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A&A
Volume 652, August 2021
Article Number A28
Number of page(s) 32
Section Stellar atmospheres
DOI https://doi.org/10.1051/0004-6361/202140605
Published online 04 August 2021

© ESO 2021

1 Introduction

One of the main problems when trying to find and study exoplanets with Doppler spectroscopy is the intrinsic variability of the host stars. Different phenomena on the surface of stars, such as solar-like oscillations (e.g. Bouchy & Carrier 2002; Butler et al. 2003; Kjeldsen et al. 2005; Bazot et al. 2012), surface granulation (e.g. Dravins 1982; Del Moro et al. 2004; Meunier et al. 2017; Cegla et al. 2019), stellar magnetic activity features such as cool spots and hot faculae (e.g. Saar & Donahue 1997; Desort et al. 2007; Lagrange et al. 2010; Meunier et al. 2010), or long-term magnetic cycles (e.g. Santos et al. 2010; Lovis et al. 2011; Suárez Mascareño et al. 2016, 2018), introduce signals in radial velocity (RV) measurements that can obfuscate planetary signatures. Moreover, since stars rotate, stellar activity features often appear as periodic signals modulated with the stellar rotation period (Prot), which can be mistakenly attributed to the periodic signal caused by a planet (e.g. Queloz et al. 2001; Desidera et al. 2004; Bonfils et al. 2007; Huélamo et al. 2008; Boisse et al. 2009; Figueira et al. 2010; Hatzes 2013; Rajpaul et al. 2016; Haywood et al. 2014; Santos et al. 2014; Robertson et al. 2015). Alongside these, long-term magnetic cycles can also result in periodic signals. Therefore, it is critical to understand how astrophysical variability affects the measurements in order to exclude rotational modulation as the origin of RV variations.

A variety of activity indicators obtained from the same stellar spectra used to extract RVs are employed to probe activity in different ways. Common examples are measurements of the flux in the core of chromospheric lines, such as the Ca II H&K lines in solar-like stars (Wilson 1968; Vaughan et al. 1978; Noyes et al. 1984; Lovis et al. 2011) or the Hα line in M dwarfs (West et al. 2004; Schöfer et al. 2019a), parametrisations of the cross-correlation function (CCF) profile (Queloz et al. 2001; Boisse et al. 2011; Figueira et al. 2013; Lanza et al. 2018; Simola et al. 2019), or wavelength-dependent changes in the RVs measured with the so-called chromatic index (CRX, Zechmeister et al. 2018). Photometric observations are also commonly used to study activity (Boisse et al. 2009; Cegla et al. 2014; Haywood et al. 2014; Bastien et al. 2014; Oshagh et al. 2017; Hojjatpanah et al. 2020). The average strength of the indicators is related to the activity level of the stars, and modulationsinferred from the indicators’ time series measure the inhomogeneity of activity across the stellar surface.

Stellar activity indicators are sensitive to stellar variability and track signals induced in RVs by activity. At the same time, by construction, they are insensitive to planet-induced modulations. Although they could be affected by star-planet interactions enhancing the stellar activity, no firm detection of this phenomenon exists so far (see e.g. Cuntz et al. 2000; Shkolnik et al. 2003). Consequently, they are necessary to distinguish between a planetary or stellar origin of periodic signals found in RVs. Correlations of activity indicators with RVs or the presence of the same periodic signal in both RV and indicators suggest the existence of activity-driven variations in the RVs. Several techniques have been developed to decorrelate or model the RV activity signal using different activity indicators (e.g. Boisse et al. 2009; Lanza et al. 2010; Haywood et al. 2014; Rajpaul et al. 2015; Herrero et al. 2016; Mallonn et al. 2018; Rosich et al. 2020; Baroch et al. 2020; Gilbertson et al. 2020). There are also a number of studies focusing on the temporal variability experienced by common indicators, the correlations between them, and their relation with RV measurements on relatively large sets of cool stars (e.g. Suárez Mascareño et al. 2015, 2017, 2018; Tal-Or et al. 2018; Schöfer et al. 2019a; Fuhrmeister et al. 2019). However, a general methodology to correct for activity in RV measurements has not yet been established.

Indicators such as asymmetry measurements of the CCF bisector inverse slope (BIS) or the CRX have been observed to show linear correlations with the RVs in M dwarfs, however, this is not always the case for, for example, the full-width-at-half-maximum (FWHM) of the CCF or indicators derived from chromospheric lines (e.g. Queloz et al. 2001; Bonfils et al. 2013; Zechmeister et al. 2018; Tal-Or et al. 2018; Gomes da Silva et al. 2012). The lack of a linear correlation does not mean that these indicators are not correlated with the RVs, but rather, they often show a more complicated relation, which could be due to being out of phase with the RVs (e.g. Santos et al. 2014; Perger et al. 2017). Usually, indicators display signals at the stellar rotation period or some of its harmonics (Boisse et al. 2011; Schöfer et al. 2019a). However, differential rotation on the photosphere can result in slight variations in the measured rotation period of the star. Complex active region patterns on the stellar surface also alter the frequencies seen in the periodograms, and the limited lifetime of active regions may also impede the detection of signals in long time series (see e.g. Schöfer et al. 2019b). Moreover, signals observed in indicators that trace different types of activity, such as activity in the photosphere or the chromosphere, do not necessarily match exactly. Due to the compound action of all these effects, the behaviour of any given activity indicator can display notable differences between individual stars. Some stars may show activity-related signals in only some indicators but not in others, while in another set of stars, the ‘useful’ indicators may be different.

The aim of this work is to study the behaviour of a set of spectroscopic activity indicators and evaluate their performance for assessing activity signals. We want to determine if there is any relation between their performance and the properties of the target stars, with the goal of finding which indicators work best for stars with certain properties. For this purpose, we used indicators from a sub-sample of the CARMENES M dwarfs and studied their time series. In Sects. 2 and 3 we present the sub-sample of selected targets, and the observations and parameters analysed. Sections 4 and 5 describe the methodology we followed to analyse the time series data and the results obtained, respectively. In Sect. 6 we evaluate the performance of the indicators and we discuss possible detection biases in Sect. 7. We study the relation between the detected activity signals and the RV scatter in Sect. 8, and with the stellar rotational velocity in Sect. 9. We conclude in Sect. 10 with a summary of our work.

2 Stellar sample

2.1 CARMENES GTO sample and previous studies on it

We used observations obtained with the CARMENES instrument (Calar Alto high-Resolution search for M dwarfs with Exo-earths with Near-infrared and optical Echelle Spectrographs, Quirrenbach et al. 2016, 2018) as part of its main survey (guaranteed-time observations– GTO program). CARMENES is installed at the 3.5 m telescope at Calar Alto Observatory in Almería, Spain, and consists of a pair of cross-dispersed, fibre-fed echelle spectrographs with complementary wavelength coverage, which allow simultaneous observationsin the visual and the near-infrared wavelength range. The visual (VIS) channel covers the spectral range λ = 5200–9600 Å at a resolution of R = 94 600, with an average sampling of 2.5 pixels per spectral element, and the near-infrared (NIR) channel covers the range λ = 9600–17 100 Å at a resolution of R = 80 400, and has an average sampling of 2.8 pixels per spectral element. The CARMENES survey has been ongoing since 2016. It monitors over 300 M dwarfs across all spectral subtypes with the main goal of detecting orbiting exoplanets (Reiners et al. 2018).

The CARMENES GTO sample has been previously used to study activity in M dwarfs. Tal-Or et al. (2018) analysed correlations between RV and activity indicators, focusing on stars with large variability in the RVs (RV scatter ≥10 m s−1), the so-called ‘RV-loud’ sample. Of the 31 stars in the RV-loud sample, about a third showed significant anti-correlations between theRVs and the CRX, while for another 20%, there was a marginal detection of an anti-correlation. For the Hα line and the differential line width (dLW, an indicator that measures changes in the width of the absorption lines), the authors excluded the existence of linear correlations with the RVs, although more complex relations could exist (as shown in e.g. Zechmeister et al. 2018).

Schöfer et al. (2019a) computed and studied the temporal variability and the correlations of chromospheric indicators and photospheric absorption band indices in almost the whole CARMENES GTO sample, over 300 M dwarfs. They identified 15 stars (out of the 133 stars with known rotation period longer than 1 d) with a significant signal related to the rotation period in more than two indicators. The indicators that were most likely to vary with the stellar period were those measured from the Hα line and one of the Ca II infrared triplet (Ca IRT) lines, as well as the ones measured from the photospheric titanium oxide bands at 7050 and 8430 Å. Fuhrmeister et al. (2019) computed chromospheric indices in a slightly different way than Schöfer et al. (2019a) and used them to look for activity-related periodicities in 16 early M dwarfs (M0–M2). Their results agree with those of Schöfer et al. (2019a): they find similar periodicities, and of the different chromospheric lines tested, the most useful ones are the Hα line and the Ca IRT lines. More recently, Schöfer et al. (2019b) performed an in-depth study of four stars in which different chromospheric lines and photospheric absorption bands display significant activity-related periodicities. The analysis of different indicators measured over time indicates changes in the surface feature distribution of the stars, which make the indicators vary with different harmonics of Prot depending on the observation time.

2.2 Targets used in this work

Here, we expand on previous studies by investigating several activity indicators using data from the CARMENES VIS observations from GTO. To ensure the reliability of our analysis we selected targets having at least 40 observations in the VIS channel, excluding 18 known binaries (Cortés-Contreras et al. 2017; Baroch et al. 2018). A preliminary search for periodic signals related to the stellar rotation period in the GTO data revealed that six stars with less than 40 measurements showed strong signals in the periodogram of RV and/or spectroscopic activity indicators. To increase the number of stars in the sample, we therefore included these stars in our analysis, bringing our final sample to 98 targets. These six additional stars have 19–39 observations (27 on average), and are active stars or have well-defined Prot. We would expect to find the same kind of activity signals if more observations were available, so considering them in the sample should not bias our results.

Compared to the previous studies mentioned above, our sample includes 8 of the total 31 RV-loud stars, for which correlations between RV and activity indicators (CRX, dLW, and Hα index) were previously analysed by Tal-Or et al. (2018). The rest of RV-loud stars were not considered here because of their low number of observations. Most stars showing large RV scatters, that is, RV-loud stars, were discarded from the GTO survey after about 11 observations. Schöfer et al. (2019a) studied chromospheric indicators in 96 of the 98 stars in our sample. The two new stars in our sample not included in Schöfer et al. (2019a) are J20451-313 (AU Mic, GJ 803), whose observations started after that work was accepted, and J18198-019 (HD 168442, GJ 710), which has spectral type K7 and therefore is not always considered as part of the GTO sample of M dwarfs. In this work, instead of focusing on the correlation between the indicators, we perform a time-series analysis, and include, in addition to the indicators mentioned above, three measurements from the CCF profile. Moreover, we use a more up-to-date GTO data release, which in most cases includes more observations per star.

Table A.1 shows the main properties of the selected stars. Histograms of the spectral type, stellar mass, average activity level, RV scatter, rotational velocity, rotational period (mostly photometric measurements), apparent brightness, and number of observations are shown in Fig. 1. All values are obtained from the latest internal release of Carmencita,the CARMENES input catalogue (Alonso-Floriano et al. 2015; Caballero et al. 2016), except for the RV scatter, which we compute from the CARMENES measurements. Figure 2 shows the activity level of our sample as a function of the stellar mass. The selected stars cover most of the M spectral subtypes, from M0 to M8 V, plus one late-K type dwarf, but most of them have early and mid M spectral subtype. The mass measurements are computed also from CARMENES observationsand other data sets as in Schweitzer et al. (2019). The sample also covers a wide range of activity levels. To quantify the average activity level of the stars, we used measurements of the pseudo-equivalent width of the Hα line (pEW′(Hα)) computed from a coadded stellar template as in Schöfer et al. (2019a), instead of averaging the pEW′ (Hα) measurements of individual observations. The templates for each star are built with the serval pipeline (Zechmeister et al. 2018), which co-adds the different observations of the star. The average pEW′ (Hα) goes from ~ 0.2 to − 10 Å, however, the majority of stars are considered Hα inactive (71 of them having pEW′(Hα) ≥ −0.3 Å, and of these, 42 have pEW′(Hα) ≥ 0 Å). Since the pEW′(Hα) values were measured from coadded templates of the same CARMENES observations that we are using in our analysis, they should accurately reflect the activity observed in our data.

A total of 61 stars have a previously measured rotation period, ranging from ~ 1 to 163 d, which mostly comefrom photometric measurements (Díez Alonso et al. 2019; Newton et al. 2016). Most of these are concentrated towards ~ 3 d (for the most active stars, all with pEW′(Hα) ≤ −2 Å) and ~ 30−40 d, and only 18 stars have Prot larger than 50 d. Stars with unknown Prot are scattered throughout the activity-mass space, but most of them are likely small-amplitude, slow rotators.

3 Data: RVs and activity parameters

To analyse the presence of activity signals, we used RVs and several activity indicators derived from the CARMENES VIS observations: three parameters derived from the CCF profile (FWHM, contrast, and BIS), CRX, dLW, and indices derived from four lines that show chromospheric emission. We describe these parameters in the following subsections.

3.1 RV

RVs from the VIS channel were obtained with the template-matching pipeline serval (Zechmeister et al. 2018), which computes the RV of a set of observations by performing a least-squares fit with a high S/N template built from the observations themselves. The RVs have been corrected for barycentric motions, secular acceleration, instrumental drifts, and nightly-zero points (Trifonov et al. 2018; Tal-Or et al. 2019).

3.2 CCF profile: FWHM, contrast, and BIS

Distortions common to the majority of the photospheric absorption lines are reflected in the CCF profile, and can be studied with different parametrisations of the CCF. We analysed the FWHM, contrast, and BIS of the CCF, computed with the raccoon code as explainedin Lafarga et al. (2020). The CCFs of the targets are computed with different weighted binary masks depending on the star spectral subtype and rotational velocity. The masks are created from high S/N stellar templates built from CARMENES observationswith serval. The resulting CCFs are fitted with a Gaussian, from which we measure the FWHM and contrast. The BIS is computed directly from the CCF profile as the difference between the average velocity of the top region of the CCF (from 60 to 90%) and the average velocity of the bottom region (from 10 to 40%), as in Queloz et al. (2001).

thumbnail Fig. 1

Distribution of the spectral type (top left), stellar mass (top right), mean activity level (pEW′ (Hα) average measured from the serval template, second row left), RV scatter (measured as the standard deviation of the serval VIS RVs, second row right), rotational velocity (v sin i, third row left), rotation period (Prot, third row right), J magnitude (bottom left), and number of observations (# obs, bottom right) of the 98 selected stars. Only 61 stars have a known Prot to date. All values compiled from Table A.1.
thumbnail Fig. 2

Average activity level (measured as the pEW′(Hα) of the serval template, in linear scale between −0.1 and 0.1, and logarithmic scale otherwise) as a function of the stellar mass of the 98 selected stars. The data points are colour-coded with the target rotation period Prot (grey points indicate targets with unknown Prot), and their size is given by the number of CARMENES VIS observations (with all the stars with more than 150 observationshaving the same size). We have indicated the name of several stars for reference. All values compiled from Table A.1.

3.3 CRX and dLW

We also used the CRX and the dLW values computed by the serval pipeline, both parameters as defined in Zechmeister et al. (2018; as mentioned above, see Tal-Or et al. 2018, for an analysis of the correlations between these indicators and RV). The CRX measures variations in the RV across the observed wavelength range. The dLW accounts for differential changes in the line widths of the observed spectrum compared to the spectral template. Indicators such as dLW, FWHM, or contrast can be affected by instrumental effects such as changes in the instrument profile, sky background (e.g. contamination by light scattered by clouds or the Moon, especially on observations of faint targets), or an artificial broadening of the lines due to barycentric motion during a long exposure.

3.4 Chromospheric emission lines: Hα and Ca IRT

To probe chromospheric activity, we used measurements of the core emission flux of the Hα line (6564.60 Å vacuum wavelength) and the Ca IRT lines (with vacuum wavelengths at 8500.35, 8544.44, and 8664.52 Å). Initially, we analysed both their I index computed as in Zechmeister et al. (2018) and pseudo-equivalent width pEW’ computed as in Schöfer et al. (2019a). The I index is defined as the ratio of flux around the centre of the line to the flux in reference bandpasses on either sides of the line (e.g. Kürster et al. 2003). The pseudo-equivalent width pEW’ measures the equivalent width of the line with respect to a pseudo-continuum region, normalised by the spectrum of a non-active star in order to remove photospheric contributions (e.g. Young et al. 1989; Montes et al. 1995). Following Schöfer et al. (2019a), a non-active star per spectral subtype has been used to compute the pEW’ values. Due to this spectral subtraction, pEW’ measurements represent an absolute measure for the (excess) emission, and is most useful when comparing different stars. Equivalent widths and line indices are closely related, as both quantities measure the integrated flux of the lines. We observe that, for the four lines under consideration, the two types of measurements show in general a similar behaviour. Therefore, to simplify our analysis, we chose to only use the I index. In the following, instead of using, for instance, IHα for the Hα index, we refer to this measurement simply as ‘Hα’ for the Hα line, and as ‘Ca IRT-a’, ‘Ca IRT-b’, and ‘Ca IRT-c’ for the three lines of the Ca IRT.

4 Time-series analysis

4.1 Periodogram analysis

For each of the selected stars, we computed the generalised Lomb-Scargle (GLS) periodogram (Zechmeister & Kürster 2009) of the time series of the RVs and the activity indicators mentioned in Sect. 3. We sampled frequencies from the inverse of the time span of the measurements of each star to 1 d−1, since the shortest known Prot of the sample starsis ~1 d. Within these limits, we used a frequency grid that approximately oversamples each peak with 10 points, to make sure that the grid is fine enough to recover all significant peaks without adding a significant amount of computing time. To assess the significance of the power of the periodogram peaks, we used the false alarm probability (FAP) computed with the analytical approximation proposed in Baluev (2008).

In each time series, we discarded observations with low S/N (average S/N per pixel < 5 around 7456 Å). We also removed outliers (values that deviate from the mean of the corresponding time series by more than 3 times their standard deviation, i.e. 3σ clipping), and data points with large error bars (also applying a 3σ clipping on the uncertainties), to avoid including in the analysis observations obtained during flare events, which can strongly affect the measured RVs and spectroscopic indicators (see e.g. Reiners 2009). On average, for each star, this process removed less than 5 observations.

All the data sets were corrected for long-term trends (using a linear model) to avoid biases due to long-term magnetic cycles or wide-orbit sub-stellar companions present in the RVs. Some of the stars in the sample are known to host planets. We did not remove the planetary signals, so the RV periodograms may reflect those signals, alongside those related to activity. We also averaged all measurements obtained during the same night.

4.2 Detection of activity-related signals

Periodograms reflect the convolution of the power spectrum of the true signals present in the data with the window function of the data. This means that each frequency f can show an alias at f + nfW, where n is an integer, and fW represents a typical sampling frequency (a strong feature in the window function). For ground-based observations, this typically results in 1-day (actually, one sidereal day, 0.99726 d) and 1-yr aliases. Harmonics of a specific frequency f can appear for periodic signals that are not strictly sinusoidal and have power at higher harmonics mf, where m is a positive integer. These harmonics can also suffer aliasing effects due to the window function. Moreover, every peak at a frequency f has a corresponding peak at a frequency − f, and both peaks in the positive and negative frequency domain are subject to aliasing. In general, aliases can appear at frequencies falias = |mf + nfW| (Dawson & Fabrycky 2010; VanderPlas 2018; Stock et al. 2020).

Therefore, we looked for significant signals related to the activity of the star, taking into account the presence of aliases and harmonics of the true periods contained in the data. Specifically, we looked for significant peaks at the rotation period of the stars, Prot, and its first two harmonics, 12$\frac{1}{2}$ Prot and 13$\frac{1}{3}$Prot. From previous analyses, we know that, for ground based observations, it is very frequent to find significant peaks at the 1-day alias of Prot, so we also looked for peaks at the regions around the 1-day aliases of Prot and its first two harmonics. For stars with unknown Prot (37 stars), we looked for coincidences between signals in the RVs and the indicators. In case of a significant peak at the same frequency (we considered the same frequency values within ~ 0.01 d−1) in two or more different indicators, we assumed it to be related to the activity of the star.

4.3 Examples

In this section we explain the detection of activity-related signals of five stars as representative examples of the analysis performed. Figures with the time series data of RV and activity indicators, as well as their periodograms, can be found in Appendix B.

4.3.1 Clear signal at known Prot: J07446+035(YZ CMi, GJ 285)

J07446+035is a mid-M dwarf (M4.5 V) with the activity level that counts among the highest in the sample (pEW′(Hα) ~ −7). It has a Prot of 2.78 d (Díez Alonso et al. 2019) and has been observed 51 times with CARMENES. This is a clear example of an active star with a very significant activity-related signal present in the RVs as well as most of the activity indicators, which has been previously studied in Zechmeister et al. (2018); Tal-Or et al. (2018); Baroch et al. (2020); Schöfer et al. (2019b). In Fig. B.1 we show the time series of the RVs and the indicators, the data folded at Prot, the correlation of the indicators with the RV, and the periodogram of each parameter.

The periodograms of RV, CRX, dLW, and the three CCF parameters all show significant (FAP < 0.1%) periodicities at Prot, and a smaller but still significant (with FAP < 0.1% and <10%) signal at 1.56 d, which corresponds to the 1-day alias of the Prot signal. The two highest peaks of the Hα periodogram are at Prot and its daily alias, but they are not significant (FAP > 10%) nor clearly above the rest of the peaks. The Ca IRT lines do not show any clear peak. We do not observe any significant power (FAP < 10%) at 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ nor its alias in any of the parameters. Therefore, for this star, we conclude that only RV, CRX, dLW, FWHM, contrast, and BIS show significant signals at both Prot and its 1-day alias. We also note that for Hα, there is a signal at Prot, but with very low significance.

4.3.2 Multiple signals related to known Prot: J22468+443 (EV Lac, GJ 873)

J22468+443 is another example of a very active (pEW′(Hα) ~ −5) mid-M dwarf (M3.5 V) with a short Prot (4.38 d, Díez Alonso et al. 2019), also previously studied in Tal-Or et al. (2018) and Schöfer et al. (2019b). The latter study finds that the periodicities change over time, indicating significant changes of the surface features. Here we use all the observations available (111 observations, Fig. B.2). The periodograms are more complex than for the case of J07446+035, with signals at both Prot and 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (and their 1-day aliases).

The periodograms of RV, CRX, BIS, and FWHM show their highest peak at 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (FAP < 0.1%), and another much less significant (with FAP between ~1 and 10%), but still very obvious peak at Prot. In contrast, dLW and contrast show their highest peak at Prot (with FAP < 0.1% and 0.1% FAP < 1%, respectively), and a much less significant peak at 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (FAP > 10%). The chromospheric lines have a periodogram with more structure around the peaks. They also display their highest peak at Prot (with 1% < FAP 10%), and we observe no significant power at 12Prot$\frac{1}{2}P_{\mathrm{rot}}$. Additionally, dLW, FWHM, and BIS show another significant peak at 13Prot$\frac{1}{3}P_{\mathrm{rot}}$ (0.1% < FAP < 1% for dLW, and FAP ~10% for FWHM and BIS), and RV and CRX also seem to have some power at this period, although much less significant.

4.3.3 Unknown Prot: J17303+055(BD+05 3409, GJ 678.1 A)

In Fig. B.3 we show an example of an early M dwarf (M0.0 V) with low activity level (pEW′(Hα) ~ 0) and unknown Prot. RV, dLW, FWHM, contrast, and the chromospheric lines show a significant peak at ~ 33.8 d (FAP < 0.1% for FWHM and chromospheric lines, and FAP ~1% for the other indicators mentioned). There is also a peak at ~1.03 d, its 1-day alias, with similar significance. We attribute the long-period peak to the true rotation period, because this is an inactive star with a low rotational velocity (vsini ≤ 2 km s−1, Reiners et al. 2018). BIS shows significant signals at 17.6 d and 1.06 d (FAP ~ 1%), which are close to 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ and its 1-day alias. CRX does not show any significant peak (no peaks with FAP < 10%).

4.3.4 Clear but formally non-significant signals: J20451-313 (AU Mic, GJ 803)

J20451-313 is an active (pEW′(Hα) ~ −2), early M dwarf (M 0.5 V) with a Prot of 4.84 d (Messina et al. 2011), for which two transiting planets have been recently announced (Plavchan et al. 2020; Martioli et al. 2021). We see clear peaks at either Prot or 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (and their 1-day aliases) in the RVs and all the indicators (Fig. B.4). However, for CRX, dLW, Hα, and Ca IRT-a, the peaks have low significance, FAP > 10%. Since these peaks are clear, isolated, and above the rest of the peaks present in the periodogram, we still consider those as probably activity-related signals, although in our final analysis, we only consider peaks with FAP < 10%.

4.3.5 Long Prot: J03133+047 (CD Cet, GJ 1057)

Low-activity stars tend to have long rotation periods that are not well constrained, which complicates their identification in periodograms. J03133+047 is an example of this. It is an M5.0 V star with a low activity level (pEW′(Hα) ~ 0) and a long Prot of ~ 126 d (Newton et al. 2016). It hosts a super-Earth orbiting on a 2.29 d orbit (Bauer et al. 2020).

dLW, FWHM, contrast, Hα, and Ca IRT-b show significant (FAP < 0.1%, except 1% < FAP < 10% for Ca IRT-b), wide peaks around Prot (Fig. B.5). In this case, we chose the peaks closest to the literature Prot value as the activity-related signal. These fall in the range from 137 to 148 d, depending on the indicator. The other indicators show some power close to Prot, but they are less clear and not significant (FAP > 10%). RV also shows some excess power close to Prot and 12Prot$\frac{1}{2}P_{\mathrm{rot}}$. The power at Prot becomes significant if the 2.29 d planetary signal is removed from the RV measurements (see Bauer et al. 2020).

5 Rotation signals in activity indicators

Table 1 shows a summary of the results obtained from the periodogram analysis, where we list the indicators for which we found a significant activity-related signal. We find at least one significant (FAP ≤ 10%) signal in 56 of the 98 stars investigated. In Appendix C, we show the specific results obtained for each indicator. Tables C.1 to C.10 contain, one for each parameter (RV, CRX, dLW, FWHM, contrast, BIS, Hα, and Ca IRT-a,b,c), the periods and FAP of the significant peaks that we identified as being related to stellar activity. Specifically, we show the values of the peaks at Prot, 12Prot$\frac{1}{2}P_{\mathrm{rot}}$, and their 1-day aliases (we do not show the values corresponding to 13Prot$\frac{1}{3}P_{\mathrm{rot}}$ because we only found significant signals for one star, J22468+443, see Sect. 4.3.2).

To visualise which of the indicators show a modulation due to activity depending on the properties of the stars, we plot a summary of the results in Fig. 3. Each panel corresponds to the results obtained for one of the parameters analysed (RVs and the nine activity indicators). All the panels show the average activity level of the selected targets on the y-axis as a function of their mass on the x-axis. We used the same quantities as in Fig. 2: average pEW′(Hα) measured from a template of the CARMENES observations themselves as in Schöfer et al. (2019a), and masses from Schweitzer et al. (2019). In all the panels, each data point corresponds to one of the 98 selected stars. For many targets, we found more than one peak related to activity (at Prot, its harmonics, or 1-day aliases). In the panels, we show the properties of the most significant peak. Different symbols indicate at which frequency the highest peak was found, and their size corresponds to the FAP of that peak, with larger sizes indicating smaller FAPs. Finally, the data points are colour-coded according to the semi-amplitude of the sinusoid corresponding to that peak. This type of representation allow us to see how the different indicators behave depending on the mass and activity level of the stars.

5.1 RV

Of the 56 stars for which we find a signal in any parameter, 44 show significant (FAP ≤ 10%) activity signals in the RVs (25% of them have signals with FAP ≤ 0.1%). In the upper left panel of Fig. 3, we see how they are distributed in the activity-mass space. Most of the stars with a relatively high mass (M ≳ 0.3−0.4 M⊙) and with high activity levels (pEW′(Hα) ≲ −0.3, stars near the top left corner of the panel) show significant (FAP ≤ 0.1%) activity signals at Prot. The only exceptions are J22468+443, for which the most significant peak is at 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (see Sect. 4.3.2), and J15218+209, for which the highest peak is found at the 1-day alias of Prot. Two other targets show slightly less significant signals (0.1% < FAP ≤ 10%) at Prot and its 1-day alias (J18174+483 and J11026+219, respectively). Some of the less massive (M ≲ 0.3 − 0.4 M⊙) but active stars (pEW′(Hα) ≲ −0.3, top right corner of the panel), also show clear signals (with FAPs from ≤ 0.1 to 10%) at either Prot or its 1-day alias, but for seven stars (all with M ≤ 0.2 M⊙ and spectral type later than M5.0 V), we do not observe any significant signal in the periodogram. Six of those seven are some of the faintest stars in the sample (J ≳ 8 mag), and another one (J23419+441), has a long Prot, of ~ 106 d (Díez Alonso et al. 2019). Regarding the stars with low activity level (pEW′(Hα) ≳ −0.3), less than half of the high-mass sub-sample (M ≳ 0.3−0.4 M⊙, bottom left corner of the panel) show clear signals at either Prot or 12Prot$\frac{1}{2}P_{\mathrm{rot}}$. In the low-mass regime (M ≲ 0.3 − 0.4 M⊙, bottom right corner of the panel), almost none of the stars show any signal.

Table 1

Parameters that show an activity-related signal with FAP ≤ 10% (bold-face indicates FAP ≤ 0.1%) of the 56 stars for which we find a detection.

thumbnail Fig. 3

Activity detections in the 98 selected stars for the ten parameters analysed (left to right, top to bottom: RV, CCF BIS, CCF FWHM, CCF contrast, CRX, dLW, Hα, Ca IRT-a, b, and c). Stars are shown as a function of their average activity level (measured as the pEW′ (Hα) of the serval template) and mass. Different markers represent the activity signal with the smallest FAP identified in the periodogram of each star (circles correspond to Prot, hexagons to 1-day Prot alias, squares to 12Prot$\frac{1}{2}P_{\mathrm{rot}}$, diamonds to 1-day 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ alias, and crosses indicate that no activity-related peak was found). Symbol sizes indicate the FAP value of the corresponding peak (larger size means smaller FAP), and the points are colour coded as a function of the semi-amplitude of the best-fitting sinusoid to the corresponding period.

5.2 CRX and BIS

Both CRX and CCF BIS show a similar behaviour (middle panels in the first and second rows of Fig. 3). For these indicators, most of the detections correspond to the most active stars (pEW′(Hα) ≲ −0.3), especially in the high-mass regime (M ≳ 0.3 − 0.4 M⊙). In the active and low-mass regime (pEW′(Hα) ≲ −0.3 and M ≲ 0.3−0.4 M⊙), the situation is similar to the RVs: over half of the targets (including some of the faintest ones) do not show any significant signal. There are some detections for the stars in the low-activity regime (pEW′(Hα) ≳ −0.3), but they arein general much less significant.

5.3 dLW, FWHM, and contrast

CCF FWHM and dLW (right panels in the first and second rows of Fig. 3) show some significant detections across all the activity levels and masses. In the high-activity regime (pEW′(Hα) ≤ −0.3), they show significant detections, mostly at Prot and its 1-day alias, for some of the lowest-mass (M < 0.3 M⊙) stars (six with FAP ≤ 0.1%), for which CRX and BIS do not show signals. About half of the more massive stars show signals (four with FAP ≤ 0.1%). For the low-activity, high-mass stars, we find significant detections, mostly at Prot, in less than half of the targets, in general common to the ones with RV detections. The low-activity, low-mass stars, do not show any signals, as for the RVs, except for two targets, J03133+047 (CD Cet) and J17578+046 (Barnard’s star). These two stars also show significant peaks in the Hα index, but not in the Ca IRT lines. CCF contrast (second row, left panel of Fig. 3) shows a behaviour similar to CCF FWHM, but with slightly lower number of detections and with lower significance.

5.4 Chromospheric lines

In the chromospheric indicators (bottom panels of Fig. 3), we find significant peaks especially in the high-mass, low-activity regime, where most of the stars with detections coincide with the ones that have detections in the RV. About half of the high-activity, high-mass stars also show some activity-related peaks. In the high-activity, low-mass regime, one to four active stars, depending on the chromospheric line, show peaks with very low significance (FAP > 10%), and, except for the two targets mentioned above for dLW and FWHM (J03133+047 and J17578+046), none of the low-activity, low-mass stars show any signals. In general, the four lines show similar results. Differences in the detections could be due to the Ca IRT lines containing a photospheric component, or to telluric contamination, which affects the targets to varying degrees, depending on their absolute RV (Schöfer et al. 2019a).

6 Performance of activity indicators as a function of stellar activity and mass

Given their similar behaviour discussed before, we can group the indicators into 3 categories: (1) CRX and BIS, which trace chromaticity and average line asymmetry, respectively, (2) dLW and FWHM, which trace changes in the width of the stellar absorption lines, and (3) Hα and Ca IRT lines, which are proxies of chromospheric emission. We do not include the contrast because its results were similar to FWHM and dLW, but less significant in general. We also grouped the 56 stars for which we find at least one activity-related signal into four subsets, depending on their activity level (high, pEW′(Hα) ≤−0.3, 22 stars, or low, pEW′(Hα) > −0.3, 34 stars), and their mass (high, M ≥ 0.35 M⊙, 40 stars, or low, M < 0.35 M⊙, 16 stars). Inthe four panels of Fig. 4, we show the performance of these three groups of indicators, together with the detections in the RVs, for each of the four subsets of stars. In each panel, the bins correspond to the four subsets of stars, and the colour code and numbers indicate how many of them show a significant (FAP ≤ 10%) activity signal. As in Fig. 3, we selected the activity-related peak with smallest FAP. Figure 5 shows the same as Fig. 4, but for signals with FAP ≤ 1% and FAP ≤ 0.1%.

6.1 RV

We find significant (FAP ≤ 10%) signals in the RVs for most of the stars (almost 80% of them, especially in the high-activity regime), except for low-mass, low-activity, where only one of the three stars in the bin (the target with the highest mass) shows a signal. The total number of detections decrease if we only consider signals with FAP ≤ 1% (64% of the stars show a detection) or FAP ≤ 0.1% (52% of the stars show a detection), by about the same fraction for each bin, that is to say, we still find more detections for the most active, highest mass stars, and significantly less for the least active, lowest mass ones. Globally, RV variations are the best tracers of stellar activity signals, which implies that nearly always activity signals can be found in RVs, but not always in the activity indicators.

6.2 CRX and BIS

As noted above, CRX and BIS are effective activity tracers for the stars showing the highest activity levels, especially for the ones with the highest mass, where 78% (seven of nine) of the targets in the high-mass high-activity subset show a signal with FAP ≤ 10%. If we restrict the FAP to values ≤1%, the number of stars with signals decreases, especially for the high-activity high-mass subset, where only the four most active targets (44%) show a signal with that significance (this number goes down to three stars, 33% for signals with FAP ≤ 0.1%). Of the low-activity stars, only five out of 34 (16%) show clear signals, all of them in the high-mass regime. For more restrictive FAPs, the number of stars with signals approaches zero: three stars (10%) show a signal with FAP ≤ 1%, and only one star (3%) has a signal with FAP ≤ 0.1%.

Both CRX and BIS seem to trace the same type of activity variability, as we observe the same behaviour in the periodogram analysis and similar correlations with RV. CRX traces RV changes with wavelength, while BIS is sensitive to changes in the average asymmetry in the absorption lines. Both indicators are sensitive to the brightness distribution over the stellar disk, that is, to the presence of active regions. Active regions such as spots create non-uniform weighting of the blueshifted and redshifted wings of the absorption lines, creating asymmetries, and have a larger effect at shorter wavelengths, that is, have a colour-dependence. Therefore, both BIS and CRX (and RV) show similar variations. Furthermore, since BIS quantifies the RV difference between the upper and the lower part of the CCF, it should be sensitive to differences between lines formed at different photospheric heights, lines with different depths. Opacity is higher at shorter wavelengths, so lines in the blue part of the spectrum are formed at larger photospheric heights than those in the red. This means that there should be a dependence on the line depth with wavelength, so that the BIS would be tracing a chromatic effect as the CRX does.

thumbnail Fig. 4

Number of stars with activity detections in RV (top left), CRX and BIS (top right), dLW and FWHM (bottom left), and chromospheric lines Hα and Ca IRT-a,b,c (bottom right). The stars are divided into four bins, depending on their average activity level and mass. Axes are the same as in Fig. 3. The colours of each bin indicate the number of stars (in percentage) for which we found an activity-related signal with FAP ≤ 10%. The text in each bin also shows that percentage, together with the absolute number of stars that have such a detection. The title of each panel shows the same numbers, but for all the stars (i.e. for the four bins together). Grey data points indicate the position of the 56 stars considered in the activity-mass space, with large circles representing the stars with a detection in the specific indicator, and crosses, stars with no detection.

6.3 Chromospheric lines

Chromospheric lines show the opposite behaviour as CRX and BIS. We find significant (FAP ≤ 10%) signals in most (almost 90%, 30 targets) of the stars with low activity levels, and in less than half of the most active ones (eight stars out of 22, 36%). The signals in most of the low activity stars are all highly significant, since all but two of the total 30 have FAP ≤ 0.1%. In the high-activity regime, the number of detections decreases with more restrictive FAPs, where only four stars show signals with FAP ≤ 1%, and of these, only three with FAP ≤ 0.1%. Regarding the mass, we detect a periodic signal in the chromospheric lines more often in the most massive stars, similarly to RV, and CRX and BIS.

6.4 dLW and FWHM

We find that dLW and FWHM perform better for the high-activity, low-mass stars, with signals with FAP ≤ 10% in 77% of them (and of these, still 62% have FAP ≤ 1% and FAP ≤ 0.1%). None of the other indicators (except RV) has that many significant signals in this regime. dLW and FWHM show significant signals for about half of the targets in the three other subsets: 56% for the high-activity high-mass stars, 55% for the low-activity high-mass stars, and 67% for the low-activity low-mass ones. These numbers slightly decrease when considering FAP ≤ 1% or FAP ≤ 0.1%, but the proportion between subsets remains more or less constant.

6.5 Overview

About half of the stars in the sample show clear activity signals in the RVs, especially the most active ones. Of the differentindicators analysed, we find that they behave differently depending on the mass and activity level of the target star. CRX and BIS work best for the most active stars, while the chromospheric lines Hα and Ca IRT are the most effective in tracing activity in targets with lower activity levels. dLW and FWHM behave similarly in all mass and activity regimes, but are especially useful for the most active and least massive stars.

We find that 50–80% (30–60%) of the stars with a high activity level show signals with FAP ≤ 10% (FAP ≤ 1% and ≤ 0.1%) in photospheric indicators (CRX, BIS, dLW, and FWHM), depending on the mass regime. For the most massive stars, CRX and BIS work best, with signals in about 80% of the targets. The other photospheric indicators (dLW and FWHM) and the chromospheric lines (Hα and Ca IRT) show signals with FAP ≤ 10% in about 50% of these stars (30–40% for FAP ≤ 1% and ≤ 0.1%). For the least massive stars, the most effective indicators are dLW and FWHM, with FAP ≤ 10% signals in over 75% of the targets (and about 60% for FAP ≤ 1% and ≤ 0.1%), followed by CRX and BIS, with signals in about 50% of them for FAP ≤ 10% and FAP ≤ 1% (40% of stars for FAP ≤ 0.1%). Only a third of these stars show signals in the chromospheric lines, all of them with large FAPs (~10%).

Regarding stars with low activity levels, most of them (~ 90% in the high-mass, and almost 70% in low-mass regime) show very significant activity signals (FAP ≤ 0.1%) in chromospheric indicators. About half of them (~50% high-mass, and 70% low-mass stars) also show signals in dLW and FWHM (most of them very significant, with FAP ≤ 0.1%). Finally, CRX and BIS indicators are not effective in tracing activity in these low activity stars, with detections in about ~ 15% of the most massive stars (most of them with relatively large FAPs, 10–1%), and none in the low-mass regime.

These results clearly show the need to use different indicators to assess the presence of activity in RV measurements depending on the characteristics of the target star. Failing to use the adequate indicators may result in RV signals classified as ‘planet detections’ that are actually false positives. It follows that it is possible to rule out the existence of planets that have only been cross-checked with a limited set of indicators (e.g. Feng et al. 2020). To show a specific example, the unrefereed manuscript Tuomi et al. (2019) claim the existence of two planets in the very active (pEW′(Hα) ~ −7.2), late-type (M6.0 V) star J10564+070 (CN Leo, GJ 406) based on RV data obtained with the HARPS (23 observations, Mayor et al. 2003) and HIRES (41 observations, Vogt et al. 1994) high-resolution spectrographs. One of the claimed planet candidates is a hot super-Earth in a ~2.68 d period orbit. The analysis of different spectroscopic activity indicators, CCF BIS and FWHM from the HARPS data, Ca II H&K S-index from both HARPS and HIRES, and photometric time series from ASAS (Pojmanski 1997), results in no significant periodicities related to the planet orbital period. Therefore, the authors conclude that the 2.68 d signal has no stellar origin. However, we have just seen that in active and low-mass stars such as this one, the chromospheric lines tend to not show activity signals, and other indicators such as CRX and BIS, or dLW and FWHM work better. In this case, CARMENES observations (see Fig. B.6) show a clear and strong (FAP < 10−13) signal at 2.71 d in the CRX data, which was not analysed in Tuomi et al. (2019; we note here that HARPS observes in a different wavelength range than CARMENES, and that indicators such as CRX or BIS could depend on the wavelength band used). This clearly points at a stellar origin for this signal. There are weaker activity-related periodicities in dLW and BIS, and none in the chromospheric lines. Moreover, Díez Alonso et al. (2019) identified the rotation period of the star to be ~ 2.7 d from photometric time series. Overall, the findings presented here strengthen the notion that caution should be exercised when vetting RV planet candidates, and that a complete activity indicator analysis needs to be performed.

thumbnail Fig. 5

Same as Fig. 4, but for signals with FAP ≤ 1% (top) and FAP ≤ 0.1% (bottom).

7 Detection biases

We selected stars with on average more than 40 observations and spanning several nights so that a peridogram analysis of their activity indicators could reveal information related to rotation, which has a time scale of days. Despite that, there are still several reasons explaining why we do not observe signals in some of the stars.

We find activity-related signals in 56 of the 98 selected stars. In Fig. 6 we show the average activity of the stars and their mass, as a function of their brightness, and we indicate for which targets we found a detection (with FAP ≤ 10%) in any of the indicators. In general, stars for which we find no detections have low activity levels, and are distributed across the entire mass range. Of the 71 stars in the low-activity regime (pEW′(Hα) ≳ −0.3), 53% (37 stars) show no detection in any parameter. This number increases if we focus only on the low-mass, low-activity regime (M ≲ 0.3 M⊙, ~ 13 stars), where only three stars show a detection: J07274+052 (Luyten’s star), J17578+046 (Barnard’s star), and J03133+047 (CD Cet). These are well-studied stars with planetary companions (see, respectively, Astudillo-Defru et al. 2017; Ribas et al. 2018; Bauer et al. 2020) and long rotation periods (Prot ≳ 100 d). Since the main aim of the CARMENES survey is to find and characterise exoplanets, these targets have been observed more frequently than other similar stars, which could explain why we have a detection. Of the most active stars (pEW′(Hα) < −0.3, 27 stars), only 19% (five stars) show no detections (J14321+081, J18482+076, J19169+051S, J23351-023, and J23419+441). They are low-mass (M ≤ 0.17 M⊙) stars, and four of them are at the faintest end of the sample (J ≥ 8.8 mag), which implies less precise measurements. The fifth star (J23419+441) is brighter (J ~ 6.9) but shows a long Prot (~ 106 d). These five targets have between 47 and 99 observations.

Clearly, for the least active stars, signals induced by activity can be below the noise floor of our measurements, making them impossible to detect. Also, stars with lower activity levels show longer rotation periods. In general, the observations of each star in the sample cover relatively long time spans, of ~ 1000 d, and most of the targets have been observed between 50 and 130 times. However, in stars with long Prot, this may not always sufficiently sample the rotational modulation so that a significant signal appears in the periodogram. As mentioned above, another observational constraint is the apparent brightness of the stars, which results in observations with lower S/N. Therefore, activity signals could be hidden in the noise. The faintness of some stars at the low-mass end of the sample could be impeding activity detections, and the combination of a relatively small number of observationsand long rotation periods could be a problem when looking for activity signals in the least active targets.

Aside from the overall S/N of the spectra, our ability to detect activity-related signals in different types of stars could also be limited by other stellar properties. CRX measurements may vary depending on the stellar temperature, since for the coolest stars, the RV information is contained in a shorter wavelength range than earlier type M dwarfs, making stellar colour more relevant than brightness. The shape of photospheric absorption lines, which depends on spectral type, can also differently affect the indicators derived from the line profiles.

The average activity level of the stars may vary with time as a result of a long-period magnetic cycle. Some of the stars could have been observed at a low-activity phase of the cycle, which would decrease the level of the activity signals, making them more difficult to detect. Also, some stars have groups of observations separated by several months, and we could be combining epochs with very different activity levels, which could also reduce the significance of the signals.

The inclination of the stellar rotation axis with respect to our line of sight also plays a role in the total amplitude of the activity signals. In stars with nearly pole-on inclination, visible active regions do not appear and disappear as the star rotates. This results in smaller-amplitude modulations, which again makes them more difficult to detect. For perfectly pole-on configurations, in principle Prot cannot be measured. However, pole-on configurations are unlikely, and statistically should only occur for a small fraction of the targets. The distribution of active regions also affects the amplitude of activity modulations. Similarly to the case of a pole-on configuration, stars with a homogeneous distribution of active regions on their surface may displaysignals with smaller amplitudes. We also do not expect a clear modulation in the case of large polar spots common in fast-rotators, for stars with edge-on inclinations (e.g. Schüssler & Solanki 1992; Piskunov & Wehlau 1994; Yadav et al. 2015). Complex activity patterns on the stellar surface may induce signals that are not exactly at Prot, but at its harmonics (e.g. Boisse et al. 2011), although we tried to account for that. Stars can also have differential rotation, which can make the very definition of Prot fuzzy. Also, active regions could have short life-spans. The fact that we are able to identify activity-related peaks in the periodograms of several sample stars could indicate persistent active region patters on these stars. Changes in the activity surface patterns on a time scale shorter than the total time span of the observations could hamper the detection of a coherent signal related to Prot.

thumbnail Fig. 6

Average activity level (pEW′(Hα)) as a function of the mass of the 98 sample stars, colour-coded with the J magnitude. Large data points indicate that a signal (FAP ≤ 10%) related to the activity of the star was found in at least one parameter, while small data points indicate non-detections. Stars with no known planetary companions are indicated with circles, while those with confirmed planetary companions are indicated with triangles.

8 RV jitter-activity relation

Next, we analyse the RV scatter of the 98 stars in the sample. Figure 7 shows the relation between the RV scatter (measured as the standard deviation of the RV, std RV), the average activity level (measured as the average pEW′(Hα)), and the stellar mass of the 98 stars in the sample. We also indicate the presence of planetary companions, and whether we detected any kind of activity-related signal in any of the parameters studied. We did not remove RV variations induced by planetary companions, so the RV scatter of stars identified as having planets is only an upper limit to the RV variation caused by activity.

8.1 High-activity stars

In the high-activity regime (pEW′(Hα) ≲ −0.3, 27 stars), the RV scatter increases with the average activity level of the stars, from values ~ 2 m s−1 to over 100 m s−1. Of these 27 stars, 11 have RV scatter ≲ 10 m s−1. They correspond mostly to low-mass stars (ten of them, i.e. 90%, have masses < 0.4 M⊙). We note that, according to our definition of active stars (Hα in emission), most low-mass stars are active. In the other 16 targets with std RV > 10 m s−1, the mass distribution is approximately equally divided between low masses (nine stars, 6%, with M < 0.4 M⊙) and high masses (seven stars,4%, with M ≥ 0.4 M⊙).

For most of these 27 stars, we were able to identify an activity-related signal in at least one of the indicators. As mentioned above (Sect. 7), there are five targets with no detections, which have low mass, are faint, or have a long Prot, which couldimpact on the possibility of detecting a signal. From Fig. 3 (top left), we also see that the RV semi-amplitudes of the stars for which we find activity signals are, in general, large (≳ 10 m s−1).

8.2 Low-activity stars

In the low-activity regime (pEW′(Hα) ≳ −0.3, 71 stars), most of the stars have low RV scatter, ≤ 10 m s−1. There are two outliers, J11417+427 (Ross 1003, GJ 1148) and J22096-046 (BD-05 5715, GJ 849), with larger RV scatter, which contain the modulation due to large planetary companions (see e.g. Trifonov et al. 2018; Butler et al. 2006, respectively). Here, 26 of the stars have M < 0.4 M⊙ and 45 stars M ≥ 0.4 M⊙. As for the high-activity regime, we find that lower RV scatter values correspond in general to the lowest mass stars, while most of the highest mass stars show larger RV scatter. Specifically, of the 33 targets with RV scatter ≤ 3 m s−1, 20 (~ 60%) have M < 0.4 M⊙, while in the 38 stars with RV scatter > 3 m s−1, only six (~16%) have M < 0.4 M⊙. This is clearly observed in the right panel of Fig. 7, where we see that the RV scatter decreases with the stellar mass. This difference in RV scatter between higher- and lower-mass M dwarfs could hint at varying manifestations of stellar variability, such as different surface granulation, active regions, or dynamo mechanisms.

Regarding activity detections, we identify signals in almost half (34 of the 71 stars, 48%) of these low-activity stars. Most of the targets with detections have RV scatter > 3 m s−1 (26 of the total of 34 stars, ~ 76%). In the group of stars with RV scatter ≤ 3 m s−1, only eight of the 33 targets (~24%) show reliable detections (J01025+716, J17578+046, J13299+102, J23492+024, J07274+052, J11511+352, and J00183+440). These eight targets all have a large number of observations, ≥ 50 (seven of them with > 110 observations), while the majority of the remaining targets with std RV ≤ 3 m s−1 and no detections have been observed significantly less (17 of the other 25 stars, ~ 70%, have <60 observations). All of the seven targets with detections show clear activity signals in their RVs (except for J17578+046, one of the stars with a planet, and J20305+654). For three of them (J07274+052, J11511+352, and J13299+102), the only activity signal found is in the RVs.

8.3 Overview

In summary,our sample stars with low activity levels (pEW′(Hα) > −0.3) show RV scatter from ~2 to 10 m s−1, while for active stars, the scatter can reach values one order of magnitude larger. The RV scatter in the active stars increases with the average activity level, and most active targets show clear periodic signals. Nevertheless, we identify activity signals in almost half of the inactive stars, especially in the ones with the largest RV scatter (std RV > 3).

In both active and inactive stars, the RV jitter shows a gradient with stellar mass. Both low- and high-mass stars show a range of RV scatters, with more active stars showing in general larger scatter values, but we observe that the minimum RV scatter decreases with stellar mass. Despite having in general higher activity levels, stars with lower RV scatters tend to be those of lower masses, while targets with a larger scatter correspond to the most massive ones. This could indicate different manifestations of activity between M dwarfs with high- and low-mass. A relevant implication of these results is that, since lower-mass stars (in general, late-type M dwarfs) show the lowest RV jitter, they may be better targets for planet searches than more massive (earlier-type) M dwarfs, independently of their activity level.

thumbnail Fig. 7

Left: RV scatter (std RV) as a function of the average activity level (pEW′ (Hα)) of the 98 stars in the sample, colour-coded with the stellar mass. Stars with no known planetary companions are indicated with circles, while those with confirmed planetary companions are indicated with triangles. Large data points correspond to the 56 stars for which we find an activity-related signal in any of the indicators, and small data points, stars with no detection. Right: RV scatter as a function of the stellar mass of the 98 stars in the sample, colour-coded with the average activity level (pEW′ (Hα)). Same symbols and sizes as in the left panel.

9 v sin i-activity relation and BIS performance

Measurements derived from the CCF bisector have been found to show significant variations related to activity in stars with large v sini, but do not provide significant information for slow rotators (Saar & Donahue 1997; Desort et al. 2007; Bonfils et al. 2007). The v sini values of the sample stars increase with the average activity level pEW′(Hα) in the high-activity regime. The results presented here show that activity modulation in BIS increases with the average pEW′(Hα) (Fig. 3). Given this behaviour of BIS with pEW′(Hα), we then could expect some correspondence between the detections in BIS and v sini.

Figure 8 (left) shows the average activity level pEW′(Hα) of the 98 sample stars as a function of their vsini, where we indicate the ones that show an activity signal in any of the parameters, and also the ones with a detection in BIS. About 60% of the targets with vsini > 2 km s−1 and an activity detection in any parameter, show a significant detection in BIS (16 out of 26 stars), while for the slower rotators, this number is of only about 13% (four out of 30 stars). This agrees with the fact that bisector measurements are usually found to be useful in fast rotators, and not in slowly-rotating stars.

If we consider the targets with detections in CRX, the other indicator that we find to behave in a way similar to BIS, we obtain comparable results (Fig. 8, right panel). About 45% of the stars with v sini > 2 km s−1 and detection in at least one of the parameters, show a significant detection in CRX (12 out of 26 stars), and about 16% of the slowest rotators show a signal (five out of 30 stars).

If we focus on the low-activity regime (pEW′(Hα) > −0.3), most of the targets have very low vsini, ≤ 2 km s−1, but there are ~10 stars with larger vsini values, up to ~4 km s−1. Half of these outliers show significant signals in BIS (although all with low FAP, see Fig. 3), but none in the CRX. This could indicate that BIS is more sensitive to activity variations in stars with a relatively large v sin i than CRX, at least in the low-activity regime.

10 Summary

We performed a search for activity-related periodicities in a sample of 98 M dwarfs observed with CARMENES. We carried out a periodogram analysis on the time series of their RVs and nine activity indicators: CCF FWHM, contrast and BIS, CRX derived from the RVs, dLW derived from the template matching method used to compute the RVs, and indices measured from four chromospheric lines, Hα and the Ca IRT.

Of the initial sample of 98 stars, we find that 56 of them show a signal that we attribute to activity (i.e. a signal related to Prot) in at least one of the ten parameters analysed. Most of these 56 stars show an activity signal in RV, which is themost effective tracer of activity (i.e. it shows an activity-related signal for most of the stars). Aside from RV, CRX and BIS are the most effective for the active stars in our sample (stars with pEW′(Hα) ≲ −0.3), but they are not as sensitive in the low-activity regime (pEW′(Hα) ≳ −0.3). Low-activity stars tend to be slow rotators, which agrees with the fact that BIS is usually not found to trace activity in such stars. For the chromospheric lines, we observe the opposite behaviour. Low-activity stars show a larger fraction of targets with periodic signals in these indicators than the most active ones. dLW and FWHM are similarly effective for all stars, but especially in the high-activity, low-mass (M ≲ 0.35 M⊙) regime, performing better than any other indicator.

This implies that none of the activity indicators can efficiently trace stellar activity for all stars. Activity in the most active stars tends to be detected in photospheric indicators. CRX and BIS work best for the active, higher-mass (M ≳ 0.35 M⊙) stars, followed by dLW and FWHM, and chromospheric lines. In active, low-mass stars, the most efficient indicators are dLW and FWHM, followed by CRX and BIS. Chromospheric lines are only effective in a small subset of such stars. Most low-activity stars show activity signals in chromopheric indicators, and about half of them also show signals in dLW and FWHM. CRX and BIS are not good activity tracers in these stars. From these results it is clear that, when assessing the presence of stellar activity in RV measurements, it is key to take into account the adequate activity indicators, depending on the characteristics of the target star. Even more importantly, an RV signal should not be assumed to be of planetary nature on the basis of only a small set of indicators, as false positives can abound.

Stars for which we detect no signature of activity are located mainly in the low-activity regime, where they account for about half of the sample. In the high-activity regime, stars with no detection are a minority and correspond to faint, low-mass targets. Our inability to detect any activity signals in these stars could be due to the weakness of these signals compared to our measurement precision (in the case of the stars with low activity levels), to complex or changing active region patterns giving rise to incoherent signals, or to observational limitations (observations not covering the rotation phase well enough so that a significant peak appears in the periodogram, or low S/N).

As expected, the RV jitter increases with the average activity level of the stars, especially in the high-activity regime, where the RV scatter (std RV) can reach values as high as ~ 100 m s−1. In the low-activity regime, the scatter is usually lower than ~10 m s−1. In general, lower RV scatter correspond to stars with no detections of signals related to activity. We observe that, independent of the activity level, stars with lower mass are the ones with lower RV scatter, which could be due to different manifestations of stellar activity. This also means that late-type M dwarfs could be better candidates for planetary searches than their earlier-type siblings.

Overall, this study highlights the fact that, depending on the properties of the star considered, different indicators of stellar activity will behave differently. We find that, in a sample of M dwarfs with a relatively large range of masses and activity levels, each type of indicator performs best (is most effective in tracing activity signals) in a specific range of mass and activity. Therefore, analyses such as the one presented here can be used as a guide for studies of activity signals in spectroscopic observations. Nevertheless, the effectiveness of the indicators depends on several factors, from observational constraints to the specific properties of the stellar active regions, so thorough studies of all available indicators should be conducted in conjunction with RV searches for planets.

thumbnail Fig. 8

Left: average activity level (pEW′(Hα)) as a functionof the rotational velocity (vsini) of the 98 stars in the sample, colour-coded with the stellar mass. Stars with activity-related signals (FAP ≤ 10%) in any of the parameters are shown with circles, and stars with no detections with triangles. For the targets with detections, large circles indicate a detection (FAP ≤ 10%) in the BIS. Right: same as the left panel, but for the CRX instead of the BIS.

Acknowledgements

We thank the anonymous referee for the very helpful review of the article. CARMENES is an instrument for the Centro Astronómico Hispano-Alemán de Calar Alto (CAHA, Almería, Spain). CARMENES is funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Científicas (CSIC), the European Union through FEDER/ERF FICTS-2011-02 funds, and the members of the CARMENES Consortium (Max-Planck-Institut für Astronomie, Instituto de Astrofísica de Andalucía, Landessternwarte Königstuhl, Institut de Ciències de l’Espai, Institut für Astrophysik Göttingen, Universidad Complutense de Madrid, Thüringer Landessternwarte Tautenburg, Instituto de Astrofísica de Canarias, Hamburger Sternwarte, Centro de Astrobiología and Centro Astronómico Hispano-Alemán), with additional contributions by the Spanish Ministry of Economy, the German Science Foundation through the Major Research Instrumentation Programme and DFG Research Unit FOR2544 “Blue Planets around Red Stars”, the Klaus Tschira Stiftung, the states of Baden-Württemberg and Niedersachsen, and by the Junta de Andalucía. Based on data from the CARMENES data archive at CAB (INTA-CSIC). We acknowledge support from the Spanish Ministry of Science and Innovation and the European Regional Development Fund through grant PGC2018-098153-B-C33, the Generalitat de Catalunya/CERCA programme, PID2019-109522GB-C51/2/3/4 (CAB, IAA, IAC, UCM), and UKRI FLF grant MR/S035214/1. SVJ acknowledges the support of the DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets (JE 701/5-1).

Appendix A Targets

Table A.1

Properties of the 98 selected stars.

Appendix B Periodogram analysis examples

thumbnail Fig. B.1

RV and indicator time series (left), data folded at Prot (middle left), correlation with the RV (middle right), and periodogram (right) of J07446+035 (YZ CMi, GJ 285). The parameters are, from top to bottom: corrected serval RV, CRX, dLW, CCF FWHM, CCF contrast, CCF BIS, Hα index, and Ca IRT-a index. We only show the first IRT line because the other two show very similar time series and periodograms with no significant signal. Each time series is corrected for a linear trend, and the periodograms are computed on nightly-averaged observations. Data points are colour-coded with the rotation phase, and outliers not considered are marked in grey (some outliers may be outside the data range shown). The text in the time series panels shows the standard deviation of the data (std) and the slope of the linear trend that is subtracted from the data (only slopes with absolute values ≥ 0.001). The text in the correlation panels indicates the Pearson correlation coefficient of the data (R). In the periodogram panels, horizontal grey lines indicate the FAP level at 10% (dotted), 1% (dashed), and 0.1% (dotted dashed), and coloured shaded regions indicate the location of Prot (blue), 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (yellow), and their 1-day aliases (lighter hatched regions).
thumbnail Fig. B.2

Same as Fig. B.1, but for J22468+443 (EV Lac, GJ 873). We now display also the Ca IRT-b and -c databecause they show significant signals. In the periodogram panels, we add a purple shaded region around 13$\frac{1}{3}$ Prot (and its corresponding 1-day alias indicated by a hatched purple region).
thumbnail Fig. B.3

Same as Fig. B.1, but for J17303+055 (BD+05 3409, GJ 678.1 A).
thumbnail Fig. B.4

Same as Fig. B.1, but for J20451-313 (AU Mic, GJ 803).
thumbnail Fig. B.5

Same as Fig. B.1, but for J03133+047 (CD Cet, GJ 1057). In this case, the periodogram shows a zoom in at the low frequency range, where we find activity-related peaks (the planetary companion shows a significant peak in the RVs at 2.29 d = 0.44 d−1, not shown here).
thumbnail Fig. B.6

Same as Fig. B.1, but for J10564+070 (CN Leo, GJ 406).

Appendix C Periodogram analysis results

Table C.1

Activity-related signals (periods and FAPs) at Prot, 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ and their 1 day aliases (1 d alias) found in the periodograms of the serval RVs.

Table C.2

Same as Table C.1, but for CRX.

Table C.3

Same as Table C.1, but for dLW.

Table C.4

Same as Table C.1, but for CCF FWHM.

Table C.5

Same as Table C.1, but for CCF contrast.

Table C.6

Same as Table C.1, but for CCF BIS.

Table C.7

Same as Table C.1, but for Hα.

Table C.8

Same as Table C.1, but for Ca IRT-a.

Table C.9

Same as Table C.1 but for Ca IRT-b.

Table C.10

Same as Table C.1, but for Ca IRT-c.

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All Tables

Table 1

Parameters that show an activity-related signal with FAP ≤ 10% (bold-face indicates FAP ≤ 0.1%) of the 56 stars for which we find a detection.

In the text
Table A.1

Properties of the 98 selected stars.

In the text
Table C.1

Activity-related signals (periods and FAPs) at Prot, 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ and their 1 day aliases (1 d alias) found in the periodograms of the serval RVs.

In the text
Table C.2

Same as Table C.1, but for CRX.

In the text
Table C.3

Same as Table C.1, but for dLW.

In the text
Table C.4

Same as Table C.1, but for CCF FWHM.

In the text
Table C.5

Same as Table C.1, but for CCF contrast.

In the text
Table C.6

Same as Table C.1, but for CCF BIS.

In the text
Table C.7

Same as Table C.1, but for Hα.

In the text
Table C.8

Same as Table C.1, but for Ca IRT-a.

In the text
Table C.9

Same as Table C.1 but for Ca IRT-b.

In the text
Table C.10

Same as Table C.1, but for Ca IRT-c.

In the text

All Figures

thumbnail Fig. 1

Distribution of the spectral type (top left), stellar mass (top right), mean activity level (pEW′ (Hα) average measured from the serval template, second row left), RV scatter (measured as the standard deviation of the serval VIS RVs, second row right), rotational velocity (v sin i, third row left), rotation period (Prot, third row right), J magnitude (bottom left), and number of observations (# obs, bottom right) of the 98 selected stars. Only 61 stars have a known Prot to date. All values compiled from Table A.1.
In the text
thumbnail Fig. 2

Average activity level (measured as the pEW′(Hα) of the serval template, in linear scale between −0.1 and 0.1, and logarithmic scale otherwise) as a function of the stellar mass of the 98 selected stars. The data points are colour-coded with the target rotation period Prot (grey points indicate targets with unknown Prot), and their size is given by the number of CARMENES VIS observations (with all the stars with more than 150 observationshaving the same size). We have indicated the name of several stars for reference. All values compiled from Table A.1.
In the text
thumbnail Fig. 3

Activity detections in the 98 selected stars for the ten parameters analysed (left to right, top to bottom: RV, CCF BIS, CCF FWHM, CCF contrast, CRX, dLW, Hα, Ca IRT-a, b, and c). Stars are shown as a function of their average activity level (measured as the pEW′ (Hα) of the serval template) and mass. Different markers represent the activity signal with the smallest FAP identified in the periodogram of each star (circles correspond to Prot, hexagons to 1-day Prot alias, squares to 12Prot$\frac{1}{2}P_{\mathrm{rot}}$, diamonds to 1-day 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ alias, and crosses indicate that no activity-related peak was found). Symbol sizes indicate the FAP value of the corresponding peak (larger size means smaller FAP), and the points are colour coded as a function of the semi-amplitude of the best-fitting sinusoid to the corresponding period.
In the text
thumbnail Fig. 4

Number of stars with activity detections in RV (top left), CRX and BIS (top right), dLW and FWHM (bottom left), and chromospheric lines Hα and Ca IRT-a,b,c (bottom right). The stars are divided into four bins, depending on their average activity level and mass. Axes are the same as in Fig. 3. The colours of each bin indicate the number of stars (in percentage) for which we found an activity-related signal with FAP ≤ 10%. The text in each bin also shows that percentage, together with the absolute number of stars that have such a detection. The title of each panel shows the same numbers, but for all the stars (i.e. for the four bins together). Grey data points indicate the position of the 56 stars considered in the activity-mass space, with large circles representing the stars with a detection in the specific indicator, and crosses, stars with no detection.
In the text
thumbnail Fig. 5

Same as Fig. 4, but for signals with FAP ≤ 1% (top) and FAP ≤ 0.1% (bottom).
In the text
thumbnail Fig. 6

Average activity level (pEW′(Hα)) as a function of the mass of the 98 sample stars, colour-coded with the J magnitude. Large data points indicate that a signal (FAP ≤ 10%) related to the activity of the star was found in at least one parameter, while small data points indicate non-detections. Stars with no known planetary companions are indicated with circles, while those with confirmed planetary companions are indicated with triangles.
In the text
thumbnail Fig. 7

Left: RV scatter (std RV) as a function of the average activity level (pEW′ (Hα)) of the 98 stars in the sample, colour-coded with the stellar mass. Stars with no known planetary companions are indicated with circles, while those with confirmed planetary companions are indicated with triangles. Large data points correspond to the 56 stars for which we find an activity-related signal in any of the indicators, and small data points, stars with no detection. Right: RV scatter as a function of the stellar mass of the 98 stars in the sample, colour-coded with the average activity level (pEW′ (Hα)). Same symbols and sizes as in the left panel.
In the text
thumbnail Fig. 8

Left: average activity level (pEW′(Hα)) as a functionof the rotational velocity (vsini) of the 98 stars in the sample, colour-coded with the stellar mass. Stars with activity-related signals (FAP ≤ 10%) in any of the parameters are shown with circles, and stars with no detections with triangles. For the targets with detections, large circles indicate a detection (FAP ≤ 10%) in the BIS. Right: same as the left panel, but for the CRX instead of the BIS.
In the text
thumbnail Fig. B.1

RV and indicator time series (left), data folded at Prot (middle left), correlation with the RV (middle right), and periodogram (right) of J07446+035 (YZ CMi, GJ 285). The parameters are, from top to bottom: corrected serval RV, CRX, dLW, CCF FWHM, CCF contrast, CCF BIS, Hα index, and Ca IRT-a index. We only show the first IRT line because the other two show very similar time series and periodograms with no significant signal. Each time series is corrected for a linear trend, and the periodograms are computed on nightly-averaged observations. Data points are colour-coded with the rotation phase, and outliers not considered are marked in grey (some outliers may be outside the data range shown). The text in the time series panels shows the standard deviation of the data (std) and the slope of the linear trend that is subtracted from the data (only slopes with absolute values ≥ 0.001). The text in the correlation panels indicates the Pearson correlation coefficient of the data (R). In the periodogram panels, horizontal grey lines indicate the FAP level at 10% (dotted), 1% (dashed), and 0.1% (dotted dashed), and coloured shaded regions indicate the location of Prot (blue), 12Prot$\frac{1}{2}P_{\mathrm{rot}}$ (yellow), and their 1-day aliases (lighter hatched regions).
In the text
thumbnail Fig. B.2

Same as Fig. B.1, but for J22468+443 (EV Lac, GJ 873). We now display also the Ca IRT-b and -c databecause they show significant signals. In the periodogram panels, we add a purple shaded region around 13$\frac{1}{3}$ Prot (and its corresponding 1-day alias indicated by a hatched purple region).
In the text
thumbnail Fig. B.3

Same as Fig. B.1, but for J17303+055 (BD+05 3409, GJ 678.1 A).
In the text
thumbnail Fig. B.4

Same as Fig. B.1, but for J20451-313 (AU Mic, GJ 803).
In the text
thumbnail Fig. B.5

Same as Fig. B.1, but for J03133+047 (CD Cet, GJ 1057). In this case, the periodogram shows a zoom in at the low frequency range, where we find activity-related peaks (the planetary companion shows a significant peak in the RVs at 2.29 d = 0.44 d−1, not shown here).
In the text
thumbnail Fig. B.6

Same as Fig. B.1, but for J10564+070 (CN Leo, GJ 406).
In the text

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