars (Bonﬁls et al. 2013). For orbital periods between 1 and 10 days, this survey estimated that less than 1% of M-dwarfs host a planetary companion with a mass between 100 and 1000 MEarths, which is an occurrence rate comparable with that of the hot Jupiters for FGK stars. For longer periods, between 10 and 100 days, this frequency increases to around 2%.

1.1.2 The radial velocity method

A very signiﬁcant part of the exoplanets discovered until now, were detected by the radial velocity (RV) method (also known as Doppler spectroscopy). This technique measures the movements of a star when pulled by an orbiting companion. These movements will produce a periodic variation in the wavelength of the stellar spectrum (the Doppler effect) which are due to the change in direction of the radial velocity of the star. This variation in wavelength is related to the RV of the star vie the Doppler Effect equation:

V r , (1.1) 0 ' c where = is the change in wavelength due to the star’s motion, the rest 0 0 wavelength of the spectral line, Vr the radial velocity (measured along the line-of-sight), and c the speed of light in the vacuum.

During the movement around the centre of mass, when the star starts moving away from the observer, its radial velocity becomes positive and the spectrum is shifted to higher wavelength values (light is redshifted, Vr > 0, > 0). When the star is approaching the observer, the measured radial velocity is negative and the spectrum is shifted towards lower wavelengths values (light is redshifted, Vr > 0, > 0). These periodic redshifts and blueshifts in the spectrum will translate into a periodic RV signal in the case of a planet moving on a edge-on circular orbit. CHAPTER 1. INTRODUCTION 17

The radial velocity method is based in the measurements of the Doppler shift of spectral lines. However, there are stellar phenomena that distorts line proﬁles and induce artiﬁcial Doppler shifts in the measurements, which are then translated into RV noise (a discussion of stellar noise is presented in section 1.2.1). After this type of noise is taken into account, the residual radial velocity will be the signal induced by the orbiting planet. From this signal, some planetary orbital and physical parameters can obtained.

The RV signal of a star having a planet moving in a non-perturbed keplerian orbit is of the form

Vr(t) = K[cos(⌫(t) + !) + e cos(!)] + (1.2) where K is the velocity semi-amplitude, 2⇡a sin i K = ? , (1.3) P(1 e2)1/2 where a? is the star’s orbital semi-major axis, i the orbital inclination, ! is the longitude of periastron, and is the systemic velocity (velocity of the barycentre). The true anomaly, ⌫(t), depends on the orbital period (P), eccentricity (e) and time of passage at periastron

(T0). Therefore, ﬁtting a radial velocity time series with this keplerian model yields six parameters: K, e, !, T0, P, and . The velocity semi-amplitude is related to the masses of the two components through the mass function,

3 (mp sin i) P = 3 2 3/2 2 K (1 e ) (1.4) (m? + mp) 2⇡G where mp is the mass of the planet, m? the mass of the star, and G the gravitational constant. The right-hand-side parameters of this equation can be obtained by the ﬁt of the RV function. When assuming that m m , Eq. 1.4 reduces to the expression of p ⌧ ? the planet minimum mass

P 1/3 m sin i Km2/3(1 e2)1/2. (1.5) p ' 2⇡G ? ✓ ◆ Only the minimum mass, mp sin i, can be obtained by this method since the inclination, i, is not known. An expression for the semi-major axis of the relative orbit can be obtained by applying the same approximation as before to the Keplers third law,

G 1/3 a a m1/3P2/3. (1.6) ' p ' 4⇡2 ? ✓ ◆ Therefore, ﬁtting radial velocity data with a keplerian model to account for the presence of a planetary companion gives four of the six orbital elements of the relative orbit (the CHAPTER 1. INTRODUCTION 18 longitude of the ascending node, ⌦, and the orbital inclination, i, remain unknown). Note however that not knowing the inclination is not statistically relevant. If inclination angles are isotropically distributed, then edge-on orbits are a lot more frequent than face-on systems. Therefore, systems with sin i > 0.5 will have a probability of about 87% (see Lovis & Fischer 2011).

By estimating the mass of the central star using other techniques, the keplerian ﬁt will deliver a lower limit of the companion’s mass together with the semi-major axis of the relative orbit. Although, only the orbital parameters and a lower limit on the mass are known from radial velocity measurements, when combined with transit photometry, the true mass, radius and, consequently, the mean planetary density can be estimated. For a planet in a circular orbit around a solar-mass star, Eq. 1.5 simpliﬁes to

1 1/3 K [m s ] 28.57 m sin i [M ] P [yr]. (1.7) ' p Jup Since the probability of detecting a planetary signal depends in a ﬁrst approximation on the value of the velocity semi-amplitude, this expression indicates that radial-velocity measurements favour the detection of planetary systems with massive and short-period planets. As an example, the radial velocity semi-amplitude induced by Jupiter and Earth 1 on the Sun is 12.4 and 0.09 m s , respectively.

1 A very high-precision of below 1 m s can be achieved, for example, via the cross- correlation function (CCF), which uses information from several thousand lines that are averaged into a single line proﬁle, whose centroid is then used to determine de RV (e.g. Baranne et al. 1996).

1.1.3 Limitations of the radial velocity method

As was stated before, the radial velocity technique is one of the most successful method for detecting (and conﬁrming) exoplanets. However, it was not until this technique was 1 able to reach the high-precision required to detect RVs of several tens of m s when the exoplanet search by RV became so successful. To achieve this, wavelength calibration of the observed spectrum became a crucial step in data processing. Wavelength calibration data was included in the target spectrum with the aim of directly detecting any instrumental effects during the observations. Two main methods have been applied: the calibration lamp or the absorption sell. The ﬁrst uses a calibration source next to the target spectrum which will be compared with the stellar spectrum (e.g. the ”ThAr method”, see Pepe et al. 2002) while the other uses an absorption cell in front of the spectrograph, which will imprint a dense forest of absorption lines from the cell onto CHAPTER 1. INTRODUCTION 19 the spectrum (e.g. the ”iodine cell”, see Butler et al. 1996). By using either of these methods, any systematic effect in the wavelength solution of the spectrum will be directly monitored at the time of observations.

Note however that the stars themselves (and stellar properties) can affect the precision that can be achieved by the RV method. One such example is stellar rotation. Stellar rotation will broaden the spectral lines, which, in the case of fast rotating stars, would blend with neighbouring lines and reduce the attainable precision of RV (Bouchy et al. 2001). To minimise this, planet search surveys normally discard fast-rotators from their samples, which includes young stars and early-types.

1 The RV method can now achieve a precision better than 1 m s (Pepe et al. 2011), enabling the detection of planets with masses close to that of Earth (Mayor et al. 2009; Dumusque et al. 2012). At these levels of precision, one of the major limitations of the RV method comes from the RV ”noise” produced by stellar intrinsic variability. Stellar magnetic activity in the form of spots, plages, changes in the convection pattern, and others, can cause RV noise which can be easily detected by high-precision spectrographs. As an example, a spot covering 0.5% of a solar-type star will induce an RV 1 signal of around 0.5 m s (Saar & Donahue 1997; Hatzes 2002), totally hiding the signal produced by an Earth-like planet around a solar-like star (which is around 0.09 1 ms ). The knowledge of how stellar activity behaves in different stars, the connection between all the activity phenomena and RV, and ﬁnding methods to correct or minimise them, is then of extreme interest for the quest of ﬁnding another Earth orbiting in the habitable zone of another star. In the following section I will discuss the magnetic activity phenomena of other stars, always keeping the exoplanet search subject in mind.

1.2 Stellar activity

Stellar activity is what we call the phenomena produced by the presence of magnetic fields in the atmosphere of cool stars. Variations in the magnetic fields topology affects all atmospheric layers of a star ranging from the cool photosphere up to the hot corona (see e.g. Hall 2008). These variations can be observed on a large range of timescales, from minutes to years (e.g. Baliunas et al. 1995; Dumusque et al. 2011b). For example, stellar flares are magnetic bursts in the atmosphere which normally causes huge variations in the brightness and spectrum of a star with a duration of seconds to minutes. On longer timescales, stellar activity cycles, like the 11 year cycle of our Sun, are the product of changes in the global magnetic configuration, and have cyclic variations that CHAPTER 1. INTRODUCTION 20 can range from months to a few decades.

The activity phenomena induced by stellar magnetic ﬁelds is thought to be produced by dynamo processes in the stellar interior which is linked to the star’s rotation and age, in solar-type stars.

The study of stellar activity is important to understand the structure and evolution of stars and the interstellar medium but also to exoplanet search and characterisation, since activity interferes with the most used exoplanet detection methods, Doppler spectroscopy and transit techniques, and can also affect the weather and habitability of orbiting planets (see e.g. Buccino et al. 2006; Kaltenegger et al. 2010). In this work, we are mostly focused in studying the long-term activity variations of cool stars and the effects of stellar activity on the observed radial velocity.

In this section, we will discuss stellar chromospheric activity, how does it arises and which stars have it (sect. 1.2.1), the mean activity levels of stars and correlations with stellar parameters and RV (sect. 1.2.3), how to detect it and the mostly used activity proxies (sect. 1.2.2), the different timescales of activity, how they affect RV, and ways to limit the interference of activity in the detection of exoplanets (sect. 1.3).

1.2.1 Stellar chromospheric activity

The Sun, and similarly other solar-type stars, have the core in its centre, where nuclear fusion generates the energy. Surrounding the core there is a layer, the radiative zone, where the energy generated in the core is carried outward in the form of energetic photons via electromagnetic radiation. This radiative layer extends up to around 70% of the solar radius. Above, and extending up to the surface, is the convection zone where energy is transferred from the radiative zone to the solar ”surface” by convection: heated matter rises to the surface and, as it cools, its density increases and it sinks back down. This phenomenon results in the structure called granulation, where the bright granules, the regions where hot plasma is rising to the surface, are surrounded by darker boundaries, where cooler plasma is sinking down (e.g. Dravins et al. 1981). The solar disk that we see with the naked eye, and which is generally called the ”surface”, is the photosphere, which lies at the outer edge of the convection zone.

Above the photosphere, is the Sun’s atmosphere which extends itself into interplanetary space. The atmosphere is characterised by an extremely low density when compared with the solar interior. The main regions of the solar atmosphere are the inner chro- CHAPTER 1. INTRODUCTION 21

Figure 1.3: A solar ﬂare representing the solar atmosphere as a dynamic environment. Pictured here is a lighten blended version of the 304 Å and 171 Å wavelengths. Credit: NASA Goddard Space Flight Centre. mosphere and the outer and more extended corona. The chromosphere is just a few thousand km in extension. After dropping from around 15 106 K in the core to around · 5800 K in the photosphere, the temperature of the solar chromosphere increases from 4300 K just above the photosphere to around 50 000 K below the corona. At the transition region between the chromosphere and the corona, the temperature jumps from around 800 000 K to 3 106 K. For the solar atmosphere, with its low density, to · increase so much in temperature, heating mechanisms other than the ones acting in the solar interior are needed.

In a stellar atmosphere in radiative equilibrium (RE), the energy is transported through the plasma via radiation. In this scenario, the heat absorbed from the radiation field and the thermal emission of the plasma are balanced so that the outward flow of energy from the deep interior is maintained. The outward temperature rise observed in the chromosphere can occur under specific conditions in RE (e.g. Auer & Mihalas 1969; Skumanich 1970). However, since emission reversals in prominent lines such as Ca II H and K are known to be signs of departures from RE (Hall 2008), other means of heating are necessary to explain the additional radiative losses in these and other lines. The effects these mechanisms of heating have in a stellar atmospheres are what is generally called activity (Hall 2008). CHAPTER 1. INTRODUCTION 22

In the Sun and other solar-type stars, there are phenomena that deposit mechanical energy into the atmosphere covering the photosphere. This dumping of energy causes heating beyond the expected RE values for the increasingly tenuous plasma. The increase of energy in the plasma can be balanced by increasing hydrogen ionisation as it warms from 5000 K to 8000 K, which sets free a large supply of electrons ⇠ ⇠ that allows the collisional radiative cooling of the chromosphere. However, as soon as the hydrogen reservoir becomes fully ionised, the plasma loses this essential cooling mechanism and the temperature jumps from chromospheric to coronal temperatures.

The chromosphere is not an homogeneous layer. On the other hand, it is variable on the short and long timescales, and characterised by regions of hot plasma which suggest a complex magnetic topology. For example, there are tightly collimated jets of plasma streaming upward through the chromosphere, spicules and macrospicules (Roberts 1945; Bohlin et al. 1975), which are bright in H↵ and gives the chromosphere its orange colour. Furthermore, dark regions of cool gas with sub-photosphere temperatures (< 4000 K) are also observed in the chromosphere layer (Solanki et al. 1994).

Numerous definitions of chromosphere have been proposed, based on height, temperature, physical processes, or some combination of these. Figure 1.4, shows the early model of the solar chromosphere produced by Vernazza et al. (1981). In this model, the chromosphere would be a layer ranging from 500 km to around 2200 km above the photosphere. In this region the temperatures start with the minimum temperature of 4400 K in the lower chromosphere, then slowly rise to a plateaux of around 6000 ⇠ K between 1000 km and 2000 km, then abruptly jumps to 24,000 K at the upper ⇠ chromosphere at 2300 km. ⇠ Due to the complexity and dynamics that characterise a stellar chromosphere, Hall (2008) avoided the use of parameters such as height or temperature and defined the chromosphere based on physical processes at work. In his definition, a chromosphere is the regions of the stellar atmosphere where:

Emission in excess of that expected in radiative equilibrium can be observed. • Cooling occurs mainly by radiation in strong resonance lines (rather than in the • continuum as is mostly the case in the photosphere) of abundant species such as Mg II and Ca II.

This deﬁnition can be translated as a thick region of the stellar atmosphere marked by non-radiative heating and cooling which occurs mainly in resonance lines rather than in the continuum. CHAPTER 1. INTRODUCTION 23

Figure 1.4: Temperature structure derived from a semi-empirical model of the solar chromosphere. The formation heights of important lines and continua are also presented. The height in the atmosphere increases from right to the left. The column mass density is shown in the lower x-axis. From Vernazza et al. (1981).

Not all stars are expected to have a chromosphere. In cool stars, dissipation of excess mechanical heating can happen through ionisation of some elements, such as hydrogen, as the temperature of the plasma increases at larger heights above the photosphere. Hot stars with partially or highly ionised photospheres cannot dissipate the excess heating via ionisation, and thus will not sustain the extended chromosphere that can be observed on their cooler counterparts. Furthermore, surface convection is a requirement for magnetic sources of activity (through its role in maintaining the magnetic dynamo via subsurface mass transport) and non-magnetic sources of activity (explicitly) (Hall 2008). For these reasons, a chromosphere will be expected for stars having a subsurface convection zone, which in terms of spectral type means stars cooler than late A dwarfs and post-main-sequence stars that have developed convective zones. CHAPTER 1. INTRODUCTION 24

There are two main forms of activity, one generated by a self-regenerating magnetic ﬁeld (e.g. Babcock 1961), and the other produced by acoustic waves originated in convective cells (e.g. Biermann 1948; Schwarzschild 1948). A self-regenerated magnetic ﬁeld could explain the principal features of visual and magnetic observations of the sunspot cycle and is found to account for much of what we observe in the chromosphere and corona, via heating of Alfven´ waves or the transport of mechanical energy along the magnetic tubes into the outer atmosphere. The rise of convective cells to the solar surface release energy in the photosphere. This could generate a continuous stream of acoustic waves that propagate into the outer atmosphere, develop into shocks and, as they dissipate, release energy. This dissipation of acoustic energy can be a source of extra heating for the chromosphere.

The magnetic ﬁelds responsible for stellar activity in late-type stars are generally accepted to be formed by the action of an ↵⌦ dynamo (Parker 1955). This dynamo is a result from the action of differential rotation at the interface between the convective layer and the radiative core, i.e., at the tachocline (Spiegel & Zahn 1992). As a result, stellar magnetic activity is related to the existence and depth of the tachocline, and consequently, to the presence of an outer convection envelope. On main sequence stars, the depth of the convection zone varies with spectral type. Mid-M dwarfs are completely convective while F dwarfs have shallow convection layers.

It is therefore particularly important to characterise the stellar activity of stars of different spectral types to understand, for example, the generation of stellar magnetic ﬁelds by dynamo processes, the relation between activity level and the presence and depth of an outer convection zone, the persistence of stellar activity on fully convective stars, the nature of coronal heating and its relation with stellar activity, the evolution of overall stellar magnetic activity with age, or the occurrence of magnetic cycles in other stars. Determination of the activity level and its temporal evolution is also important in other ﬁelds like the detection and characterisation of extra solar planets. Since stellar activity interferes with the measured radial velocity, by adding noise or periodic signals, understanding the connection between activity and radial velocity is of extreme interest to planet hunters (e.g. Saar & Donahue 1997). The brightness of a star is also affected by rotating active regions produced by activity, and therefore its study is very important for detecting exoplanets via the transit method (e.g. Henry et al. 1997). The effect of magnetic activity on the formation and evolution of planets and their atmospheres has also been of interest in more recent years (e.g. Cuntz et al. 2000).

In this work, we are mostly concerned with exoplanet detection, mainly on the effect that stellar activity has on the measured radial velocity. We therefore will discuss the origins CHAPTER 1. INTRODUCTION 25 and consequences of stellar activity having this objective in mind.

For further reading about chromospheric activity I direct the reader to the following works: Lyra & Porto de Mello (2005), Zhao et al. (2011), and Pace (2013) have enquired about the nature of the chromospheric activity evolution; Hall (2008) presents a review of recent advances in the subject; Soderblom (2010) reviews the connection between activity and stellar ages; Strassmeier (2009) discussed its link to stellar spots; Linsky (1980) provides a review of how the chromosphere, transition region, and corona may be deﬁned (together with other topics, see also Ulmschneider 1979); and the subject of generation and propagation of acoustic waves in the solar atmosphere is discussed in Ulmschneider et al. (1977) and following papers of the same series.

1.2.2 Activity proxies

Stellar activity can be detected mainly by spectroscopy or photometry. Rotationally modulated active regions with different contrast from the surrounding photosphere result in variability of the brightness of a star. Activity studies using photometry have nowadays a great potential due to the large data gathered by the Kepler mission. This activity phenomena together with the inhibition of convection by magnetic fields, which destabilises the granulation pattern, also affect the stellar spectrum. For example, in the visible, there are lines such as Ca ii H & K and H↵ which are sensitive to the chromospheric temperature rise. In the presence of strong magnetic fields, these lines enter in emission and can be used as proxies of magnetic activity. Magnetic fields can also be measured directly by means of the Zeeman effect4 (see Reiners & Basri 2009, and references therein).

There are other activity proxies, as for example emission in UV lines and x-rays (that detects activity in the corona), which are not observed from the ground. However, dedicated satellites such as the International Ultraviolet Explorer (IUE) and the Einstein X-ray Observatory opened up these spectral windows for stellar activity research. In the NIR there is the CaII triplet, which is also widely used, mainly for cooler stars which have their emission peak in the redder area of the spectrum (e.g. Linsky et al. 1979). However not all spectrographs operate at these wavelengths and the precision of RV measurements in the NIR is lower than in the optical (Figueira et al. 2010b).

4The Zeeman e↵ect is the splitting a spectral line into several elements in the presence of a static magnetic field. The distance between the Zeeman sub-levels is a function of the magnetic field. Therefore, magnetic fields in the Sun and other stars can be calculated by measuring these distances. CHAPTER 1. INTRODUCTION 26

Active regions which are modulated by stellar rotation affect the shape of the CCF proﬁle, because it represents an average of the ﬂux in all spectral lines (e.g Queloz et al. 2001). As a result, CCF parameters such as line bisector, FWHM, or line depth, might all be affected by rotating active regions, and can therefore be used to detect RV variability induced by stellar phenomena (e.g. Queloz et al. 2001; Figueira et al. 2010a; Santos et al. 2010).

Spectral lines are formed by radiative and collisional processes. In the conditions similar to those of solar-like chromospheres, the lines of ionised metals are dominated by collisional processes while those of neutral metals are shaped by radiative processes. Collisionally dominated lines such as Ca ii H & K reveal the local plasma conditions since collisionally processes are a consequence of the local electron temperature. This can be observed in the emission reversal at the line cores. Neutral metals in general reflect continuum radiation and show no such reversal. However, strong lines such as the H↵ line, whose core is formed high in the chromosphere, are marginally photoionization- dominated in solar-like stars (Jefferies & Thomas 1959; Fosbury 1974). Due to the increase of collisional processes in the hot, high density conditions that occur during flares (or in extremely active stars), these lines start to fill in or become emission lines. For this reason, the H↵ line core has been, together with the calcium lines, extensively used in stellar activity studies.

I will now describe in more detail some of the activity proxies which were used in this thesis, namely the Ca ii H & K, H↵, Na i D, He i, and CCF parameters which are the most used optical spectroscopic activity proxies and more easily accessible to the HARPS spectrograph, which was the instrument used to produce the work described in this thesis.

Ca II H and K lines It is known for a long time that the ﬂux on the Ca ii H & K lines has a direct relationship with the number of active regions in the Sun (see e.g. Baliunas & Soon 1995), and therefore these lines are the most used activity proxies nowadays.

The use of the double ionised calcium H and K lines as an activity index was made popular among activity researchers by the Mt. Wilson ”HK program”, a project aimed at measuring the long-term activity of solar-like stars which was started in 1966 by O. Wilson (Wilson 1978). Vaughan et al. (1978) introduced the S -index, a dimensionless proxy for the Ca ii activity measured by the Mt. Wilson Observatory spectrometers. This index was based on the flux integrated in 1.09 Å passbands centred on the H (3933.66) and K (3968.47) lines and normalised to the flux in two 20 Å wide surrounding pseudo- CHAPTER 1. INTRODUCTION 27 continuum bands centred at 3901 (V band) and 4001 (R band) Å. The S -index can be defined as5 F + F S = ↵ H K , (1.8) F F B V where ↵ is a calibration constant, FH and FK the fluxes in the H and K lines, and FB and

FV the ﬂuxes in the two reference lines (e.g. Boisse et al. 2009).

The S -index can be used to control the variations of activity of a given star. However, when the S value of stars of different spectral type is compared, one needs to consider the colour and photospheric contributions to the index. The first arises from the normal- isation of the index to the two pseudo-continuum bands, one bluer and the other redder than the calcium line cores. Stars of different spectral types have different levels of flux on these spectral regions, which will affect the S value. The photospheric contribution is a result of the fact that the H & K line cores are not purely chromospheric in origin, there is also some photospheric flux in the lines. To remove the colour dependence and the photospheric component, Middelkoop (1982) and Noyes et al. (1984) developed a transformation of the S -index into a value R0 which is a function of B V and is HK normalised to the bolometric flux.

Halpha line As stated before, the most used activity diagnostic are the Ca ii H & K lines which are easily accessible in FGK dwarfs. However, when we move to cooler stars, the energy distribution starts to move to redder wavelengths and the signal-to-noise ratio decreases drastically in the H and K lines. An alternative has been the use of other spectral activity proxies at longer optical wavelengths, and one of the most used is the core of the H↵ line at 6562.808 Å (Giampapa & Liebert 1986; Stauffer & Hartmann 1986; Herbst & Layden 1987; Herbst & Miller 1989; Stauffer et al. 1991; Pasquini & Pallavicini 1991; Montes et al. 1995).

Worden & Peterson (1976) noted the central emission line reversal in H↵ lines. While studying 17 dM and dMe stars, Worden et al. (1981) found that this emission is prevalent among the ﬂare (dMe) stars.

5This method, however, is problematic for fast-rotating stars. In rapid rotators, the wings of the H and K lines fill up the centre of the absorption line and the emission line flux in the core is also lost due to rotational broadening. But in the context of planets searches the fast rotators are normally ignored since, due to the connection between stellar rotation and activity (the faster is the rotation, the higher is the activity), these stars will have a large RV jitter. Nevertheless, Schroder¨ et al. (2009) developed a method to measure Ca ii H & K emission in very rapid rotating stars by comparing the line shapes from known inactive slowly rotating template stars that have been artificially broadened to those of fast rotators. CHAPTER 1. INTRODUCTION 28

It has been suggested that the H↵ line may be formed in two distinct layers of the atmosphere: the broad emission component in the low-lying chromosphere and any displaced absorption in the outer parts of the stellar wind (Heidmann & Thomas 1980).

Cram & Mullan (1979) studied the behaviour of the Balmer lines (H↵,H,H). These are weak absorption lines when no chromosphere is present. However, as the amount of chromospheric material (from Te = 5500 K to 50 000 K) increases, these absorption lines first become deeper, then develop emission peaks on the outer edges of their wings, and finally, when the chromosphere is sufficiently massive, they become strong emission lines.

The stellar continuum near H↵ varies along with bolometric luminosity (Hall 1996; Walkow- icz et al. 2004; Cincunegui et al. 2007b) and as a consequence, the ﬂux in the line is expected to vary not only with chromospheric activity but also with spectral type. Therefore, a bolometric correction is needed before the H↵ line can be used to compare the activity of different stars (see Walkowicz et al. 2004).

A positive correlation between the chromospheric fluxes of the Ca ii H & K and H↵ lines has been suggested by several authors (Montes et al. 1995; Strassmeier et al. 1990; Robinson et al. 1990; Giampapa et al. 1989). But the majority of the studies where this relation was observed used averaged fluxes for both lines which were not obtained simultaneously. On the other hand, Thatcher & Robinson (1993) measured the fluxes at a particular moment of each star by using simultaneous observations but they were only observed once. Cincunegui et al. (2007b) measured the long-term variations of the H↵ and Ca ii lines over 7 years for 109 mid-F to mid-M stars and found a wide range of correlations, from strongly positive to strongly negative, to cases with no correlation at all. They found no evidence of dependence of the correlations on spectral type or level of activity. Even when the analysis is restricted to hydrogen line emission stars (dMe), where the conditions on the chromosphere are supposed to produce mechanisms of formation of the lines that are similar, the correlation is different from star to star. The authors also found that the observed correlations are the product of the dependence of each flux on stellar colour and not of similar activity levels. Since both the H↵ and Ca ii H & K lines are generally formed under different conditions, their behaviour can be different when observing different stars with different chromospheric conditions (Soderblom et al. 1993).

Na I D1 and D2 lines The Na i D1 and D2 resonance lines (D1: 5895.92 Å; D2: 5889.95 Å) can be observed in the spectra of all stellar types, however, for cooler stars (late- CHAPTER 1. INTRODUCTION 29

G to M) the doublet starts to develop strong absorption wings. For the most active stars, chromospheric emission in the core of the D lines becomes visible, which is an indication of collision-dominated formation processes. For instance, Worden et al. (1981) observed central emission in the cores of the Na i D lines for dMe stars, and that the emission is strongly correlated with H↵ line emission. The sodium D lines can be used as a complement to the H↵ line for M dwarfs since they provide information of the conditions in the middle-to-lower chromosphere, as opposed to H↵ that is a diagnostic of the conditions of the upper chromosphere and low transition region (Andretta et al. 1997; Short & Doyle 1998; Mauas 2000).

D´ıaz et al. (2007a) studied different features of the D lines using medium-resolution echelle spectra of 84 late F to middle M dwarfs. They deﬁned an index N similar to the

Mount Wilson S index: they divided the flux in the core of the D1 and D2 lines by the flux in two redder and bluer pseudo-continuum reference bands. The authors found that when the colour dependence of N and S is taken into account, the correlation between both indices varies from tightly correlated for some stars to cases of no correlation. However, the two indices are well correlated for active stars with emission in the Balmer lines. They conclude that the N index can be useful when comparing the activity variations of individual stars, mainly for later types where little emission is observed in the Ca ii H & K lines. To compare the activity levels on stars of different spectral types, they defined an enhanced index, R0D (analogous to R0HK for the calcium lines) that takes into account the photospheric contribution to the flux both in the lines and in the continuum windows. As was expected, earlier stellar types do not show any signs of correlation between both indices. However, the R0D index was found to correlate well with

R0HK for the most active stars which exhibit the Balmer lines in emission, even though some of these stars do not present a line reversal at the core of the D lines. Therefore,

R0D is also a good activity indicator for these stars.

HeI D3 line Another useful diagnostic of chromospheric activity in the optical domain is the He i D3 line centred at 5876 Å. This line is normally seen as an absorption feature in F-dwarfs and moderately active G and K-dwarfs (Huenemoerder 1986; Biazzo et al. 2007). The He i absorption requires a temperature of 10 000 K to be formed and ⇠ therefore, it is a diagnostic of the upper chromosphere, and particularly useful for F- stars in which the other activity indicators in the optical are more difﬁcult to be observed due to the strong continuum ﬂux (e.g. Rachford & Foight 2009) CHAPTER 1. INTRODUCTION 30

Parameters of the CCF profile As was stated previously, one widely used and very precise method for the determination of the RV of a star is to measure the wavelength shifts observed in the CCF of the stellar spectrum (for a detailed description see e.g. Baranne et al. 1996; Pepe et al. 2002). The CCF corresponds to an average of all the spectral lines used in the correlation mask (Mayor 1985). As a result, any stellar ”phenomenon” having the ability to influence the lines included in the mask will also influence the CCF line profile (e.g. changing its shape, width, or depth). Asymmetries in the profile of spectral lines can be produced by active regions rotating with the stellar surface (see next section). These effects will be detected in the parameters of the CCF that quantify its profile, such as the line bisector, the full-width-at-half-maximum (FWHM), and contrast (line depth). Consequently, the parameters of the CCF are good proxies of RV induced by activity phenomena. If simultaneous measurements of RV and these parameters are correlated, then it is very probable that the RV variations are being induced by stellar atmospheric changes (e.g. Queloz et al. 2001; Santos et al. 2001; Boisse et al. 2009; Santos et al. 2010).

There are various ways to quantify the shape of the spectral line bisector. The bisector velocity span is the difference in bisector velocity between the upper and lower regions of the line, discarding the core and the wings (Toner & Gray 1988; Hatzes 1996; Queloz et al. 2001). The bisector inverse slope (BIS) is the difference between the mean bisector velocity in the 10-40% of the line depth (at the continuum is 0%), and the mean bisector velocity in the 55-90% region of the line (Queloz et al. 2001; Santos et al. 2002). The bisector curvature is the difference between the upper and the lower halves of the line bisector (e.g. Hatzes 1996; Nowak & Niedzielski 2008). For example, an anti-correlation between BIS and RV is often used as a diagnostic of RV induced by spots (Queloz et al. 2001), while positive correlations have been observed for long-term (cycle) observations (e.g. Dumusque et al. 2011a). At these timescales, the FWHM of the CCF proﬁle is also generally correlated with RV while the CCF contrast is normally anti-correlated (e.g. Dumusque et al. 2011a).

1.2.3 Mean activity level of stars

The study of stellar activity is now decades old (e.g. Baliunas et al. 1995; Hall et al. 2007), and the results start to accumulate. In 1957, Wilson & Bappu (1957) detected a positive correlation between the width of the Ca ii K emission and the absolute visual magnitude of stars which is independent of spectral type – the so called Wilson-Bappu effect. This effect can be used to estimate the absolute magnitude of nearby stars by CHAPTER 1. INTRODUCTION 31 measuring the Ca ii K width (Wallerstein et al. 1999). Another important result is the distribution of mean activity level. Vaughan & Preston (1980) found that the activity level distribution is not continuous from low activity to hight activity stars, but that there is a gap in the number of moderately active stars. This gap became known as the Vaughan- Preston gap. The majority of the stars with a Solar-like activity cycle appear to have activity levels at around log R0 = 4.9 while the rest have higher activity levels near HK log R0 = 4.5, with the gap being at log R0 = 4.75 (Henry et al. 1996). However, HK ⇠ HK more recently, early results from the Kepler mission appear to show that the proportion of active stars might be higher than what was expected (Basri et al. 2010).

Stellar activity is also known to have a connection with stellar age. The chromospheric emission in the Ca ii H & K lines and the rotational velocity were shown to be inversely proportional to the square root of the age of the stars – the Skumanich law (Skumanich 1972).

Another important result from the study of the mean activity level of stars is the direct evidence of the dynamo related activity in late-type stars that was shown by Noyes 6 et al. (1984) in the form of a correlation between the Rossby number and log R0HK level. Because of this, the activity level of a star is related to its rotational period (Noyes et al. 1984).

The majority of the activity surveys found in the literature are based on measurements of the Ca II H & K lines. The HK Project at Mount Wilson Observatory operated from 1966 through 2003 and obtained an extensive collection of multiple observations of 1300 ⇠ stars over a period of 40 years, contributing with a large dataset and long timespan to analyse magnetic cycles in other solar-like stars (Wilson 1978; Duncan et al. 1991; Baliunas et al. 1995). Other large datasets include Henry et al. (1996) ( 800 stars), ⇠ Strassmeier et al. (2000) ( 1000 stars), Wright et al. (2004) ( 1200 stars), Gray et al. ⇠ ⇠ (2006) ( 1700 stars), Isaacson & Fischer (2010) ( 2600 main-sequence and giant ⇠ ⇠ stars). Lovis et al. (2011) used the HARPS GTO sample to study the relation between magnetic cycles and RV of 304 FGK stars over a timespan of 7 years. More recently, Zhao et al. (2013) published a huge catalog of over 13 000 F, G and K disk stars with measured Ca ii H & K emission. Other large surveys using the H↵ line include that of West et al. (2004) ( 8000 late-type dwarfs). ⇠ Not only is the study of the activity level of stars important per se, but it is also crucial for the ﬁeld of extrasolar planet research. The activity level of stars is also correlated to the observed RV noise or ”jitter” and can prevent the detection of extrasolar planets

6The Rossby number describes the Coriolis accelerations arising from a body in rotation CHAPTER 1. INTRODUCTION 32 by hiding their RV signal. Strong photospheric features like spots or the inhibition of convection, which are directly related to the activity level of stars, can induce RV noise 1 with amplitudes up to tens of m s (Saar & Donahue 1997; Saar et al. 1998; Santos et al. 2000). Apart from the average activity level of stars which is proportional to their RV jitter, the time evolution of activity is also extremely important for planet hunters. That will be the subject of the following section.

1.3 Stellar activity at di↵erent time scales and its inﬂuence on RV

Three distinct stellar intrinsic physical phenomena contribute to perturbations on RV that are considered by exoplanet hunters as ”stellar noise”: oscillations, granulation, and magnetic activity. These physical phenomena have different timescales, or manifest themselves in RV at different timescales. The timescales range from minutes to several years and can add RV noise to potential planetary signals, or even induce periodic signals which can simulate the ones produced by exoplanets. Table 1.1 summarises these types of stellar induced RV noise and gives some examples on how to correct them. In the following sections, we will describe the different types of stellar noise that affect the RV based on their timescales, starting from the short-term effects produced by stellar oscillation modes and granulation phenomena, moving to the effect of rotationally modulated magnetic active regions which affect the RV on timescales similar to the stellar rotation period, and ﬁnishing with the long-term effects of magnetic cycles which have periodicities of several years.

1.3.1 Oscillations and Granulation

P-mode oscillations Turbulent convection can excite pressure waves which propagate at the surface of stars with outer convective envelopes and leads to the dilatation and contraction of the stellar external envelopes. These oscillations have timescales of a few minutes in solar-type stars (5–15 min for the Sun; Schrijver & Zwaan 2000) and cause RV variations with amplitudes per mode of up to a few centimeters per second (e.g. Bouchy & Carrier 2001; Kjeldsen et al. 2005). However, the superposition of a large number of these modes can induce RV signals that can reach several meters per second (Schrijver & Zwaan 2000; Bouchy & Carrier 2003; Bedding & Kjeldsen 2003; CHAPTER 1. INTRODUCTION 33

Table 1.1: Stellar activity at di↵erent timescales and correction of RV.

Activity type Typical timespan Typical RV correction Pulsations (p-mode) 5-15 min Average signal over typical timespan Granulation min-hours Average signal over typical timespan Modulated active regions days to months Simultaneous activity measurements

(stellar Prot) and removal of signal Using activity-RV slope Activity cycles years Simultaneous activity measurements and removal of signal Using activity-RV slope

Bedding et al. 2007). Modern spectrographs such as HARPS, can reach radial-velocity precisions of sub-meter-per-second using short exposure times for bright stars (typically 1 1ms in 1 min for a V = 7.5 K dwarf, Pepe et al. 2005). As a consequence, RV variability produced by p-mode oscillations can be observable and will interfere with the detection of exoplanets (Fig. 1.5).

The frequency of the oscillations scale with the square root of the mean stellar density, while the RV amplitudes scale with the luminosity-to-mass ratio, L/M (Kjeldsen & Bed- ding 1995; O’Toole et al. 2008). As a result, the period of oscillations and amplitude of the produced RV signal will increase towards early-types and evolved stars. This means that F dwarfs will have longer oscillation periods and higher RV amplitudes than K dwarfs and subgiants will have longer period of oscillations and higher RV amplitude than dwarfs.

On the other hand, the lower-mass dwarf stars will be less affected by this type of ”noise” and will, therefore, be easier targets for planet searches. Nevertheless, the noise is still present in these types of stars and can affect the detection of the lower semi-amplitude RV signals induced by planets with low-mass or in longer orbits. It is then necessary to average out this signal in order to increase the RV precision to the sub-meter level. A careful observation strategy, with integer times longer than one or two typical oscillation 1 periods, will be sufﬁcient to decrease the effect of this type of noise below the 1 m s level for dwarf stars (e.g. Santos et al. 2004; Dumusque et al. 2011b).

Tinney et al. (2005) suggested that exposure times of integer multiples of the peak 1 oscillation periods could decrease oscillations induced jitter by 1 to 2 m s . Mayor et al. (2003) recommended using exposure times of around 15 min to minimise the impact of CHAPTER 1. INTRODUCTION 34

Figure 1.5: RV variations produced by oscillations for ↵ Cen A (upper panel) and Hyi (lower panel). From O’Toole et al. (2008). oscillations.

Granulation Solar-type stars with an outer convection zone will have a granulation pattern visible at the photosphere. This pattern is made of bright cells, where the hot plasma is rising to the surface, surrounded by darker ﬁlaments, where the plasma cooled down and returns to the stellar interior. As a result, these granulation features have positive or negative radial velocity signatures. But, since the brighter granulation patterns are larger than the darker ones, there will be a non-zero average radial velocity – the convective blueshift (see Fig. 1.6). This is what produces the ”C”-shapes observed on the line bisectors of solar-type stars (e.g. Dravins et al. 1981). On the 1 Sun, the typical radial velocities of convective motions are 1-2 km s . However, the disk-averaged radial velocity jitter will be of the order of the meters per second for the Sun and maybe less for cooler stars (e.g. Palle et al. 1995; Dravins 1990). Granulation has typical timescales up to 25 min (Title et al. 1989; Del Moro 2004). On larger scales in terms of size and lifetime, there is mesogranulation (Palle et al. 1995; Schrijver & Zwaan 2000) and, with timescales that can reach 33h in the Sun (Del Moro 2004), supergranulation, which corresponds to larger convective structures. In active regions, these convective phenomena will be attenuated due to the presence of strong magnetic CHAPTER 1. INTRODUCTION 35

Figure 1.6: Illustration of spectral line asymmetries and wavelength shifts caused by granulation. Left: Schematic of the granulation pattern in a solar-type star. Here 75% of the surface is covered by bright outflow granules while the rest is covered by intergranular downflow dark lanes. Centre: Spectral lines representing the bright granules (top profile) and dark lanes (lower profile). Right: The dashed profile is the undisturbed line resulting from a static atmosphere without velocity patterns. The solid profile is the line profile resulting from the combination of the two profiles in the centre panel (average over many granules). The bisector line shows the asymmetry of the profile caused by the granulation pattern. It can also be seen that the core of the line has been blueshifted by this e↵ect. From Dravins et al. (1981).

ﬁelds and, consequently, the overall convective blueshift will be lower – there will be an inhibition of convection – and this will affect the measured radial velocity of the star (e.g. Dravins 1982; Livingston 1982; Brandt & Solanki 1990; Gray 1992; Meunier et al. 2010). The effect of granulation on RV has amplitudes similar to those induced by p- mode oscillations, at the meter-per-second level (e.g. Dravins 1999; Schrijver & Zwaan 2000; Kjeldsen et al. 2005; Dumusque et al. 2011b).

The impact of granulation and oscillation modes on RV can be reduced by using careful observational strategies. Dumusque et al. (2011b) arrived at the conclusion that the best observing strategy to attenuate these two effects is to make 3 measurements per night of 10 min each and two hours apart. Using this strategy, they found that a 3 MEarth at the habitable zone (HZ) of a K1 dwarf (with a period of 200 days) can be detectable with HARPS, and therefore, granulation and oscillations will not prevent the detection of Earth-like planets in the HZs of stars. The RV variations induced by granulation and oscillations are dependent on the spectral type and surface gravity of the stars CHAPTER 1. INTRODUCTION 36

(Dumusque et al. 2011b). The induced RV amplitude will increase towards early-types and lower gravity stars, implying that an evolved G star will be more affected by this kind of noise than a non-evolved K dwarf.

1.3.2 Rotationally modulated active regions

Active regions are inhomogeneities in the stellar photosphere that are produced by magnetic ﬁelds at the surface of solar-type and M-type stars. These features can be dark spots, which have temperatures lower than the surrounding photosphere, and bright plages, which have higher temperatures. In fact, normally active regions consist of both spots and plages.

Since these features have different temperatures than the photosphere, they will affect the spectral lines, by decreasing its flux in the case of spots, or increasing it in the case of plages. As the star rotates, these active regions will move from the blueshifted half of the stellar disk to the redshifted half, attenuating or increasing the flux in the spectral lines as they move, varying the line shapes. This effect will distort the lines and make their centroid, the minimum of the line where RV is measured, move from blueshifted to redshifted, introducing temporal modulations (see Fig. 1.7 for an illustration of this effect). Therefore, an artificial RV signal with timescales similar to that of the rotation period of the star can be produced which will interfere with the signal induced by an orbiting planet by adding noise or simulating false planetary signals (Vaughan et al. 1981; Baliunas et al. 1983; Saar & Donahue 1997; Saar et al. 1998; Santos et al. 2000; Queloz et al. 2001; Henry et al. 2002; Wright 2005; Huelamo´ et al. 2008; Queloz et al. 2009; Lagrange et al. 2010; Boisse et al. 2011). Since spectral lines are distorted due to the presence of spots and plages, one natural diagnostic of activity is the line bisector. An anti-correlation between BIS and RV is normally observed in cases of RV induced by rotating active regions (e.g. Queloz et al. 2001; Huelamo´ et al. 2008; Queloz et al. 2009; Boisse et al. 2011).

For a given spectral type, the properties of active regions depend mainly on their mean activity level, which depends on stellar age. In general, solar-type stars have a tendency to decrease in rotational velocity with time. As they age, their rotational velocities will slow down from around 1-2 days at Myrs to around 20-50 days at 5 Gyrs. As a consequence, the activity produced by the magnetic dynamo will decrease, and active regions will become less proeminent. As a result, younger fast rotating stars will have higher amplitude RV noise. For example, main sequence stars younger than 1 Gyr can CHAPTER 1. INTRODUCTION 37

Figure 1.7: Example of a radial-velocity shift induced by a single spot for two contrast values. Three di↵erent phases of the star rotation are shown. Top panel: location of the spot on the stellar disk at di↵erent phases. Centre panel: line profiles (solid) and residuals between the profile of the quiet photosphere and the profile of the spotted star (dashed). Black lines represent a cool spot and red lines a hot spot. Lower panel: observed radial- velocity shift at the di↵erent phases. From Reiners et al. (2010).

1 have dark spots causing RV variations in excess of 100 m s , enough to completely hide a Jupiter-like planet orbiting a Sun-sized star7 To avoid this, young stars are normally not included in planet search surveys. Old, slowly rotating stars are more quiet and, in favourable conditions and a good treatment of activity noise, can enable RV precisions 1 to arrive at the 1 m s level, or even lower (e.g. Queloz et al. 2009; Dumusque et al. 2012). Another approach would be to use near-infrared observations since the contrast of dark spots is expected to be lower than at optical wavelengths (see e.g. Reiners et al. 2010; Huelamo´ et al. 2008).

The effects that spots and plages have on spectral lines could cancel each other if their temperatures were symmetric when compared to the photosphere and their ﬁlling factors (the fraction of the disk total area that they cover) the same. However, this is

7 1 Note that for very young stars still in the formation stage, these e↵ects be of the order of km s (e.g. Melo 2003). CHAPTER 1. INTRODUCTION 38 generally not the case (e.g. Chapman et al. 2001). Furthermore, another effect of activity is the inhibition of convection by strong magnetic ﬁelds in active regions (e.g. Dravins 1982; Livingston 1982; Gray 1992). This will add to the overall RV noise produced by 1 rotating active regions to values that vary between 40 cm s at minimum of activity to 1 140 cm s at maximum for the case of the Sun (Meunier et al. 2010).

The induced RV signal will have a period similar to that of the rotation period of the star and the corresponding harmonics (Boisse et al. 2011). These signals can be diagnosed if simultaneous measurements of RV and activity proxies like the ﬂux of chromospheric Ca ii H & K lines are carried out. If the RV signal has the same periodicity than the activity indicator, then the observed signal could be due to intrinsic stellar phenomena (e.g. Queloz et al. 2001). However, since the lifetime of spots on the stellar disk is typically of a few rotational periods (Howard 2000), the distribution of spots will be different after several rotations, and therefore the amplitude and phase of the signal will be different. Nevertheless, rotational activity induced RV can be modelled if the radial velocity is selected over time intervals of a few rotations and sinusoidals are ﬁtted at the rotational period and its harmonics (Boisse et al. 2011). Furthermore, precisions 1 as high as 10 cm s can be achieved if a large quantity of data is binned and averaged over rotational period timescales. In this case, it would be possible to detect Earth-sized planets orbiting in the habitable zone of solar-type stars.

The number of active regions present on a star vary drastically with the star’s magnetic cycle: with more of these regions at the maximum of the cycle and less, or even none, at the cycles’s minimum. This will be a another source of stellar noise at a longer timescale and will be discussed in the following section.

1.3.3 Long-term activity: magnetic cycles

It is well known that the Sun has a 11 year-long activity cycle and a 22-year period in which the polarity of its global magnetic ﬁeld is reversed. During the activity cycle the activity level of the Sun varies between log R0 = 5 at the minimum and around HK log R0 = 4.75 at the maximum. As the Sun moves from low activity to high activity HK levels, active regions start to arise at latitudes of around 30. With increasing activity level, the number of active regions increases, but the latitude at which they appear starts to decrease. The maximum of activity is reached at 15. From this moment on, the ± number of active regions (and therefore activity level) decreases while migrating further towards the equator, at which point, the minimum of activity is again reached, and no CHAPTER 1. INTRODUCTION 39

Figure 1.8: Upper panel: The Sun’s butterﬂy diagram showing the sunspot area appearing at di↵erent latitudes. Lower panel: Average daily sunspot area during activity cycles. Credit: Nasa/NSST. active regions are present. The Sun has different rotation rates at different latitudes, with faster rotation for latitudes closer to the equator. Furthermore, active regions tend to appear at preferred longitudes (e.g. Berdyugina & Usoskin 2003; Ivanov 2007) which will turn with the Sun’ differential rotation. This 11-year sunspot cycle with varying latitudes can be observed in the butterﬂy diagram (Fig. 1.8).

Other stars are also known to possess long-term activity variations similar to the Sun’s 11-year cycle (e.g. Baliunas et al. 1995; Buccino & Mauas 2008). The pioneer work of O. Wilson at the Mt. Wilson Observatory (MWO) gave us a solid base of information regarding the magnetic activity cycles of other stars (Wilson 1978; Duncan et al. 1991; Baliunas et al. 1995, 1998). It was found that 60% of the sample showed periodic cyclic variations, while 25% presented irregular variability, and 15% had ﬂat activity. Flat activity stars are suspected of being in a Maunder minimum state (Baliunas & Jastrow 1990), similar to that of the Sun in the seventeenth century when solarspots were extremely rare to observe for a period of around 30 years. Stars having cycles with multiple periodicities were also found in the sample (Baliunas et al. 1995). An example of three stars from the MWO programme showing the three different cycle classiﬁcation CHAPTER 1. INTRODUCTION 40

Figure 1.9: Example of three stars from the MWO survey showing the three long-term classiﬁcation: variable or irregular cycle (upper); periodic cycle (middle); ﬂat activity (lower). From Baliunas et al. (1998).

can be observed in Fig. 1.9. More recently, Lovis et al. (2011) studied a sample of FGK stars using HARPS and detected a similar distribution of stars with cycles. They also found that the cycle amplitude is proportional to the average activity level.

It is generally accepted that the ↵⌦-dynamo (Parker 1955) is the model which describes the generation of strong magnetic fields in solar-type stars. This model was later extended to include F- and M- type stars (e.g. Robinson & Durney 1982; Saar & Brandenburg 1999; Lorente & Montesinos 2005). As explained before, the dynamo model explains the generation of magnetic field via a interaction between the differential rotation, ⌦-effect, and convective motions, ↵-effect, at the tachocline. As a result, the existence of magnetic activity cycles are dependent on the presence and depth of an outer convection layer. This will restrict the stellar types with cycles to those between F- and early-M stars. However, there is observational evidence that low-mass fully- convective stars do possess strong magnetic fields and even activity cycles (e.g. West et al. 2004; Reiners & Basri 2007; Cincunegui et al. 2007a; D´ıaz et al. 2007b; Reiners & Basri 2010; Shulyak et al. 2011). A pure ↵2-dynamo driven by turbulent convection CHAPTER 1. INTRODUCTION 41 could be able to generate large-scale magnetic fields in these cool stars (see Chabrier &Kuker¨ 2006; Dobler et al. 2006). Browning (2008) developed a 3-D dynamo model for fully-convective M stars which indicates that these stars are able to produce kG- strength magnetic fields without the need of a tachocline. However, it is still uncertain if there is an abrupt transition from a rotational to a turbulent dynamo at the fully-convetive boundary or if this transition is gradual. This will have implications for long-term cyclic activity, and therefore, it is of special interest to study the long-term activity of M-dwarfs, in particular near the fully-convective limit.

The length of the activity cycles is related to the stellar rotation period and other stellar parameters. Baliunas et al. (1996) found an inverse relation between cycle length and rotation period, i.e., faster rotating stars have shorter activity cycles, and that this relation can be explained via dynamo theory. A similar correlation was also found by Olah´ & Strassmeier (2002) using photometric data of active stars. A dependence between the activity cycle, the rotational frequency, and Rossby number was later found by Brandenburg et al. (1998) and Saar & Brandenburg (1999).

Long-term activity cycles are expected to induce artificial RV signals which interferes with planets searches (Campbell et al. 1988; Dravins 1985). The influence of long- term activity cycles on RV has been investigated with no definite conclusions (Paulson et al. 2002, 2004; Wright 2004, 2005; Isaacson & Fischer 2010; Santos et al. 2010) until recently, when Dumusque et al. (2011a) and Lovis et al. (2011) showed that such a correlation exists for FGK stars. The previous failures to establish a correlation were attributed to the lack of precision in RV, long timespan of observations and sample limitations (Lovis et al. 2011).

The correlation between long-term activity and RV is supposed to be caused by the inhibition of convection produced by active regions (Dravins 1985; Meunier et al. 2010). As the activity level gets higher during the cycle, the ﬁlling factor of active regions increases. This will decrease the total convection in the star, and consequently the convective blueshift, making the star look redder (Dravins 1982; Livingston 1982; Brandt & Solanki 1990; Gray 1992; Meunier et al. 2010). Consequently, a positive correlation between long-term activity and RV can be expected during these cycles (Saar & Fischer 2000; Lindegren & Dravins 2003; Meunier et al. 2010; Lovis et al. 2011; Dumusque et al. 2011a)8. This was in fact detected by Dumusque et al. (2011a) and used to correct the RV of the planet hosts HD 137388, HD 204941, and HD 7199. The authors ﬁtted the activity signal observed in the log R0HK time series, and applied the same solution to

8Other e↵ects may add signiﬁcant RV noise during activity cycles. For example, Makarov (2010) suggested 1 that global changes in large-scale surface ﬂows can be responsible for RV rms of 1.4 m s . CHAPTER 1. INTRODUCTION 42

Figure 1.10: Long-term correlations between RV and the activity proxies log R0HK, BIS, FWHM, and contrast for HD 7199. The RV residuals (O–C) are the raw RVs after removing the detected planet. Blue points correspond to all the measurements. Red squares are 3 month-bins to average out short-term activity scatter. From Dumusque et al. (2011a).

the RV data, efﬁciently removing the artiﬁcial RV. Apart from the activity-RV correlation, other long-term correlations were also detected between RV and the CCF parameters BIS, FWHM, and contrast (Fig. 1.10).

So, if RV and activity indicators are measured simultaneously, the RV data can be easily corrected from the effect of magnetic cycles by using two different approaches: by adding a periodic component in the keplerian model with the same period and phase as the ones observed in the activity indices as in Dumusque et al. (2011a), or by using the sensitivity model presented by Lovis et al. (2011) to correct the RV based on a ﬁt of the magnetic cycle on the activity data.

Meunier et al. (2010) suggested that the magnetic cycle of the Sun could be responsible 1 for an RV of around 10 m s . For other solar-type stars, the amplitude of the induced RV CHAPTER 1. INTRODUCTION 43

1 can be up to 25 m s (Lovis et al. 2011). While studying the activity cycle-RV correlation for a sample of FGK stars, Dumusque (2010) found that G dwarfs are more sensitive to induced RV than K dwarfs (also pointed out by Santos et al. 2010). If this trend can be extrapolated to M dwarfs, it could suggest that these stars would have the less induced long-term RV noise, and are thus easier to detect smaller-mass or longer-period planets. However, a comprehensive study of the long-term correlation between activity and RV for M dwarfs using a large sample was never carried out before. This is one of the results of this thesis that we will discuss in the following chapter.

1.4 Motivation

In this thesis I study the topic of stellar activity and its inﬂuence on the detection of exoplanets. The main focus is on long-term effects of activity on RV in the smaller and cooler stars of the HR diagram, namely M dwarfs. This topic was chosen for two main reasons:

M dwarfs are optimal targets for the search of small habitable zone exoplanets • using the RV method. A planet orbiting an M dwarf will produce an higher RV semi-amplitude than if it is orbiting a larger mass star. Furthermore, since M dwarfs are cooler, the habitable zone of the star will be at a shorter distance to the star, and thus, increasing the RV semi-amplitude induced by an habitable zone planet when compared to solar-type stars (Kasting et al. 1993). The majority of the stars in the solar neighbourhood are M dwarfs (around 75%, according to Henry 2009), as a result, it will be increase the statistically chances of detecting an Earth analog around these stars. Recent statistical studies also suggested that there is a tendency for the smaller planets to orbit lower mass stars (Bonﬁls et al. 2013).

M dwarfs are the least studied stellar types in terms of long-term activity. To date • there are no comprehensive studies using large samples that focused on activity cycles of M dwarfs, nor how those cycles can affect the observed RV. Only a few studies were done where attempts were made at detecting activity cycles, or where long-term activity was compared with RV (e.g. Cincunegui et al. 2007a) There is also an interest in the study of activity of M dwarfs due to the fact that at mid-M types these stars become fully convective and a different type of dynamo process might be responsible for the generation of magnetic ﬁelds. It is still not CHAPTER 1. INTRODUCTION 44

known if this change in activity generation is an abrupt process or happens in a smooth transition from eary-M to later-M dwarfs.

The chromospheres of M dwarfs might be very different from those of solar-type stars due to higher depth of the convection layer, or to the lack of a radiation core in the case of later-M types. Therefore, activity indices that are used in FGK stars can behave differently in M dwarfs. Furthermore, since these stars have their emission peak at redder wavelengths, other indices might be more appropriate than the famous log R0HK index based on the Ca ii H & K emission lines. The H↵ line is a widely used activity proxy used for later type stars, however there are indications that a strict relation between this index and the ﬂux in the Ca ii lines is not so linear (e.g. Cincunegui et al. 2007b). It is then very important to establish the relation between these two indices and to compare them with others to try to ﬁnd a more appropriate activity index (that can also follow the Ca ii lines) for these stars in order to fully understand the behaviour of long term activity in M dwarfs.

Another topic of this thesis is the correlation between two widely used activity proxies: the ﬂux in the Ca ii H & K and in the H↵ lines. These two indices are normally used to follow stellar activity of different stellar types, but it is known that they are not always correlated (e.g. Cincunegui et al. 2007b). Since activity measurements are very important to diagnose RV noise of stellar origin when searching for planets, understanding how to use and how activity indicators behave is crucial to this ﬁeld.

In the next three chapters I will discuss and try to give answers to the questions:

1. How do different indices behave when measuring the activity of M dwarfs?

2. Do M dwarfs have activity cycles similar to those of the Sun and other stars?

3. What is the effect of long-term activity variations on the RV of M dwarfs?

4. Why do some stars show long-term correlation between Ca ii H & K and H↵ lines while others show anti-correlation or no correlation at all?

The ﬁrst two papers (chapters 2 and 3) investigate points 1 to 3 while the last paper (chapter 4) discusses question 4. My contribution in these three works was to analyse, interpret the data and to write the papers. Chapter 2

Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program I. Comparison of activity indices

45 A&A 534, A30 (2011) Astronomy DOI: 10.1051/0004-6361/201116971 & c ESO 2011 Astrophysics

Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program I. Comparison of activity indices

J. Gomes da Silva1,2,N.C.Santos1,2,X.Bonﬁls3,X.Delfosse3,T.Forveille3,andS.Udry4

1 Centro de Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal e-mail: [email protected] 2 Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Portugal 3 UJF-Grenoble 1 / CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, 38041 Grenoble, France 4 Observatoire de Genève, 51 Ch. des Maillettes, 1290 Sauverny, Switzerland Received 28 March 2011 / Accepted 25 August 2011

ABSTRACT

Context. The search for extra-solar planets similar to Earth is becoming a reality, but as the level of the measured radial-velocity 1 reaches the sub-m s ,stellarintrinsicsourcesofnoisecapableofhidingthesignaloftheseplanetsfromscrutinybecomemore important. Aims. Other stars are known to have magnetic cycles similar to that of the Sun. The relationship between these activity variations and the observed radial-velocity is still not satisfactorily understood. Following our previous work, which studied the correlation between activity cycles and long-term velocity variations for K dwarfs, we now expand it to the lower end of the main sequence. In this first paper our aim is to assess the long-term activity variations in the low end of the main sequence, having in mind a planetary search perspective. Methods. We used a sample of 30 M0–M5.5 stars from the HARPS M-dwarf planet search program with a median timespan of observations of 5.2 years. We computed chromospheric activity indicators based on the Ca HandK,H↵,HeD3, and Na D1 and D2 lines. All data were binned to average out undesired e↵ects such as rotationally modulated atmospheric inhomogeneities. We searched for long-term variability of each index and determined the correlations between them. Results. While the S Ca II,H↵,andNaindices showed significant variability for a fraction of our stellar sample (39%, 33%, and 37%, respectively), only 10% of our stars presented significant variability in the He index. We therefore conclude that this index is apooractivityindicatoratleastforthistypeofstars.AlthoughtheH↵ shows good correlation with S Ca II for the most active stars, the correlation is lost when the activity level decreases. This result appears to indicate that the Ca H↵ correlation is dependent on the activity level of the star. The Na lines correlate very well with the S Ca II index for the stars with low activity levels we used, and are thus a good chromospheric activity proxy for early-M dwarfs. We therefore strongly recommend the use of the Na i activity index because the signal-to-noise ratio in the sodium lines spectral region is always higher than for the calcium lines. Key words. techniques: spectroscopic – stars: late-type – stars: activity

1. Introduction by extra-solar planets (Queloz et al. 2001; Bonfils et al. 2007; Huélamo et al. 2008). It is therefore extremely important to study The increase in precision of the radial-velocity instruments is and try to understand how stellar activity produce these signals leading to the detection of smaller reflex semi-amplitude signals and how they can be corrected for. induced by extra-solar planets (e.g. the 1.9 M planet discovered by Mayor et al. 2009). Also, as the observation timespan Studies conducted at the Mount Wilson observatory uncov- increases, the detection of planets in longer orbital periods is be- ered that many solar-like stars have magnetic cycles similar to coming possible (e.g. Wright et al. 2008). that of the Sun (Wilson 1978; Baliunas et al. 1995). These stud- 1 ies concluded that around 85% of the stars have stellar activity As these keplerian semi-amplitudes reach the sub-m s level, the signals induced by intrinsic sources (e.g. oscillations, variability (Baliunas et al. 1998). Although the Mt. Wilson sur- rotating spots and plages, inhibition of convection) become more vey covered a broad range of spectral types, only one M-dwarf significant (e.g. Saar & Donahue 1997; Santos et al. 2000; was included in the sample. This star, HD95735, has an av- Paulson et al. 2002; Bouchy et al. 2004; Meunier et al. 2010; erage S MW value of 0.424 and a variable activity cycle (with Dumusque et al. 2011a,b; Boisse et al. 2011). It is well-known the cycle period poorly defined as yet). More recently, evidence that stellar activity can be a source of radial-velocity “noise” and for cyclic activity was found for a few M dwarfs. Cincunegui can even induce periodic RV signals similar to those produced et al. (2007a)claimedamagneticcyclewitha 442 day period for the dMe 5.5 Prox Centauri & Díaz et al. (⇠2007b)founda ? Based on observations made with the HARPS instrument on P = 763 day activity period for the dMe 3.5 spectroscopic bi- the ESO 3.6-m telescope at La Silla Observatory under programme nary⇠ Gl375. Aditionally, activity cycles were also claimed to be ID 072.C-0488(E). present on Gl229A (M1/2) and Gl752A (M2.5) with periods of Article published by EDP Sciences A30, page 1 of 17 A&A 534, A30 (2011)

4yrand 7yr,respectively(Buccino et al. 2011). Apart from these⇠ few cases,⇠ not much is known about the magnetic cycles of the largest population of stars in the solar neighborhood. In a recent paper we studied a sample of seven late-G and early-K dwarfs with well-known magnetic cycles and compared the activity level of these stars with their radial-velocity variations over a timespan of five years (Santos et al. 2010). We found that generally the S index was correlated with H↵ and anti- correlated with the He index. Also, the long-term variations of the S index could be detected in the cross-correlation function parameter’s line bisector span, full-width-at-half-maximum and contrast, implying that these parameters could be used to follow the activity cycles of these stars. In this first paper we extend this study to the lower end of the main sequence and use a more extended sample. We study for the first time the e↵ect of long-term chromospheric activity of a sample of dwarfs of spectral types from M0 to M5.5, covering the range of stars from partially convective to the beginning of fully convective interiors. We used the same HARPS M-dwarf sample as in the search of extra-solar planets in the southern hemisphere (see Bonfils et al. 2011). The outline of this paper is as follows: we first describe our sample and observations in Sect. 2,inSect.3 we explain the computation of our four activity indices, we search for activity variability in Sect. 4 and for maxima or minima of activity in Fig. 1. Cores of the lines used to calculate the indices for three stars Sect. 5,comparetheindicesinSect.6,andourconclusionsare with similar color (V I 2.10) and di↵erent activity levels plus one of the most active stars in the⇠ sample (green, Gl479). In blue is Gl1, black finally presented in Sect. 7. is Gl526, and red is Gl205.

2. Sample and observations selection. The timespan of observations ranges from 1.9 to The sample comes from the HARPS (Mayor et al. 2003)M- 6.5 years, which should be sucient to detect activity cycle vari- dwarf planet search program, which corresponds to a volume ations in these stars if they are present. limited selection of stars brighter than V = 14 mag and with 1 aprojectedrotationalvelocityv sin i 6.5kms (see Bonfils et al. 2011). They obtained high-resolution spectra (spectral res- 3. Activity indices olution =115 000) for these stars from 2003 to 2009, with 15 min The Ca HandKlinesarewell-knownandwidelyusedstellar integration times. magnetic activity proxies. Our Ca index was computed as in For the calculation of our S index1 we selected all spectra Boisse et al. (2009)andSantos et al. (2000)withslightmod- with a signal-to-noise ratio at spectral order 6 (corresponding ifications to the wavelength bands at the core of the lines. We to the Ca ii Kline, 3933 Å) higher than 2, the value at which chose bands of 0.6 Å centered at the Ca H(3968.47) and the relation between⇠ the index and S/Ndisappears.Allotherin- K(3933.66) lines instead of the 1.09 Å band used by Boisse dices were not a↵ected by this selection except for cases where et al. (2009)becausethislastoneincludespartsofthelinewings we compared them with S .Thedatawerethennightlyav- Ca II and thus undesirable photospheric flux (see Fig. 1,asimilar eraged and bins of 150 days were used to suppress any rota- smaller band for the K line was also used by Livingston et al. tionally modulated signals caused by short-term activity. Each (2007)forthesamereasons).ThesumofthefluxinthetwoH bin included at least three nights, and cases where this condition and K lines was then weighted by the square of their respective was not met were discarded. At this stage only stars with four or more bins were considered for the rest of this study. This se- errors taken as pN where N is the number of counts inside each lection enabled us to compare the di↵erent parameters and look band. Our reference bands were two 20 Å windows centered at for correlations with enough data points. From now on, we refer 3900 and 4000 Å. Because the Mt. Wilson survey only includes to the binned data unless specified. We ended up with a sample one M dwarf, we did not have enough stars to calibrate our S Ca II of 30 stars matching these conditions (23 for the S index) with index to the S MW scale. Furthermore, we could not compute a spectral types ranging from M0V to M5.5V. photospheric free RHK0 index (Noyes et al. 1984)becausethereis The errors used for each bin are the errors on the average, no calibration for stars with B V higher than 1.2. A comparison of the indices with color is discussed in Sect. 6.6. / pN,where is the root-mean-square (rms) of the nightly av- The H↵ index is also a widely used chromospheric indica- eraged data in each bin and N the number of measurements used tor, and some authors recommend it for the study of later-type to calculate the average. stars owing to the increasing flux in the red part of the spec- Table 1 presents some basic parameters and the observation tra for these stars (e.g. Pasquini & Pallavicini 1991; Cincunegui log for these stars. The start and end dates, number of nights, et al. 2007b). Our H↵ index was also computed as in Boisse et al. timespan of observations, and signal-to-noise ratios were calcu- (2009)butusingaslightlybroadercentralband.Insteadofthe lated for the nightly averaged data without using the S/N 2 0.6 Å window centered at 6562.808 Å, we used a 1.6 Å band 1 From now on the index based on the Ca ii lines will be referenced as that seems to include more contribution from chromospheric ac- S index or S Ca II. tivity (see Fig. 1). Pasquini & Pallavicini (1991)obtainedbands

A30, page 2 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Table 1. Basic parameters of the stellar sample and observation log.

a e d Star Sp. type V V I BJDstart 2400000 BJDend 2400000 Nnights Tspan S/N [mag] [mag] [days] [days] [years] (sp.h orderi 6) GJ361 M1.5 Vb 10.40 2.01 54 455.84 55 169.84 34 2.0 3.9 GJ2049 M1 Ve 11.17d 1.77 54 455.70 55 155.86 25 1.9 3.2 GJ3218 M2 Ve 11.12 1.65e 54 396.89 55 141.67 40 2.0 2.0 Gl1 M3 V 8.57 2.13 52 985.60 55 048.83 43 5.6 11.5 Gl176 M2.5 V 9.97 2.25 52 986.71 55 132.82 70 5.9 4.2 Gl205 M1.5 V 7.92 2.08 52 986.73 54 386.81 75 3.8 15.0 Gl273 M3.5 V 9.89 2.71 52 986.77 55 126.87 61 5.9 6.5 Gl382 M2 V 9.26 2.18 52 986.84 54 174.65 30 3.3 8.0 Gl393 M2 V 9.76d 2.26 52 986.86 54 883.74 28 5.2 6.9 Gl433 M2 V 9.79 2.15 52 989.84 55 057.47 60 5.7 5.3 Gl436 M2.5 Vb 10.68 2.02 53 760.83 54 999.46 105 3.4 2.6 Gl479 M3 V 10.64 1.90 53 158.55 54 571.70 57 3.9 4.2 Gl526 M1.5 V 8.46 2.07 53 158.60 55 001.58 34 5.0 11.6 Gl551 M5.5 V 11.05 3.62 52 684.86 55 057.54 37 6.5 1.2 Gl581 M2.5 V 10.57 2.53 53 152.71 55 056.53 128 5.2 3.6 Gl588 M2.5 V 9.31 2.40 53 152.75 54 956.80 25 4.9 9.2 Gl667C M2 V 10.22 2.08e 53 158.76 55 053.69 147 5.2 4.0 Gl674 M3 V 9.36 2.40 53 158.75 54 732.48 44 4.3 8.4 Gl680 M1.5 V 10.14 2.27 53 159.71 55 057.65 28 5.2 4.3 Gl699 M4 V 9.54 2.52 54 194.89 55 054.65 25 2.4 6.6 Gl832 M1 V 8.67 2.18 52 985.52 55 122.65 57 5.9 10.4 Gl849 M3 V 10.42 2.50 52 990.54 55 122.62 48 5.8 4.5 Gl876 M3.5 V 10.17 2.77 52 987.58 55 122.63 37 5.8 4.8 Gl877 M2.5 Ve 10.55d 2.43 52 857.83 54 704.73 39 5.1 2.8 Gl887 M2 V 7.34 2.02 52 985.57 54 392.68 63 3.9 15.7 Gl908 M1 V 8.98 2.04 52 986.58 55 057.85 50 5.7 11.6 HIP12961 M0 Vc 9.7 1.64 52 991.63 55 109.79 45 5.8 3.4 HIP19394 M3.5 Ve 11.81 2.5 52 942.80 55 105.79 29 5.9 1.2 HIP38594 Me 9.96 1.64 52 989.79 55 105.90 16 5.8 2.8 HIP85647 M0 Vb 9.59 1.85 53 917.75 55 117.49 27 3.3 3.8

References. (a) Bonfils et al. (2011)unlessindividuallyspecified;(b)Hawley et al. (1996); (c) Koen et al. (2010); (d) ESA (1997); (e) Simbad (http://simbad.u-strasbg.fr/simbad/). in the region 1.6 1.7 Å for the chromospheric contribution of flux. Therefore, we tried narrower bands of 0.5 Å for the lines the H↵ line by subtracting the spectra of inactive stars to those and noticed that the correlation with the S Ca II index improved of active stars of the same spectral type (the same band was also drastically (see the results section). These narrower bands were found by Herbig 1985). Recently, Cincunegui et al. (2007b)also formally adopted for the rest of this work. used a window of 1.5 Å to calculate the flux in the H↵ line. We The He D3 line (5875.62) was observed to show good spa- divided the flux in the central line by the flux in two reference tial correlation with plages (Landman 1981)andcantherefore lines of 10.75 and 8.75 Å centered at 6550.87 and 6580.31 Å, be used as an activity proxy (see Saar et al. 1997; Montes et al. respectively. 1997,andreferencestherein).Weuseda0.4Åbandcenteredat Díaz et al. (2007b)proposedthattheNaD1 and D2 lines the line and divided its flux by the flux in two reference windows could also be used to follow the chromospheric activity level of of 5 Å centered at 5869.0 and 5881.0 Å, following the procedure very active late-type stars with (B V) > 1.1. In this sample in Boisse et al. (2009). we do not have very active stars, but we decided to study these The errors of the four indices were estimated by di↵erentiat- lines as a complement to the other widely used activity prox- ing the respective equations, and taking into account the flux in ies. The Na Dlinesprovideinformationabouttheconditionsin each band. But because we are interested only on the long-term the middle-to-lower chromosphere (Mauas 2000)andthusarea variations of the indices and we binned the data into 150 day good complement to the upper chromosphere indicator H↵ and bins, the final errors are the statistical errors on the mean as ex- lower chromosphere proxy Ca index. We first computed our plained in Sect. 2.Theindividualerrorsofthenightlyobserva- Na index in a similar fashion as Díaz et al. (2007b)bycalcu- tions are always lower than the estimated statistical errors on the lating the average flux in the core of the D1 (5895.92) and D2 mean used for the binned data. (5889.95) lines using 1 Å bands. We used two reference bands Figure 1 shows spectra in the region around the lines used with windows of 10 and 20 Å centered at 5805.0 and 6090.0 Å, to calculate the activity proxies. The four lines in each plot rep- respectively. For each band we selected the 10 higher flux values resent three stars with di↵erent activity levels but similar color and calculated the average. The averagevaluesof the two D1and (V I 2.10) plus one of the most active stars in the sample. D2 lines were then divided by the average of the two reference By increasing⇠ activity, the blue line stands for Gl1 ( S = h Ca IIi bands. We noticed that the 1 Å bands include a significant part of 0.0147, V I = 2.13), the black line for Gl526 ( S Ca II = 0.0307, the line wings and thus possible photospheric contribution to the V I = 2.07), the red line represents Gl205 ( hS i = 0.0920, h Ca IIi A30, page 3 of 17 A&A 534, A30 (2011)

V I = 2.08), and the green line illustrates the lines for one of is expected because the ability to detect magnetic cycle activity the most active stars in the sample, Gl479 with S Ca II = 0.0960 variations should increase with timespan. but slightly di↵erent color (V I = 1.90). The dashedh i lines mark Figure 2 show the time-series of the four activity indica- the line centers, while the dotted lines delimitate the band win- tors for the selected stars as having significant variability. Small dow. The flux in all figures was normalized by dividing it by the points without errorbars are the data averaged per night, points mean flux in the reference bands of each index. with error bars represent the binned data, where the errors are the For these four stars the Ca and Na lines show a similar be- standard error on the mean, the numbers are number of nights havior. Both increase in emission with increasing activity level used in each bin, and the dashed lines are the second-order poly- in the S -index. On the other hand, the H↵ and He lines do not nomials best-fitted to the data. In each plot there is a reference show the same trend. The H↵ first decreases its emission as ac- to the peak-to-peak variation ()andtothestandarddeviations tivity increases and then exceedsthelevelofthestarwithless of the binned data (). The values in parenthesis are the percent- activity, ultimately arriving at a level similar to that of the con- ages of the variations relative to the average values. tinuum (if the activity increases even more it is expected to be- Although we may not have enough data to detect full cycles, come an emission line). This behavior was explained by Cram there are some hints for the cycle phase at which some of these &Mullan(1979)throughnon-LTEmodelchromospheresfor stars could be. For example, in Fig. 2 the time-series of S Ca II for dK and dM stars. These authors explained that the stronger ab- Gl433 seems to show a maximum of activity for this star, while sorption in the line with increasing chromosphere heating rate for Gl581 a minimum is clearly visible. is caused by an increase of the n = 2boundlevelpopulation of hydrogen and that when the heating reaches a certain level, the chromosphere electron density becomes so high that the line 4.1. S Ca II variability becomes collisionally excited, which increases the emission at Although the spectral orders of the Ca H&Klinesaretheones its core. The He D3 triplet is observed in Fig. 1 in absorption. with the lower signal-to-noise ratio, the S Ca II index still shows This is generally the case for surges, eruptive prominences, and agreatnumberofstarswithvariability.Fromoursampleof23 weaker flares, while emission is correlated with more intense stars, 9 have P-values lower than or equal to 0.05, which rep- flares (Zirin 1988). The behavior observed in the figure is that resents 39% of the sample. These stars are Gl1, Gl273, Gl433, of an anti-correlation with Ca :astheCa lines emission in- Gl581, Gl588, Gl667C, Gl832, Gl908, and HIP85647. If we increases, there is a tendency for the He lines to increase in ab- clude the three stars with P-value below 0.1 (GJ361, Gl876, and sorption. Gl887; in general they have short observation timespans or only afewnightsandthusanyvariationscausedbytheirhypothetic cycle might be underestimated) we have 52% of the sample with 4. Activity indices variability significant mid-term activity variations. Moreover, all stars with significant variations (P 0.05) in the S Ca II index also present After obtaining the four activity indices for our sample we now significant variations in at leastoneoftheotherindices,which try to infer which stars show long-term variability and if mag- reinforces this variable behavior. netic activity cycles are present in the data. With this in mind we calculated the rms (e)andaverageerrors(i )forthein- dices and compared them using an F-statistics withh i the F-value 4.2. H↵ variability computed as F = 2/ 2 following a similar procedure as in e h ii The H↵ index indicates significant variability (P 0.05) for Zechmeister et al. (2009). This approach will give the probabil-  ity, given an F-value, that the observed variability ( )canbe 10 stars (Gl1, Gl433, Gl436, Gl581, Gl588, Gl699, Gl849, e Gl877, HIP19394, and HIP38594) out of 30, representing 33% explained by the mean errors of the data (i). In this case, the error of the data depends on the high-frequency activity variations of the sample. All these stars, apart from Gl699, HIP19394 and of the nightly averaged data and number of bins (as explained HIP38594, also have significant variations in the other indices. in Sect. 2). Therefore, lower values of probability (P(F)) will If we include the three stars with a P-values below 0.1 (GJ3218, indicate that the variability is not due to the scatter induced by Gl273, and HIP85647), then around 43% of the sample shows the errors. The results of this study are presented in Table 2.For variability in this index, and two of these stars present a strong variability in the S Ca II and Na indices. the S index we used the S/N 2selection,resultinginNbins(S ) bins. Where there are less than four bins, the columns relating to the variability of the S Ca II index appear empty. For the other 4.3. Na i variability indices we used no selection, resulting in Nbins shown in Col. 3. The probability that the variation is caused by the errors is pre- In terms of variability, the Na index seems to be one of the best sented in the form of a P-value, where values lower than 0.05 we have. Out of 30 stars, 11 present significant scatter (Gl273, (95% significance) are highlighted in bold. Gl433, Gl436, Gl526, Gl588, Gl667C, Gl832, Gl849, Gl876, Because we averaged the data by 150 day bins, we inten- Gl877, and Gl908, representing 37% of the sample), and there are six more with 0.05 < P 0.1(GJ361,GJ2049,GJ3218, tionally removed the short-timescale variations, and only long-  term variations are to be detected. As a result of this, we expect Gl581, HIP38594, and HIP85647), which, if these are included, to find variability in stars with longer periods of observation, amounts to 57% of the sample. Apart from Gl526, all stars with P 0.05 also have a strong variability or hints of variability in where their activity cycle pattern becomes detectable. Indeed, of  the four stars with a timespan shorter than three years only one the other indices. (Gl699) shows significant variability, and just in one of the four indices. Furthermore, from the 18 stars that show variability, 13 4.4. He i variability have timespans longer than or equal to five years. Indeed, 72% of the stars with timespans equal to or longer than five years The He index is the one with fewer stars presenting variability present significant variability in at least one activity index. This in the F-tests. Only three stars in the sample (Gl205, Gl908 and

A30, page 4 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Fig. 2. Variations of S Ca II,H↵ ,Nai and He i with time for the 12 stars with long-term variability (see Sect. 4). For visualization purposes, the y-axis is deﬁned as the mean of the data plus and minus 0.35 times the maximum of the average errors of each index. The x-axis is constant for all stars. Note that Gl877 does not have data for the S Ca II index.

A30, page 5 of 17 A&A 534, A30 (2011)

Fig. 2. continued.

A30, page 6 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Fig. 2. continued.

A30, page 7 of 17 A&A 534, A30 (2011)

Fig. 2. continued.

A30, page 8 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Fig. 2. continued.

A30, page 9 of 17 A&A 534, A30 (2011)

Fig. 2. continued.

A30, page 10 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I. ) const F ( 0.028 0.010 0.015 P i i h He e 0.0064 0.0035 0.081 0.00013 0.00011 0.32 0.00011 0.000079 0.17 0.00013 0.000075 0.13 0.00017 0.000056 0.00013 0.00011 0.40 0.00020 0.000074 0.00013 0.000062 0.070 0.000120.00015 0.000097 0.0000820.00016 0.31 0.18 0.000067 0.088 0.00019 0.00015 0.37 0.000270.00018 0.00015 0.000060 0.097 0.00023 0.00014 0.22 0.00028 0.00012 0.096 0.00025 0.00015 0.18 0.00013 0.00012 0.42 0.00019 0.00020 0.53 0.000140.00019 0.000068 0.00016 0.13 0.40 0.00016 0.00015 0.49 0.000039 0.000054 0.78 0.000055 0.00014 0.97 0.000067 0.000075 0.58 0.000054 0.000075 0.71 0.000079 0.00014 0.82 0.000081 0.00010 0.66 0.000049 0.000091 0.87 0.000098 0.00012 0.65 ) const F ( 0.014 0.013 0.026 0.024 0.044 0.047 0.041 0.032 0.043 0.0064 0.0026 P i i Na h e 0.043 0.046 0.56 0.0022 0.0013 0.072 0.00330.0031 0.0011 0.00097 0.0040 0.0016 0.055 0.00400.0032 0.00081 0.0014 0.00330.0029 0.0015 0.0016 0.10 0.0033 0.0014 0.0039 0.0015 0.0032 0.00140.0018 0.10 0.0011 0.18 0.0036 0.0011 0.0022 0.00250.00320.0054 0.0013 0.58 0.0017 0.0039 0.0014 0.063 0.00640.0045 0.0038 0.00290.0051 0.12 0.0027 0.17 0.12 0.0027 0.0026 0.48 0.0024 0.0018 0.31 0.0037 0.0029 0.33 0.0058 0.0020 0.055 0.0036 0.0021 0.12 0.00360.0077 0.0013 0.0030 0.059 0.077 0.0065 0.0011 0.0020 0.0016 0.35 ) const F ( 0.015 0.018 0.038 0.044 0.031 0.044 0.0016 0.0064 0.00093 0.00068 P i i ↵ H the average of the error on the mean for the binned activity data of each star. h i i h e 0.014 0.0078 0.11 0.0012 0.00070 0.16 0.0013 0.00045 0.055 0.00029 0.000096 0.00035 0.00015 0.067 0.00018 0.00012 0.20 0.000220.00017 0.00015 0.00019 0.18 0.62 0.000360.00031 0.000065 0.000065 0.00051 0.00011 0.00012 0.00013 0.53 0.00034 0.00020 0.21 0.00043 0.00022 0.080 0.00015 0.00011 0.31 0.00012 0.000140.00033 0.00015 0.63 0.11 0.000380.00061 0.00011 0.00029 0.00043 0.000290.00075 0.21 0.00043 0.49 0.15 0.00045 0.00047 0.53 0.000190.00065 0.00014 0.00019 0.00029 0.31 0.00012 0.000310.00040 0.00012 0.000063 0.00019 0.00011 0.22 0.00028 0.00023 0.36 0.00047 0.00018 ) const F ( 0.016 0.033 0.017 0.034 0.046 0.016 0.0041 0.0074 0.0071 P i i Ca II h S is the rms of the index (binned) and e e 0.0015 0.00210.0041 0.75 0.0016 0.0018 0.00064 0.0019 0.00080 0.0028 0.0012 0.087 0.00360.0031 0.00270.0037 0.00260.0035 0.0010 0.27 0.0031 0.35 0.0024 0.00085 0.41 0.00350.0015 0.0024 0.00077 0.28 0.0020 0.15 0.00044 0.00120.0019 0.00300.0011 0.00150.0037 0.0015 0.92 0.0016 0.0011 0.37 0.0036 0.0012 0.68 0.00140.0029 0.23 0.0022 0.075 0.0011 0.00060 0.077 0.0015 0.00054 0.00095 0.00056 0.13 where 2 i i bins h / N 2 e ) = S ( F 46 44 44 44 47 45 44 < < < < < < < bins N -value used was Star GJ361 4 4 Gl433 5 6 Gl667CGl674Gl680 8 4 4 7 5 4 Gl382 5 5 Gl849 6 6 Gl479 4 4 HIP19394 HIP38594 Gl551 Gl887 4 4 GJ2049 Gl588 4 4 Gl876Gl877 Gl908 4 6 4 8 GJ3218 Gl1Gl176 5 6Gl436 5 7 6 7 Gl832 6 5 Gl393 Gl205Gl273 6 5 6 Gl526 6 4 4 Gl699 4 4 HIP85647 5 5 Gl581 9 10 HIP12961 6 6 F Variability F-tests for the activity indices. Bold values indicate probabilities lower than 0.05 (95% signiﬁcance level). The Table 2. Notes.

A30, page 11 of 17 A&A 534, A30 (2011)

Table 3. F-tests for trends in our activity indices.

Star Nbins(S ) Nbins S Ca II H↵ Na He Fpoly P(Fpoly) Fpoly P(Fpoly) Fpoly P(Fpoly) Fpoly P(Fpoly) GJ361 4 4 0.475 0.72 3.13 0.37 0.00785 0.99 414 0.035 GJ2049 <44 0.187 0.85 0.0204 0.98 0.0733 0.93 GJ3218 <44 5.44 0.29 5.46 0.29 0.00831 0.99 Gl1 5 5 27.9 0.019 3.61 0.12 22.5 0.023 0.729 0.34 Gl176 6 7 1.33 0.24 0.579 0.41 0.442 0.46 0.827 0.34 Gl205 6 6 0.00533 0.56 0.0243 0.56 0.166 0.53 0.0851 0.55 Gl273 5 6 0.0998 0.52 0.0967 0.55 5.18 0.059 0.0761 0.55 Gl382 5 5 0.511 0.39 0.820 0.32 0.150 0.50 0.136 0.51 Gl393 <44 0.0149 0.99 27.6 0.13 0.0533 0.95 Gl433 5 6 17.6 0.030 5.15 0.059 18.4 0.011 0.0255 0.56 Gl436 6 7 0.196 0.52 2.79 0.098 0.769 0.35 0.111 0.56 Gl479 4 4 24.1 0.14 6.86 0.26 2.92 0.38 10.9 0.21 Gl526 4 4 6.02 0.28 0.666 0.66 9.94 0.22 0.168 0.87 Gl551 <47 0.193 0.54 0.795 0.35 0.510 0.44 Gl581 9 10 11.9 0.0022 12.2 0.0010 10.7 0.0016 4.45 0.019 Gl588 4 4 0.469 0.72 0.290 0.80 0.322 0.78 0.0387 0.96 Gl667C 8 7 0.713 0.38 3.55 0.070 1.26 0.24 4.06 0.057 Gl674 4 5 0.128 0.89 0.826 0.32 0.467 0.40 0.0445 0.54 Gl680 4 4 0.0706 0.94 1.48 0.50 4.78 0.31 0.905 0.60 Gl699 4 4 2.92 0.38 62.9 0.089 1.74 0.47 0.0186 0.98 Gl832 6 5 0.153 0.54 63.7 0.0084 0.0227 0.54 0.996 0.29 Gl849 6 6 0.285 0.49 0.673 0.37 0.325 0.48 1.08 0.28 Gl876 4 4 1.08 0.56 4.78 0.31 1.63 0.48 6.21 0.27 Gl877 <45 3.56 0.12 1.41 0.24 0.00635 0.54 Gl887 4 4 9.44 0.22 0.465 0.72 0.756 0.63 0.00450 0.99 Gl908 6 8 1.16 0.27 0.689 0.39 0.970 0.30 2.29 0.11 HIP12961 6 6 0.0851 0.55 0.136 0.54 2.15 0.16 0.451 0.43 HIP19394 <46 1.37 0.23 2.15 0.16 5.83 0.051 HIP38594 <44 1399 0.019 37.3 0.12 0.322 0.78 HIP85647 5 5 4.15 0.11 3.66 0.12 15.3 0.034 0.133 0.51

Notes. The F-value used was F = (N 3)(2 2 )/2 ,where2 is the chi-squared of the straight line model, 2 the chi-squared of poly slope poly poly slope poly the polynomial model, and N the number of bins. This test will give the probability that a second-order polynomial is a better ﬁt to the data than a straight line. Bold values indicate probabilities lower than 0.05 (95% signiﬁcance level).

HIP85647, 10% of the sample) have P 0.05 and five (Gl176, used P-values lower than 0.05 as a limit for statistically signifi- Gl551, Gl680, Gl887, and HIP12961) have 0.05 < P 0.1, cant improvements to the fit.  which yields an overall of 27% of the sample with variability. The S Ca II index shows three stars having maxima or minima, This indicates that this index, although in a region of the spec- namely Gl1, Gl433, and Gl581, whose data are statistically bet- trum with high signal-to-noise ratio, does not vary with a su- ter fitted by a second-order polynomial than by a straight line. ciently high amplitude to be detected in M dwarfs. It is curious Both Gl1 and Gl433 show a maximum of activity in the time- that Gl205, although having a strong variability in the He index, series plots (Fig. 2), while Gl581 presents a minimum (Fig. 2). does not present any significant scatter either in S Ca II (P = 0.35) The Na i index shows the same behavior in the tests as the or H↵ (P = 0.49). The same is true of Gl176 and HIP12961. calcium lines apart from HIP85647. This star passed the test and On the other hand, there are a large number of stars that have shows a maximum in the time-series (Fig. 2)withasimilarbe- strong variations in the other indices, but their P-values for He havior also observed on S Ca II (P = 0.11) and H↵ (P = 0.12). indicate no variability. Therefore, this index does not seem to Two other stars passed the test for the H↵ index, Gl832 and be a good proxy of medium to long-term activity variations of HIP38594, but without similar variations observed for the other early-M type dwarfs. activity indicators. For Gl581 we observe a maximum instead of the minimum produced by the Ca ii and Na ii lines. 5. Activity maxima and minima Two stars present significant maximum or minimum in He . These are Gl361, which has passed the test for the other three Apart from the variability tests we also performed F-tests to try indices, and Gl581 with a minimum. to find maxima or minima in our data that could indicate the presence of magnetic cycles. We fitted straight lines and second- order polynomials to the time-series and calculated an F-test 6. Comparision between activity indicators using F = (N 3)(2 2 )/2 ,where2 is the poly slope poly poly slope After assessing the variability for our four indices, we now com- 2 chi-squared of the straight line model, poly the chi-squared of pare them to assess their mid-term correlations. Table 4 shows the polynomial model, and N the number of bins. The proba- the Pearson correlation coecients between the activity indices bility that the data are better fitted by a polynomial than by a for our sample (⇢). Nbins is the number of bins for each star straight line is given in Table 3 by low values of P(Fpoly). We (Nbins(S )forcomparisonsusingtheS index). The false-alarm

A30, page 12 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Fig. 3. Pearson correlation coecients for the relations between S Ca II,H↵,Na,andHeas a function of mean S Ca II for the 23 stars with values of S index. Open squares are values with FAP 0.01, open circles for 0.01 < FAP 0.05, and “plus” (“+”) symbols for FAP > 0.05.   probability (FAP) was computed by bootstraping the nightly av- the anti-correlation found for Gl526 with a Pearson correlation eraged data, then binning the data every 150 days, and calculat- coecient of 0.78 (FAP = 13%) can be an indication that the ing the coecient for each of the 10 000 permutations. A signif- plages and filaments are spatially well-correlated for that star. icant FAP was then chosen for values <0.05 (95% significance Stars with strong positive correlations (and higher levels of ac- level) and highlighted in bold. tivity) such as Gl176, Gl205, Gl382, and Gl479 probably have asaturatedfilamentcontributiontoH↵ that therefore does not influence the index as much as the plage contribution. 6.1. S Ca II vs. H↵ Figure 3 (left panel) shows the Pearson correlation coe- Six stars (out of 23, correspondingto 26% of the sample) show a cient between these two indices against the mean values of the S -index. Open squares are values with FAP 0.01, open circles significant positive correlation between the S Ca II and H↵ indices for 0.01 < FAP 0.05, and “plus” (“+”) symbols for FAP values (Table 4). Around 57% of the sample have a positive correlation  between S and H↵ higher than 0.5. Although it has been claimed higher than 0.05. that a strong correlation between these two indices exists, it is As was found by Cincunegui et al. (2007b), we obtain a not clear if that is the case for all stellar types or levels of activity great variety of correlations from around –0.8 to 1. Nevertheless, (e.g. Montes et al. 1995; Strassmeier et al. 1990; Robinson et al. there is a tendency in our sample for the positive correlations. A 1990; Giampapa et al. 1989). trend can be observed when the correlation coecient is plot- Cincunegui et al. (2007b)studiedthecorrelationbetween ted against the mean S Ca II:forvaluesofS lower than around these two indices for a sample of 109 stars ranging in spectral 0.035 there are no significant correlations and for S higher than 0.035, there are only positive correlations and some of them type from F6 to M5. These authors found a great variety of cor- ⇠ relations between 1and1. with statistical significance. This trend is not observed when the More recently,Walkowicz & Hawley (2009)comparedsi- correlation is plotted against the mean values of H↵. multaneous spectra of Ca and Balmer lines for a sample of M 3 An interpretation of this could be that because the H↵ is dwarfs and observed that the relationship between calcium and more sensitive to filaments than the S -index, as the activity gets H↵ is not linear: weak absorption of the H↵ line can correspond stronger (higher S Ca II)thecontributionofplagesbecomesmore either to weak or intermediate Ca Kemission,asproposedby important to the H↵ index than the contribution coming from Cram & Giampapa (1987)andpreviouslyobservedbyStau↵er filaments, because their contribution saturates at a certain ac- &Hartmann(1986;seealsoRauscher & Marcy 2006). tivity level (Meunier & Delfosse 2009). This will produce the Meunier & Delfosse (2009)alsostudiedtheseindicesforthe observed positive correlation between the two indices for higher Sun, and although we used 150 day bins and they used individ- values of S .Wecouldalsoarguethatthisisane↵ect of the dif- ual measurements, their discussion about the relation between ficulty of obtaining statistically significant correlations for stars Ca ii and H↵ can provide interesting insights here. These au- with lower activity values but this seems not to be the case be- thors pointed out that if the timescale of the observations cov- cause we found significant correlations for the cases of Na and ered less than the solar cycle, the correlation could decrease to He for low values of S (middle and right panels of Fig. 3). We negative values. We do not have information about the length of therefore attribute this trend to the decrease of the importance of the cycles of these stars (or if they have periodic cycles), but be- filaments and the increase of the contribution of plages to the H↵ cause our maximum timespans are in the 6-year range or less, index as the activity level of the stars increases. the conclusion by Meunier & Delfosse (2009)forthelowpos- We found no dependence of the correlation between these itive or negative values of the correlation coecient might be a indices and color. We note, however, that this was observed with possibility. Another possibility to explain the low and negative very low signal-to-noise ratio for the (bluer) spectral regions that values of the correlation coecients might be explained by the contain the Ca HandKlines. di↵erent sensitivity of the indices to di↵erent activity phenomena. For the Sun, the surface coverage of plages as measured 6.2. S Ca II vs. Na i by the two indices is not exactly the same: it is smaller for H↵ than for the Ca ii lines (Meunier & Delfosse 2009). This will Table 4,Fig.3 (middle panel), and the time-series presented in reduce the correlation between them. Furthermore, the H↵ line Fig. 2,showthattheNabehaves similarly to the S Ca II index. is more sensitive to the presence of dark filaments. As Meunier Díaz et al. (2007a)studiedtheNaD1 and D2 lines for a &Delfosse(2009)pointedout,thiswillreducethecorrelation sample of late-F to mid-M and found that these lines could be coecient to values closer to zero if the filaments and plages used as chromospheric activity indicators for very active stars. are not sharing the same positions on the disk of the star. If the In our sample of low-activity stars, 16 out of 23 (around 70% filaments are spatially well-correlated with plages, the correla- of the sample) have a strong correlation (with FAP 0.05) tion between the two indices will tend to negative values. Thus, between the Na i index and our S -index. We have no negative

A30, page 13 of 17 A&A 534, A30 (2011)

Table 4. Pearson correlation coecients between the activity indices.

Star Nbins(S ) Nbins S Ca II vs. H↵ S Ca II vs. Na S Ca II vs. He H↵ vs. Na H↵ vs. He Na vs. He ⇢ FAP ⇢ FAP ⇢ FAP ⇢ FAP ⇢ FAP ⇢ FAP GJ361 4 4 0.58 0.27 0.73 0.12 0.43 0.35 –0.07 0.46 0.86 0.13 –0.24 0.41 GJ2049 <44 –0.04 0.47 –0.89 0.083 0.43 0.33 GJ3218 <44 1.00 0.0006 0.39 0.36 0.36 0.37 Gl1 5 5 0.12 0.41 0.89 0.031 0.56 0.24 0.37 0.33 0.14 0.45 0.84 0.067 Gl176 6 7 0.85 0.016 0.33 0.27 0.76 0.033 0.40 0.24 0.77 0.034 –0.04 0.48 Gl205 6 6 0.98 0.0015 0.94 0.0079 0.58 0.17 0.83 0.054 0.57 0.17 0.69 0.10 Gl273 5 6 0.06 0.46 0.90 0.024 0.45 0.25 –0.40 0.24 0.80 0.038 0.08 0.44 Gl382 5 5 0.99 0.0007 0.98 0.0017 0.42 0.24 0.98 0.0021 0.46 0.23 0.56 0.15 Gl393 <44 –0.10 0.45 0.91 0.044 0.17 0.42 Gl433 5 6 –0.28 0.32 0.98 0.0012 –0.50 0.29 –0.32 0.25 –0.39 0.30 –0.31 0.33 Gl436 6 7 –0.06 0.45 0.87 0.010 0.42 0.20 0.49 0.19 –0.15 0.38 0.21 0.32 Gl479 4 4 0.99 0.0044 0.94 0.034 0.87 0.060 0.94 0.033 0.82 0.10 0.91 0.050 Gl526 4 4 –0.78 0.13 0.99 0.013 0.21 0.36 –0.86 0.12 0.42 0.24 0.10 0.43 Gl551 <47 0.59 0.086 0.96 0.0007 0.55 0.11 Gl581 9 10 –0.44 0.094 0.82 0.0036 0.75 0.024 –0.75 0.0035 –0.14 0.37 0.58 0.063 Gl588 4 4 0.73 0.11 0.94 0.026 0.88 0.067 0.63 0.17 0.93 0.036 0.73 0.15 Gl667C 8 7 –0.31 0.23 0.89 0.0016 –0.04 0.40 0.11 0.40 0.35 0.23 –0.15 0.34 Gl674 4 5 0.35 0.36 0.91 0.045 0.60 0.23 0.59 0.18 0.81 0.036 0.85 0.028 Gl680 4 4 0.96 0.022 0.85 0.085 0.89 0.087 0.95 0.021 0.13 0.39 –0.04 0.50 Gl699 4 4 0.57 0.21 0.43 0.32 0.25 0.38 0.32 0.35 0.89 0.062 0.48 0.27 Gl832 6 5 0.64 0.083 0.97 0.0006 0.05 0.47 –0.17 0.37 0.49 0.15 –0.02 0.49 Gl849 6 6 0.80 0.063 0.71 0.069 0.44 0.24 0.71 0.077 0.82 0.041 0.84 0.025 Gl876 4 4 0.76 0.14 1.00 0.0005 0.58 0.24 0.88 0.054 0.88 0.053 0.93 0.032 Gl877 <45 0.90 0.032 0.57 0.20 0.79 0.088 Gl887 4 4 0.85 0.12 0.91 0.063 0.63 0.21 0.98 0.018 0.82 0.10 0.86 0.082 Gl908 6 8 –0.24 0.33 0.89 0.016 0.31 0.30 0.12 0.39 –0.16 0.37 0.07 0.44 HIP12961 6 6 0.35 0.25 0.30 0.32 0.63 0.098 –0.38 0.23 0.83 0.018 –0.78 0.033 HIP19394 <46 0.39 0.21 0.08 0.45 0.26 0.31 HIP38594 <44 0.59 0.19 0.19 0.41 –0.15 0.43 HIP85647 5 5 0.94 0.011 0.99 0.0016 0.94 0.012 0.92 0.019 0.88 0.037 0.77 0.087

Notes. FAPs calculated using bootstrap permutations (see text). In bold are given FAP values below 0.05. Nbins is the number of bins for each star. values of the correlation coecient and all the stars except three variation of the coecient with mean S -index. Although there is have ⇢ > 0.5. Note that neither of these three stars passed the atendencyforpositivecorrelationsasshownintheotherindices, variability test for these two indices. Furthermore, we found no the coecients are more scattered than for the S –Na i case and relation between the correlation coecient and the average val- less significant. A similar trend as the one observed for H↵ can ues of S ,Nai,orwithV I.ThismeansthattheNai lines can also be observed here, where for stars with lower S Ca II there is be used as a proxy of the long-term activity as measured by Ca ii atendencyforlowerornegativevaluesofthecoehcient.i for low-activity early-M dwarfs. This can be important because the Ca H&Klinesarelocatedinthebluepartofthespectrum and in these late-type stars the flux in this region is very low 6.4. H↵ vs. Na i, H↵ vs. He i,andNa i vs. He i compared to the redder regions where the Na i D1 and D2 lines are located. That Díaz et al. (2007a)havenotfoundthistrendfor Because the correlation between the calcium and the sodium the least active stars of their sample might be because they used lines is very strong for almost all stars in our sample, it is ex- medium-resolution spectra, while we used spectra obtained with pected that the relation between these two indices and H↵ will high resolution. be similar. This is the case, because the majority of the stars that show strong correlations here also have strong correlations be- 6.3. S vs. He i tween S and the hydrogen line, except for Gl581, which shows Ca II an anti-correlation for the two cases. Therefore, the discussion When we studied the variability of the activity indices in Sect. 4, in Section 6.1 could also make sense in this case. we noted that the He i index was not showing as much variability Nine stars out of 30 show strong a correlation between H↵ as the other three indices. Only three stars present a variability and He i (around 30% of the sample) with four more stars having with P-value below 0.05. Now, when we studied the correlation 0.05 < FAP 0.1. This shows that the He i index is more similar coecient between this index and the S Ca II,weobservedthat  in behavior to H↵ than to S Ca II,whereonlythreeoutof23stars the correlation between the two is very weak. Only three stars showed a strong correlation. show correlation below a FAP value of 0.05 and the correlation coecients vary between 0.50 and 0.94. This further confirms As expected from the S –He i comparison, the correlation be- that the He i index is a poor activity proxy (as measured by the tween the Na i and He i indices is weak. Only 17% of the stars S -index) for early-M dwarfs. Figure 3 (right panel) shows the have FAP values lower than 0.05.

A30, page 14 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Fig. 4. Comparison between the average values of S Ca II,H↵ ,Nai,andHei for the 23 stars with values of S index. Errorbars are the standard deviations, the dashed line the best linear ﬁt, ⇢ is the Pearson correlation coecient, and N the number of stars used.

Fig. 5. Comparison between the average values of H↵ ,Nai,andHei for 29 stars. Gl551 was excluded from these plots because it has very high activity values. Symbols as in Fig. 4.

6.5. Nightly averaged correlations

Although the aim of this work was not to study the correlations between the four indices on short timespans (our concern was with long-term, cycle-type variations), we also calculated the correlation coecients for the relations S Ca II–H↵ and S Ca II–Na for the nightly averaged data. The correlations observed for the binned data were maintained. The trend observed for the correlation between S and H↵ when plotted against average S is also present and Na maintains a very good correlation with the S index that is independent of the activity level. The FAP values in general were lower because here we had more data points and therefore it was more dicult to obtain higher correlations by permutating individual points. Again, this result supports the use of the Na index as a proxy of activity of M dwarfs even for Fig. 6. Relation between the four activity indices and V I color. high-frequency variations as does the fact that the H↵ activity Symbols as in Fig. 4. indicator does not vary linearly with activity as measured by the S index. This study will be presented in more detail in a future paper. S were maintained with similar correlation coecient values excepth i for He i vs. Na i ,whichdecreased⇢ from 0.80 to 0.55. Althoughh thei averageh i values of these three indices are cor- 6.6. Mean activity indices and color related, the scatter is still high. It is known that the fraction of active M dwarfs is not constant with spectral type but, increases We compared the average values of the four activity indicators for spectral types later than M 4 (Delfosse et al. 1998). This of each star to look for correlations (Figs. 4 and 5). We found could be a source of biasing toward the redder end of spectral that the mean values of S Ca II,Nai and He i are linearly corre- color. However, in this sample only two stars have spectral type lated, but the same is not true when we compared them with the later than or equal to M 4 and the redder of them (Gl551, with hydrogen line. Because these activity proxies were not corrected spectral type M 5.5) was discarded from these corrections. for the contribution of photospheric ﬂux, we expect these indices It is clear from Figs. 7 and 8 that direct comparisons between to be dependent on the spectral type when we compare stars with H↵ and the other three indices are not possible because there is di↵erent colors. As we can see in Fig. 6,thesamethreeindices no correlation between them. This reinforces the idea that the that have a linear correlation between their average values ap- hydrogen line does not measure activity in the same way as Ca ii, pear to have a similar trend with V I:allofthemdecreasewith Na i,orHei for early-M dwarfs. The strong intra-star correla- color. On the other hand, the H↵ index increases with V I. tions observed between the S and Na i lines are also observed We corrected the average values of the four indices using the when the activity level of di↵erent stars is compared. Therefore, residuals of the best-ﬁt lines shown in Fig. 6.Figures7 and 8 the sodium lines can be used not only to measure the relative show the relations between the residuals of the indices after cor- activity variations for a given star, but also to compare activity rection. The linear trends between Na i vs. S and He i vs. between stars. h i h i h i A30, page 15 of 17 A&A 534, A30 (2011)

Fig. 7. Comparison between the average values of S Ca II,H↵ ,Nai,andHei for the 23 stars with values of S index after correction for color. Symbols as in Fig. 4.

Fig. 8. Comparison between the average values of H↵ ,Nai,andHei for 29 stars after correction for color. Gl551 was excluded from these plots because of its very high activity values. Symbols as in Fig. 4.

7. Conclusions (left panel). This ambiguous relation between the calcium and H↵ lines was also observed in Fig. 1 where we compared the We used more than five yearsof HARPS high-resolution spectra shape of the activity lines for di↵erent activity levels. This be- of a sample of M0–M5.5 stars from the HARPS M-dwarf planet havior might be a consequence of the di↵erent contribution of search survey to study the behavior of the S Ca II,H↵,Nai,and filaments to both indices, their di↵erent spatial distribution in He i chromospheric activity indicators. The data were binned to the stellar disk, and the fact that its contribution to the H↵ index average-out unwanted short time-scale variations. We first ad- saturates at a given level of activity (see Meunier & Delfosse dressed the question of the mid- to long-term variability of the 2009). We thus conclude that, although the H↵ is able to detect activity indices using F-tests. We found that some stars in our long-term activity variations in early-M dwarfs, it is not the same sample were showing obvious signs of these variations in S Ca II, physical phenomena that is being probed by both indices and H↵,andNa.ThesamewasnotasevidentfortheHeindex. thus their variations cannot be naively compared. Nevertheless, The most obvious cases of detected long-term activity variations the simultaneous study of S Ca II (or Na )andH↵ might be use- are Gl1, Gl273, Gl433, Gl436, Gl581, Gl588, Gl667C, Gl832, ful to gather new information about the presence of di↵erent Gl849, Gl877, Gl908, and HIP85647. This selection was made activity-related features such as filaments and plages in stellar by choosing stars with statistically significant variation in at least disks. two indices. We also performedF-tests to detect possible maxima or min- The He index has not only the smallest variation of the three ima of activity. Gl1 and Gl433 have statistically significant max- lines, we also found it to correlate less well with activity and thus ima in at least two indices. Gl581 appears to be in a statisti- we do not recommend its use for the long-term activity study of cally significant minimum of activity in all indices except for Mdwarfs. H↵,whichshowsamaximum. We found a very good correlation between S Ca II and Na .A Our next step was to compare the activity indicators using great number of stars display a similar behavior for both indices the Pearson correlation coecient. Similarly to what was found and there is no relation between the correlation coecient and by Cincunegui et al. (2007b)weobtainedagreatvarietyofcor- the activity level. This index consequently is a proxy of activity relations between the S and H↵ in the range 0.8 < ⇢ < 1. Ca II variations as measured by S Ca II.Becausethesestarshavemore We found that there is a trend of the correlation coecient with flux in the redder part of the spectrum, the Na index should the level of activity as measured by the S -index. For the least be preferred over the Ca ii lines because the measurements will active stars there is a tendency for low- or anti-correlation, while have a far better signal-to-noise ratio. We can then extend the for the most active stars in our sample the correlation becomes Díaz et al. (2007a)suggestionoftheuseoftheselinestomeasure strongly positive. mid- to long-term activity in the least active stars of later spectral We attribute this e↵ect to the fact that as activity increases, type. the H↵ lines first start as a weak absorbing line, then become strongly absorbing, and as the activity further increases, they In a following paper we will compare the behavior of the start to fill in, becoming weak absorbers again, and finally at long-term activity from these results with the radial-velocity high-activity levels become a full emission line, as predicted measurements and the cross-correlation function parameters bi- by Cram & Mullan (1979)(seealsoCram & Giampapa 1987; sector span, full-width-at-half-maximum, and contrast, with the Stau↵er & Hartmann 1986; Walkowicz & Hawley 2009). A re- aim of investigating if long-term cycle-like activity variations are lation like this would produce the correlation observed in Fig. 3 able to influence themeasuredradialvelocityofMdwarfs.

A30, page 16 of 17 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. I.

Acknowledgements. Wewould like to thank our anonymous referee for the help- Giampapa, M. S., Cram, L. E., & Wild, W. J. 1989, ApJ, 345, 536 ful comments and suggestions. This work has been supported by the European Hawley, S. L., Gizis, J. E., & Reid, I. N. 1996, AJ, 112, 2799 Research Council/European Community under the FP7 through a Starting Grant, Herbig, G. H. 1985, ApJ, 289, 269 as well as in the form of a grant reference PTDT/CTE-AST/098528/2008, funded Huélamo, N., Figueira, P., Bonfils, X., et al. 2008, A&A, 489, L9 by Fundação para a Ciência e a Tecnologia (FCT), Portugal. J.G.S. would like Koen, C., Kilkenny, D., van Wyk, F., & Marang, F. 2010, MNRAS, 403, 1949 to thank the financial support given by FCT in the form of a scholarship, namely Landman, D. A. 1981, ApJ, 244, 345 SFRH/BD/64722/2009. N.C.S. would further like to thank the support from Livingston, W., Wallace, L., White, O. R., & Giampapa, M. S. 2007, ApJ, 657, FCT through a Ciência 2007 contract funded by FCT/MCTES (Portugal) and 1137 POPH/FSE (EC). Mauas, P. J. D. 2000, ApJ, 539, 858 Mayor, M., Pepe, F., Queloz, D., et al. 2003, The Messenger, 114, 20 Mayor, M., Bonfils, X., Forveille, T., et al. 2009, A&A, 507, 487 References Meunier, N., & Delfosse, X. 2009, A&A, 501, 1103 Meunier, N., Desort, M., & Lagrange, A. 2010, A&A, 512, A39 Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ, 438, 269 Montes, D., Fernandez-Figueroa, M. J., de Castro, E., & Cornide, M. 1995, Baliunas, S. L., Donahue, R. A., Soon, W., & Henry, G. W. 1998, in Cool Stars, A&AS, 109, 135 Stellar Systems, and the Sun, ed. R.A.Donahue,&J.A.Bookbinder,ASP Montes, D., Fernandez-Figueroa, M. J.,deCastro,E.,&Sanz-Forcada,J.1997, Conf. Ser., 154, 153 A&AS, 125, 263 Boisse, I., Bouchy, F., Hébrard, G., et al. 2011, A&A, 528, A4 Noyes, R. W., Weiss, N. O., & Vaughan, A. H. 1984, ApJ, 287, 769 Boisse, I., Moutou, C., Vidal-Madjar, A., et al. 2009, A&A, 495, 959 Pasquini, L., & Pallavicini, R. 1991, A&A, 251, 199 Bonfils, X., Mayor, M., Delfosse, X., et al. 2007, A&A, 474, 293 Paulson, D. B., Saar, S. H., Cochran, W. D., & Hatzes, A. P. 2002, AJ, 124, 572 Bonfils, X., Delfosse, X., Udry, S., et al. 2011, A&A, submitted Queloz, D., Henry, G. W., Sivan, J. P., et al. 2001, A&A, 379, 279 Bouchy, F., Pont, F., Santos, N. C., et al. 2004, A&A, 421, L13 Rauscher, E., & Marcy, G. W. 2006, PASP, 118, 617 Buccino, A. P., Díaz, R. F., Luoni, M. L., & Mauas, P. J. D. 2011, AJ, 141, 34 Robinson, R. D., Cram, L. E., & Giampapa, M. S. 1990, ApJS, 74, 891 Cincunegui, C., Díaz, R. F., & Mauas, P. J. D. 2007a, A&A, 461, 1107 Saar, S. H., & Donahue, R. A. 1997, ApJ, 485, 319 Cincunegui, C., Díaz, R. F., & Mauas, P. J. D. 2007b, A&A, 469, 309 Saar, S. H., Huovelin, J., Osten, R. A., & Shcherbakov, A. G. 1997, A&A, 326, Cram, L. E., & Giampapa, M. S. 1987, ApJ, 323, 316 741 Cram, L. E., & Mullan, D. J. 1979, ApJ, 234, 579 Santos, N. C., Mayor, M., Naef, D., et al. 2000, A&A, 361, 265 Delfosse, X., Forveille, T., Perrier, C., & Mayor, M. 1998, A&A, 331, 581 Santos, N. C., Gomes da Silva, J., Lovis, C., & Melo, C. 2010, A&A, 511, A54 Díaz, R. F., Cincunegui, C., & Mauas, P. J. D. 2007a, MNRAS, 378, 1007 Stau↵er, J. R., & Hartmann, L. W. 1986, ApJS, 61, 531 Díaz, R. F., González, J. F., Cincunegui, C., & Mauas, P. J. D. 2007b, A&A, 474, Strassmeier, K. G., Fekel, F. C., Bopp, B. W., Dempsey, R. C., & Henry, G. W. 345 1990, ApJS, 72, 191 Dumusque, X., Santos, N. C., Udry, S., Lovis, C., & Bonfils, X. 2011a, A&A, Walkowicz, L. M., & Hawley, S. L. 2009, AJ, 137, 3297 527, A82 Wilson, O. C. 1978, ApJ, 226, 379 Dumusque, X., Udry, S., Lovis, C., Santos, N. C., & Monteiro, M. J. P. F. G. Wright, J. T., Marcy, G. W., Butler, R. P., et al. 2008, ApJ, 683, L63 2011b, A&A, 525, A140 Zechmeister, M., Kürster, M., & Endl, M. 2009, A&A, 505, 859 ESA 1997, VizieR Online Data Catalog, 1239, 0 Zirin, H. 1988, Astrophysics of the sun, ed. H. Zirin

A30, page 17 of 17 Chapter 3

Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program II. Activity and radial velocity

63 A&A 541, A9 (2012) Astronomy DOI: 10.1051/0004-6361/201118598 & c ESO 2012 Astrophysics

Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program II. Activity and radial velocity,,

J. Gomes da Silva1,2,N.C.Santos1,2,X.Bonﬁls3,X.Delfosse3,T.Forveille3,S.Udry4,X.Dumusque1,4,andC.Lovis4

1 Centro de Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal e-mail: [email protected] 2 Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Portugal 3 UJF-Grenoble 1 / CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, 38041 Grenoble, France 4 Observatoire de Genève, Université de Genève,51Ch.desMaillettes,1290Versoix,Switzerland Received 6 December 2011 / Accepted 7 February 2012

ABSTRACT

Owing to their low mass and luminosity, M dwarfs are ideal targets if one hopes to ﬁnd low-mass planets similar to Earth using the radial velocity (RV) method. However, stellar magnetic cycles could add noise or even mimic the RV signal of a long-period companion. We extend our previous study of the correlation between activity cycles and long-term RV variations for K dwarfs to the lower-end of the main sequence. Our objective is to detect any correlations between long-term activity variations and the observed RV of a sample of M dwarfs. We use a sample of 27 M-dwarfs with a median observational timespan of 5.9 years. The cross-correlation function (CCF) with its parameters RV, bisector inverse slope (BIS), full width at half maximum (FWHM), and contrast are computed from the HARPS spectrum. The activity index is derived using the Na Ddoublet.Theseparametersarecomparedwiththeactivity 1 level of the stars to search for correlations. We detect RV variations up to 5ms that we can attribute to activity cycle e↵ects. However, only 36% of the stars with long-term activity variability appear to⇠ have had their RV a↵ected by magnetic cycles, on the typical timescale of 6years.Therefore,wesuggestacarefulanalysisofactivitydatawhensearchingforextrasolarplanetsusing long-timespan RV data.⇠ Key words. planets and satellites: detection – stars: activity – stars: late-type – techniques: radial velocities – techniques: spectroscopic

1. Introduction regions on line profiles, hence RV measurements, can easily hide or mimic the signal of orbiting companions (e.g. Saar & The majority of extrasolar planets discovered so far were either 1 Donahue 1997; Santos et al. 2000; Queloz et al. 2001). In some detected or confirmed via the radial velocity (RV) method .This cases, these e↵ects can be diagnosed e.g. by the anti-correlation technique measures the Doppler e↵ect caused by the wobble of between instantaneous measurements of RV and the bisector in- the star around the centre of mass of the star-planet system. As verse slope (BIS) (Queloz et al. 2001; Boisse et al. 2011), and an indirect method, it is sensitive to stellar sources of noise such corrected by either subtracting the anti-correlation slope from as oscillations, granulation, rotating active regions, and magnetic the RV measurements (e.g. Melo et al. 2007; Boisse et al. 2009) cycles. or fitting an extra Keplerian orbit to the RV data with the pe- Stellar oscillations and granulation induce RV variations on riod detected in the activity time-series (e.g. Bonfils et al. 2007; timescales of up to some hours and these variations can eas- Forveille et al. 2009). Queloz et al. (2009)andBoisse et al. ily be suppressed if an optimized observational strategy is used (2011)proposedtothefittingoftheactivitysignalwithsinusoids (Dumusque et al. 2011). However, this is not true in the case of di↵erent periods: the rotation one and its harmonics. In con- of rotationally modulated active regions, for which the observed trast, Saar & Fischer (2000)usedadi↵erent technique to correct variations have longer timescales. The e↵ect of rotating active the RV induced by long-term activity. These authors used the slope of the S IR–RV correlation to remove the activity influence ? Based on observations made with the HARPS instrument on from the RV signal. the ESO 3.6-m telescope at La Silla Observatory under programme ID 072.C-0488(E). Long-term stellar magnetic cycles can also be a source of ?? Tables with the data used for Figs. A.1–A.27 are only available at noise for precise RV measurements. Kürster et al. (2003)studied the CDS via anonymous ftp to the correlation between the RV and the H↵ index of the nearby cdsarc.u-strasbg.fr (130.79.128.5) or via Barnard’s star (Gl699). They found an anti-correlation between http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/541/A9 the RV and the activity index with a correlation coecient of ??? Appendix A is available in electronic form at ⇢ = 0.50. The authors concluded that the activity measured http://www.aanda.org by the hydrogen line produces a blueshift of the photospheric 1 Cf. http://exoplanet.eu/ absorption lines. Article published by EDP Sciences A9, page 1 of 25 A&A 541, A9 (2012)

By using simulations, Meunier et al. (2010)showedthat compare the long-term activity with RV and the CCF parame- magnetic activity cycles can induce RV variations in the case ters; in Sect. 6,weexamineindividualstarswithstrongactivity- of the Sun as seen edge-on, with amplitudes that can reach the RV correlation and other interesting cases; and finally in Sect. 7, 1 10 m s level. These kinds of variations in a star with a pe- we draw our conclusions from the present work. riodic⇠ activity cycle might be able to mimic the signal of a long-period extra-solar planet. In this context, Santos et al. (2010)usedasampleof8solar- 2. Sample and observations type stars to determine whether a correlation between long- Our sample was selected from the HARPS M-dwarf planet term activity and RV variations exists. The long-term variations search program that started in 2003 and ended in 2009 (see were detected in the S MW,H↵,andHeindices and in the BIS, Bonfils et al. 2012). We used this sample in Paper I to study full-width-at-half-maximum(FWHM), and contrast of the cross- four known chromospheric activity indices and to select stars correlation function (CCF) but only two stars were found to have with long-term activity variability. However, we now comple- correlations with RV stronger than ⇢ > 0.75 :onepositivecorre- ment this data set with data taken in 2010 as part of the Bonfils | | lation and one anti-correlation. The authors concluded then that et al. (2012)programextension.Wethereforedecidedtoredo the possible amplitudes of induced RV variations for the early-K the same analysis as in Paper I using the new data to detect any 1 dwarfs was low, of the 1ms level and similar to the HARPS new cases of activity variability that could arise from more data ⇠ precision. points. Using a larger sample of around 300 stars from the HARPS We obtained simultaneous RV, BIS, FWHM, contrast, and FGK high precision program, Lovis et al. (2011)studiedthecor- the Na activity indicator. The median RV error of the nightly 1 relation between long-term activity variations and the RV in a averaged data was 1.2 m s .AlthoughHARPSiscapableof similar fashion to Santos et al. (2010). They found a correlation more precise measurements (e.g. Mayor et al. 2011), our sample between the slope of the RV–activity index (RHK0 )correlation,ef- includes dim stars for which it is more dicult to acquire high fective temperature (Te↵), and metallicity ([Fe/H]). The slope is signal-to-noise ratio (S/N) data and therefore higher-precision weaker for late-type dwarfs than for early ones, hence the RVs of RVs. To measure activity 2,weusedtheindexbasedonthe later-K dwarfs appear to be less a↵ected by magnetic cycles than Na D1 and D2 lines in a same way as in Paper I (see also the RVs of early-G dwarfs. Therefore, the influence of long-term Díaz et al. 2007a). The CCF parameters were used because of activity could be corrected if the activity level, e↵ective temper- their potential as complementary long-term activity proxies (e.g. ature, and metallicity of the star can be inferred from the slope Santos et al. 2010). of the RV–log(RHK0 )relation. Owing to an instrumental drift detected in the HARPS data Hints of long-term RV variations produced by activity cy- that a↵ected the FWHM and contrast of the CCF, these parame- cles were found by Moutou et al. (2011)inthestarsBD-114672 ters were corrected using the expressions and HIP21934, with periods of 1692 and 1100 days respec- 6 9 2 tively. Ségransan et al. (2012)alsofoundalong-termperiodof FWHMcorr = FWHM + 5.66 10 D 1.77 10 D , (1) 5 8 2 500 days in the RV data of HD104067 (K2V). The activity in- contrastcorr = contrast + 4.59 10 D 2.75 10 D , (2) dex⇠ of this star, hosting a 55-day period Neptune-like planet, was found to have a correlation with the RV residuals (with where D is (BJD 2454500)days.However,thiscorrection 1 is very small and represents a long-term drift. For example, the RV = 4.6ms )aftertheplanetarysignalwasremoved. More recently, three exoplanets were discovered in three FWHM drift is only 0.1% in five years. early-K stars with magnetic cycles by correcting the activity Since this sample includes some stars very close to the Sun, signals in the RV data (Dumusque et al. 2012). The planets these stars may undergo significant secular acceleration that were found by fitting simultaneously two Keplerians: one for could produce a trend in the observed RV. We corrected all the planet and one for the magnetic cycle. All the parameters of stars for this e↵ect using the proper motions and parallaxes that the Keplerian fitting the cycle, except the amplitude, were fixed were retrieved from the H catalog (ESA 1997). The sec- to the ones obtained when fitting the activity index only. This ular accelerations were calculatedfollowingthedescriptionin proves that (i) the magnetic activity cycles of stars can influence Zechmeister et al. (2009)andtheradial-velocitiesweresubse- RV and hide the signal of long-period planets, and (ii) a correc- quently corrected (see also Bonfils et al. 2012). tion of the long-term activity-induced RV is possible and can be Some of the stars in this sample are known to be planetary used to recover the embedded signal of a planet. hosts, namely Gl 176, Gl 433, Gl 436, Gl 581, Gl 667 C, Gl 674, In Gomes da Silva et al. (2011,hereafterPaperI)wecom- Gl 832, Gl 849, Gl 876, HIP12961, and HIP85647 (Bonfils et al. pared the long-term activity variations using four activity indices 2012). Since we are only interested in variations caused by ac- for a sample of M-dwarf stars from the HARPS program. We tivity, these planetary signals were subtracted from the observed arrived at the conclusion that the Na index was the most ap- RVs by fitting Keplerian functionsbased on the published orbital parameters. propriate of the four available indices (which included the S CaII, H↵,andHeindices) to study the activity of these type of stars. The selection criteria was the same as in our previous paper. In this paper, we use the Na index as a proxy of activity to We nightlyaveragedand binnedthe data into 150-daybinsto av- enable us to compare long-term activity to RV and some other erage out short timescale variability, since we are only concerned relevant CCF parameters using the same sample of stars. This with long-term variations. Only bins of more than three nights paper therefore extends our first study in Santos et al. (2010)to and stars with at least four bins were selected. The errors used p the case of early-M dwarfs. for each bin are the statistical errors in the average, i = / N, This paper is organised as follows: in Sect. 2,wepresent where is the root-mean-square (rms) of the nightly averaged our sample and observation log and explain our data analysis; in data in each bin, and N is the number of nights included in the Sect. 3,wedescribeourselectionofasubsampleofstarswith bin. long-term activity variability; in Sect. 4,wedeterminewhich 2 From now on, we use the terms activity, Na ,andsodiumlinesinter- stars have hints of periodic magnetic cycles; in Sect. 5,we changeably.

A9, page 2 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Table 1. Basic parameters and observational log of the sample.

a d e Star Other names Sp. Type V V I BJDstart 2400000 #Nights Tspan S/N i(Vr) h ih1 i [mag] [mag] [days] [days] (order 56) [m s ] Gl 1 M3V 8.57 2.13 52 985.60 45 2063 95.6 0.7 Gl 176† M2.5V 9.97 2.25 52 986.71 71 2146 47.6 1.2 Gl 205 M1.5V 7.92 2.08 52 986.73 75 1400 108.5 0.8 Gl 273 M3.5V 9.89 2.71 52 986.77 62 2140 57.3 0.8 Gl 382 M2V 9.26 2.18 52 986.84 30 1188 66.7 1.1 Gl 393 M2V 9.76 2.26 52 986.86 29 1897 67.0 1.0 Gl 433† M2V 9.79 2.15 52 989.84 61 2245 56.6 1.2 b Gl 436† M2.5V 10.68 2.02 53 760.83 115 1532 32.9 1.4 Gl 479 M3V 10.64 1.90 53 158.55 58 1413 43.3 1.2 Gl 526 M1.5V 8.46 2.07 53 158.60 34 1843 101.6 0.8 Gl 551 Prox Cent M5.5V 11.05 3.62 53 152.60 42 2140 21.1 1.3 Gl 581† M2.5V 10.57 2.53 53 152.71 194 2306 36.4 1.2 Gl 588 M2.5V 9.31 2.40 53 152.75 32 2200 75.4 0.8 Gl 667 C† M2V 10.22 2.08 53 158.76 173 2201 42.9 1.3 Gl 674† M3V 9.36 2.40 53 158.75 44 1574 70.6 0.8 Gl 680 M1.5V 10.14 2.27 53 159.71 35 2269 41.2 1.4 Gl 699 Barnard’s star M4V 9.54 2.52 54 194.89 32 1291 34.3 0.8 Gl 832† M1V 8.67 2.18 52 985.52 59 2424 88.9 0.8 Gl 849† M3V 10.42 2.50 52 990.54 49 2423 41.9 1.3 Gl 876† M3.5V 10.17 2.77 52 987.58 67 2508 42.6 1.1 Gl 877 M2.5V 10.55 2.43 52 857.83 40 2636 36.5 1.2 Gl 887 M2V 7.34 2.02 52 985.57 63 1407 131.3 0.8 Gl 908 M1V 8.98 2.04 52 986.58 66 2511 76.0 0.9 c HIP 12961† M0V 9.7 1.64 52 991.63 46 2226 46.5 3.0 HIP 19394 M3.5Vd 11.81 2.5 52 942.80 35 2495 23.3 2.0 HIP 38594 Md 9.96 1.64 52 989.79 17 2229 41.1 2.0 b HIP 85647† GJ 676 A M0V 9.59 1.85 53 917.75 38 1520 36.6 2.4

( ) Notes. The average RV errors, (V ) ,aretakenafterremovaloftheplanetarycompanion’ssignals. † Stars with published planetary companions. h i r i References. (a) Bonﬁls et al. (2012)unlessindividuallyspeciﬁed;(b) Hawley et al. (1996); (c) Koen et al. (2010); (d) Simbad (http://simbad. u-strasbg.fr/simbad/); (e) ESA (1997).

We also decided to select only stars with data for at least statistically significant variability in their long time scale activity three years of observations, which resulted in GJ 361, GJ 2049, that has not been detected before.Wethereforedecidedtorepeat and GJ 3218 being discarded from the sample. Our final sample the variability F-tests, this time using only the Na i index. consisted of 27 stars that passed the selection criteria, whose ba- The Na activity proxy was determined as explained in sic parameters are presented in Table 1.Thesestarshavespectral Paper I, by measuring the flux in the centre of the sodium D1 types in the range M0–M5.5 V and have V magnitudes between and D2 lines relative to the flux in two reference bands. This in- 7.34 and 11.81, with V I colours ranging from 1.64 to 3.62 mag. dex has not been calibrated to the bolometric flux of the stars, In the same table, we also present the observation log, with in- hence depends on the e↵ective temperature of each star (see dis- formation about the number of nights of observation, the time cussion on Sect. 6.6 of Paper I). As a consequence, this index span in days, the average S/N at spectral order 56 (the order of cannot be used to compare the activity of stars with di↵erent the Na doublet, 5893 Å) and the average RV error. The time e↵ective temperatures. Nevertheless, it can be used to detect ac- span of the observations⇠ range from 3.3 to 7.2 years (with a me- tivity variability with time for a given star. dian value of 5.9 years). The average errors on RV per star for In a similar fashion to our analysis in Paper I, we investi- 1 the nightly averaged data vary between 0.8 and 3.0 m s . gated whether the long time scale variations observed in our data were of statistical significance. As previously done in Paper I, we used the F-test with an F-value of F = 2/ 2,where e h ii 3. Na I index variability e is the standard deviation and i the average of the error in the mean of the binned parameterh i for each star (see Endl In Paper I, we compared four activity indices, namely S Ca II, et al. 2002; Zechmeister et al. 2009; Bonfils et al. 2012). This H↵,Nai,andHei,andarrivedattheconclusionthatthe F-test gives the probability that the observed standard deviation Na i index is the most suitable for monitoring the long-term ac- can be explained by the random scatter due to the internal er- tivity of M-dwarf stars. We also tested our sample for variabil- rors. Therefore, a low value of P(F)willdiscriminateagainstthe ity and found that Gl1, Gl273, Gl433, Gl436, Gl581, Gl588, stars that have experienced significant variability that is not jus- Gl 667 C, Gl 832, Gl 849, Gl 877, Gl 908, and HIP 85647 showed tified by the internal errors. The results of these tests are shown significant (P(F) 0.05) long-term activity variability in at least in Table 2.Boldfacevaluesindicateprobabilitieslowerthan two indices. However, we are now using the latest data with new 0.05 (95% significance level). The F-value used to calculate the 2 2 measurements from 2010 (previously we used data covering the probabilities was F = e(Na i) / i(Na i) ,wheree stands for years 2003–2009) and consequently other stars might now show the rms of the (binned) data and h is thei average of the error in h ii A9, page 3 of 25 A&A 541, A9 (2012)

Table 2. Statistics for RV and Na ,andprobabilitiesP(F)ofthevariabilityF-testsforactivity.

Star Nbins Sel. e(Vr) i(Vr) Na i e(Na i) i(Na i) P(F) 1 h 1 ih i h i [m s ][ms ] Gl 1 5 Yes 0.58 0.71 0.104 0.0021 0.0013 0.18 Gl 176 7 No 2.7 0.94 0.188 0.0074 0.0044 0.12 Gl 205 6 No 2.9 0.82 0.179 0.0046 0.0029 0.16 Gl 273 6 Yes 1.5 0.49 0.075 0.0037 0.0016 0.042 Gl 382 5 No 2.1 2.2 0.196 0.0052 0.0027 0.12 Gl 393 5 No 1.6 0.71 0.146 0.0037 0.0023 0.18 Gl 433 6 Yes 1.2 0.71 0.141 0.0034 0.0011 0.011 Gl 436 8 Yes 0.43 0.52 0.100 0.0042 0.0012 0.0017 Gl 479 4 No 2.0 0.97 0.186 0.0040 0.0029 0.31 Gl 526 4 No 1.8 0.69 0.158 0.0035 0.0011 0.042 Gl 551 6 No 1.5 0.83 0.493 0.057 0.044 0.28 Gl 581 13 Yes 0.96 0.51 0.071 0.0026 0.0013 0.012 Gl 588 5 Yes 1.3 0.39 0.131 0.0059 0.0010 0.0025 Gl 667 C 8 Yes 0.73 0.61 0.096 0.0030 0.0014 0.031 Gl 674 5 No 2.3 0.73 0.138 0.0037 0.0029 0.32 Gl 680 6 No 5.9 0.93 0.146 0.0048 0.0022 0.059 Gl 699 5 No 1.5 0.61 0.059 0.0082 0.0027 0.027 Gl 832 5 Yes 0.30 0.66 0.132 0.0039 0.0015 0.047 Gl 849 6 Yes 0.29 0.77 0.124 0.0032 0.0013 0.032 Gl 876 6 No 2.3 1.8 0.081 0.0047 0.0017 0.020 Gl 877 5 Yes 2.7 1.3 0.106 0.0074 0.0020 0.014 Gl 887 4 No 1.6 1.1 0.173 0.0038 0.0014 0.062 Gl 908 9 Yes 1.2 0.55 0.131 0.0031 0.0014 0.020 HIP 12961 6 No 1.3 0.89 0.172 0.0028 0.0016 0.12 HIP 19394 7 No 5.3 2.0 0.094 0.0033 0.0019 0.096 HIP 38594 4 No 2.6 1.2 0.169 0.0058 0.0020 0.055 HIP 85647 6 Yes 1.5 1.3 0.145 0.0041 0.0017 0.039

Notes. All parameters were calculated for the data with 150 day bins. the mean. We also show the number of bins Nbins,anindication From now on, we consider only these 14 stars for the rest of of whether the star passed the variability tests in Paper I, Sel., the study, unless specified. the RV rms e(Vr) and the average error in the mean i(Vr) , and the averageh valuei of the Na index, Na i . h i h i Fourteen of the 27 stars displayed long-term activity vari- 4. Activity cycle fits ability with P(F) 0.05, representing 52% of the sample.  Some stars show clear long-term variation in their activity, that These stars are Gl 273, Gl 433, Gl 436, Gl 526, Gl 581, Gl 588, is clearly visible with a general trend (increase or decrease in Gl 667 C, Gl 699, Gl 832, Gl 849, Gl 876, Gl 877, Gl 908, and activity over several observational seasons). These include stars HIP 85647. These are the same stars that passed the tests in that have not passed the variability F-tests of Sect. 3.Thereis Paper I plus Gl526, Gl699, and Gl876, and less Gl1. Four evidence that the periodic activity cycles of M-dwarf stars can more stars, Gl 680, Gl 887, HIP 19394, and HIP 38594, have be well-fitted by a sinusoidal function (see Cincunegui et al. 0.05 < P(F) 0.1, which if they are considered increases the  2007; Díaz et al. 2007b; Buccino et al. 2011). Given the usu- percentage of stars with variability to 67%. In Paper I, we found ally smaller number of points in our study, fitting other func- that 17 stars out of 30 showed variability in the Na index with tions (e.g. Keplerian) would not provide tighter constraints since P(F) 0.1, representing 57% of the sample. This represents an  it would increase the number of free-fitting parameters close to increase in the number of variable stars by 10% from our previ- the number of data points. We therefore tried to fit a sinusoidal ous work which has been achieved by simply adding one more signal to the Na data to obtain the periods of these cycles (min- year of observations, thus more of these stars might have shown imum periods in the case of data covering less than one period). long-term variability if data of a longer time-span had been con- The fitted sinusoidal signal was of the form sidered. We note that Gl 1 passed the variability test on Paper I but not here. This is because in Paper I this star passed the test 2⇡ Na i = A sin t + + , (3) because of its variability in both the S Ca and H↵ indices, while sine ii Pcycle not showing significant variability in Na .Sinceweonlyused the Na index and for Gl 1 we did not have more data points in where A is the semi-amplitude in units of Na , Pcycle the activity 2010, we found that this star failed to pass the F-test based solely cycle period in days, t the observation epoch in days, the phase, on Na . and aconstanto↵set. The quality of the fit was obtained by a By using a sample of old FGK stars in the solar neighbour- p-value, which gives the probability that the data is more accu- hood that had been studied for up to seven years, Lovis et al. rately fit by a straight line than a sinusoidal signal. This p-value (2011)foundthat61%haveamagneticactivitycycle.Although was calculated via an F-value given by we cannot confirm the cyclic nature of our detected long-term 2 2 activity variations, our results are compatible with those of Lovis F(2) = (N 4) line sine , (4) et al. (2011). 2 sine A9, page 4 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II. where line and sine identify whether the model used was the linear fit or sinusoidal fit, respectively, and N is the number of data points. The chi-squared function used was

N Na i Na i 2 2 = n n, sine , for 1 n N, (5) i(Na i)n   1 where Na in are the observed values of the activity index, Na in, sine are the activity values obtained from the fitted sine model, and i(Na i)n are the internal errors in each individual Na in. Smaller p-values indicate that the data were more tightly fitted by a sinusoid. We note that these fits were carried out without taking into consideration whether the star passed the variability F-tests in Sect. 3.Inaddition,itwasonlypossibletocalculate the probabilities for the stars that have five or more data points, otherwise (N 4) 0. Eight stars had their long-term activity successfully fitted by a sinusoidal signal, with P(2) 0.1. These stars are Gl 1, Gl 382, Gl 433, Gl 581, Gl 667 C, Gl 680, Gl 832, and HIP 85647. However, Gl 1, Gl 382, and Gl 680 did not pass the long-term variability F-tests hence were discarded from further discussion. The others are discussed individually in Sect. 6.

5. RV, activity, and CCF parameters Figures A.1–A.27 present the time-series of RV data, activity, and the CCF parameters’ BIS, FWHM, and contrast for the 27 stars that passed the selection criteria (prior to the variability F-tests). Small points are nightly averaged data used to calcu- Fig. 1. Top: RV scatter versus Na scatter. Bottom: RV scatter versus relative Na scatter. late the bins, and points with errorbars are the binned data (the errors are explained in Sect. 2). The peak-to-peak variation () and rms ()arealsoshown.Theknownplanetarycompanions’ signal were subtracted from the RV time-series. The most active star in the sample, Gl 551, also has the After removal of secular acceleration, HIP38594 showed largest absolute scatter in Na index (and 12% relative scatter). a trend in the RV time-series with a slope of 50.83 However, its RV dispersion is not particularly high, having a 1 1 ± 1 0.51 m s yr .Thiscorrespondstoavariationof(Vr) = standard deviation of e(Vr) = 1.5ms . 1 307.5ms across the time span of our data and is probably due Meunier et al. (2010)simulatedthee↵ects of spots, plages, to a stellar companion. A Keplerian fit gives an orbit for a com- and inhibition of convection in the solar RV during a solar activ- panion with a minimum period (only a linear trend is observed ity cycle with the Sun seen edge-on and observed as a star, by in the data) of 4941 1516 days. Since we are only concerned measuring its integrated flux over the whole disk. The authors with low-amplitude and± long-term variations, we removed this found that the signal induced by the three e↵ects on the solar 1 trend. RV during the cycle had an rms of (Vr) = 2.40 m s ,witha 1 Other stars appear to have linear trends in RV, such as Gl205 peak-to-peak variation of 10.6 m s . 1 1 1 (with (Vr) = 9ms )andGl680((Vr) = 15 m s ), but The median RV rms of 1.5 m s for our sample is smaller since these trends have smaller amplitude variations we decided than the results of Meunier et al. (2010)andthereforeinagree- to keep them for the rest of the study (see Sect. 5.2 for more ment with the extrapolation towards M dwarfs of Lovis et al. information). (2011), who found that later-type stars have lower amplitude RV influenced by long-term activity than earlier-type stars. The stronger contribution to RV from magnetic activity cycles is ex- 5.1. Activity and RV scatter pected to originate from the inhibition of convection (Meunier Table 2 shows the RV rms after the subtraction of the orbits to- et al. 2010). Since the cell-convection structure depends strongly gether with the mean and rms of the Na i index for the binned on the e↵ective temperature of the stars, the impact of their inhi- data of the full sample. The scatter in RV, e(Vr), varies between bition should also depend of spectral type. Thus, activity cycles 1 1 0.29 m s for Gl 849 and 5.9 m s for Gl 680. The most active are expected to have a di↵erent influence on RV for di↵erent star in the sample is Gl551 (Proxima Centauri) with an aver- types of stars. age Na i index of 0.49, while the most inactive star is Gl 699 Figure 1 shows the rms variation in RV against the rms (Barnard’s star) with an average Na i value of 0.059 (but the in Na index (top panel) and the relative variation in Na largest relative scatter in Na of 14%). We note, however, that (lower panel). A relation between these parameters is clearly the average Na index values depend⇠ on stellar colour (see Fig. 6 visible: stars with a larger long-term scatter in their activity of Paper I) and should not be used to compare the activity of also have a larger long-term scatter in RV. The minimum long- stars with di↵erent colours for which the index is not calibrated term relative variation we could detect in the Na index was for the photospheric contribution and the bolometric flux is not around 2%, with the highest scatter reaching around 14%. The taken into consideration. star Gl 699 appears to be an outlier, more evidently when we

A9, page 5 of 25 A&A 541, A9 (2012)

Table 3. Pearson correlation coecients and their respective FAPs.

Star Vr vs. Na i Na i vs. BIS Na i vs. FWHM Na i vs. Contrast ⇢ FAP ⇢ FAP ⇢ FAP ⇢ FAP Gl 273 0.84 0.022 –0.64 0.094 0.60 0.13 –0.89 0.0074 Gl 433 0.91 0.0018 –0.70 0.11 0.70 0.031 –0.53 0.14 Gl 436 0.83 0.0091 0.28 0.29 0.82 0.0074 0.44 0.15 Gl 526 0.86 0.13 0.27 0.34 0.90 0.057 –0.76 0.13 Gl 581 0.24 0.25 0.11 0.38 0.60 0.019 –0.38 0.13 Gl 588 0.82 0.033 0.03 0.49 –0.51 0.24 –0.40 0.25 Gl 667C 0.45 0.12 –0.35 0.26 –0.27 0.22 0.37 0.17 Gl 699 0.32 0.31 –0.12 0.42 0.55 0.15 –0.79 0.070 Gl 832 –0.20 0.36 –0.41 0.30 0.57 0.19 0.08 0.46 Gl 849 -0.37 0.25 -0.38 0.26 0.69 0.097 –0.29 0.29 Gl 876 0.63 0.091 0.45 0.15 0.27 0.30 –0.15 0.39 Gl 877 0.77 0.11 –0.74 0.085 0.93 0.023 –0.45 0.21 Gl 908 0.85 0.0038 –0.61 0.051 0.82 0.0075 0.43 0.093 HIP 85647 –0.03 0.48 0.32 0.30 0.81 0.039 –0.87 0.014

Notes. Only the 14 stars that passed the activity variability tests in Sect. 3 are considered. Bold face text indicates FAP values lower than 0.05 (95% signiﬁcance level). The FAPs were calculated via bootstraping as in Paper I. consider the relative activity values. Although this star has an average value of (Vr), when compared to the rest of the sample, it has the highest relative activity variation, almost twice that of the star with the second highest relative activity variation.

5.2. Correlation between RV and activity Table 3 shows the correlation coecients of the relation between RV and Na and the respective FAPs. The FAPs were calculated using bootstrapping of the nightly averaged data, in addition to a re-binning and a subsequent determination of the correlation coecient for each of the 10 000 permutations (see also Paper I). The tendency for positive correlations is clear, with an average correlation coecient of ⇢ = 0.49. Five stars have a significant correlation coecienth (withi 5% false-alarm probability) Fig. 2. Slope of the correlation between RV and activity against (V I) between activity and RV, which represents 36% of the sample. colour. Symbol sizes depend on the value of the correlation coecient between RV and activity: large for ⇢ 0.75, medium for 0.50 ⇢ < These stars are Gl 273, Gl 433, Gl 436, Gl 588, and Gl 908 and  their coecients range between 0.82 and 0.91. One more star, 0.75, and small for ⇢ < 0.50. The data points have three colours based on the FAP values: black for FAP 0.01, grey for 0.01 < FAP 0.05, Gl 876, has a FAP value lower than 10%, with a correlation co- and white for FAP > 0.1. The errorbars are the errors in the slope. ecient of 0.63. If a FAP lower than 10% is taken as the limit, then we can conclude that for 43% of the variable stars the RV is induced by long-term activity.⇠ correlation observed in their Fig. 18 (lower panel) reaches a Figure 2 shows the slope of the correlation between RV and plateau for lower e↵ective temperatures or that the variations Na index as a function of (V I)colour.Thesymbolshavethree induced by long-term activity in the RV of M dwarfs are so sizes that depend on the correlation coecient values: large for small that they are more dicult to observe (some of the ob- ⇢ 0.75, medium for 0.50 ⇢ < 0.75, and small for ⇢ < 0.50. served scatter reaches the same level as the instrument preci- The data points have three colours based on the FAP values: sion). Another possibility could be that still undetected small black for FAP 0.01, grey for 0.01 < FAP 0.05, and white planets might interfere with theRVdata,preventinganyclear for FAP > 0.1. The errorbars are the errors in the slope. We can hypothetical correlation. see in the figure that there is a clear tendency for positive slopes in the correlation RV–Na .Thisimpliesthatapositivechange in activity will induce a positive change in the apparent stellar 5.3. Correlation between activity and the CCF parameters velocity. All the cases of a significant correlation have positive 5.3.1. Na I versus BIS coecients and the slopes of the correlation range from 1 1 1 1 85 m s Na to 338 m s Na .Incontrasttothefindings We found a marginal tendency for negative correlations be- of Lovis et al. (2011)forFGKstars,wefoundnostrongrela- tween Na and BIS, with ⇢ = 0.18. We detected no cases h i tionship between the slopes and stellar colour (a proxy of Te↵) of significant coecients with a FAP 5%. Three cases of for this sample of early-M dwarfs. Furthermore, we found no marginal (5% < FAP 10%) anti-correlation, Gl 273 with ⇢ = cases of significant anti-correlations as would be expected from 0.64, Gl 877 with ⇢= 0.74, and Gl 908 with ⇢ = 0.61 the author’s study. Possible explanations are that the author’s (21% of the sample). Owing to the lack of significant cases of

A9, page 6 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II. correlation with activity, the line bisector thus does seem not to be a very good long-term activity indicator for early-M dwarfs. This is di↵erent from the trend found between activity and BIS for early-K stars, where the two were found to be positively correlated (e.g. Santos et al. 2010). While the BIS values found here were all negative, Santos et al. (2010)measuredpositive BIS values in all stars. Althoughthe absolute value of BIS would increase with activity, in the case of the negative values found in this study it means that the increase was a negative increase, hence anti-correlated with activity. We can speculate that the difference in the signal of the BIS values might be attributed to either the bisectors of K and M dwarfs that have inverse shapes, or the use of di↵erent cross-correlation masks to obtain the CCF line profiles (see e.g. Dall et al. 2006). Fig. 3. RV relation with Na i index for Gl 273. Small dots without errorbars are nightly averaged data points and points with errorbars are 5.3.2. Na I versus FWHM averaged over 150 days. The dashed line is the best linear fit. The correlation coecient ⇢ and the respective FAP are shown. We found a tendency for positive correlations between our activity indicator and width of the CCF profile, with ⇢ = 0.53 (the strongest average correlation coecient betweenh i parameters). We also found, a positive trend for early-K stars (e.g. Santos et al. 2010), hence we conclude that the qualitative behaviour of Gl 433. In Paper I, we found that this star reaches a maximum FWHM with activity is similar for di↵erent spectral types, an ef- in activity, which is typical of cycle-type long-term activity vari- fect also shown in Lovis et al. (2011). Six stars have strong corre- ations. Figure 4 (middle and bottom panels) shows that the RV lations in the range 0.60–0.93 with FAP 1%, representing 43%  time-series, after removal of the planetary signal (Delfosse et al. of our 14-star sample. These are Gl 433, Gl 436, Gl 581, Gl 877, 2012), follows a similar pattern to the Na index. The correlation Gl908, and HIP 85647. Two more stars display a marginal cor- coecient between the two is ⇢ = 0.91 with a FAP of 0.0018 relation, Gl 526 and Gl 849. If we count them, then 57% of our (Fig. 4,toppanel).TheNaindex also shows correlations with stars have a long-term correlation between activity and FWHM. CCF parameters of 0.70 and 0.70 for BIS and FWHM, respec- This means that the use of FWHM should be useful to detect tively. We can therefore confirm that the activity cycle maximum long-term activity-like variations in M-dwarfs and can be used is inducing the maximum in RV. The slope of the RV–Na corre- in addition to other activity proxies. 1 1 lation is 328 m s Na and we measured an overall variation 1 1 in RV of 3.29 m s (with e(Vr) = 1.22 m s ). The amplitude and period of the cycle in both Na or RV scales could not be in- 5.3.3. Na I versus contrast ferred because we do not have an entire cycle period in our data. As found by Santos et al. (2010)forearlier-typestars,wemea- However, a minimum limit for the amplitude and period could sured an apparent anti-correlation, ⇢ = 0.30 between the ac- be calculated by fitting a sinusoid to the activity time-series. We tivity level and the contrast of the CCF.h i However we found only found that the minimum activity cycle period is 1665 days with two cases of significant coecients, Gl 273 with ⇢ = 0.89 and aminimumamplitudeof0.004inNa(Fig. 4,middlepanel).A HIP 85647 with ⇢ = 0.87. This represents only 14% of the similar minimum period was also found for the RV signal with a 1 sample, an indication that the depth of the CCF line is not an value of 1758 days and an amplitude of 1.45 ms (Fig. 4,bot- optimal measure of the activity level of M dwarfs (at least that tom panel). This star therefore represents a good example of an measured by the Na /Ca lines). Two other cases of marginal RV signal induced by an activity cycle. correlation, Gl 699 with ⇢ = 0.79 and Gl 908 with ⇢ = 0.43 are present. Gl 436. This star has the smallest slope of the RV–activity cor- 1 1 relation with a value of 85 m s Na .FromFig.5,wecan observe a large scatter in the nightly averaged data. Ballard et al. 6. Individual cases (2010)reportedthemeasurementofshort-termnoiseinphotom- etry that they attributed to stellar spots. Furthermore, Knutson 6.1. Stars with significant RV–activity correlation et al. (2011)detectedevidenceofocculted spots during the transits of Gl 436 b (Butler et al. 2004). It is probable that short-term Gl 273. This star has the highest slope in the RV–activity rela- activity variability is producing the large scatter in Na and con- tion of the stars with significant correlation. Its slope has a value tributing to a reduction in the slope’s value. Nevertheless, the 1 1 of 338 m s Na with the RV having a peak-to-peak varia- correlation coecient of the RV–activity relation is ⇢ = 0.83 1 1 tion of = 5ms and a rms of 1.5 m s .ItsRV–activity with a FAP of 0.9%, providing clues for the influence of long- correlation coecient is 0.84 with a⇠ FAP of 2% (Fig. 3). This term activity on the observed RV of the star. A strong correlation star also has a strong anti-correlation between Na and contrast coecient between Na and FWHM of 0.82 (FAP = 0.7%) was with ⇢ = 0.89 (FAP = 0.0074). A moderate anti-correlation is also found. However, we tried to fit a sinusoidal signal to both also observed between Na and BIS (⇢ = 0.64, FAP = 0.094). the RV and Na time series but obtained no significant results. Although we found signs of a correlation between activity and The activity time series in Fig. A.8 shows a decreasing trend in RV we were unable to properly fit a sinusoidal to the Na time activity, which might be due to a long-period magnetic cycle, but series. more data will be needed to firmly prove this.

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Fig. 5. RV relation for the Na i index in the case of Gl 436. Small dots without errorbars are nightly averaged data points and points with errorbars are averaged over 150 days. The dashed line is the best linear ﬁt. The correlation coecient ⇢ and the respective FAP are shown.

Fig. 6. RV relation for the Na i index in the case of Gl 588. Small dots without errorbars are nightly averaged data points and points with er- Fig. 4. Top: RV relation with Na index for Gl 433. Middle: sinusoidal rorbars are averaged over 150 days. The dashed line is the best linear fit to the Na index for Gl 433. Bottom: sinusoidal fit to RV of Gl 433. fit. The correlation coecient ⇢ and the respective FAP are shown. Small dots without errorbars are nightly averaged and points with errorbars are averaged over 150 days. The dashed lines represent the best linear (top)andsinusoidal(middle, bottom)fitstothedata. has a magnetic “cycle” with no clear period, i.e., a star with a long-term aperiodic magnetic-activity variability, the variations of which are often classified as var (variable) by (Baliunas et al. Gl 588. With a correlation coecient of 0.82 (FAP = 3.3%), 1995). this star also has a strong long-term relationship between RV and 1 1 activity (Fig. 6). This correlation has a slope of 181 m s Na . 6.2. Other interesting cases The RV time series (Fig. A.13)hasaperiodic-likesignalwitha 1 peak-to-peak variation of 3.6 m s , which is similar to the Na Gl 176. This star has what appears to be a long-term periodic time series apart from a point at BJD 2453560d.Thisisa signal with P 2043 d in RV (see the time-series plot Fig. A.2). point that includes data for only four nights⇠ and might be influ- The same trend⇠ is not observed in the Na index and the data enced by short-term activity variability. It is therefore impossible for this star did not pass the variability tests. This star has to conclude anything about the periodicity of this stars’ activity aconfirmedplanetarycompanion,Gl176bwithP = 8.7d, cycle. and a rotationally modulated activity signal with a period of P = 39 d (Forveille et al. 2009). However, none of these signals can explain the 2000 d variation, which might be due to a Gl 908. This is another good example of a long-term correla- yet undiscovered long-period⇠ planet. tion between RV and activity. The correlation coecient has a value of 0.85 (FAP = 0.4%) and the trend can be observed in both the binned and the nightly averaged data (Fig. 7). The slope Gl 581. This star has the highest probability that its activity data 1 1 of the correlation is 322 m s Na and we measured an RV can be fitted by a periodic sinusoidal signal instead of a linear 1 peak-to-peak variation of 3.85 m s . A strong correlation be- trend. We obtained a signal with a period of P = 3.85 years tween Na and FWHM with ⇢ = 0.82 (FAP = 0.75%) was also (P(2) = 0.01%) and our timespan for this star is long enough to detected. Although we have strong evidence that the RV was cover more than one activity cycle period (Fig. 8). Furthermore, induced by long-term activity, we could not fit a sinusoidal sig- Gl 581 also passed the variability tests. To date, four planets are nal to both time series with significant p(2). This star probably known to orbit the star, and the possibility of two more planets

A9, page 8 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. 9. Sinusoidal ﬁt to the activity time series of Gl 667 C.

Fig. 7. RV relation for the Na i index in the case of Gl 908. Small dots without errorbars are nightly averaged data points and points with errorbars are averaged over 150 days. The dashed line is the best linear ﬁt. The correlation coecient ⇢ and the respective FAP are shown.

Fig. 10. Sinusoidal ﬁt to the activity time series of Gl 832.

Fig. 8. Sinusoidal fit to the activity time series of Gl 581. has been discarded (Bonfils et al. 2005; Udry et al. 2007; Mayor et al. 2009; Forveille et al. 2011a). We removed the signal of the four confirmed planets resulting in a long-term RV rms of 1 0.96 m s ,whichisoftheorderoftheinstrumentprecision.No correlation was found between the long-term RV and activity but the Na index is correlated with FWHM (⇢ = 0.60, FAP = 1.9%). Fig. 11. Sinusoidal fit to the activity time series of HIP 85647. Owing to of the large number of detected planets, we note that their orbits might not have been properly subtracted from the data. We therefore draw no conclusions about thepossibilityof the activity cycle having influence on the RV signal of this star. correlated with both FWHM (⇢ = 0.55, FAP = 0.15) and contrast (⇢ = 0.79, FAP = 0.070). Gl 667C. Two planets are known to orbit this star (Delfosse et al. 2012). It is also a member of a triple system and orbits Gl 832. This star passed the activity variability tests but we the A + Bbinarysystem.ThissystemintroducesatrendinRV found no correlation with RV after the removal of the planetary that was subtracted together with the planetary companions sig- companion (Bailey et al. 2009). None of the other parameters nal. The Na activity index passed the variability F-test and a are correlated apart from a marginal correlation between activ- sinusoidal function with a period of P = 3.18 years is well-fitted ity and FWHM of ⇢ = 0.57 but with a high FAP of 19%. The to the activity time series (with P(2) = 3.3%, Fig. 9). However, activity time series is well-fitted by a sinusoidal function with the RV signal is only marginally correlated with activity, hav- P(2) = 3.2% and a minimum period of 4.73 years (Fig. 10). ing a correlation coecient of ⇢ = 0.45 with a FAP of 12%. No correlations between the other parameters are detected. HIP 85647. After removal of the signal of the planetary companion (Forveille et al. 2011b)ofthisstarandalineartrend Gl 699. Kürster et al. (2003)foundananti-correlationbetween caused by a stellar companion, we found no correlation between RV and the H↵ index for Bernard’s star with a coecient of ⇢ = RV and activity. There are strong correlations between Na and 0.50. Using a longer timespan for the same star, Zechmeister the CCF parameters FWHM and contrast with ⇢ = 0.81 (FAP = et al. (2009)detectedasimilarcorrelationwith⇢ = 0.42. We 3.9%) and ⇢ = 0.87 (FAP = 1.4%), respectively. We success- found only a marginal positive correlation with the Na index fully fitted a sinusoidal signal to the activity time series and ob- (⇢ = 0.32, FAP = 0.32). The Na index of this star is moderately tained a period of 2.74 years (with P(2) = 3.4%, Fig. 11).

A9, page 9 of 25 A&A 541, A9 (2012)

7. Conclusions in M dwarfs, as a complement to activity indices. A similar result was previously found in the case of early-K dwarfs by We have used a sample of 27 M0 to M5.5 dwarfs to study the Santos et al. (2010). relationship between long-term activity, RV, and parameters of – When compared with activity, the contrast appeared to fol- the CCF given by the HARPS pipeline. As the indicator for ac- low negative correlations, which in only 14% of the cases tivity, level we used the Na index as suggested in Paper I. We was significant. This finding of anti-correlations was also binned the data into 150-day binstoaverageouthigh-frequency found by Santos et al. (2010)forearly-Kdwarfs,butsince noise and removed any RV signals induced by known stellar or the fraction of significant coecients is very low, this pa- planetary companions. rameter does not seem to be a strong tool to help us diagnose Aselectionofstarswithlong-termactivityvariabilitywas long-term activity variability. carried out by using F-tests. This resulted in a subsample of 14 variable stars, which means that around half of the stars in We found some cases of RV variations induced by long-term ac- our sample have significant long-term activity variations. tivity, although this does not seem to be a general trend. These The activity time series of some stars were closely fitted variations may have several causes. One possibility is the poor by sinusoidal functions to infer the activity cycle’s period or frequency sampling of observations: since this is a program that minimum period. Five stars could be statistically well-fitted was dedicated to the search for planets, most of the observa- by sinusoids and the inferred periods varied between 2.8 and tions either were focused on short-term RV variability to identify 4.7 years. We should note, however, that our data covered close short-period planets or had bad high-frequency sampling when to one period or less of the fitted signals and therefore the cyclic the aim was to detect long-period companions. Another possible nature of the signals cannot be fully established. Even if these cause is the short time span of the data, although we found some stars have cyclic activity variability, the periods obtained by the activity cycle periods to be of the order of three-years, some sinusoidal fitting should be regarded as minimum periods since could have periods longer than the approximately six-year span the timespan is not long enough to cover two periods. of our observations. Alternatively, some of the stars might have We measured a long-term RV rms in the range 0.30 to low-mass and/or long-period planets that have not yet been de- 1 5.9 m s and a relative scatter in the Na index for the 14-star tected, thus their RV signal could be creating confusion in our variable subsample in the range 2–14%. These two parameters, ⇠ activity study. A longer time span of observations will certainly (Vr)and(Na i), appear to be correlated. The median RV rms 1 help to improve our understanding of how long-term activity cy- of 1.5 m s that can possibly be induced by activity is lower than cles influence the detected RV of these late-type stars. the one obtained in the case of the Sun by Meunier et al. (2010) In light of these results, we advise planet hunters to carefully as predicted by extrapolation of the trend in Fig. 18 (lower panel) check for long-term activity variations when analysing long- of Lovis et al. (2011)tothecaseoflate-typestars. timespans of RV data since activity cycles could be adding noise We then searched for correlations between RV, activity, and 1 to the data or even mimicking the low-amplitude ( 5ms )sig- the CCF parameters BIS, FWHM, and contrast. The main gen- nals of planetary companions.  eral results we obtained can be summarised as: – We found overall evidence of positive correlations between long-term activity and RV variations. No relation between Acknowledgements. Wewould like to thank our anonymous referee for the help- the slope of the correlation and stellar colour was found. ful comments and suggestions. This work has been supported by the European – Five out of 14 stars with long-term variability have a sig- Research Council/European Community under the FP7 through a Starting Grant, as well as in the form of a grant reference PTDT/CTE-AST/098528/2008, funded nificant correlation between activity and RV. This amounts by Fundação para a Ciência e a Tecnologia (FCT), Portugal. J.G.S. would like to 36% of our subsample. These stars are Gl273, Gl433, to thank the financial support given by FCT in the form of a scholarship, namely Gl436, Gl588, and Gl908. The maximum peak-to-peak RV SFRH/BD/64722/2009. N.C.S. would further like to thank the support from variation we obtained for stars with significant correlation FCT through a Ciência 2007 contract funded by FCT/MCTES (Portugal) and 1 POPH/FSE (EC). between long-term activity and RV was 5ms .Onlyfor Gl 433 was the activity closely fitted by a⇠ sinusoidal signal, even though the signal spans less than a full period. We de- References termined a minimum period of 4.6 years for the activity cycle of this star, and a similar minimum period of 4.8 years was Bailey, J., Butler, R. P., Tinney, C. G., et al. 2009, ApJ, 690, 743 found for the RV signal. The other stars could have aperi- Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ, 438, 269 Ballard, S., Christiansen, J. L., Charbonneau, D., et al. 2010, ApJ, 716, 1047 odic activity cycles but more data is needed to confirm this Boisse, I., Moutou, C., Vidal-Madjar, A., et al. 2009, A&A, 495, 959 hypothesis. Boisse, I., Bouchy, F., Hébrard, G., et al. 2011, A&A, 528, A4 – Although we found a general tendency for BIS to be anti- Bonfils, X., Forveille, T., Delfosse, X., et al. 2005, A&A, 443, L15 correlated with activity, those correlations were not statis- Bonfils, X., Mayor, M., Delfosse, X., et al. 2007, A&A, 474, 293 Bonfils, X., Delfosse, X., Udry, S., et al. 2012, A&A, in press tically significant. Only 21% of the stars with long-term Buccino, A. P., Díaz, R. F., Luoni, M. L., Abrevaya, X. C., & Mauas, P. J. D. variability displayed marginal correlations between activity 2011, AJ, 141, 34 and BIS. While we found a general trend for anti-correlations Butler, R. P., Vogt, S. S., Marcy, G. W., et al. 2004, ApJ, 617, 580 between activity and BIS for M dwarfs, Santos et al. (2010) Cincunegui, C., Díaz, R. F., & Mauas, P. J. D. 2007, A&A, 461, 1107 found positive correlations between the S activity index Dall, T. H., Santos, N. C., Arentoft, T., Bedding, T. R., & Kjeldsen, H. 2006, MW A&A, 454, 341 and BIS for early-K stars. This is a curious result that should Delfosse, X., Bonfils, X., Forveille, T., et al. 2012, A&A, submitted be investigated further. [arXiv:1202.2467] – We found that the long-term activity level was in general Díaz, R. F., Cincunegui, C., & Mauas, P. J. D. 2007a, MNRAS, 378, 1007 well-correlated with FWHM, where 43% of the stars with Díaz, R. F., González, J. F., Cincunegui, C., & Mauas, P. J. D. 2007b, A&A, 474, 345 long-term variability had their activity level significantly cor- Dumusque, X., Udry, S., Lovis, C., Santos, N. C., & Monteiro, M. J. P. F. G. related with FWHM. This is a good indication that the width 2011, A&A, 525, A140 of the CCF profile can be used to follow long-term activity Dumusque, X., Lovis, C., Ségransan, D., et al. 2012, A&A, 535, A55

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Endl, M., Kürster, M., Els, S., et al. 2002, A&A, 392, 671 Mayor, M., Marmier, M., Lovis, C., et al. 2011, A&A, submitted ESA 1997, VizieR Online Data Catalog, 1239, 0 [arXiv:1109.2497] Forveille, T., Bonfils, X., Delfosse, X., et al. 2009, A&A, 493, 645 Melo, C., Santos, N. C., Gieren, W., et al. 2007, A&A, 467, 721 Forveille, T., Bonfils, X., Delfosse, X., et al. 2011a, A&A, submitted Meunier, N., Desort, M., & Lagrange, A.-M. 2010, A&A, 512, A39 [arXiv:1109.2505] Moutou, C., Mayor, M., Lo Curto, G., et al. 2011, A&A, 527, A63 Forveille, T., Bonfils, X., Lo Curto, G., et al. 2011b, A&A, 526, A141 Queloz, D., Bouchy, F., Moutou, C., et al. 2009, A&A, 506, 303 Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2011, A&A, 534, A30 Queloz, D., Henry, G. W., Sivan, J. P., et al. 2001, A&A, 379, 279 Hawley, S. L., Gizis, J. E., & Reid, I. N. 1996, AJ, 112, 2799 Saar, S. H., & Donahue, R. A. 1997, ApJ, 485, 319 Knutson, H. A., Madhusudhan, N., Cowan, N. B., et al. 2011, ApJ, 735, 27 Saar, S. H., & Fischer, D. 2000, ApJ, 534, L105 Koen, C., Kilkenny, D., van Wyk, F., & Marang, F. 2010, MNRAS, 403, 1949 Santos, N. C., Mayor, M., Naef, D., et al. 2000, A&A, 361, 265 Kürster, M., Endl, M., Rouesnel, F., et al. 2003, A&A, 403, 1077 Santos, N. C., Gomes da Silva, J., Lovis, C., & Melo, C. 2010, A&A, 511, A54 Lovis, C., Dumusque, X., Santos, N. C., et al. 2011, A&A, submitted Ségransan, D., Mayor, M., Udry, S., et al. 2012, A&A, 535, A54 [arXiv:1107.5325] Udry, S., Bonfils, X., Delfosse, X., et al. 2007, A&A, 469, L43 Mayor, M., Bonfils, X., Forveille, T., et al. 2009, A&A, 507, 487 Zechmeister, M., Kürster, M., & Endl, M. 2009, A&A, 505, 859

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Fig. A.1. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 1.

Fig. A.2. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 176.

Appendix A: Data times series In the following ﬁgures, we present the time series for all the parameters of the sample we used in this work. Black points are nightly averaged data points, red squares with errorbars are the 150-day bins, is the peak-to-peak variation, and the standard deviation in the data. The errorbars are the error in the mean rms/pN,whereN is the number of measurements in each bin.

A9, page 12 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.3. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 205.

Fig. A.4. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 273.

A9, page 13 of 25 A&A 541, A9 (2012)

Fig. A.5. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 382.

Fig. A.6. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 393.

A9, page 14 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.7. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 433.

Fig. A.8. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 436.

A9, page 15 of 25 A&A 541, A9 (2012)

Fig. A.9. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 479.

Fig. A.10. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 526.

A9, page 16 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.11. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 551.

Fig. A.12. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 581.

A9, page 17 of 25 A&A 541, A9 (2012)

Fig. A.13. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 588.

Fig. A.14. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 667C.

A9, page 18 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.15. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 674.

Fig. A.16. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 680.

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Fig. A.17. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 699.

Fig. A.18. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 832.

A9, page 20 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.19. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 849.

Fig. A.20. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 876.

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Fig. A.21. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 877.

Fig. A.22. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 887.

A9, page 22 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.23. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for Gl 908.

Fig. A.24. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for HIP 12961.

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Fig. A.25. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for HIP 19394.

Fig. A.26. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for HIP 38594.

A9, page 24 of 25 J. Gomes da Silva et al.: Long-term magnetic activity of a sample of M-dwarf stars from the HARPS program. II.

Fig. A.27. Time-series of RV, Na index data, and the BIS, FWHM, and contrast of the CCF line proﬁle for HIP 85647.

A9, page 25 of 25 Chapter 4

On the long-term correlation between the ﬂux in the Ca ii H & K and Halpha lines of FGK stars

89 A&A 566, A66 (2014) Astronomy DOI: 10.1051/0004-6361/201322697 & c ESO 2014 Astrophysics

On the long-term correlation between the ﬂux in the Ca ii H&K and H↵ lines for FGK stars? J. Gomes da Silva1,2, N. C. Santos1,2, I. Boisse1, X. Dumusque1,3, and C. Lovis3

1 Centro de Astrofísica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal e-mail: [email protected] 2 Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal 3 Observatoire de Genève, Université de Genève, 51 ch. des Maillettes, 1290 Versoix, Switzerland Received 17 September 2013 / Accepted 21 November 2013

ABSTRACT

The re-emission in the cores of the Ca ii H & K and H↵ lines are well known proxies of stellar activity. However, these activity indices probe di↵erent activity phenomena: the first is more sensitive to plage variation, while the other is more sensitive to filaments. In this paper, we study the long-term correlation between log RHK0 and log IH↵, two indices based on the Ca ii H & K and H↵ lines, respectively, for a sample of 271 FGK stars using measurements obtained over a 9 year time span. Because stellar activity is one of the main obstacles to the detection of low-mass and long-period planets, understanding⇠ this activity index correlation further can give us some hints about the optimal target to focus on ways to correct for these activity e↵ects. We found a great variety of long-term correlations between log RHK0 and log IH↵. Around 20% of our sample has a strong positive correlation between the indices while about 3% show strong negative correlation. These fractions are compatible with those found for the case of early-M dwarfs. Stars exhibiting a positive correlation have a tendency to be more active when compared to the median of the sample, while stars showing a negative correlation are more present among higher metallicity stars. There is also a tendency for the positively correlated stars to be more present among the coolest stars, a result which is probably due to the activity level e↵ect on the correlation. Activity level and metallicity therefore seem to be playing a role on the correlation between log RHK0 and log IH↵. Possible explanations based on the influence of filaments for the diversity in the correlations between these indices are discussed in this paper. As a parallel result, we show a way to estimate the e↵ective temperature of FGK dwarfs that exhibit a low activity level by using the H↵ index. Key words. stars: activity – stars: chromospheres – stars: solar-type – planetary systems

1. Introduction It is known that there is a long-term correlation between the emission in the Ca ii H & K and H↵ lines that follow the Stellar activity is one of the main limitations to the detection Sun’s 11-year activity cycle (Livingston et al. 2007). Other au- of low-mass and/or long-period planets using the radial-velocity thors have suggested that the correlation is also present in other method (e.g. Saar & Donahue 1997; Santos et al. 2000; Queloz stars (Giampapa et al. 1989; Robinson et al. 1990; Strassmeier et al. 2001; Boisse et al. 2009, 2011; Dumusque et al. 2011b; et al. 1990; Pasquini & Pallavicini 1991; Montes et al. 1995). Lovis et al. 2011; Gomes da Silva et al. 2012). Fortunately, the However, when Cincunegui et al. (2007) measured simultane- radial-velocity noise induced by these e↵ects can be corrected ously the flux in the two lines for a sample of 109 southern in some cases if for example the activity is simultaneously mea- FGK and M stars, they found a large scatter in correlations, from sured using activity indices (e.g. Dumusque et al. 2011a, 2012). very strong positive correlations to negative ones. They also sug- Therefore, understanding the behaviour of activity indices and gested that the mean values of the flux in the Ca ii and H↵ lines their relation with radial-velocity is vital to reduce the impact are correlated due to the e↵ect of stellar colour on both fluxes. of activity in radial-velocity measurements and thus improve its Meunier & Delfosse (2009) studied the contribution of sensitivity to planetary signals. plages and filaments to the emission in Ca ii and H↵ lines dur- The re-emission in the Ca ii H & K lines are widely used ing a solar cycle. In their work, plages contribute to an increase proxies of activity-induced signals in radial-velocity measure- in emission in both fluxes while filaments increase absorption ments. However, the relation between this index and H↵ is not in H↵ only. They found that the contribution of filaments to H↵ well understood for solar-type stars. Since these two activity in- can be responsible for the decrease in the correlation coecient dices are a↵ected by di↵erent activity phenomena in di↵erent between the two fluxes depending on their spatial distribution ways (the emission in the centre of the Ca ii and H↵ lines are and contrast compared to those of plages. They also noted that not formed at the same temperature in the chromosphere), un- the filament filling factor saturates at higher activity levels (e.g. derstanding their relationship and di↵erences might bring new cycle maxima) and the correlation between the two fluxes in- insights not only to stellar physics but also to the detection and creases. Other factors contributing to a decrease in the measured characterisation of extrasolar planets. correlation can be the time-span of observations, cycle phase at which they are measured, and stellar inclination angle. For ex- ? Appendices are available in electronic form at ample, the correlation is underestimated if the time-span is less http://www.aanda.org than the cycle period (or the activity range is not well spanned).

Article published by EDP Sciences A66, page 1 of 18 A&A 566, A66 (2014)

Santos et al. (2010) studied the long-term activity of 8 FGK on the S -index, which is calculated as the sum of the flux in stars using the Ca ii H & K based S MW and H↵ indices and found two 0.6 Å bands centered at the calcium H (3968.47 Å) and a general long-term correlation between the two. However, their K (3933.66 Å) lines divided by two 20 Å reference bands cen- sample was not large enough to have any statistical significance. tered at 3900 and 4000 Å (see e.g. Boisse et al. 2009). Gomes da Silva et al. (2011) expanded the comparison between The H↵ index and errors were calculated as in Gomes these two activity sensitive lines to early-M dwarfs. Similarly da Silva et al. (2011). We used a 1.6 Å band centered at to Cincunegui et al. (2007) they detected a large variety of cor- 6562.808 Å and divided the flux in the central line by the flux relation coecients, including anti-correlations for the least ac- in two reference bands of 10.75 and 8.75 Å that are centered at tive stars in their sample. The most active stars were all, how- 6550.87 and 6580.31 Å, respectively. The flux errors were cal- ↵ ever, positively correlated. They also found hints that the H culated as the photon noise in the line core, pN, where N is the index was following an “anti-cycle” relative to their S -index in number of photons in the band. The activity indices errors were some cases, i.e., the maxima and minima measured in the two obtained via error propagation. The calibration of H↵ for the ef- indices were anti-correlated. However, their time-span was not fects of photospheric flux is presented in Appendix A and results long enough to detect full cycles and confirm this e↵ect. in the I ↵ index. In this paper, we analyse the behaviour of the flux in Ca ii H H & K and H↵ lines in FGK stars via two activity indices corrected for the e↵ects of photospheric flux. We describe our sample and 3.1. Statistics of the log RHK0 index data in Sect. 2. The activity indices derivation, statistics, correlations between mean values, and activity cycle detectability are Our sample, which is biased towards inactive stars to increase R presented in Sect. 3 and Appendix A. The correlations between the chances of finding low-mass planets, has a median log HK0 . . the two indices are discussed in Sect. 4. The distribution of the of 4 948 and a mean of 4 923. In this 271-star sample, only 22 (around 8%) are considered active stars with log R 4.75, correlations in mean values of activity are discussed in Sect. 5. HK0 The e↵ects of metallicity on the correlation are studied in Sect. 6, which lies on the higher activity region above the “Vaughan- and the distribution of the correlations in e↵ective temperature Preston gap” (Vaughan & Preston 1980). is presented in Sect. 7. We discuss possible causes for the exis- The star with the highest activity level is HD 224789 = . tence of positive correlations and anti-correlations, and compare with log RHK0 4 433 and the most inactive star is HD 181433 with log R = 5.144. The median of the errors obtained for our results with those found for early-M dwarfs in Sect. 8.We HK0 conclude in Sect. 9. A possible use of the H↵ index to estimate the log RHK0 index is 0.003, or in relative terms, 0.06% around the the e↵ective temperature of low activity level FGK dwarfs is pro- mean. In terms of variability, the median standard deviation of posed in Appendix B. the sample is 0.0154 (0.3% around the mean) with HD 177758 being the least variable star with (log RHK0 ) = 0.0035 (0.07% around the mean) and HD 7199 being the star that varies the most 2. Sample and data with (log RHK0 ) = 0.08 (1.6% around the mean). The sample comes from 400 FGK stars High Accuracy Radial Velocity Planet Searcher⇠ (HARPS, spectral resolution =115 000) 3.2. Statistics of the log IH↵ index high-precision sample that has been already used by Lovis et al. In terms of log I ↵, our sample has a median value of 1.7129 (2011) to study the long-term activity of FGK stars and its e↵ect H and a mean of 1.7118. The star with the highest log IH↵ mean on the measurement of precise radial velocities. A description of value is HD 85119 with an activity level of 1.6562, and the the sample is presented in their paper. The spectra used in this most inactive star is HD 82516 with log I ↵ = 1.7299. The me- work were obtained between February 2003 and February 2012. H dian of the errors we obtained for the log IH↵ index is 0.0002, We used e↵ective temperature, metallicity, and surface grav- or in relative terms, 0.01% around the mean. As stated before, ity that were already calculated for this sample by Sousa et al. we are only considering photon noise as a source of errors, and (2008). Absolute magnitude and luminosity were both obtained since the H↵ line is in a brighter area of the spectrum compared from the Hipparcos catalogue. to the Ca ii H & K lines, we expect the photon noise to be lower We selected only spectra with S/N 100 at spectral or- for IH↵ than for RHK0 . In terms of variability, the median standard der 56 ( 5870 Å) and nightly averaged our measurements. Only ⇠ deviation of the sample is 0.0019 (0.11% around the mean) with stars with 10 or more nights of observations were selected. Then, HD 74014 being the least variable star with (log IH↵) = 0.0008 we selected just the main sequence (MS) stars as in Lovis et al. (0.05% around the mean) and HD 224789 being the star that (2011): we fitted a straight line through the H-R diagram and varies the most with (log IH↵) = 0.0063 (0.4% around the then excluded all stars with luminosity greater than +0.25 dex mean). above that line. From these simple statistics, we can see that the log R0 is We ended up with 271 MS stars with a median time span HK more sensitive to activity variations than log IH↵. While log R0 of 7 years that we used for the rest of this work. This sample HK ⇠ has a median standard deviation of 0.3% of the mean, log IH↵ is comprised of 11 432 data points with a median of 23 nights only has a median standard deviation of 0.1% of the mean, which of observations per star (and a maximum of 279). The sample means that log R0 has a more noticeable variation. ranges in spectral type from F8 to K6, e↵ective temperature from HK 4595 to 6276 K, and metallicity from 0.84 to +0.39 dex. 3.3. Mean activity level correlations

3. The activity indices Our activity indices are corrected for the e↵ects of photospheric flux and can, if they are not dependent on other factors other The log RHK0 index, which is already corrected for the photo- than chromospheric flux, be used to compare the activity levels spheric flux (Noyes et al. 1984), and respective errors were between di↵erent stars. Figure 1 (upper panel) shows the corre- directly obtained from the HARPS DRS. This index is based lation between the mean values of log RHK0 and log IH↵. These A66, page 2 of 18 J. Gomes da Silva et al.: On the long-term correlation between the flux in the Ca ii H & K and H↵ lines for FGK stars

3.4. Activity cycles: detectability To detect activity cycles, we fitted sinusoids to the time-series of the two activity indices. The significance of the fitting pro- 2 2 cess was addressed by using an F-test, where F = const/sin, to compare the fitting of a sinusoid with that of a constant model with being the standard deviation of the residuals of the fitted model. The probability p(F) gives the probability that the data is better fitted by a constant model than a sinusoidal function. We selected stars with cycles as the ones where probabilities, p(F)HK and p(F)H↵, are lower than 0.05 and, similarly to Lovis et al. (2011), we searched for periods in the region between 2 and 11 years. Based on this selection criteria and using log RHK0 , we detected 69 stars (26%) with significant activity cycles with periods varying between 2.0 and 10.8 years. The log IH↵ index, however, is not so sensitive at detecting magnetic cycles. Only 9 stars (3.3%) showed significant cycles with periods varying between 3.9 and 9.5 years. As a comparison, Robertson et al. (2013) detected activity cycles with periods longer than one year in 5% of their sample of 93 K5-M5 stars using an H↵ index similar to ours. In their study of activity cycles based on this sample but with a di↵erent selection criteria, Lovis et al. (2011) found that 99 stars (35%1) showed long-term activity cycles in their log RHK0 index, out of their 284-star sample. Their slightly higher fraction of stars with cycles is probably due to their use of a different selection criteria with a di↵erent restriction on the number of data points (some of their stars with detected cycles have less than 10 observations). We use only data with S/N 100, and we have more data points.

4. Correlations between log R0 and log I ↵ HK H For all stars, we calculated the Pearson correlation coecient between log RHK0 and log IH↵. As was detected by Cincunegui et al. (2007) for the flux in the Ca ii H & K and H↵ lines, we also find a great variety of correlation coecients between log R Fig. 1. Upper panel: relationship between log R0 and log IH↵ mean ac- HK0 HK and log I in the range 0.78 ⇢ 0.95 (Fig. 2). Although tivity levels. Open triangles are stars with positive correlation between H↵   the two indices with ⇢ 0.5, open squares stars with negative correla- there is a tendency for the stronger correlations to be positive, tion with ⇢ 0.5, and dots stars with no correlations. Lower panel: we found a few cases of anti-correlations with ⇢ 0.5.   relationship between the logarithms of S MW and H↵ indices. Since we are interested in studying the cases of strong long- term correlations between the flux in the Ca ii H & K and H↵ lines, we made a new selection of stars with good quality data that we are going to describe in the following section. mean values were calculated by averaging the two indices over 4.1. Stars with “strong” long-term correlations all our nightly measurements and represent the average activity level of each star. Open triangles are stars with a correlation We are interested in measuring the long-term Pearson corre- coecient of ⇢ 0.5, squares are stars with ⇢ 0.5, and lation coecient (⇢) between the log RHK0 and log IH↵ indices. dots stars with no strong correlations. There is a correlation be- Therefore, We need therefore to ensure that we have (a) a long 2 tween the indices with a correlation coecient of 0.53, but the time-span to certify that we are measuring long-term variations , scatter is large and the relation does not appear to be linear (cf. (b) variability in the long term so that we are not measuring cor- Cincunegui et al. 2007, Fig. 12). However, if we choose only the relations due to noise, (c) no short-term variations that can in- positively correlated stars (open triangles), they show a slightly terfere with or hide the long-term ones, (d) enough quantity of more well defined relationship for the mean values with a corre- points to calculate a significant ⇢, and (e) strong correlations. To . lation coe cient of 0 65. When Cincunegui et al. (2007) studied 1 the correlation between the mean values of the flux in Ca ii and We should note that they do not find cycles for 165 stars but they H↵, they concluded that the correlation between them is due to cannot exclude cycles either. In their conclusions, they arrive at a final value of 61% of stars with cycles when they exclude these stars from the dependence of the mean fluxes on stellar colour. Indeed, we the fraction. have a stronger correlation with ⇢ = 0.79 when we plot the log- 2 Since this sample derives from a planet hunt selection of stars, active arithm of the mean indices S MW vs. H↵ (without colour correc- stars with log RHK0 4.7 were monitored early and only rarely mea- tion) (Fig. 1, lower panel).We can therefore confirm that stellar sured. Therefore, stars with higher activity have fewer measurements colour is playing a role in the correlation between the mean flux and possibly a lower time-span of observations. This selection thus re- levels of the Ca ii and H↵ lines. duces even more the number of active stars in the sample.

A66, page 3 of 18 A&A 566, A66 (2014)

Table 1. Variability and correlations using binned data for the stars with strong long-term correlations.

Star Nbins Tspan ⇢ FAP log RHK0 log IH↵ [days] P(F) P(F) e h ii e h ii HD 100508 4 766 0.93 0.047 0.0199 0.0034 0.0082 0.00102 0.00031 0.040 5 5 HD 13808 13 2245 0.97 0.0001 0.0794 0.0043 <10 0.00302 0.00065 <10 HD 154577 7 2117 0.92 0.0014 0.0302 0.0030 0.00001 0.00242 0.00047 0.00046 HD 209100 7 829 0.92 0.0021 0.0278 0.0048 0.00022 0.00282 0.00088 0.0062 5 HD 215152 9 1160 0.83 0.0034 0.0322 0.0028 <10 0.00144 0.00045 0.0016 HD 4915 5 646 0.98 0.0046 0.0343 0.0041 0.00062 0.00185 0.00062 0.029 HD 63765 8 1936 0.88 0.0024 0.0374 0.0077 0.00023 0.00290 0.00068 0.00052 5 HD 71835 10 2618 0.85 0.0010 0.0403 0.0048 <10 0.00165 0.00046 0.00040 5 HD 7199 11 2237 0.82 0.0009 0.0758 0.0071 <10 0.00207 0.00048 0.00003 HD 78612 4 2902 0.88 0.050 0.0135 0.0036 0.029 0.00187 0.00057 0.042 4 5 5 HD 85512 12 2906 0.93 <10 0.0495 0.0026 <10 0.00395 0.00052 <10 HD 88742 5 1729 0.93 0.015 0.0323 0.0043 0.00089 0.00308 0.00086 0.015

4. We also applied the variability F-test for the log IH↵ index in a similar way as described above. 5. To select significant correlation coecients between log RHK0 and log IH↵, we calculated the False Alarm Probability (FAP) of having absolute values of ⇢ higher than the ones obtained for each star by bootstrapping the binned data and calcu- lating the fraction of cases with higher ⇢ values. We used 10 000 permutations per star to calculate| | the FAP values. Only stars with FAP 0.05 (95% significance level) were selected.  6. Stars with strong correlations were selected as the ones having ⇢ 0.70. | | From the 129 stars that passed selection criteria (1) and (2), 95 stars (73.6%) show long-term variability in log RHK0 , 51 stars (39.5%) show long-term variability in log IH↵, and 45 stars (34.9%) show long-term variability on both indices. Out of the 45 stars that show variability on both indices, 12 stars (26.7%) show strong positive correlations between the indices, 10 of Distribution of correlation coecients between log R0 and Fig. 2. HK them (22.2%) have positive correlations, while two (4.4%) have log IH↵ for the whole sample (black line). The grey-filled histogram anti-correlations. shows the distribution of correlations for the 101 stars in Cincunegui et al. (2007) sample that have their correlations calculated. Table 1 shows the variability and correlations data for the 12 stars with strong long-term correlations, where Nbins the number of bins for each star, ⇢ the correlation coecient value, FAP the false alarm probability of ⇢, and the parameters of the F-tests achieve this, we perform the following selection criteria on our for both activity indices. The time series of log RHK0 , log IH↵, 271-star sample: and their respective correlations for these 12 stars are shown in Fig. B.1. We also tried to fit sinusoids to these stars (see 1. All data was binned into 100-day averages. Each bin has at Sect. 3.4) using the binned data of both indices to check if these least three nights of observations, where the errors were cal- stars have significant activity cycles. These fits appear in Fig. B.1 culated as the standard error on the mean, /p(N), where if the p(F)HK of the fit is lower than 0.05 (95% significance is the standard deviation of the observations and N the num- level). Two stars, HD 100508 and HD 78612, only have four bins ber of observations. This reduces the variation induced by and therefore do not have enough free parameters to calculate the short-term activity modulated by stellar rotation. probability of the fit. From the stars with more than four bins, 2. We selected stars with at least four bins. This selection en- three have p(F) values lower than 0.05 for the log RHK0 index, sures that we have enough points to calculate ⇢ and that the namely HD 4915, HD 63765, and HD 88742. These are all stars time span is at least 400 days. with strong positive correlations. The seven stars with signifi- 3. Only stars that showed long-term variability in log RHK0 were cant cycles in log RHK0 have periods in the range 1528 to 10 665 selected. This ensures that we are not detecting random vari- days, and five of them could be fitted in log IH↵ with the same ations due to noise. We performed an F-test on the binned period found for log RHK0 and a p(F)H↵ value lower than 0.05 data, where F = 2/ 2, with the standard deviation of (HD 13808, HD 154577, HD 215152, HD 7199, and HD 85512). e h ii e the binned data and the mean of the errors on the bins For this sample, no star showed a period in log I ↵ that was not h ii H (e.g. Zechmeister et al. 2009). We calculated the probabil- also found in log RHK0 and at a higher significance. ity of the F-test, P(F), such that the variations are due to To try to understand why some stars have positive correla- the internal errors of the binned data, and selected stars with tions while others are negative, we compared the correlations P(F) 0.05 (95% probability that the variability in not due with the basic stellar parameters shown in Table 2. The two stars to the internal errors). with negative correlations are shown in bold. First, we observe

A66, page 4 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

Table 2. Stellar parameters of the stars with strong long-term correlations.

Star log RHK0 log IH↵ [Fe/H] Te↵ log g MV B VProt h ih i 2 [K] [cm s ] [days] HD 100508 5.055 1.7198 0.39 0.05 5449 61 4.42 0.09 5.16 0.83 48.4 ± ± ± HD 13808 4.892 1.7138 0.20 0.03 5087 41 4.40 0.08 6.08 0.87 42.8 ± ± ± HD 154577 4.878 1.7019 0.70 0.02 4900 37 4.52 0.08 6.70 0.89 41.3 ± ± ± HD 209100 4.781 1.7153 0.20 0.04 4754 89 4.45 0.19 6.89 1.06 37.2 ± ± ± HD 215152 4.871 1.7157 0.10 0.04 4935 76 4.40 0.14 6.45 0.97 42.0 ± ± ± HD 4915 4.798 1.7038 0.21 0.01 5658 13 4.52 0.03 5.26 0.66 20.4 ± ± ± HD 63765 4.741 1.7044 0.16 0.01 5432 19 4.42 0.03 5.53 0.74 25.0 ± ± ± HD 71835 4.889 1.7194 0.04 0.02 5438 22 4.39 0.04 5.38 0.77 35.2 ± ± ± HD 7199 4.946 1.7270 0.28 0.03 5386 45 4.34 0.08 5.29 0.85 45.9 ± ± ± HD 78612 5.004 1.7154 0.24 0.01 5834 14 4.27 0.02 4.06 0.61 21.7 ± ± ± HD 85512 4.898 1.7023 0.32 0.03 4715 102 4.39 0.28 7.43 1.16 47.3 ± ± ± HD 88742 4.688 1.7031 0.02 0.01 5981 13 4.52 0.02 4.60 0.59 11.4 ± ± ±

Notes. The average values of log RHK0 and log IH↵ were calculated using the binned data. that the two stars with the negative correlations are two of the 5. Mean activity level and correlations most inactive in terms of both log RHK0 and log IH↵. Second, Here, we investigate the distribution of the positively and neg- while all the stars with positive correlation coecient have negatively correlated stars in terms of log R0 and log I ↵ activity ative metallicity (median value of 0.20 dex), the two stars with HK H levels. negative correlations have positive metallicity (median value of Figure 3 (upper panel) shows the distribution of activity as 0.34 dex). measured by the log RHK0 index. The black line is the histogram Although we can see hints that activity level and metallicity of the selected sample of 271 main sequence stars. We can ob- could be influencing the correlation between the two indices, the serve the selection bias against active stars as the great majority small number of stars we are using is insucient to clearly show of the sample lies between 5.1 and 4.8 dex with a median of a solid trend between these parameters. We therefore chose to 4.95 dex. The hatched and filled grey histograms show the dis- relax our selection criteria to increase the number of stars in our tribution in average activity level of the stars with positive and sample and check if the trends with activity level and metallicity negative log RHK0 –log IH↵ correlations, respectively. The median are maintained. of the negatively correlated stars is close to the median of the full sample (but with a tendency to be less active) with a value of 4.97 dex, while the median of the positively correlated stars 4.2. “Relaxed” selection of stars with correlations lies in a higher activity zone with a value of 4.81 dex. In gen- To increase the number of stars in our study, we discarded the eral, the majority of the least active stars show no strong cor- variability tests, or FAPs on the correlation coecients and used relations between the two indices. However, it is obvious from the full data sets based on the nightly averaged data. The cor- the plot that there is a tendency for the positively correlated relation coecient limit was also decreased to ⇢ 0.5. This stars to be more active in general, and all stars more active than | | log R = 4.7 have positive correlations between log R and produced a larger sample, which includes weaker correlations HK0 HK0 that can be due to a lower number of data points, shorter time- log IH↵. The relative histogram in Fig. 3 (lower panel) illustrates spans, and/or short-term variations. We shall therefore take this very well this tendency. part of the study as an indication and not as a proof. However, The separation between positively and negatively correlated we are now be able to do statistical tests to this sample. stars is further confirmed by the Kolmogorov-Smirnov (K-S) test that shows that the two populations are distinct with a p-value of Using this selection, we found that out of the 271 stars in 3 our original sample, 58 (21.4% of the sample) have positive 0.002 and a D value of 0.664. A similar distribution was found for log IH↵ (Fig. 4). The correlation between the two indices have correlations between log RHK0 and log IH↵, and 8 (3.0% of the sample) have anti-correlations. Table B.1 shows the 66 stars di↵erent distributions according to activity level with negatively with ⇢ 0.5 with their activity mean levels and standard de- correlated stars being the least active ones and the positively cor- viations,| | stellar parameters, and correlation coecient between related stars increasing in number with IH↵ activity level. In this the two indices. Stars with correlations coecients in the range case, the K-S test have a D = 0.513 and p-value = 0.03. The 0.5 < ⇢ < 0.5 (no correlations) are presented in Table B.2. histograms also show that the values in log IH↵ are very well . . All the eight stars with negative correlations (⇢ 0.5) have constrained between 1 73 and 1 70, and only a few cases of  higher activity stars exists beyond these values. In the relative low log RHK0 activity levels with a median value of 4.97 and a median super-solar metallicity with a value of 0.20. The 58 stars histogram (lower panel) note that the “hole” in the region be- . . with positive correlations (⇢ 0.5) have log R with a median tween 1 675 and 1 660 is due to lack of data. HK0 value of 4.81 and a median sub-solar metallicity with a value 3 The K-S D value is the highest value of the di↵erence between of 0.16. This “relaxed” selection appears to maintain the trends the cumulative distributions of the two populations. The p-value gives found in Sect. 4.1. In the next sections, we study these trends for the probability that the two populations come from the same parent this sample of stars. distribution.

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Fig. 3. Upper panel: distribution on log RHK0 activity for the full sam- Fig. 4. Upper panel: distribution on log IH↵ activity for the full sample (black), stars with a positive correlation coecient higher than 0.5 ple (black), stars with positive correlation coecient higher than 0.5 (hatched grey), and stars with negative correlation coecient lower than (hatched grey), and stars with negative correlation coecient lower than 0.5 (ﬁlled grey). Vertical lines are the medians of the distributions 0.5 (ﬁlled grey). Vertical lines are the medians of the distributions with a black line for the full sample, a dashed line for the positively with a black line for the full sample, a dashed line for the positively correlated stars, and a dotted line for the negatively correlated stars. correlated stars, and a dotted line for the negatively correlated stars. Lower panel: same as the upper panel but using a relative distribution Lower panel: same as the upper panel but using a relative distribution on log RHK0 . The values in each bin are divided by the total number of on log IH↵. stars in the respective bin.

6. Metallicity and correlations This is further corroborated by the K-S test, which gives a probability of 0.04% that the two populations are indistinct (with a Is stellar activity the only variable playing a role in the definition K-S D value of 0.733). The relative histogram of Fig. 5 (lower of the correlation or anti-correlation observed? In Table B.1, it is panel) confirms this with the negatively correlated stars peak- noticeable that there is a tendency for the eight stars with nega- ing at the super-solar metallicity, while the positively correlated tive correlation between the log RHK0 and log IH↵ indices to have stars peaks at the sub-solar metallicity. Nevertheless, there are super-solar metallicity. We plotted the histogram of the two pop- some stars with negative correlation that have sub-solar metallic- ulations: the ones with a positive and those with a negative cor- ity and stars with positive correlation with super-solar metallic- relation against metallicity (Fig. 5). Symbols and colours are the ity. We plotted metallicity histograms for two bins where there same as that presented in Fig. 3. In Fig. 5 (upper panel), the me- is superposition of positively and negatively correlated stars in dian of the negatively correlated stars is not coincident with the activity in the region 4.8 log RHK0 5.0 (Fig. 6). The ten- medians of both the sample and the positively correlated stars. dency for stars with higher metal content to have negative corre- The histogram shows that, again, there seems to be two distinct lations is maintained in each activity bin. In the lower panel of populations of stars: the majority of the stars with positive corre- the figure for the three stars with metallicity between 0.1 and lations have negative metallicity while the negatively correlated 0.2 dex, the positively correlated star has [Fe/H] = 0.20 dex, stars appear to be of super-solar metallicity (mainly if compared while the two negatively correlated stars have [Fe/H] = 0.16 to the overall sample). The sample median is 0.10 dex, and the and [Fe/H] = 0.15 dex. These plots show that metallicity still median of positively correlated stars lies at 0.15 dex, but the has an impact on the correlation between log RHK0 and log IH↵ for negatively correlated star’s median is at a metallicity of 0.20 dex. a given activity range.

A66, page 6 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

Fig. 5. Upper panel: distribution of metallicity for the full sample Fig. 6. Upper panel: distribution of metallicity for stars with positive (black), stars with positive correlation coecient higher than 0.5 correlation coecient higher than 0.5 (hatched grey), and stars with (hatched grey), and stars with negative correlation coecient lower than negative correlation coecient lower than 0.5 (filled grey) with activ- 0.5 (filled grey). The black vertical line is the median of the full sam- ity in the range 4.9 log R0 4.8. Lower panel: same as the top  HK  ple, the dashed vertical line is the median of the positively correlated panel but using just stars with activity in the range 5.0 log RHK0 stars, and the dotted line is the median of the negatively correlated stars. 4.9.   Lower panel: same as the top panel but for relative distributions. The K-S test gives a p-value of 0.01% for the probability that the two populations are drawn from the same distribution. stars having positive correlations than hotter stars relative to the full sample distribution. This can be easily observed in the lower panel of Fig. 7. Stars with negative correlations appear also well Our analysis was based on a small number of anti-correlated distributed in e↵ective temperature but are only restricted to the stars, and our conclusions can be a consequence of small-number range between 5000 and 6100 K. It would be easier then to statistics. Also, as was stated before, this sample is not rigorous find positively⇠ correlated stars⇠ among the cooler dwarfs. This in terms of long-term variability of the stars or the significance e↵ect is probably because cooler stars in our sample have a ten- of the correlations used. Further studies with a larger number dency to be more active than the hotter ones (Fig. 8). All the stars of metal-rich stars would be crucial to confirm or refute these in our sample with log R > 4.7 have e↵ective temperatures results. HK0 lower than 5500 K. As we saw before in Sect. 5, all stars with activity higher than 4.7 have positive correlations. 7. Effective temperature and correlations Since the Mount Wilson survey, it is known that stellar age and mean activity level are related: younger stars exhibit higher We also analysed what would be the e↵ect of temperature on the activity levels than their older counterparts (Baliunas et al. correlations between log RHK0 and log IH↵. Figure 7 (upper panel) 1995). Stars with 0.55 < B V < 0.9, which are evolved, have shows the distributions of the correlations for the full sample lower activity levels than non-evolved stars (do Nascimento et al. (black), the positively correlated stars (hatched grey), and neg- 2003). Furthermore, Wright (2004) found that most of the stars atively correlated stars (filled grey). There is an observational classifieds as “flat” or “Maunder minimum”, which show very bias toward brighter stars and therefore hotter ones. However, low activity and no variability, were evolved or sub-giant stars. the positively correlated stars seem very well distributed across Recently, Schröder et al. (2013) showed that the mean activity the temperature range, which implies that there are more cooler level decreases with relative MS-age. This confirms theorectical

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Fig. 8. Activity level measured by log RHK0 against e↵ective temperature. Triangles are stars with ⇢ 0.5 and squares stars with ⇢ 0.5 

is negligible). On the other hand, filaments contribute to the absorption in the flux of H↵, while plages contributes to emission. However, the filling factor of filaments saturates at a given activity level, while plages filling factor continues to increase as the activity level increases further. This saturation contributes to an increase in the correlation between the flux in the two line cores for higher activity levels. For the Sun, the filaments are not only found in active regions. They explain that, as the activity gets stronger (higher emission in the Ca ii lines), the positive correlation between the two indices is because the contribution of plages becomes more important for the H↵ index than the contribution coming from filaments which saturates at a certain activity level. This produces the observed strong positive correlation between the two indices for higher activity stars as observed in ↵ Fig. 7. Upper panel: distribution of e ective temperature for the full Figs. 3 and 9. On the other hand, the low-activity stars with anti- sample (black), stars with positive correlation coecient higher than ii 0.5 (hatched grey), and stars with negative correlation coecient lower correlation between the emission in Ca and H↵, which appear than 0.5 (filled grey). The black vertical line is the median of the full in Figs. 3 and 9, can be explained if these stars have the filaments sample, the dashed vertical line is the median of the positively corre- with a strong contrast (compared to plages) and which have not lated stars, and the dotted line is the median of the negatively correlated reached their saturation limit (due to their low activity levels). stars. Lower panel: same as the top panel but for relative distributions. The occurrence of positively correlated stars at higher activity levels and negatively correlated stars at lower activity levels, which we observe in Sect. 5, can then be explained by the e↵ect work by Reiners & Mohanty (2012). In other words, cooler K of filaments on the flux of the H↵ line. and M dwarfs did not had enough time to evolve (and decrease ↵ their activity level) so much as F-stars which evolve faster. We If the positively and negatively correlated stars are two di er- therefore observe cooler stars at a relative younger stage and, ent populations in terms of metallicity as discussed in Sect. 6 and if the ratio of the contrast/filing factor of filaments to plages is re- consequently, higher activity levels than their hotter counter- ii parts. sponsible for the anti-correlation between the flux in the Ca H ↵ ↵ The tendency for more earlier types in our sample is then & K and H lines, then metallicity might have an e ect on the / a consequence of the bias towards fewer active stars due to the presence of filaments (or their contrast and or filling factor) in planetary search nature of this survey. the stellar corona. This could be used to predict the correlation between these two indices and to forecast the presence, contrast, and/or filling factor between plages and filaments for a given 8. Discussion star. 8.1. Interpretation of the correlations via the effect of filaments and plages 8.2. Comparison with M dwarfs So, why we sometimes see stars with anti-correlations (and In a previous work, Gomes da Silva et al. (2011) studied the “anti-cycles”) when we measure the flux in the H↵ line? Meunier long-term activity of 30 M0-M5 dwarfs and found hints of H↵ & Delfosse (2009) studied the contribution of plages and fila- “anti-cycles” (inverted in comparison to the log RHK0 cycles) on ments to the S MW and H↵ indices for the case of the Sun. They some stars of their sample. The potential maxima and minima of noted that the emission in the Ca ii lines increases in the presence some stars were anti-correlated. This can be an indication that of plages but is almost una↵ected by filaments (their contribution the physical mechanisms responsible for the anti-correlation,

A66, page 8 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

and include the spatial distribution and di↵erence in contrast of filaments relative to plages. To study the correlation between the log RHK0 and log IH↵ indices, we first selected only the stars showing “strong” long-term correlations between the two indices by applying a rigorous selection criteria based on variability F-tests, using FAPs on the correlation coecients and binning the data to 100-day bins. This selection criteria returned a sample of 12 stars, where two of them have anti-correlations and the rest positive correlations. We observed that the two stars with anti-correlations have tendency to have lower activity levels and super-solar metallicity when compared to the positively correlated stars. Since this rigorous selection returned a small number of stars, we relaxed the selection criteria to increase our sample and study the trends found with the rigorous selection. Using this selection criteria we found that: – 58 stars (21% out of 271) have positive correlations (with Fig. 9. Correlation coecient of the relation between log R0 and ⇢ 0.5) and 8 stars (3% out of 271) show anti-correlations HK ⇢ . log IH↵ against mean log RHK0 level. The vertical line at log RHK0 = 4.7 (with 0 5). These numbers are compatible with those marks the limit after which all stars have positive correlations. found byGomes da Silva et al. (2011) for early-M dwarfs. Some of the stars with strong anti-correlations show “anti- I and thus “anti-cycles” between the two indices are present in cycles” measured in log H↵: negative activity cycles when compared to those measured by log R . both solar-type stars and at least in the earlier M dwarfs. The HK0 authors also found that all M-dwarfs in their sample have pos- – The stars with positive correlation between the two indices itive correlations after a certain value of S -index activity and have a tendency to be more active than those with negative correlations. All the stars with log R 4.7 have positive found a case of an anti-correlation with a correlation coecient HK0 value lower than 0.5 in the least active stars zone (see their correlation between the indices. We interpret this behaviour Fig. 3). We should note, however, that their S -index was not cor- using the results from Meunier & Delfosse (2009) that the ↵ rected for the e↵ects of photospheric flux, and therefore there is contribution to absorption in the H line by filaments sat- a temperature contribution to the mean index values that varies urates after a certain level of activity, and only plages con- ii ↵ from star to star. Nevertheless, their distribution of correlations tribute to emission in both Ca and H . is compatible with ours in the sense that after a certain level of – We also found a tendency for the stars with negative corre- activity all active stars have positive correlations, and there are lations to be more metal rich than the rest of the sample and some cases of low activity stars with anti-correlations (Fig. 9). that this holds for stars of similar activity level. ↵ Since both FGK and early M stars have radiative cores with con- – The distribution of the correlations in e ective temperature vective envelopes, their activity phenomena might not be too dif- was also studied, and we detected that there are more cooler ferent (contrary to later M dwarfs which are fully convective). stars showing positive correlations than hotter stars in rela- Therefore, if the contribution of filaments to the H↵ absorption tive terms. This is because cooler stars in our sample are in is the sole responsible to the anti-correlation between the flux in general more active than hotter ones, and there is a tendency the Ca ii and H↵ lines, then it is possible that this phenomenon for the more active stars to have positive correlations. ↵ is occurring in a similar way for the two types of stars. – As a parallel result, we found that our H index can be used to estimate the e↵ective temperature of a low-activity Further studies of the correlations between the two indices FGK star. for later M dwarfs would be interesting to understand how the behaviour of the two indices evolve in spectral type and infer These results might a↵ect planet detections since activity is one about the presence of filaments in fully convective stars. of the main source of errors in radial velocity (and photometric) measurements. It would be interesting to compare the correlation between the flux in the Ca ii H & K and H↵ lines with the 9. Conclusions measured radial velocity and see if this correlation has any e↵ect on the observed radial velocity signal. We studied the correlation between the flux in the Ca ii H&K and H↵ lines via two activity indices, RHK0 and IH↵, corrected for photospheric flux. A sample of 271 low activity FGK stars Acknowledgements. This work has been supported by the European Research Council/European Community under the FP7 through a Starting Grant, as well observed during 9 years was used to this e↵ect. This study was ⇠ as in the form of a grant reference PTDT/CTE-AST/098528/2008, funded by the larger scale study (in both sample number and time-span) Fundação para a Ciência e a Tecnologia (FCT), Portugal. J.G.S. would like to of the correlation between these two chromospheric indices for thank the financial support given by FCT in the form of a scholarship, namely solar-type stars. SFRH/BD/64722/2009. N.C.S. would further like to thank the support from FCT through a Ciência 2007 contract funded by FCT/MCTES (Portugal) and We detected significant activity cycles in 69 stars (26% of POPH/FSE (EC). I.B. also acknowledges the financial support given by FCT in our sample) using the log RHK0 index but only in 9 stars (3.3%) the form of grant reference SFRH/BPD/81084/2011. using log IH↵. The H↵ line is not so sensitive at measuring long- term variations as the Ca ii lines. We also found a great variety of correlation coecients in the range 0.78 ⇢ 0.95, similar References   to what was found by Cincunegui et al. (2007). Possible expla- Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ, 438, 269 nations for this variety are given by Meunier & Delfosse (2009) Barklem, P. S., Stempels, H. C., Allende Prieto, C., et al. 2002, A&A, 385, 951

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Boisse, I., Moutou, C., Vidal-Madjar, A., et al. 2009, A&A, 495, 959 Noyes, R. W., Hartmann, L. W., Baliunas, S. L., Duncan, D. K., & Vaughan, Boisse, I., Bouchy, F., Hébrard, G., et al. 2011, A&A, 528, A4 A. H. 1984, ApJ, 279, 763 Bouchy, F., Queloz, D., Deleuil, M., et al. 2008, A&A, 482, L25 Pasquini, L., & Pallavicini, R. 1991, A&A, 251, 199 Cincunegui, C., Díaz, R. F., & Mauas, P. J. D. 2007, A&A, 469, 309 Queloz, D., Henry, G. W., Sivan, J. P., et al. 2001, A&A, 379, 279 do Nascimento, Jr., J. D., Canto Martins, B. L., Melo, C. H. F., Porto de Mello, Reiners, A., & Mohanty, S. 2012, ApJ, 746, 43 G., & De Medeiros, J. R. 2003, A&A, 405, 723 Robertson, P., Endl, M., Cochran, W. D., & Dodson-Robinson, S. E. 2013, ApJ, Dumusque, X., Lovis, C., Ségransan, D., et al. 2011a, A&A, 535, A55 764, 3 Dumusque, X., Santos, N. C., Udry, S., Lovis, C., & Bonfils, X. 2011b, A&A, Robinson, R. D., Cram, L. E., & Giampapa, M. S. 1990, ApJS, 74, 891 527, A82 Saar, S. H., & Donahue, R. A. 1997, ApJ, 485, 319 Dumusque, X., Pepe, F., Lovis, C., et al. 2012, Nature, 491, 207 Santos, N. C., Mayor, M., Naef, D., et al. 2000, A&A, 361, 265 Fuhrmann, K., Axer, M., & Gehren, T. 1993, A&A, 271, 451 Santos, N. C., Pont, F., Melo, C., et al. 2006, A&A, 450, 825 Giampapa, M. S., Cram, L. E., & Wild, W. J. 1989, ApJ, 345, 536 Santos, N. C., Gomes da Silva, J., Lovis, C., & Melo, C. 2010, A&A, 511, A54 Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2011, A&A, 534, Schröder, K.-P., Mittag, M., Hempelmann, A., González-Pérez, J. N., & Schmitt, A30 J. H. M. M. 2013, A&A, 554, A50 Gomes da Silva, J., Santos, N. C., Bonfils, X., et al. 2012, A&A, 541, A9 Sousa, S. G., Santos, N. C., Mayor, M., et al. 2008, A&A, 487, 373 Livingston, W., Wallace, L., White, O. R., & Giampapa, M. S. 2007, ApJ, 657, Sozzetti, A., Torres, G., Charbonneau, D., et al. 2007, ApJ, 664, 1190 1137 Sozzetti, A., Torres, G., Charbonneau, D., et al. 2009, ApJ, 691, 1145 Lovis, C., Dumusque, X., Santos, N. C., et al. 2011, A&A, submitted Strassmeier, K. G., Fekel, F. C., Bopp, B. W., Dempsey, R. C., & Henry, G. W. [arXiv:1107.5325] 1990, ApJS, 72, 191 Meunier, N., & Delfosse, X. 2009, A&A, 501, 1103 Vaughan, A. H., & Preston, G. W. 1980, PASP, 92, 385 Montes, D., Fernandez-Figueroa, M. J., de Castro, E., & Cornide, M. 1995, Wright, J. T. 2004, AJ, 128, 1273 A&A, 294, 165 Zechmeister, M., Kürster, M., & Endl, M. 2009, A&A, 505, 859

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A66, page 10 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

Fig. A.1. Calibration of H↵ index as a function of (B V) colour. The Fig. B.1. Calibration of Te↵ by using H↵ activity index for all main se- solid curve line is the best ﬁt to the data and the dashed lines correspond quence stars except the most active (log IHK 4.75, open circles). The to the 1– limits. grey line is the best quadratic ﬁt to the data.

polynomial, which resulted in a standard deviation of the ﬁt of 0.0004. Our corrected IH↵ activity index is then I = H↵+0.019(B V)3 0.054(B V)2 +0.037(B V). (A.1) H↵ Figure A.2 shows that the resulting index is not dependent on (B V) and can therefore be used to compare the activity level of stars of di↵erent colour. This calibration is valid for main sequence stars with (B V) colour between 0.5 and 1.2 and has mean H↵ activity levels between 0.012 and 0.021.

Appendix B: Estimating effective temperature using the ﬂux in H↵ line The H↵ line wings are known to be a proxy of e↵ective temperature (e.g. Fuhrmann et al. 1993; Barklem et al. 2002) and are sometimes used to conﬁrm more accurate results by other meth-

Fig. A.2. Dependence of the log IH↵ index on stellar colour. ods. For example, Bouchy et al. (2008) used the wings of the H↵ line to derive a temperature of 5450 120 K for the star CoRoT-Exo-2. Sozzetti et al. (2007) compared± the H↵ wings Appendix A: The IH↵ hydrogen line based activity to those of synthetic spectra to obtain a temperature region of index 5750 6000 K for TrES-2 (other authors that used the same technique as a rogue estimate of temperature include Santos et al. The H↵ index is calculated from the fraction of the flux in the 2006; Sozzetti et al. 2009). H↵ line centre to the flux in two continuum reference bands, We found that our H↵ activity index is also a good proxy of where one bluer other redder than the hydrogen line. This is suf- Te↵. Figure B.1 shows a quadratic fit to the correlation between ficient if we are interested in determining the activity evolution these parameters. Active stars (open circles) were not used due over time for a star. However, stars with di↵erent colours have to their contribution to a larger scatter. We obtained an rms of di↵erent amounts of flux in the continuum, and this makes the the T ↵ residuals of = 68 K, and a correlation coecient of average H↵ level not comparable between di↵erent stars due to a e ⇢ = 0.96. The calibrated T ↵ is of the form systematic error introduced by the photospheric flux interference e 4 2 in the measurements (e.g. Cincunegui et al. 2007). Te↵ = 10 (2109 H↵ 85.65 H↵ + 1.341). (B.1) To be able to compare the average H↵ index between di↵erent stars, the photospheric contribution to the index needs to be This equation can be used for dwarfs with log IHK 4.70, taken into account. Figure A.1 shows the calibration of H↵ to mean H↵ activity in the range 0.012 H↵ 0.021, and ef-   the e↵ects of stellar colour. We fitted H↵ to (B V) using a cubic fective temperatures in the range 4600 Te↵ 6280 K.  

A66, page 11 of 18 A&A 566, A66 (2014)

Fig. B.1. Time-series of log RHK0 , log IH↵, and correlation between the Fig. B.1. continued. two for the 12 stars with “strong” correlations. Grey dots are nightly averaged data, black points are binned data. Error bars are the standard errors on the mean. Black lines are best ﬁt to the binned data. A sinusoid will appear in the time-series if well ﬁtted, i.e., having p(F) 0.05. 

A66, page 12 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

Fig. B.1. continued. Fig. B.1. continued.

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Fig. B.1. continued. Fig. B.1. continued.

A66, page 14 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

Table B.1. Parameters for the 66 stars with ⇢ 0.5 from the nightly averaged 271-star sample. | |

Star N T ⇢ [Fe/H] T log R (log R ) log I (log I ) obs span e↵ h HK0 i HK0 h H↵i H↵ [days] [K] HD 105837 21 2651 0.78 0.51 0.01 5907 17 4.825 0.019 1.7012 0.0024 ± ± HD 106275 17 2648 0.62 0.09 0.03 5059 45 4.867 0.065 1.7130 0.0037 ± ± HD 109200 118 2866 0.60 0.31 0.02 5134 38 4.938 0.033 1.7079 0.0023 ± ± HD 110619 17 2677 0.76 0.41 0.01 5613 15 4.874 0.019 1.7065 0.0019 ± ± HD 114747 32 1472 0.55 0.21 0.04 5172 57 4.850 0.073 1.7246 0.0027 ± ± HD 119638 31 3276 0.50 0.15 0.01 6069 16 4.920 0.015 1.7112 0.0017 ± ± HD 119782 14 2194 0.69 0.07 0.02 5160 34 4.691 0.020 1.7067 0.0028 ± ± HD 124364 13 2635 0.81 0.27 0.01 5584 14 4.828 0.037 1.7039 0.0025 ± ± HD 125072 24 2173 0.59 0.18 0.07 5007 103 4.959 0.052 1.7241 0.0025 ± ± HD 125455 17 2164 0.63 0.18 0.02 5162 41 4.897 0.043 1.7156 0.0032 ± ± HD 13060 18 2522 0.60 0.02 0.03 5255 45 4.825 0.061 1.7073 0.0023 ± ± HD 130992 18 1830 0.61 0.13 0.06 4898 75 4.841 0.022 1.7241 0.0037 ± ± HD 13789 10 397 0.86 0.06 0.06 4740 71 4.498 0.026 1.6822 0.0049 ± ± HD 13808 128 2964 0.81 0.20 0.03 5087 41 4.908 0.074 1.7142 0.0033 ± ± HD 140901 24 1545 0.63 0.09 0.01 5610 21 4.711 0.032 1.7103 0.0019 ± ± HD 14374 17 1804 0.60 0.04 0.02 5425 24 4.659 0.031 1.6987 0.0034 ± ± HD 144585 14 2538 0.51 0.33 0.02 5914 22 5.073 0.019 1.7188 0.0020 ± ± HD 145666 20 1410 0.64 0.04 0.01 5958 12 4.773 0.014 1.7069 0.0015 ± ± HD 148303 25 2162 0.78 0.03 0.06 4958 91 4.660 0.041 1.7113 0.0051 ± ± HD 154577 123 2606 0.81 0.70 0.02 4900 37 4.888 0.030 1.7029 0.0025 ± ± HD 157830 50 2624 0.77 0.25 0.01 5540 16 4.792 0.033 1.7023 0.0031 ± ± HD 162236 14 965 0.62 0.12 0.02 5343 25 4.693 0.030 1.6931 0.0032 ± ± HD 16297 10 2052 0.66 0.01 0.02 5422 22 4.706 0.031 1.7088 0.0033 ± ± HD 172513 40 1081 0.50 0.05 0.01 5500 18 4.774 0.020 1.7154 0.0019 ± ± HD 18386 14 405 0.67 0.14 0.02 5457 29 4.616 0.039 1.7152 0.0036 ± ± HD 18719 12 340 0.54 0.08 0.02 5241 32 4.585 0.015 1.7120 0.0044 ± ± HD 188559 25 1145 0.54 0.11 0.04 4786 100 4.804 0.055 1.7233 0.0044 ± ± HD 19034 18 2962 0.51 0.48 0.01 5477 15 4.904 0.018 1.7044 0.0018 ± ± HD 192961 11 2690 0.64 0.35 0.04 4624 73 4.882 0.033 1.7172 0.0040 ± ± HD 197210 12 2218 0.75 0.03 0.01 5577 20 4.890 0.022 1.7133 0.0018 ± ± HD 197823 18 1056 0.53 0.12 0.02 5396 32 4.738 0.051 1.7088 0.0023 ± ± HD 206172 11 2550 0.53 0.24 0.01 5608 14 4.860 0.029 1.7074 0.0025 ± ± HD 20619 26 2138 0.84 0.22 0.01 5703 13 4.806 0.032 1.7069 0.0033 ± ± HD 208272 28 527 0.81 0.08 0.03 5199 40 4.489 0.020 1.6825 0.0049 ± ± HD 209100 49 2949 0.58 0.20 0.04 4754 89 4.782 0.028 1.7155 0.0033 ± ± HD 209742 11 2911 0.95 0.16 0.03 5137 49 4.825 0.049 1.7111 0.0031 ± ± HD 215152 194 2761 0.55 0.10 0.04 4935 76 4.870 0.033 1.7156 0.0025 ± ± HD 21749 47 2224 0.53 0.02 0.08 4723 143 4.720 0.042 1.7211 0.0046 ± ± HD 219249 26 2942 0.50 0.40 0.01 5482 13 4.907 0.017 1.7077 0.0010 ± ± HD 220339 10 2122 0.82 0.35 0.03 5029 52 4.798 0.049 1.7011 0.0037 ± ± HD 222237 18 1513 0.51 0.38 0.04 4780 64 4.958 0.037 1.7044 0.0027 ± ± HD 222595 26 1334 0.56 0.01 0.01 5648 16 4.813 0.055 1.7135 0.0022 ± ± HD 224393 11 2560 0.78 0.38 0.01 5774 17 4.848 0.028 1.7034 0.0021 ± ± HD 224789 33 2833 0.81 0.03 0.02 5185 38 4.433 0.020 1.6792 0.0063 ± ± HD 23356 11 2227 0.65 0.17 0.03 5004 60 4.756 0.015 1.7096 0.0038 ± ± HD 27063 39 1575 0.75 0.05 0.01 5767 14 4.756 0.018 1.7111 0.0014 ± ± HD 34688 11 2713 0.78 0.20 0.02 5169 39 4.895 0.062 1.7109 0.0038 ± ± HD 40307 193 2990 0.50 0.31 0.03 4977 59 4.948 0.056 1.7097 0.0034 ± ± HD 44573 25 2353 0.77 0.07 0.03 5071 56 4.591 0.029 1.7040 0.0038 ± ± HD 4915 39 1822 0.86 0.21 0.01 5658 13 4.796 0.037 1.7036 0.0025 ± ± HD 63765 46 2302 0.83 0.16 0.01 5432 19 4.742 0.039 1.7046 0.0031 ± ± HD 65277 18 2974 0.62 0.31 0.04 4802 88 4.999 0.034 1.7223 0.0022 ± ± HD 67458 25 3158 0.68 0.16 0.01 5891 12 4.908 0.018 1.7104 0.0026 ± ± HD 70889 16 1579 0.69 0.11 0.01 6051 15 4.798 0.033 1.7145 0.0026 ± ± HD 71835 70 2697 0.58 0.04 0.02 5438 22 4.898 0.035 1.7198 0.0018 ± ± HD 7199 84 2872 0.78 0.28 0.03 5386 45 4.988 0.081 1.7257 0.0027 ± ± HD 72673 66 3025 0.53 0.41 0.01 5243 22 4.920 0.027 1.7091 0.0020 ± ± HD 80883 13 526 0.78 0.25 0.03 5233 35 4.670 0.042 1.6913 0.0055 ± ± HD 8389A 13 2998 0.54 0.34 0.05 5283 64 5.040 0.030 1.7242 0.0027 ± ± HD 85119 19 480 0.84 0.20 0.02 5425 25 4.440 0.015 1.6562 0.0043 ± ± HD 85512 242 2973 0.82 0.32 0.03 4715 102 4.905 0.041 1.7026 0.0039 ± ± HD 8859 16 2914 0.52 0.09 0.01 5502 18 4.986 0.011 1.7122 0.0021 ± ± HD 88742 24 1868 0.91 0.02 0.01 5981 13 4.699 0.045 1.7042 0.0040 ± ± HD 90812 17 2306 0.64 0.36 0.02 5164 35 4.945 0.039 1.7124 0.0025 ± ± HD 92719 21 2941 0.54 0.10 0.01 5824 16 4.861 0.024 1.7079 0.0014 ± ± HD 95521 19 2968 0.79 0.15 0.01 5773 18 4.875 0.041 1.7103 0.0019 ± ±

A66, page 15 of 18 A&A 566, A66 (2014)

Table B.2. Parameters for the 205 stars with ⇢ 0.5 from the nightly averaged 271-star sample. | | 

Star N T ⇢ [Fe/H] T log R (log R ) log I (log I ) obs span e↵ h HK0 i HK0 h H↵i H↵ [days] [K] HD 10002 12 838 0.08 0.17 0.03 5313 44 5.083 0.013 1.7115 0.0019 ± ± HD 100508 32 2283 0.31 0.39 0.05 5449 61 5.049 0.030 1.7200 0.0015 ± ± HD 10180 220 2974 0.08 0.08 0.01 5911 19 5.006 0.013 1.7173 0.0018 ± ± HD 102365 33 2965 0.03 0.29 0.02 5629 29 4.944 0.010 1.7102 0.0015 ± ± HD 102438 39 2243 0.22 0.29 0.01 5560 13 4.950 0.008 1.7090 0.0018 ± ± HD 104006 24 2232 0.00 0.78 0.02 5023 37 4.960 0.011 1.6881 0.0016 ± ± HD 104067 86 2270 0.39 0.06 0.05 4969 72 4.742 0.025 1.7178 0.0030 ± ± HD 104263 27 2244 0.13 0.02 0.02 5477 23 5.042 0.021 1.7141 0.0023 ± ± HD 104982 40 2270 0.32 0.19 0.01 5692 14 4.954 0.010 1.7101 0.0019 ± ± HD 106116 106 2697 0.31 0.14 0.01 5680 15 5.023 0.011 1.7159 0.0021 ± ± HD 10700 230 3125 0.08 0.52 0.01 5310 17 4.959 0.006 1.7047 0.0012 ± ± HD 108309 21 2676 0.08 0.12 0.01 5775 14 5.019 0.017 1.7273 0.0012 ± ± HD 111031 26 2244 0.08 0.27 0.02 5801 22 5.067 0.009 1.7166 0.0012 ± ± HD 11226 28 1766 0.05 0.04 0.01 6098 14 5.002 0.005 1.7187 0.0022 ± ± HD 114853 36 3031 0.34 0.23 0.01 5705 14 4.935 0.017 1.7124 0.0032 ± ± HD 11505 17 2944 0.02 0.22 0.01 5752 10 5.000 0.005 1.7128 0.0012 ± ± HD 115585 17 2640 0.20 0.35 0.02 5711 29 5.116 0.013 1.7251 0.0014 ± ± HD 115617 142 2910 0.12 0.02 0.01 5558 19 4.990 0.010 1.7113 0.0015 ± ± HD 115674 38 2251 0.10 0.17 0.01 5649 20 4.900 0.015 1.7101 0.0015 ± ± HD 117105 18 2657 0.45 0.29 0.01 5889 14 4.947 0.006 1.7113 0.0018 ± ± HD 117207 16 2680 0.22 0.22 0.02 5667 21 5.060 0.004 1.7157 0.0013 ± ± HD 122862 17 2294 0.09 0.12 0.01 5982 13 5.015 0.007 1.7198 0.0009 ± ± HD 123265 16 2641 0.02 0.19 0.03 5338 44 5.097 0.011 1.7143 0.0022 ± ± HD 12345 15 2472 0.21 0.21 0.02 5395 29 4.992 0.010 1.7139 0.0011 ± ± HD 12387 15 2838 0.06 0.24 0.01 5700 18 4.980 0.009 1.7114 0.0013 ± ± HD 124292 28 3100 0.12 0.13 0.02 5443 22 4.995 0.011 1.7120 0.0029 ± ± HD 125881 24 3002 0.02 0.06 0.01 6036 17 4.873 0.024 1.7137 0.0015 ± ± HD 126525 48 2805 0.24 0.10 0.01 5638 13 4.981 0.007 1.7120 0.0018 ± ± HD 128674 19 2262 0.41 0.38 0.01 5551 15 4.916 0.007 1.7082 0.0014 ± ± HD 129642 45 1085 0.07 0.06 0.04 5026 76 4.962 0.019 1.7126 0.0018 ± ± HD 130930 14 1781 0.30 0.01 0.03 5027 61 5.017 0.015 1.7077 0.0010 ± ± HD 1320 13 1957 0.09 0.27 0.01 5679 14 4.874 0.016 1.7100 0.0009 ± ± HD 132648 27 2623 0.47 0.37 0.01 5418 16 4.841 0.033 1.7064 0.0035 ± ± HD 134060 105 2897 0.13 0.14 0.01 5966 14 5.000 0.009 1.7150 0.0018 ± ± HD 134606 121 2448 0.07 0.27 0.02 5633 28 5.082 0.008 1.7150 0.0016 ± ± HD 134664 27 1066 0.41 0.10 0.01 5865 19 4.881 0.027 1.7178 0.0016 ± ± HD 136352 148 2809 0.23 0.34 0.01 5664 14 4.949 0.005 1.7080 0.0017 ± ± HD 136713 41 2202 0.33 0.07 0.05 4994 74 4.795 0.038 1.7220 0.0022 ± ± HD 136894 37 2044 0.28 0.10 0.02 5412 22 4.995 0.005 1.7051 0.0016 ± ± HD 13724 26 2134 0.01 0.23 0.02 5868 27 4.760 0.026 1.7172 0.0025 ± ± HD 137388 30 2148 0.36 0.18 0.03 5240 53 4.894 0.049 1.7257 0.0024 ± ± HD 138549 22 2621 0.18 0.00 0.01 5582 19 4.828 0.044 1.7152 0.0021 ± ± HD 1388 64 3025 0.09 0.01 0.01 5954 10 4.979 0.007 1.7140 0.0016 ± ± HD 142709 13 2523 0.18 0.35 0.03 4728 65 4.999 0.051 1.7155 0.0022 ± ± HD 143114 19 1789 0.19 0.41 0.01 5775 18 4.946 0.005 1.7088 0.0012 ± ± HD 144628 51 2105 0.28 0.41 0.02 5085 34 4.952 0.022 1.7114 0.0020 ± ± HD 145598 32 2107 0.30 0.78 0.02 5417 21 4.916 0.011 1.7010 0.0018 ± ± HD 1461 193 3027 0.06 0.19 0.01 5765 18 5.020 0.013 1.7128 0.0014 ± ± HD 146233 51 2602 0.20 0.04 0.01 5818 13 4.928 0.025 1.7142 0.0014 ± ± HD 14747 14 2860 0.06 0.39 0.01 5516 16 4.945 0.018 1.7070 0.0020 ± ± HD 147512 29 1734 0.08 0.08 0.01 5530 15 4.990 0.006 1.7121 0.0014 ± ± HD 150433 58 2223 0.05 0.36 0.01 5665 12 4.961 0.005 1.7041 0.0016 ± ± HD 151504 14 1897 0.01 0.06 0.02 5457 31 5.038 0.004 1.7139 0.0019 ± ± HD 15337 29 1975 0.35 0.06 0.03 5179 44 4.916 0.038 1.7214 0.0017 ± ± HD 154088 124 2014 0.04 0.28 0.03 5374 43 5.064 0.015 1.7129 0.0020 ± ± HD 154363 19 2529 0.24 0.62 0.04 4723 89 4.820 0.050 1.6810 0.0043 ± ± HD 157172 82 2266 0.06 0.11 0.02 5451 27 4.996 0.036 1.7182 0.0020 ± ± HD 157338 24 1460 0.04 0.08 0.01 6027 13 4.969 0.010 1.7154 0.0017 ± ± HD 157347 20 2892 0.26 0.02 0.01 5676 16 5.014 0.006 1.7132 0.0017 ± ± HD 1581 130 2624 0.12 0.18 0.01 5977 12 4.936 0.007 1.7095 0.0009 ± ± HD 161098 75 2015 0.42 0.27 0.01 5560 15 4.911 0.021 1.7099 0.0017 ± ± HD 161612 31 2154 0.09 0.16 0.02 5616 22 5.032 0.006 1.7182 0.0015 ± ± HD 162396 39 1884 0.17 0.35 0.01 6090 19 4.973 0.010 1.7114 0.0014 ± ± HD 165920 18 2326 0.04 0.29 0.04 5339 55 5.085 0.014 1.7191 0.0021 ± ± HD 166724 19 2567 0.46 0.09 0.03 5127 52 4.734 0.026 1.7077 0.0035 ± ± HD 16714 24 2089 0.22 0.20 0.01 5518 18 4.965 0.008 1.7133 0.0018 ± ± HD 168871 25 2951 0.01 0.09 0.01 5983 13 4.980 0.009 1.7149 0.0018 ± ± HD 170493 12 2101 0.17 0.14 0.11 4751 08 4.814 0.061 1.7216 0.0029 ± ± HD 171665 12 1730 0.34 0.05 0.01 5655 12 4.906 0.017 1.7146 0.0018 ± ±

A66, page 16 of 18 J. Gomes da Silva et al.: On the long-term correlation between the ﬂux in the Ca ii H & K and H↵ lines for FGK stars

Table B.2. continued.

Star N T ⇢ [Fe/H] T log R (log R ) log I (log I ) obs span e↵ h HK0 i HK0 h H↵i H↵ [days] [K] HD 174545 13 2574 0.23 0.22 0.04 5216 57 4.929 0.041 1.7198 0.0017 ± ± HD 176986 79 2625 0.06 0.00 0.03 5018 59 4.835 0.024 1.7201 0.0026 ± ± HD 177409 16 1979 0.37 0.04 0.01 5898 10 4.863 0.028 1.7083 0.0012 ± ± HD 177565 26 1684 0.33 0.08 0.01 5627 19 4.939 0.041 1.7159 0.0026 ± ± HD 177758 10 2834 0.39 0.58 0.02 5862 23 4.929 0.003 1.7049 0.0015 ± ± HD 17970 19 2962 0.07 0.45 0.04 5040 48 5.008 0.012 1.7015 0.0023 ± ± HD 180409 11 2834 0.12 0.17 0.01 6013 18 4.925 0.004 1.7103 0.0015 ± ± HD 181433 123 3011 0.07 0.33 0.13 4962 34 5.144 0.014 1.7130 0.0023 ± ± HD 183658 16 2171 0.14 0.03 0.01 5803 17 4.987 0.008 1.7128 0.0022 ± ± HD 183783 11 2676 0.09 0.20 0.07 4595 73 4.907 0.049 1.7163 0.0020 ± ± HD 185615 19 2297 0.10 0.08 0.02 5570 20 5.043 0.014 1.7156 0.0016 ± ± HD 188748 20 2133 0.26 0.12 0.01 5623 17 4.967 0.013 1.7088 0.0018 ± ± HD 189567 174 2941 0.41 0.24 0.01 5726 15 4.916 0.016 1.7142 0.0014 ± ± HD 189625 16 1743 0.42 0.18 0.02 5846 22 4.810 0.041 1.7133 0.0025 ± ± HD 190248 136 2942 0.02 0.33 0.03 5604 38 5.095 0.010 1.7168 0.0010 ± ± HD 190954 11 2204 0.29 0.41 0.02 5430 24 4.969 0.012 1.7070 0.0022 ± ± HD 192031 11 519 0.45 0.84 0.01 5215 16 4.954 0.006 1.7030 0.0019 ± ± HD 192310 206 3082 0.14 0.04 0.03 5166 49 4.991 0.040 1.7136 0.0017 ± ± HD 193193 30 1134 0.09 0.05 0.01 5979 13 4.933 0.016 1.7158 0.0018 ± ± HD 19467 21 2941 0.15 0.14 0.01 5720 10 5.002 0.015 1.7131 0.0019 ± ± HD 196761 10 2822 0.17 0.31 0.01 5415 16 4.918 0.025 1.7102 0.0026 ± ± HD 199190 23 762 0.23 0.15 0.01 5926 17 5.052 0.014 1.7198 0.0014 ± ± HD 199288 16 2602 0.02 0.63 0.01 5765 19 4.895 0.005 1.7042 0.0013 ± ± HD 199960 28 854 0.37 0.28 0.02 5973 26 5.012 0.019 1.7217 0.0013 ± ± HD 20003 104 2280 0.25 0.04 0.02 5494 27 4.988 0.040 1.7203 0.0014 ± ± HD 203432 33 1405 0.19 0.29 0.02 5645 25 4.858 0.057 1.7201 0.0022 ± ± HD 20407 20 3062 0.04 0.44 0.01 5866 14 4.899 0.007 1.7078 0.0010 ± ± HD 204313 70 2026 0.03 0.18 0.02 5776 22 5.019 0.017 1.7202 0.0015 ± ± HD 204385 13 2889 0.13 0.07 0.01 6033 16 4.976 0.009 1.7164 0.0014 ± ± HD 204941 38 2546 0.31 0.19 0.03 5056 52 4.952 0.030 1.7146 0.0020 ± ± HD 205536 22 2218 0.33 0.05 0.02 5442 23 5.016 0.006 1.7152 0.0020 ± ± HD 207129 79 1875 0.32 0.00 0.01 5937 13 4.903 0.030 1.7112 0.0016 ± ± HD 207700 13 2111 0.30 0.04 0.01 5666 18 5.006 0.010 1.7207 0.0015 ± ± HD 20781 124 2966 0.14 0.11 0.02 5256 29 5.035 0.011 1.7171 0.0022 ± ± HD 20782 55 2983 0.30 0.06 0.01 5774 14 4.919 0.015 1.7149 0.0019 ± ± HD 20794 279 3033 0.12 0.40 0.01 5401 17 4.981 0.006 1.7034 0.0018 ± ± HD 207970 12 2955 0.44 0.07 0.02 5556 25 5.028 0.010 1.7148 0.0016 ± ± HD 20807 39 2308 0.12 0.23 0.01 5866 11 4.881 0.013 1.7082 0.0017 ± ± HD 208704 12 2638 0.02 0.09 0.01 5826 11 4.957 0.011 1.7194 0.0019 ± ± HD 210752 14 2534 0.03 0.57 0.01 5923 23 4.874 0.004 1.7045 0.0018 ± ± HD 210918 31 1857 0.25 0.09 0.01 5755 12 5.002 0.015 1.7157 0.0013 ± ± HD 211415 13 2997 0.24 0.21 0.01 5850 14 4.919 0.023 1.7117 0.0012 ± ± HD 21209A 12 3022 0.05 0.41 0.04 4671 65 4.840 0.022 1.7082 0.0024 ± ± HD 212708 30 1058 0.34 0.27 0.02 5681 27 5.076 0.014 1.7187 0.0020 ± ± HD 213628 12 2608 0.26 0.01 0.01 5555 20 4.957 0.010 1.7145 0.0025 ± ± HD 213941 26 2217 0.35 0.46 0.01 5532 18 4.909 0.013 1.7095 0.0023 ± ± HD 214385 11 2911 0.04 0.34 0.01 5654 15 4.924 0.016 1.7094 0.0016 ± ± HD 21693 141 2951 0.02 0.00 0.02 5430 26 4.909 0.055 1.7161 0.0021 ± ± HD 21938 18 3019 0.10 0.47 0.01 5778 18 4.939 0.007 1.7076 0.0021 ± ± HD 220256 22 1217 0.08 0.10 0.03 5144 48 5.022 0.016 1.7088 0.0013 ± ± HD 220507 48 2220 0.02 0.01 0.01 5698 17 5.052 0.010 1.7186 0.0019 ± ± HD 221356 23 2941 0.29 0.20 0.03 6112 37 4.919 0.004 1.7062 0.0010 ± ± HD 222669 46 1403 0.13 0.05 0.01 5894 17 4.863 0.022 1.7118 0.0022 ± ± HD 224619 15 2992 0.10 0.20 0.01 5436 16 4.975 0.013 1.7148 0.0012 ± ± HD 22879 50 2686 0.05 0.83 0.02 5857 27 4.908 0.007 1.6987 0.0015 ± ± HD 23456 20 2200 0.10 0.32 0.01 6178 18 4.909 0.010 1.7079 0.0019 ± ± HD 26965A 24 2998 0.35 0.31 0.03 5153 38 4.944 0.034 1.7040 0.0027 ± ± HD 283 11 2592 0.46 0.54 0.02 5157 28 4.949 0.011 1.7085 0.0018 ± ± HD 28471 17 2683 0.04 0.05 0.01 5745 14 4.991 0.021 1.7140 0.0018 ± ± HD 28701 17 1263 0.08 0.32 0.01 5710 12 4.986 0.012 1.7114 0.0011 ± ± HD 28821 18 2904 0.08 0.12 0.01 5660 13 4.975 0.013 1.7151 0.0025 ± ± HD 30278 21 1513 0.05 0.17 0.02 5394 29 5.006 0.013 1.7124 0.0019 ± ± HD 30306 21 2904 0.43 0.17 0.02 5529 26 5.074 0.013 1.7156 0.0020 ± ± HD 31527 182 3011 0.01 0.17 0.01 5898 13 4.955 0.006 1.7131 0.0018 ± ± HD 31822 43 2352 0.03 0.19 0.01 6042 16 4.865 0.007 1.7113 0.0018 ± ± HD 32724 21 2954 0.02 0.17 0.01 5818 13 5.032 0.013 1.7150 0.0011 ± ± HD 33725 17 3011 0.10 0.17 0.02 5274 30 4.972 0.035 1.7154 0.0015 ± ± HD 34449 13 2626 0.12 0.09 0.01 5848 17 4.883 0.013 1.7102 0.0017 ± ±

A66, page 17 of 18 A&A 566, A66 (2014)

Table B.2. continued.

Star N T ⇢ [Fe/H] T log R (log R ) log I (log I ) obs span e↵ h HK0 i HK0 h H↵i H↵ [days] [K] HD 35854 17 2958 0.47 0.13 0.03 4928 56 4.799 0.037 1.7110 0.0038 ± ± HD 36003 57 1494 0.08 0.20 0.06 4647 88 4.872 0.040 1.7080 0.0032 ± ± HD 36108 23 3275 0.25 0.21 0.01 5916 12 4.992 0.006 1.7156 0.0030 ± ± HD 36379 45 2341 0.22 0.17 0.01 6030 14 4.976 0.006 1.7174 0.0018 ± ± HD 37986 19 2975 0.24 0.26 0.03 5507 38 5.082 0.013 1.7245 0.0021 ± ± HD 3823 33 2265 0.00 0.28 0.01 6022 14 4.988 0.007 1.7137 0.0010 ± ± HD 38277 10 3019 0.12 0.07 0.01 5871 10 5.019 0.007 1.7228 0.0013 ± ± HD 38858 66 3009 0.01 0.22 0.01 5733 12 4.918 0.013 1.7102 0.0015 ± ± HD 38973 22 2353 0.07 0.05 0.01 6016 17 4.972 0.013 1.7138 0.0010 ± ± HD 39194 156 3008 0.18 0.61 0.02 5205 23 4.951 0.014 1.7003 0.0015 ± ± HD 40397 21 3060 0.42 0.13 0.01 5527 20 5.013 0.009 1.7104 0.0014 ± ± HD 44120 18 3019 0.33 0.12 0.01 6052 15 5.070 0.017 1.7206 0.0010 ± ± HD 44420 17 2898 0.14 0.29 0.02 5818 22 5.036 0.024 1.7188 0.0012 ± ± HD 44447 23 2989 0.23 0.22 0.01 5999 14 4.977 0.015 1.7117 0.0015 ± ± HD 44594 21 2903 0.01 0.15 0.01 5840 14 5.004 0.020 1.7175 0.0024 ± ± HD 45184 102 3013 0.24 0.04 0.01 5869 14 4.905 0.026 1.7126 0.0013 ± ± HD 45289 16 3023 0.44 0.02 0.01 5717 18 5.033 0.008 1.7169 0.0024 ± ± HD 45364 62 2917 0.16 0.17 0.01 5434 20 4.959 0.022 1.7092 0.0021 ± ± HD 47186 104 2879 0.28 0.23 0.02 5675 21 5.051 0.009 1.7131 0.0014 ± ± HD 50590 12 2193 0.05 0.22 0.04 4870 67 4.974 0.032 1.7150 0.0021 ± ± HD 51608 126 2966 0.12 0.07 0.01 5358 22 4.982 0.020 1.7141 0.0023 ± ± HD 55693 27 3278 0.43 0.29 0.02 5914 26 4.999 0.020 1.7221 0.0028 ± ± HD 59468 141 2754 0.17 0.03 0.01 5618 20 4.996 0.012 1.7101 0.0010 ± ± HD 59711A 16 2911 0.22 0.12 0.01 5722 13 4.946 0.010 1.7107 0.0013 ± ± HD 65562 15 2945 0.43 0.10 0.03 5076 47 4.954 0.035 1.7069 0.0018 ± ± HD 65907A 61 2608 0.30 0.31 0.01 5945 16 4.914 0.010 1.7059 0.0013 ± ± HD 66221 17 2350 0.04 0.17 0.02 5635 25 5.058 0.020 1.7158 0.0028 ± ± HD 6735 17 2960 0.26 0.06 0.01 6082 15 4.877 0.014 1.7141 0.0012 ± ± HD 68607 29 1209 0.26 0.07 0.03 5215 45 4.728 0.036 1.7166 0.0024 ± ± HD 68978A 60 2339 0.03 0.04 0.02 5965 22 4.879 0.015 1.7169 0.0018 ± ± HD 69655 21 2905 0.06 0.18 0.01 5961 12 4.943 0.009 1.7112 0.0014 ± ± HD 71334 21 2973 0.29 0.09 0.01 5694 13 4.987 0.010 1.7076 0.0016 ± ± HD 7134 16 1767 0.09 0.29 0.01 5940 14 4.949 0.005 1.7142 0.0015 ± ± HD 71479 21 2974 0.14 0.24 0.01 6026 18 5.040 0.015 1.7264 0.0020 ± ± HD 72579 23 2974 0.35 0.20 0.02 5449 30 5.087 0.009 1.7187 0.0018 ± ± HD 72769 21 2703 0.07 0.30 0.02 5640 27 5.090 0.015 1.7183 0.0022 ± ± HD 73121 19 2708 0.07 0.09 0.01 6091 16 5.061 0.013 1.7211 0.0021 ± ± HD 73524 64 2975 0.12 0.16 0.01 6017 13 5.002 0.017 1.7137 0.0014 ± ± HD 74014 17 2963 0.29 0.22 0.02 5561 27 5.072 0.010 1.7189 0.0008 ± ± HD 7449 84 2926 0.38 0.11 0.01 6024 13 4.850 0.015 1.7089 0.0015 ± ± HD 78429 57 1960 0.24 0.09 0.01 5760 19 4.927 0.029 1.7194 0.0023 ± ± HD 78558 20 2969 0.04 0.44 0.01 5711 18 4.974 0.009 1.7108 0.0023 ± ± HD 78612 22 2968 0.37 0.24 0.01 5834 14 5.005 0.017 1.7155 0.0025 ± ± HD 78747 42 2553 0.07 0.67 0.01 5778 18 4.921 0.008 1.7019 0.0008 ± ± HD 81639 18 2706 0.03 0.17 0.02 5522 20 4.990 0.013 1.7143 0.0019 ± ± HD 82342 27 3008 0.01 0.54 0.03 4820 61 4.943 0.032 1.6983 0.0030 ± ± HD 82516 53 2319 0.04 0.01 0.04 5104 60 4.955 0.044 1.7299 0.0026 ± ± HD 83529 22 2706 0.40 0.22 0.01 5902 12 4.970 0.009 1.7133 0.0020 ± ± HD 8406 14 3002 0.12 0.10 0.01 5726 12 4.856 0.009 1.7113 0.0010 ± ± HD 85390 63 2965 0.06 0.07 0.03 5186 54 4.959 0.026 1.7145 0.0022 ± ± HD 86140 10 2699 0.40 0.25 0.04 4903 59 4.806 0.020 1.7042 0.0017 ± ± HD 8638 33 1826 0.15 0.38 0.02 5507 26 4.953 0.006 1.7034 0.0016 ± ± HD 88084 18 2692 0.20 0.10 0.01 5766 11 4.973 0.009 1.7124 0.0016 ± ± HD 8828 45 2223 0.38 0.16 0.02 5403 25 4.996 0.010 1.7080 0.0020 ± ± HD 89454 48 1467 0.46 0.12 0.01 5728 17 4.701 0.029 1.7182 0.0024 ± ± HD 90156 83 2937 0.01 0.24 0.01 5599 12 4.947 0.006 1.7066 0.0016 ± ± HD 90711 17 2305 0.38 0.24 0.03 5444 39 5.004 0.034 1.7215 0.0021 ± ± HD 93385 136 2908 0.07 0.02 0.01 5977 18 4.988 0.007 1.7133 0.0019 ± ± HD 94151 21 2724 0.02 0.04 0.01 5583 19 4.974 0.031 1.7168 0.0015 ± ± HD 95456 77 2338 0.08 0.16 0.02 6276 22 4.982 0.019 1.7208 0.0014 ± ± HD 96423 22 2722 0.05 0.10 0.01 5711 18 5.035 0.013 1.7142 0.0021 ± ± HD 96700 168 3270 0.22 0.18 0.01 5845 13 4.948 0.011 1.7148 0.0017 ± ± HD 97037 18 2668 0.35 0.07 0.01 5883 14 4.998 0.009 1.7155 0.0013 ± ± HD 97343 21 2695 0.03 0.06 0.01 5410 20 5.015 0.009 1.7132 0.0019 ± ± HD 9782 27 2216 0.35 0.09 0.01 6023 19 4.974 0.007 1.7146 0.0011 ± ± HD 9796 15 2573 0.42 0.25 0.02 5179 28 4.874 0.025 1.6902 0.0017 ± ± HD 97998 17 2351 0.28 0.42 0.01 5716 21 4.902 0.007 1.7085 0.0016 ± ± HD 98281 54 2226 0.47 0.26 0.02 5381 23 4.887 0.027 1.7071 0.0023 ± ±

A66, page 18 of 18 Chapter 5

Conclusions

In this thesis I studied the long-term activity of M dwarfs (chapter 2) and its inﬂuence on the measured RV (chapter 3) and the long-term behaviour of the two activity indices based on the Ca ii H & K and H↵ lines for a sample of FGK stars (chapter 4). These studies resulted in three peer-reviewed papers (Gomes da Silva et al. 2011, 2012, 2013). In the following sections I will describe the results from these three papers and ﬁnish with the future prospects on these subjects.

5.1 Activity indices for M dwarfs

In the ﬁrst paper (Gomes da Silva et al. 2011) we studied the long-term behaviour of four well known activity indices based on the Ca ii H & K, H↵, Na i D1 &D2, and He i

D3 lines. We used a sample of 30 M0–M5.5 dwarf stars observed with HARPS during a timespan of around 5 years. All data was binned into 150-day bins to average out short- to mid-term sources of noise like rotationally modulated active regions. The objective of the work was to detect long-term activity variability in M dwarfs and also to compare the four activity proxies to test their behaviour for these types of stars with the aim of selecting the most appropriate index for further comparison with simultaneous RV measurements (see Section 5.3).

We compared the four indices using Pearson correlation coefficients and false alarm probability (FAP) tests to determine the most significative cases of correlations (see Chapter 2 for a description of the tests). We found that 26% of our stars have significant positive correlation between Ca ii and the H↵. As was detected by Cincunegui et al.

108 CHAPTER 5. CONCLUSIONS 109

(2007a), we found a very broad range in correlation coefficient values between the Ca ii and the H↵ indices, ranging from negative to strong positive correlations. However, there seems to be a trend between the correlation coefficient of these two indices and the average activity level of the stars as measured by the calcium lines: for mean activity levels higher than a given value of activity (S 0.04), all stars show positive CaII ' correlation between the Ca ii and H↵, while for lower values there are positive and negative correlations. We interpret this behaviour as due to the different contribution of filaments to the Ca ii and H↵ lines and due to the saturation of the filament contribution to the hydrogen line for higher activity levels. As discussed by Meunier & Delfosse (2009), both indices are sensitive to plages, and both emit in these regions. However, only H↵ is sensitive to filaments which increases the absorption of the line. This as the filling factor of plages increases, the filling factor of filaments also increases, but will saturate at a given activity level (contrarily to the filling factor of plages). This will cause the H↵ to cease absorption and start to fill in as activity increases further. As a result the value of both indices will increase, which justifies the correlation for higher activity levels. For activity levels lower than the filament saturation limit, the correlation might depend on the plages to filaments filling factor ratio and levels of contrast (which depend on temperature). On the other hand, we found a very good correlation between the Ca ii and Na i indices, with 70% of our sample having significant positive correlations. We detected no cases of anti-correlations between these indices and only around 11% of the stars presented correlation coefficient values lower than 0.5. This shows that the Na i D lines follow very closely the long-term activity measured by the Ca ii H & K lines for early-M dwarfs. D´ıaz et al. (2007a) has previously suggested that a positive correlation between Na i D and Ca ii H & K lines existed for stars with emission in the Balmer lines only. However, none of the stars in our sample have H↵ emission, showing that the Na i D lines can be used to follow the long-term activity level of early-M dwarfs even for the least active stars. And since the flux of M dwarfs peaks at redder wavelengths than than that of the hotter FGK stars, this index might be more appropriate than the use of the Ca ii lines due to the higher signal-to-noise ratio.

Although we found a tendency for positive correlations between He i and Ca ii, the majority of them were not statistically signiﬁcant. Only 11% of the stars showed signiﬁcant correlation between these two indices. This can be due to the lack of He i variability that we detected in our M dwarfs sample. CHAPTER 5. CONCLUSIONS 110

5.2 Long-term activity variability and cycles of M dwarfs

In Gomes da Silva et al. (2011), before the comparison of the four activity indices discussed in the previous section we analysed the variability of the stars using the four indices based on the Ca ii H & K, H↵, Na i D, and He i D3 lines. We used F-tests to determine which stars showed statistically significative long-term variability (see Chapter 3 for more information). We found that the Ca ii,H↵, and Na i indices were equally efficient at detecting long-term activity variations for early-M dwarfs, by detecting 39%, 33%, and 37% of stars, respectively, with significant long-term activity variability. From these numbers we conclude that around 1/3 of early-M dwarfs show long-term activity variability. However, He i was not as efficient as the other activity proxies by detecting long-term variability on only 10% of the stars. Actually, the flux in the He i line is more appropriate for hotter stars since the maximum absorbed flux in the D3 line decreases with B V, and if extrapolated to M dwarfs, its maximum flux is almost two orders of magnitude lower for these stars than for F dwarfs (see Saar et al. 1997, Fig. 3).

In Gomes da Silva et al. (2012) we extended the timespan of the sample used in Gomes da Silva et al. (2011) by one more year and reduced the sample to 27 early-M dwarfs whose activity was followed using an activity indicator based on the Na i doublet. This index was chosen after a careful comparison of four activity indicators in Gomes da Silva et al. (2011) (see Chapter 5.1). We detected signiﬁcant long-term variability in 67% of our sample (with a FAP 0.1). This fraction of stars with variability can be compared  to the work of Lovis et al. (2011) who studied the long-term variability of a sample of FGK dwarfs and showed that around 61% of their sample present activity cycle-like variability (a similar result to the 60% detected by the Mt. Wilson survey, Baliunas et al. 1998)). This shows that the fraction of stars with long-term variability does not change too much when we move from solar-type stars to early-M dwarfs. This might be expected since their activity is supposed to be operated by the same type of dynamo model (↵⌦- dynamo) (Saar & Brandenburg 1999; Lorente & Montesinos 2005). It’s only after around M5.5 that M dwarfs are completely convective, and a different dynamo, maintained by turbulent convection (↵2-dynamo), becomes the magnetic ﬁelds generator (Chabrier & Kuker¨ 2006; Dobler et al. 2006). Therefore, some change in long-term activity behaviour can be expected for later-M dwarfs when compared with early-Ms or FGKs. Actually, Chabrier & Kuker¨ (2006) state that an observational signature of the ↵2-dynamo model would be the absence of cycles in fully convective stars.

We could fit sinusoidal signals with statistically significant results in 19% of our stars. ⇠ This might indicate that the fraction of M dwarfs that show periodic cycles is lower than CHAPTER 5. CONCLUSIONS 111 for FGK stars and that the majority (48%) have variable long-term activity (folowing the classification of Baliunas et al. 1995). For example, Baliunas et al. (1998) found that 60% of their FGKM sample showed periodic cyclic activity, while only 25% was variable with no defined period. The only M dwarfs included in their sample, HD 95735 (M2) was classified as having variable long-term activity. Does this means that we are detecting a smooth transition from the ↵⌦-dynamo (stars with tachocline) to the ↵2- dynamo (fully convective stars) where long-term activity variability is non-periodic? We need to note that our sinusoidal fitting can be affected by short-term variations produced by the growth and decay of active regions (Donahue et al. 1997), by the fundamental variability of the activity cycles (e.g. for the Sun the period ranges from 9 to 13 years, Donahue & Baliunas 1992), and by the ”small” timespan of our data. Our timespan covers 6 years, which might not be enough to detect full cycles. In fact, the periods of ⇠ our fitted sinusoids varied between 2.8 and 4.7 years. These periods should be regarded as minimum cycle periods. Nevertheless we were able to detect some stars with cycle periods longer that the timespan of their observations. For example, we detected for the first time and with a high probability of 99.9% that the planet host Gl 581 has a magnetic activity cycle with a period of 3.85 years. We also found that the planet host Gl 667C also has an activity cycle with a period of 3.18 years (probability of 96.7%). These activity cycles could produce RV signals that can affect the search for planetary companions and should therefore be taken into account when fitting keplerian orbits. In the next section we will discuss our results regarding the effects of long-term variability on the RV of M dwarfs.

5.3 Inﬂuence of long-term activity on the RV of M dwarfs

In the previous section I discussed the results obtained in Chapter 3 related to the long- term activity variations in 27 early-M dwarfs. In that work we obtained simultaneous measurements of the activity indicator based on the Na i lines and RV (together with the CCF parameters BIS, FWHM, and contrast). As we stated before, all data was binned to 150 days to average out short-term variability. We compared the activity variations with RV and found that long-term activity can be able to induce RV signals with amplitudes of 1 up to 5 m s . However, only 36% of the stars with long-term activity variability appear to have had their RV signiﬁcantly (with FAP 0.05) affected by magnetic cycles, on the  typical timescale of 6 years. This means that 19% of early-M dwarfs might have their ⇠ ⇠ 1 RV affected by long-term activity with amplitudes as high as 5 m s , which is enough to hide a low-mass planet. We note that the median of the rms of the detected RV CHAPTER 5. CONCLUSIONS 112 signals (after removal of the signals induced by planetary companions and after binning 1 1 the short-term noise) was 1.5 m s , comparable to the instrument precision ( 1ms ) ⇠ which means that more stars might be inﬂuencing the RV measurements with lower, undetected amplitudes. Very low RV amplitudes produced by activity cycles can be expected. Lovis et al. (2011) showed that, for a given activity level, the sensitivity of the RV to long-term activity decreases with decreasing stellar temperature. As a result, for a given activity level, G-type stars are more affected by this cyclic variability than K dwarfs and, if we extrapolate the model to M dwarfs, these stars will show very low (or even negative) slopes of the correlation between activity and RV (see their Fig. 18, 1 lower panel). They detected RV amplitudes of up to 25 m s in their FGK sample. Our ⇠ smaller induced RV amplitudes are therefore in agreement with their model.

Almost all of the stars with variability that we studied presented a positive correlation between activity and RV (although some with low signiﬁcance). This means that as the activity level increases and more active regions are present in the star, there will be higher levels of inhibition of convection which will decrease the convective blueshift and therefore increase the star overall redshift (positive RVs). This is a similar behaviour as the one observed for the Ca ii lines (e.g. Lovis et al. 2011; Dumusque et al. 2011a).

Recently, Robertson et al. (2013) used the Na i D features to reveal the long-period 1 stellar activity cycle of the K7/M0 dwarf GJ 328, which induces a 6-10 m s amplitude signal in the star’s RV data. This showed the advantage of using this line when following activity for this type of stars in cases where the Ca ii H & K lines are not available or the S/N in the Ca ii region is too low. Their RV amplitude is also comparable to the maximum 1 RV amplitude we detected in our M dwarf sample (5.9 m s ).

5.4 The long-term correlation between Ca II and Halpha for FGK stars

In Gomes da Silva et al. (2013) we tried to understand what affects the correlation between the ﬂux in the Ca ii and H↵ chromospheric lines in FGK stars. Several surveys use these indices to measure the activity variability of stars, and in some cases to search for activity effects on RV when looking for planets. However, as noted by Cincunegui et al. (2007a) the relation between these two indices is not straightforward. This is very important to diagnose RV variations due to activity when searching for exoplanets. Normally Ca ii is correlated with RV, and the Ca ii signals can be used to subtract RV CHAPTER 5. CONCLUSIONS 113 effects from the time series (e.g. Dumusque et al. 2011a). In some cases, it is known that these indices are anti-correlated or not correlated at all (Cincunegui et al. 2007a). Therefore, when trying to detect RV variability induced by activity with the H↵ line, we could ﬁnd a different correspondence between the index and RV, and the signal might be misinterpreted. We need to know the behaviour of these indices, and what might cause their correlation to vary from star to star, in order to correctly diagnose activity signals and their induced RV variations.

With this in mind we used a sample of 271 FGK stars with measurements from the HARPS spectrograph during a timespan of 9 years. We obtained simultaneously two ⇠ indices based on the Ca ii and H↵ lines, the log R0HK (Noyes et al. 1984) and log IH↵, respectively. Similarly to Cincunegui et al. (2007a), we found a great variety of long-term correlations between the two indicators. We found strong positive correlations on 20% of our stars, while around 3% showed strong negative correlations. These results are comparable to what we found for the case of M dwarfs in Gomes da Silva et al. (2011). When comparing with the average activity level we detected that stars which exhibit positive correlations are normally the most active stars. At low activity levels, one can ﬁnd both negative correlations and stars showing no correlations (cf. Gomes da Silva et al. 2011). We also compared the correlations we obtained with the metallicity of the stars. All the stars with anti-correlations between the two indices have higher metallicity content that the average of the sample. These two results suggests that metallicity and activity level are playing a role in the way these indices relate to each other.

In light of the study by Meunier & Delfosse (2009) about the correlation between the flux in Ca ii and H↵ for the Sun we can interpret our results based on the effect of filaments on the flux of the H↵ line (see discussion in Section 5.1). Following this, metallicity might be influencing the contrast or filling factor of the filaments to plages ratio, and controlling the emission or absorption of the H↵ line when compared to the emission in Ca ii as activity increases.

5.5 Future prospects and things to be done

The work included in this thesis is a contribution the the knowledge about the influence of long-term activity on the RV of M dwarfs. For the first time, a moderate-size sample of early-M dwarfs was used to confirm that activity cycles are frequent (however less frequent than in FGKs) and indeed induce measurable RV variations capable of hiding low-mass planets or simulating the signals produced by long-period planets (Gomes da CHAPTER 5. CONCLUSIONS 114

Silva et al. 2012). As a result, we shown that it is crucial to include activity cycle analysis when searching for low-mass and/or long-period planets around these stars. Using the same sample, we also studied for the first time the long-term behaviour of four well known activity indices for early-M dwarfs and confirmed that the flux in the Ca ii H&K and H↵ lines are not always correlated but that the correlation depends on the activity level of the star(Gomes da Silva et al. 2011). In the same work we also confirmed that the Na i D lines follow very well the behaviour of the Ca ii lines and that the former are more suitable to follow the activity level of M dwarfs. The use of Na i on M stars can then be a solution to the problem of the lack of correlation between Ca ii H & K and H↵. Finally, we confirmed the complex behaviour between Ca ii H & K and H↵ for FGK stars and found indications that metallicity, along with the mean activity level of the stars, might be playing a role on the correlation between these two indices (Gomes da Silva et al. 2013).

In the following sections I will discuss how these results can be improved or expanded along with some of the limitations of the present work.

5.5.1 Activity cycles in M dwarfs

During this thesis we found that a small fraction of early-M dwarfs have activity cycles similar to that of the Sun (Gomes da Silva et al. 2012). However, this fraction is smaller for these stars than for FGK stars (Lovis et al. 2011). Dynamo theories predict that stars with a tachocline (FGK and early-Ms) have their magnetic ﬁelds generated by a ↵⌦-dynamo (e.g. Saar & Brandenburg 1999) but fully convective stars (later-M dwarfs) have their activity driven by an ↵2-dynamo (e.g. Chabrier & Kuker¨ 2006). The results of this thesis show that there is a decreasing fraction of stars with cycles as we move from FGKs to M-types. According to Chabrier & Kuker¨ (2006), one of the observational results of having an ↵2-dynamo operating on a star would be the lack of a magnetic cycle. Therefore, expanding our study of the magnetic cycles to include mid- and later- M dwarfs would be one way to test the ↵2-dynamo model of fully convective stars. That expansion could also answer to the question of whether the transition from one dynamo model to the other is a smooth transition or an abrupt transition at some speciﬁc stellar subtype.

Our activity studies could also be expanded in terms of timespan. The observations we used covered around six years. However, activity cycles can last longer than that, with some stars in the Mt. Wilson survey having activity cycles as long as 20 years, and CHAPTER 5. CONCLUSIONS 115 some others showing trends that might be of cycles lasting even longer (Baliunas et al. 1995). Several trends in our data can be long activity cycles that were not detected due to timespan limitations. Therefore, the fraction of M-dwarf stars with cycles can be higher than the one we detect, which will affect the discussion regarding the dynamo models. It is therefore important to continue following the long-term activity of these type of stars (and later types) and gather more data so we can be able to detect full activity cycles, study their frequency, and possible correlations between the cycle parameters (amplitude, period) and other stellar parameters.

Regarding the inﬂuence of long-term activity and RV, I shown that amplitudes of around 1 5ms can be induced on early-M dwarfs (Gomes da Silva et al. 2012). It appears that, as we move from FG to K-dwarfs, and then to early-Ms, the amplitude of the RV induced by long-term activity tends to decrease (Lovis et al. 2011). However, nothing is known when we move to later-Ms. It would then be interesting to make similar tests for these stars. Furthermore, some of the stars we used in our survey might have undetected planets capable of inducing low-amplitude RV signals that interfere with our comparisons with the activity variations. A more careful analysis of the RV data with the aim of separating planetary signals from those of activity would contribute to a better assessment of the activity interference on RV.

5.5.2 Activity indices

In two of the works published during this thesis I studied the long-term behaviour of different activity indices for early-M and FGK stars (Gomes da Silva et al. 2011, 2013). These works showed that different indicators behave differently for different stars. This is because they are formed at different heights in the chromosphere, and are then mapping different layers of the star’s atmosphere. The Ca ii lines are known to follow very well the activity changes in stars and to correlate well with RV (e.g. Lovis et al. 2011; Dumusque et al. 2011a). However other activity features like ﬁlaments are undetected by these lines (Meunier & Delfosse 2009). These type of features, which are not detected by Ca ii and might affect RV, are not taken into consideration when this index is the sole activity indicator and compared to RV to remove sources of noise in planet searches. The same can be told about the use of any other index that is based only on a single chromospheric species. It would then be very interesting to explore the advantages of a new homogenius index that could be based on different species, and used for a wide range of spectral types, like for example, combining the Ca ii H & K and H↵ lines. CHAPTER 5. CONCLUSIONS 116

In our study of the long-term correlation between the Ca ii H & K and H↵ lines, we found indications that metallicity could be having an influence on the relation between them (Gomes da Silva et al. 2013). However, our sample included only a few cases of stars with anti-correlations. A larger sample including more anti-correlated stars would help establish if metallicity is in fact influencing the behaviour of these two indices. These anti-correlations might also have an effect on the induced RV noise by activity. A comparison between the flux on the Ca ii H & K and H↵ lines and RV for different stars having different correlations would answer that question. References

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