© ESO 2018

1. Introduction

Stellar activity is a common phenomenon in M dwarfs. In particular, the Hα line is often used as an activity indicator for these stars because it is more easily accessible than more traditional activity tracers used for solar-like stars such as the Ca ii H&K lines. In all but the earliest M dwarfs, the photosphere is too cool to show the Hα line in absorption. Therefore, Hα emission and absorption must stem from the chromosphere. As the level of activity increases, the Hα line first appears as a deepening absorption line, then fills in, and, finally, goes into emission for the most active stars (Cram & Mullan 1979). These latter stars are called active “dMe”, while M dwarfs with Hα in absorption are usually called inactive. M dwarfs with neither emission nor absorption in the Hα line may either be very inactive or medium active; a different activity indicator is needed for a discrimination in this case (see e. g. Walkowicz & Hawley 2009).

Newton et al. (2017) found a threshold in the mass–rotationperiod plane, separating active and inactive M dwarfs. This is in line with Jeffers et al. (2018), who reported that the detection of Hα active stars is consistent with the saturation rotational velocity observed in X-rays by Reiners et al. (2014). The saturation period increases from 10 d for spectral types < 2.5 (Jeffers et al. 2018), to 30–40 d for M3.0 to M4.5 (Jeffers et al. 2018; Newton et al. 2017), and 80–90 d in late-M stars (> 5.0) (West et al. 2015; Newton et al. 2017).

For the more slowly rotating active M dwarfs, where the emission profile is not dominated by rotation, the Hα line can exhibit a complex double peaked profile, which is reproduced by non-local thermal equilibrium chromospheric models (Short & Doyle 1998). Observations additionally often show an asymmetric pattern for which static models cannot account (e.g. Cheng et al. 2006).

The surface of the Sun can be resolved in great detail, and thus numerous reports of solar observations accompanied by broadened and asymmetric chromospheric line profiles exist (e. g. Schmieder et al. 1987; Zarro et al. 1988; Cho et al. 2016; see also the review by Berlicki 2007). While symmetric line broadening can be caused by the Stark effect or turbulence (Švestka 1972; Kowalski et al. 2017b), asymmetric line broadening is sometimes attributed to bulk motion, for example in the form of socalled coronal rain (e.g. Antolin & Rouppe van der Voort 2012; Antolin et al. 2015; Lacatus et al. 2017) or chromospheric condensations (Ichimoto & Kurokawa 1984; Canfield et al. 1990; see also Sect. 6.3). Following previous studies, we use the terms red and blue asymmetry to refer to line profiles with excess emission in each respective part of the line profile.

While red-shifted excess emission is frequently observed on the Sun, blue asymmetries are less often observed in solar flares. In fact, Švestka et al. (1962) found that of 92 studied flares only 23% showed a blue asymmetry, while 80% exhibited a red asymmetry. A similar result was derived by Tang (1983), who reported an even lower fraction of 5% of flares with blue asymmetries.

Other stars are far less intensively monitored with highresolution spectroscopy than the Sun, so that spectral time series of stellar flares often result from chance observations (e.g. Klocová et al. 2017). Also, flares on other stars are generally only observed in disk-integrated light. Nonetheless, also during stellar flares, Hα line profiles with broad wings and asymmetric profiles have been observed (e.g. Fuhrmeister et al. 2005, 2008).

In a systematic flare study of the active M3 dwarf AD Leo, Crespo-Chacón et al. (2006) detected a total of 14 flares, out of which the strongest three showed Balmer line broadening and two also showed red wing asymmetries, with the more pronounced asymmetry for the larger flare. Additionally, the same authors detected weaker red asymmetries during the quiescent state, which they tentatively attributed to persistent coronal rain. Notably, Crespo-Chacón et al. (2006) did not find any asymmetry or broad wings for Ca ii H&K.

During a flare on the M dwarf Proxima Centauri, Fuhrmeister et al. (2011) found blue and red asymmetries in the Balmer lines, the Ca ii K line, and one He I line. A similar observation was made during a mega-flare on CN Leo, where Fuhrmeister et al. (2008) detected asymmetries in the Balmer lines, in two He I lines, and the Ca ii infrared triplet lines. Both studies reported a blue asymmetry during flare onset and a red asymmetry during decay, along with temporal evolution in the asymmetry pattern on the scale of minutes.

Montes et al. (1998) studied the Hα line of highly active binary stars and weak-line T Tauri stars and reported the detection of numerous broad and asymmetric wings in Hα, possibly related to atmospheric mass motion. In a study of two longlasting (>1 day) flares on the RS Canum Venaticorum binary II Peg, Berdyugina et al. (1999) found broad, blue-shifted components in the He I D₃ line as well as many other strong absorption lines. The narrow components of these lines exhibited a red shift. The authors attributed these phenomena to up-and down flows. A blue wing asymmetry during a long duration flare on the active K2 dwarf LQ Hydrae was reported by Flores Soriano & Strassmeier (2017). The blue excess emission persisted for two days after the flare and was interpreted as a stellar coronal mass ejection. Gizis et al. (2013) observed a broadened Hα line during a strong flare on the field L1 ultracool dwarf WISEP J190648.47+401106.8 accompanying amplified continuum and He emission. Therefore, also very late-type objects undergo these type of event. As an example of line broadening on a more inactive M dwarf, we point out the observations of a flare on Barnard’s star by Paulson et al. (2006). During the event, the Balmer series went into emission up to H13 and showed broadening, which the authors attributed to the Stark effect. A marginal asymmetry may also have been present.

All these examples of searches on individual stars or serendipitous flare observations show that M dwarfs regularly exhibit broadened and asymmetric Balmer lines though even strong flares do not need to produce broad components or asymmetries (e.g. Worden et al. 1984). We are not aware of any systematic study of such effects using high-resolution spectroscopy in a large sample of active M dwarf stars. Therefore, we utilise the stellar sample monitored by the CARMENES (Calar Alto high-Resolution search for M dwarfs with Exo-Earths with Near-infrared and optical Echelle Spectrographs) consortium for planet search around M dwarfs (Quirrenbach et al. 2016) to systematically study chromospheric emission-line asymmetries. The CARMENES sample spans the whole M dwarf regime from M0 to M9 and comprises inactive as well as active stars. Since the most active M dwarfs are known to flare frequently, we focus on a sub-sample of active objects, which we consider the most promising sample for a systematic study of chromospheric line profile asymmetries. Specifically, we want to study how often such asymmetries occur, if they are always associated with flares, and if there are physical parameters such as fast rotation that favour their occurrence.

Our paper is structured as follows: in Sect. 2 we describe the CARMENES observations and data reduction. In Sect. 3 we give an overview of our stellar sample selection, and we describe our flare search criterion in Sect. 4. In Sect. 5 we present the detected wing asymmetries and discuss them in Sect. 6. Finally, we provide our conclusions in Sect. 7.

2. Observations and data reduction

All spectra discussed in this paper were taken with CARMENES (Quirrenbach et al. 2016). The main scientific objective of CARMENES is the search for low-mass planets (i.e. super-and exo-Earths) orbiting mid to late M dwarfs in their habitable zone. For this purpose, the CARMENES consortium is conducting a 750-night exo-planet survey, targeting ∼300 M dwarfs (Alonso-Floriano et al. 2015; Reiners et al. 2018). The CARMENES spectrograph, developed by a consortium of eleven Spanish and German institutions, is mounted at the 3.5 m Calar Alto telescope, located in the Sierra de Los Filabres, Almería, in southern Spain, at a height of about 2200 m. The two-channel, fibre-fed spectrograph covers the wavelength range from 0.52 µm to 0.96 µm in the visual channel (VIS) and from 0.96 µm to 1.71 µm in the near infrared channel (NIR) with a spectral resolution of R ∼ 94 600 in VIS and R ∼ 80 400 in NIR.]

The spectra were reduced using the CARMENES reduction pipeline and are taken from the CARMENES archive (Caballero et al. 2016b; Zechmeister et al. 2017). For the analysis, all stellar spectra were corrected for barycentric and stellar radial velocity shifts. Since we were not interested in high-precision radial velocity measurements, we used the mean radial velocity for each star computed from the pipeline-measured absolute radial velocities given in the fits headers of the spectra; the wavelengths are given in vacuum. We did not correct for telluric lines since they are normally weak and rather narrow compared to the Hα line, which is the prime focus of our study. The exposure times varied from below one hundred seconds for the brightest stars to a few hundred seconds for most of the observations, with the maximum exposure time being 1800 s for the faintest stars in the CARMENES sample.

3. Stellar sample

Since line wing asymmetries in Hα have so far been reported primarily during flares, we selected only active stars with Hα in emission. For the selection we used the CARMENES input catalogue Carmencita (Caballero et al. 2016a), which lists Hα pseudoequivalent widths, pEW(Hα), from various sources (see Table 1). The term pseudo-equivalent width is used here since around Hα there is no true continuum in M dwarfs, but numerous molecular lines, defining a pseudo-continuum. We took into consideration all stars with a negative pEW(Hα) in Carmencita and ten or more observations listed in the archive as of 28 February 2017. Since pEW(Hα) values higher than −1.0 Å need not correspond to true emission lines, but are sometimes due to flat or even shallow absorption lines, we visually inspected all such Hα lines in the CARMENES spectra and excluded stars showing absorption lines or flat spectra. Moreover, we rejected one known binary star. There is another star, Barta 161 12, which was listed by Malo et al. (2014) as a very young double-line spectroscopic binary candidate based on observations with ESPaDOnS, and which indeed shows suspicious changes in the Hα line but not in the photospheric lines in CARMENES spectra. Since its Hα profile shows in many cases a more complex behaviour than the other stars (see Sect. 6.10) we excluded it from the general analysis but list it for reference in the tables and the appendix.

We did not exclude stars with an Hα line profile consisting of a central absorption component and an emission component outside the line centre, since we interpret these stars to be intermediate cases with Hα between absorption and emission; the corresponding stars are V2689 Ori, BD–02 2198, GJ 362, HH And, and DS Leo. These selection criteria left us with a sample of 30 stars listed in Table 1, where we specify the Carmencita identifier, the common name of the star, its spectral type, the pEW(Hα), the projected rotation velocity (v sin i), and a rotation period, all taken from Carmencita with the corresponding references.

For technical reasons, such as too low signal-to-noise ratio in the region of Hα, we had to exclude a number of spectra from the analysis. Unfortunately, this affected all spectra of the latest object in our sample, namely LSR J1835+2839, reducing the number of stars in our sample to 28 with a total of 473 usable spectra (not counting Barta 161 12). The final sample then comprised stars with spectral types ranging from M0 through M8, among which the mid M spectral types are the most numerous.

4. Characterisation of the activity state

To assess the activity state of the star for each spectrum we define an Hα index following the method of Robertson et al. (2016). In particular, we use the mean flux density in a spectral band centred on the spectral feature (the so-called line band) and divide by the sum of the average flux density in two reference bands. We use the definition$$I_{\mathrm{line}}=w(1-\frac{\overline{F_{\mathrm{line}}}}{\overline{F_{\mathrm{ref}\mathrm{1}}}+\overline{F_{\mathrm{ref}\mathrm{2}}}}),$$(1)

where w is the width of the line band, and F_line, F_ref1, and F_ref2 are the mean flux densities in the line and the two reference bands. Our definition slightly differs from that of Robertson et al. (2016). For equidistant wavelength grids, which are an accurate approximation for the spectra used in our study, the index I_Hα can easily be converted into pEW(Hα) by the relation pEW(Hα) = 2I_Hα − w and, therefore, carries the same information content. In I_Hα, the transition between absorption and emission occurs at 0.5 w. According to its definition, changes in I_Hα can be caused by variations of the line, a shift in the continuum level, or both.

For the definition of the width w of the line band we follow Robertson et al. (2016) and Gomes da Silva et al. (2011), adopting 1.6 Å for the (full) width of the line band. We note that during flares the line width can easily amount to 5 Å or even more. In that case, line flux is left unaccounted for and the true value of I_line is underestimated. However, using a larger bandwidth reduces the sensitivity of the index, and since we are not interested in a detailed study of the index evolution during flares, but only want to identify more active phases, we refrain from adapting the width of the line band. We use the red reference band of the Hα line to locally normalise our spectra for graphical display. The two reference bands are centred on 6552.68 and 6582.13 Å and are10.5 and 8.5 Å wide, respectively.

Because line asymmetries have been reported to occur during flares, we coarsely categorise the spectra as flare or quiescent spectra according to the Hα index I_Hα. Since the sequencing of the CARMENES observations is driven by the planet search (Garcia-Piquer et al. 2017), we lack a continuous time series, which precludes a search for the characteristic flare temporal behaviour with a short rise and a longer decay phase. Finding flares based on a snapshot spectrum and especially on Hα emission line strength alone is difficult, since there is intrinsic non-flare variation. Other studies (e.g. Hilton et al. 2010) used Hβ (4861.28 Å) additionally in flare searches, but this is not covered by our spectra. We therefore define a threshold for I_Hα below which we define the star to be in a flaring state. Since especially the more active stars display a considerable spread in the values of the I_Hαalso during their bona-fide quiescent state, we had to empirically define this threshold. In particular, we mark all spectra with an I_Hα lower than 1.5 times the median I_Hα as flaring. This flare definition is thus compatible with the 30% variability during quiescence found by Lee et al. (2010) and adopted also by Hilton et al. (2010). We are aware that this method is insensitive to small flares, and also to the very beginning and end of stronger flares where the lines show relatively little excess flux. To identify these cases one would need a continuous time series and shorter exposure times.

In Fig. 1 we show, as an example, the temporal behaviour of the I_Hα time series of EV Lac and YZ CMi. Both stars show continuous variability in their I_Hα also during the quiescent state, which is, in fact, more reminiscent of the quiescent flickering observed in the X-ray emission of active M dwarfs (Robrade & Schmitt 2005). Nonetheless, we continue to refer to this state as quiescent. While for EV Lac the four flares in the I_Hα time series are set apart from the quiescent state, the I_Hα light curve of YZ CMi reveals the difficulty of finding small flares without continuous observations. Following our flare definition, there are no flares in the YZ CMi light curve. Yet the star seems to be more variable in the second half of the light curve, indicating some transition in its state of activity.

In Table 2 we provide the minimum and maximum of the measured I_Hα, as well as its median and median absolute deviation (MAD) for all our sample stars. While for the stars EV Lac and YZ CMi the spread in I_Hα during quiescence as measured by MAD is about the same (≈0.22 Å; cf. Table 2), the sample stars show a considerable range with DS Leo and CN Leo marking the lower and upper bounds with MADs of 0.02 Å and 0.6 Å.

Both the median(I_Hα) and its dispersion as measured by the MAD describe the stellar activity level, and we compare both values in Fig. 2. A correlation seems to be present, indicating lower variability levels for less active stars. This is consistent with the results reported by Bell et al. (2012) and Gizis et al. (2002), who also found larger scatter for more active stars. For our sample, Fig. 2 suggests a flattening of the variability distribution for higher activity levels, which was found neither by Bell et al. (2012) nor Gizis et al. (2002). We therefore consider this to be a spurious result, attributable to the low number statistics for high-activity stars in our sample or to the underestimation of I_Hα for broadened profiles in the stars with the highest activity level.

5. Line wing asymmetries

5.1. Overview

In our M dwarf CARMENES spectra we find diverse examples of Hα lines with broad line wings with both relatively symmetric or highly asymmetric profiles. An example of a symmetric profile is given in Fig. 3, which shows four out of the 17 spectra of OT Ser considered in this study. In particular, we show two spectra representing the typical quiescent state of OT Ser (in black), while the spectra plotted in red and cyan represent a more active state. As is shown in Fig. 3, the states are nearly identical in the line core, yet the cyan spectrum exhibits rather broad line wings, reaching about 4 Å beyond the emission core.

To quantify the profile and its asymmetry, we follow Fuhrmeister et al. (2008), Flores Soriano & Strassmeier (2017), andotherstudiesandfirstobtainaresidualspectrumbysubtracting the spectrum with the highest (i.e. least active) I_Hα. By subtraction of the spectrum representing the quiescent state, we infer the additional (potentially flaring) flux density and how it is distributed between the narrow line core and the broad line component. We then fit the residual flux density with a narrow and a broad Gaussian profile, representing the line core and wing. The fit with this two-component model results in a reasonably good description of the line profile even in the most asymmetric cases. We nevertheless caution that the fit may be not unique. For example this may happen when one Gaussian flank of the broad component is hidden in the narrow component (see the example in the next section and Fig. 5).

5.2. Red and blue line asymmetries: CN Leo and vB 8

A rather striking example of line asymmetries can be found in the CARMENES spectra of vB 8 shown in Fig. 4 (and with two- Gaussian fit in Fig. D.3). Three example spectra show the typical variation during the quiescent state. One spectrum shows an extreme blue line asymmetry with only marginal emission in the line core. Two more example spectra both exhibit nearly identical line cores with large amplitudes, but only one of them shows an additional red asymmetry. This demonstrates the variety of profiles encountered in our analysis.

To illustrate our fits of red and blue line asymmetries, we consider the case of CN Leo. In Fig. 5 we plot the residual Hα line profile (i.e. the profile after subtraction of the quiescent state) with a rather moderate red asymmetry along with a two-component fit; in this case we require both the Gaussian component representing the line core and the one representing the wing to be rather narrow. The profile of the emission line core is not entirely Gaussian, especially at the top. Nonetheless, we consider the resulting characterisation of the width and area of the line core sufficiently accurate for our purposes. The problem of the non-uniqueness of the fit is apparent: the width of the wing component cannot tightly be constrained because the blue flank of this component is hidden in the core component. Fortunately, this problem occurs only rarely and the parameters derived for most of the broad components are trustworthy. To further illustrate the quality of our fits, we show the strongest and weakest asymmetry with its corresponding fit for blue and red asymmetries and for more symmetric profiles in Appendix D in Figs. D.1–D.6.

5.3. CARMENES sample of broad and asymmetric Hα line profiles

In the fashion described above we analysed all Hα line profiles. In Table 4 we list all detected asymmetries for all sample stars, number them for reference, and provide the best-fit parameters for each of the two Gaussian components: the area in Å, the shift of the central wavelength with respect to the nominal wavelength of the Hα line v_central, and the standard deviation σ in Å. Moreover, we list the full width at half maximum (FWHM), the ratio of the Gaussian area A determined for the broad and total components, the epoch of each observation as Julian Date-2 400 000 in days, and the exposure time in seconds. In Appendix A we show all Hα line profiles with detected asymmetries, and in Table 2 we summarise statistical aspects of our findings. Specifically, we give the number of detected flares and broad components (categorised into red, blue, and symmetric) and how often both coincide.

6. Discussion

6.1. Overview: statistics

In the 473 CARMENES spectra selected for our study we find a total of 41 flares and 67 line wing asymmetries. Only in eight out of the 28 sample stars, we do not find any Hα line observations with broad wings. This indicates a mean duty cycle of 9% and 15% for flares(following our definition) and Hα line asymmetries averaged over the studied sample, respectively. Therefore, broad and asymmetric Hα line profiles appear to be a rather common phenomenon among active M stars. Also, line asymmetries are not necessarily linked to flares; in fact, we observe flares without line asymmetries and line asymmetries without flares. Red asymmetries occur more often than blue asymmetries, and symmetric broadening is detected least frequently.

6.2. Limits of the line-profile analysis

The CARMENES observations provide a comprehensive and temporally unbiased sample of M dwarf line profiles, the nature of which imposes, however, some limitations on the analysis. As we lack continuous spectral time series, the course of spectral evolution cannot be resolved, and because integration times vary between less than 100 s and up to 1800 s for the faintest objects, variability on short timescales remains elusive. In the specific case of flares, we remain ignorant of the phase covered by the spectrum. Nonetheless, the spectra allow both a statistical evaluation of the sample properties and meaningful analyses of individual profiles. In particular, any sufficiently strong or long-lived structure will be preserved in the individual spectra.

6.3. Physical scenario for line broadening with potential asymmetry

6.3.1. Symmetrically broadened lines

Symmetricline broadening can be caused by the Stark effect or non thermal turbulence. For the Sun, Švestka (1972) argued that symmetric Balmer line broadening is caused by Stark broadening and not Doppler broadening. More recently, Kowalski et al. (2017b) introduced a new method to handle the Balmer line broadening caused by the elevated charge density during flares to better reconcile modelling and observations.

Another explanation for the more symmetric lines is the long exposure time, possibly blurring phases with blue and red shifts into relatively symmetric, broad lines. Indeed, we see a tendency for broader lines to be more symmetric in our data, but that may be caused by Stark broadening as well (see Sect. 6.9).

6.3.2. Red line asymmetries

As to line asymmetries, Lacatus et al. (2017) presented solar Mg ii H&K line profiles with a striking red asymmetry, observed with the Interface Region Imaging Spectrograph (IRIS) following an X2.1-class flare; the relevant data and fits are shown in their Fig. 2. The authors ascribed the observed line profiles to coronal rain, which is cool plasma condensations travelling down magnetic field lines from a few Mm above the solar surface.

This coronal rain is thought to result from catastrophic cooling and is not only observed in the context of flares, but appears to be a rather ubiquitous coronal phenomenon (Antolin & Rouppe van der Voort 2012; Antolin et al. 2015). In fact, Antolin & Rouppe van der Voort (2012) supposed that coronalrainisanimportantmechanisminthebalanceofchromospheric and coronal material and estimated the fraction of the solar corona with coronal rain to be between 10% and 40%.

Based on the Mg ii line profiles, Lacatus et al. (2017) derived a net red shift of 60 km s⁻¹, which they attributed to bulk rain motion. Velocities on the order of 100 km s⁻¹ are, indeed, rather typical for such condensations (e.g. Schrijver 2001; de Groof et al. 2005; Antolin & Rouppe van der Voort 2012; Verwichte et al. 2017), which is also the maximum shift we observed.

Along with the red shift, Lacatus et al. (2017) observed broad wings with a Doppler width of ≈100 km s⁻¹, appearing about six minutes after the impulsive flare phase. Their lines are far broader than the net red shift, which is also true for the majority of our measurements. The authors argue that these widths are best explained byunresolvedAlfvénicfluctuations.BroadeningbyAlfvénicwave turbulence was first suggested by Matthews et al. (2015), based on observations of a solar flare associated with a Sun-quake in the Mg ii H&K lines (see also Judge et al. 2014).

In a study of spatially resolved Hα emission during a solar flare, Johns-Krull et al. (1997) found quiescence subtracted spectra exhibiting weak asymmetries with slightly more flux in the red wing. We completely lack spatial resolution, and the amount of asymmetry reported by Johns-Krull et al. (1997) is so small that we would most likely not have detected it in our spectra. Johns-Krull et al. (1997) interpreted the red wing asymmetry as being caused by rising material absorbing at the blue side of the line.

Also chromospheric condensations produce red asymmetries on the Sun. Such condensations normally occur during the impulsive phases of flares driven by non-thermal downward electron beams (e. g. Ichimoto & Kurokawa 1984; Canfield et al. 1990). These so-called red streaks reach velocities between 40 to 100 km s⁻¹ with the velocities decreasing on short timescales and the emission ceasing before Hα emission reaches its maximum. Canfield et al. (1990) measured only velocities up to 60 km s⁻¹ and ascribed this low maximum velocity to their comparably low time resolution of 15 s. Also Graham & Cauzzi (2015) found lower velocities and very short decay times of only about one minute, which even partially preceded the also observed up-flows.

For the Si IV and C II transition region lines, Reep et al. (2016) found red emission asymmetries lasting more than 30 min and attributed these to the successive energisation of multiple threads in an arcade-like structure. The authors argue against coronal rain because no blue shifts were detected at the beginning of the flare. Instead, the red shifts started simultaneously with a hard X-ray burst. Reep et al. (2016) further argue that a loop needs some time to destabilise for coronal rain to start after the heating ceases. Rubio da Costa et al. (2016) and Rubio da Costa & Kleint (2017) modelled solar flare observations in Hα, Ca ii 8542 Å, and Mg ii H&K with multi-threaded down-flows but still had trouble reproducing the observed wing flux in their models.

Since we lack information about when during the flare the emission responsible for the broad components occurred (and if at all in some cases), we cannot properly distinguish between the coronal rain and chromospheric condensation scenario. While coronal rain is expected to take place later in the decay phase, chromospheric condensations are thought to be associated with the impulsive phase. We consider it improbable though that transient events lasting only about a minute can account for the strongest asymmetric signatures in our up to 30-minutes-long exposures. Moreover, the blue asymmetries found in our sample are never associated with large amplitudes in the narrow main component, suggesting coverage of the flare onset only (as expected; see Sect.6.3.3 and 6.3.1). In contrast, elevated emission in the narrow component was detected for some lines with red asymmetries, which indicates that at least the onset of the decay phase was covered; however, the impulsive phase may be covered, too. While it appears to us that the coronal rain scenario is more easily compatible with the majority of our observations, we cannot ultimately discriminate between the scenarios on the basis of our data, and both phenomena may actually have occurred.

6.3.3. Blue line asymmetries

On the Sun, blue asymmetries are also observed. For instance, Cho et al. (2016) reported the appearance of a blue asymmetry in the Hα line associated with the start of a rising filament preceding a solar flare. The authors attribute the asymmetry to a mixture of material moving at velocities between −138 km s⁻¹ and 38 km s⁻¹. While Cho et al. (2016) reported an excess absorption in Hα, blue shifted emission has also been observed on the Sun (Švestka et al. 1962; Tang 1983). In fact, the flare observations of the mid-M dwarfs CN Leo and Proxima Centauri, which also cover the flare onset, show both blue asymmetries during flare onset, followed by red asymmetries later on during the decay phase (Fuhrmeister et al. 2008, 2011). Accordingly, we ascribe the blue shifted components to chromospheric evaporation.

6.4. Strength of the asymmetries

As a way to measure the strength of the asymmetry, we compute the area of the broad Gaussian multiplied by the shift of its central wavelength. We show this asymmetry strength in Fig. 6.

Based on this measure, we find three outstandingly strong asymmetries. The one with the blue shift belongs to vB 8 and the corresponding spectrum is shown in Fig. 4. The remaining two correspond to asymmetries no.50 and 55 in Table 4, are red shifted, and stem from EV Lac. The associated spectra are shown in Fig. A.19 (and with Gaussian fit in Fig. D.1). The first of these asymmetries (no. 50) also shows the second highest flux level in the narrow line along with broad wings in the Na I D lines. It is clearly associated with a large flare on EV Lac.

6.5. Connection of asymmetries to flares

As evidenced in Table 2, broad wings in Hα with more or less pronounced asymmetries of the broad component appear to be quite common among M stars. In contrast to the literature, where wings and asymmetries therein are normally connected to flares, many asymmetries found in our study do not coincide with flares (using our flare definition). Assuming that stellar flares show a sufficiently uniform pattern of chromospheric line evolution, this finding shows that: (i) line asymmetries may not in all cases be connected to flares; (ii) they may be found also in smaller flares, (iii) they may persist up to or even beyond the end of the decay phase of stronger flares, or, (iv) they occur during the impulsive phase, where the chromospheric lines just start to react to the flare. We cannot distinguish the first three scenarios since we do not have time series, but only snapshots. The last possibility is rather unlikely, since the impulsive phase of flares typically lasts only a few tens of seconds, while the typical exposure times of our sample stars is a few hundred seconds, so that in most cases also the flare peak should be covered by the exposure.

Despite the lack of a clear association between asymmetries and flares, asymmetries generally seem to be accompanied by somewhat enhanced activity states: only in six cases, where an asymmetry was detected, did the narrow Gaussian component area remain small (<0.5 Å), indicating that the stellar activity state was only marginally higher than the minimum state that we subtracted. In all other cases, we found indications for enhanced emission in the narrow component, albeit not sufficiently strong to be qualified as a flare.

Moreover, we find that the pEW(Hα) of the broad component increases as the strength of the narrow component of the Hα line increases (see Fig. 7). A similar correlation between the stellar activity state and the strength of the broad component was found by Montes et al. (1998). Formally, we obtain a Pearson correlation coefficient of 0.43, taking all spectra into account where we found a broad component. Excluding the four values pertaining to CN Leo and vB 8 (see Fig. 7), we compute a correlation coefficient of 0.88. CN Leo and vB 8 are the only two stars in the sample with spectral type M6 or later for which we found asymmetries, but we are not aware of any physical reason why these two stars should behave differently, though they may have higher contrast to photospheric emission in this wavelength region.

6.6. Occurrence rate of asymmetries and activity state or spectral type

According to our analysis the four fastest rotators in our sample (V374Peg,LSRJ1835+3259,StKM2-809, andGL Vir) with v sin i ranging from 21 km s⁻¹ to 43 km s⁻¹ all show asymmetries. For the fastest rotator, V374 Peg, a member of the roughly 300 Myr old Castor moving group (Caballero 2010, but see Mamajek et al. 2013), we also detect the highest fraction of asymmetries. On the other end of the activity range, we find that three out of the eight stars without any detected asymmetry are less active, showing weak Hα emission (DS Leo, HH And, and BD–02 2198). Both hint at a relation between activity state and the frequency of asymmetries.

In Fig. 8 we show the fraction of spectra exhibiting asymmetries as a function of (projected) rotational velocity (top) and median(I_Hα) (bottom). With a mean fraction of 5%, the probability of showing an asymmetry is smaller for slowly rotating stars (< 3.5 km s⁻¹) than for fast rotators, where the mean fraction is 23%.At-testshowsaprobabilityofabout1%thatthetwomeansare equal.

The picture is similar for the rate of asymmetries as a function of the median(I_Hα) (Fig. 8, bottom panel). We find the highest fractions of asymmetric line profiles among the more active stars. In fact, the distribution suggests the existence of an upper envelope indicated by the dashed line in Fig. 8. While we cannot determine any formal justification, the presence of an upper envelope appears to be plausible, if the asymmetries are related to the release of magnetic energy into the stellar atmosphere. At lower activity levels such releases would then be expected to occur less frequently than at higher activity levels, where they can – but apparently do not need to – lead to detectable line profile asymmetries.

Another parameter that may relate to the occurrence of asymmetries is spectral type. We plot the distribution of the fraction of asymmetries as a function of spectral type in Fig. 9. There seems to be a concentration of a high occurrence rate of asymmetries around the mid-M spectral types. The mean occurrence rate for early spectral types (M0 – M2.5 V) is 0.07, while for mid spectral type (M3 – M5.0 V) it is 0.17, and for even later spectral types it is 0.14. We caution though, that this may be caused by selection effects, since for example all our early stars are slow rotators.

6.7. The narrow Gaussian component

The mean width of the narrow Gaussian component as measured by its FWHM found in our analysis is 65 km s⁻¹ with a standard deviation of 10 km s⁻¹. The mean absolute shift of the narrow Gaussian core components is 3.9 km s⁻¹, which is significantly lower than its mean width and about an order of magnitude less than the mean absolute shift of 35 km s⁻¹ found for the broad component. For only nine spectra we measure a shift exceeding 10 km s⁻¹. Of these, five originate from the fast rotator V374 Peg, for which we suspect a rotational contribution to the shift (see also Sect. 6.10). The four remaining cases are due to TZ Ari, OT Ser, vB 8, and WX UMa, where the shift cannot be explained by rotation. In the specific case of OT Ser, the spectrum also appears to suffer from some spectral defects that may influence the fit.

We find only small shifts in the position of the core component of the Hα line as measured by the narrow Gaussian component, in particular when compared with the line width. The shift in the position of the narrow Gaussian component is uncorrelated with its area. The distribution is shown in Fig. 10. At any rate, the two-component Gaussian model only provides an approximate representation of the true line profile, which is generally more complex, so that some residual shifts are expected. The scatter appears to decrease for stronger emission line cores, which may be due to a better constrained fit in these cases. Therefore, we consider the measurements consistent with a stationary emission line core.

6.8. Shift of the broad Gaussian component

The measured shift of the broad component varies between about −100 and 100 km s⁻¹. There are 15 (22%) spectra showing a shift of less than ±10 km s⁻¹ in the broad component. In analogy with the distribution of shifts in the narrow component (see Sect. 6.7), we consider these shifts insignificant and the profiles symmetric. In our sample, we also find a surplus of red shifted broad wings. Only considering broad components with an absolute shift larger than 10 km s⁻¹, we find 20 blue shifted (30%) and 32 red shifted (48%) components, while for absolute shifts larger than 50 km s⁻¹, there are four (6%) blue shifted and 13 (19%) red shifted components. An excess of red asymmetries is also consistent with observations of solar flares (Švestka et al. 1962; Tang 1983).

In the context of our envisaged scenario, the asymmetric line profiles do require atmospheric motions. We note that all measured velocities are far below the escape velocity of 500 to 600 km s⁻¹ for mid to early M dwarfs. Theoretically, a (radial) mass ejection at the limb would be observed at much lower velocity due to projection effects, but we consider improbable the possibility of observing ejections only at the stellar limb and not at the centre. Assuming a strictly radial motion and a true velocity of 500 km s⁻¹, only 20% of all directions yield projected velocities of ±100 km s⁻¹ or less. Thus, we consider it unlikely that the observed blue shifts are exclusively due to limb ejections, although we cannot rule out the possibility in individual cases. However, even the extreme case of a blue asymmetry in vB 8 (Fig. 4) does not require any material near the escape velocity because the largest shifts in the line flank at about 6561 Å correspond to velocities of only 160 km s⁻¹.

Turning now to red shifts, the observed red shifts are comparable with the speeds measured for solar coronal rain, and we consider a phenomenon similar to coronal rain a viable explanation for the observed line shifts. An alternative explanation could be chromospheric condensations.

In the context of our scenario (see Sect. 6.3), blue asymmetries would be associated with rising material, primarily in the early phases of flares. In Fig. 10 we show the shift of the broad component as a function of continuum-normalised flux, which shows a striking absence of blue shifts for fluxes in the narrow component higher than about 3 Å. A single exception corresponds to a spectrum of CN Leo, showing a rather marginal blue shift (which anyway makes it a symmetric case). For weaker narrow components, the distribution is more balanced. We argue that spectra showing strong blue shifted asymmetries with weak narrow components cover primarily the onset of a flare, where the line cores do not yet show a strong response. The case of CN Leo may be explained by the exposure covering both the flare onset, peak, and potentially a fraction of the decay phase. Then, both blue and red asymmetries would mix and give the appearance of a broad line with only marginal net shift and substantial flux in the narrow component.

While the observed shifts can, therefore, be reconciled with our scenario, red and blue shifts are caused by completely different physical processes. In light of this, it appears remarkable that the maximum velocities of the observed blue and red shifts are so similar and we currently lack a concise physical explanation for this.

6.9. Width of the broad component

The fitted widths of the broad component vary between 0.5 and 3.6 Å with a mean of 1.72 Å, corresponding to a velocity of 184.9 km s⁻¹ as FWHM. In Fig. 11 we show the distribution of the width of the broad and narrow Gaussian components as a function of their shift; the numbers are given in Table 4. Typical values range between 100 and 200 km s⁻¹ with a maximum of 390 km s⁻¹. Visual inspection of the fits shows, however, that the top two widths of 390 and 365 km s⁻¹, corresponding to flares on EV Lac and GT Peg, are probably overestimated.

The distribution shown in Fig. 11 suggests a decrease in the width as the shift increases either to the red or the blue side. This impression is corroborated by a value of −0.54 for Pearson’s correlation coefficient between the width and the absolute value of the shift (excluding the two outliers); the p-value for a chance result is 3 × 10⁻⁶. A stronger contribution of Stark broadening at smaller shifts is conceivable. Also the coarse time resolution may play a role, because most exposures that cover the short flare onset should also cover the flare peak and the start of the decay phase. In our sample, we do not find strong blue asymmetries in combination with strong narrow components. We argue that this indicates that evaporation was accompanied by red asymmetries in all cases studied here. This could indicate that evaporated material increases the density in the coronal loops, leading to more efficient cooling, followed by Hα rain. A red coronal rain asymmetry from the flare peak then adds to the broadening, making the profile more symmetric.

When the shift of the broad component is sufficiently small for the Hα line to be considered symmetric, we cannot distinguish if the lines are broadened by high charge density, turbulence, or downward and upward moving material, whose distinct signatures are smeared out due to the long integration time. In fact, the latter effect may account for widths in excess of 300 km s⁻¹, which appear high for an interpretation in terms of turbulence. However, the majority of the broadened lines show substantial asymmetry in the broad component for which Stark broadening does not appear to be a viable explanation. In their modelling of a chromospheric condensation computed to represent a solar flare event, Kowalski et al. (2017a) find that Stark broadening does play a significant role for the Balmer lines but not for other lines. The authors find red asymmetries with the line width from instantaneous model snapshots to be actually lower than that observed. The inclusion of moderate micro-turbulence, together with the velocity evolution of the shifts in the model accumulated over the exposure time, leads to a realistic broadening in their study. The determined widths of the broad component are comparable to those observed in the Mg ii lines by Lacatus et al. (2017) on the Sun. By analogy, we consider magnetic turbulence a viable broadening mechanism to explain the observed widths of the Hα lines.

6.10. Hα line profiles of the fast rotators Barta 161 12, StKM 2-809, and V374 Peg

The three fastest rotators Barta 161 12, StKM 2-809, and V374 Peg show complex features in the Hα line profiles observed by CARMENES. For all three stars the Hα line profile continuously varies. In Fig. 12 we show three Hα line profiles (prior to subtraction) of StKM 2-809, namely, those with the weakest and strongest detected Hα lines and a spectrum with intermediate line strength. The lowest-activity Hα line profile shows a more pronounced blue wing than the intermediate-activity spectrum shown here. Subtracting the lowest-activity state spectrum produces relative absorption features in the residual spectrum in the blue flank of the Hα line. For StKM 2-809, we find such features in two out of three spectra with asymmetry, but some spectra without marked asymmetry show also complex Hα line profiles. In this case, the absorption features may influence our fits but not to a degree that would call the presence of additional shifted emission into question. Therefore, we include the star in our normal analysis since we believe that the main effect is similar to that in slower rotators.

For V374 Peg only one spectrum shows a significant relative absorption feature along with an asymmetry (see Fig. A.18, fourth from bottom). Therefore, we believe that also for V374 Peg the asymmetries are mainly caused by the same mechanism, although some profiles also show plateaus and one profile is double-peaked (second from bottom in Fig. A.18).

Barta 161 12 shows the most pronounced variety of Hα profiles, which in many cases need more than two Gaussians for fitting (Fig. A.3) representing a different case of asymmetries. Only one spectrum of this star seems to fall into the category of asymmetries discussed in this paper. Therefore, we exclude it from our analysis as already mentioned in Sect. 3. For the other two fast rotators the situation is less extreme. All three stars show significant shift in the narrow Hα line component but never higher than their rotational velocity.

Whether or not the relative absorption features seen in the subtracted spectra of the three fast rotators are due to true absorption, for example caused by a prominence, or are the results of excess emission in the lowest-activity spectrum used in the subtraction cannot be determined on the basis of our data. We also want to note the possibility that the plateaus and multi-peaked spectra of especially Barta 161 12 (Fig. A.3, top two spectra) may originate in distinct active regions, rotating along with the stellar surface.

6.11. Broad components and asymmetries in other lines

6.11.1. The optical Na I D and He I D₃ lines

The optical arm of CARMENES covers further known activity indicators beyond the Hα line. In particular, we investigated the Na I D and He I D₃ lines and, indeed, found asymmetric components in a number of spectra of EV Lac, OT Ser, and StKM 2-809.

In Fig. 13 we show an example for the star OT Ser; the corresponding Hα line profiles are presented in Fig. 3 with the same colour coding. While two enhanced spectra in the Hα line are nearly identical, this is not true for the corresponding He I D₃ and Na I D lines, indicating a different state of the chromosphere at the two times.

Because the broad components of the two Na I D lines overlap, we fit them simultaneously with a total of four Gaussian components, representing two narrow and two broad components. We fix the offset in wavelength of the narrow and broad components to the known doublet separation and also couple their respective widths. The best-fit values for the three spectra with broad wings in Na I D and He I D₃ are given in Table 3; the spectra are also indicated in the notes column of Table 4.

The narrow Gaussian component is in all cases only slightly shifted, and its width stays about the same, with the He I D₃ line being slightly broader than the Na I D lines. Both lines are significantly narrower than the narrow component of the Hα line, which is broader because it is optically thick for our sample stars. For the broad component, the picture is more complicated with most of the fit results for the individual lines – also compared to the broad component of the Hα line – differing significantly.

These differences may be caused by the different height at which the lines originate in the atmosphere; Hα is thought to be formed in the upper chromosphere, while the Na I D lines originate in the lower chromosphere. Although we consider the fits satisfactory (see Figs. B.1–B.3), part of the differences may also be attributable to problems in the fit itself such as the approximation by Gaussian profiles. However, Figs. B.1–B.3 demonstrate that the He I D₃ line shows a red asymmetry in StKM 2-809, while the Na I D lines are more symmetric, exhibiting emission in the blue wing as well. Thus we are confident that a physical reason underlies the line profile differences, which may be related to distinct sites of line formation and radiative transfer. Again, however, we caution that the phenomena may actually not have occurred simultaneously, but arise from time averaging during the exposure (see Sect. 6.2).

The spectrum of OT Ser showing broadening in the Na I D lines also exhibits relatively symmetric, broad wings in the Hα line. While the latter may be caused by Stark broadening, the Na I D lines are not thought to be affected by this. Therefore, the broadened Na I D lines suggest a different broadening mechanism, probably turbulence, at least in this individual case.

6.11.2. The He I and Paβ near-infrared lines

The infrared arm of CARMENES also covers known chromospherically-sensitive lines such as the Paβ line and the He I line at 10833.31 Å, the latter of which has primarily been used in the solar context (e.g. Andretta et al. 2017). We searched all 72 spectra with asymmetries in Hα also for asymmetries in He I 10833 Å and Paβ. Unfortunately, not all available optical spectra have infrared counterparts (cf., Table 4). For the analysis, 40 spectra were available of which we discarded four because of the telluric contamination was too severe. Of the 36 usable spectra, 19 show no excess in the He I line, two show a weak excess, and 15 a clear excess. Unfortunately, the low excess flux in the Paβ lines precludes a meaningful analysis of its symmetry here.

We show the 15 excess spectra in Appendix C in Figs. C.1 to C.8 along with the corresponding Paβ excess fluxes. Also for the He I 10833 Åline, the degree of asymmetryis hard to assessin most cases because the red side of the line is contaminated by strong air glow or telluric lines.

In Fig. 14, we show the He I and Paβ lines of EV Lac (the corresponding spectra are also marked by “IR” in Table 4). The infrared regime is more heavily affected by telluric contamination and air glowlines (Rousselot et al. 2000). Because a number of strong lines are located in the direct vicinity of the He I line (cf., Fig. 14), and an appropriate correction is very challenging, we limit ourselves to a qualitative analysis. In Fig. 14, we show four spectra with enhanced emission in the quiescent subtracted flux density. While three spectra do not show clear signs of an asymmetry, one spectrum does exhibit a strong blue asymmetry (taken at JD 2 457 632.6289 d, cf., Table 4) and also the corresponding Hα line shows a blue asymmetry in this case. In the Paβ line, we find enhancements in the line flux for the three flare spectra as can be seen in the bottom panel of Fig. 14. Like the spectrum described above, this one also suggests a blue asymmetry.

The two infrared lines studied here clearly react to different activity states. In our spectra, emission in the He I 10833 Å line is clearly detected in 34% of the available infrared spectra also showing an Hα asymmetry, while the Paβ line appears to be less sensitive to chromospheric states causing broad wings. Asymmetries are difficult to assess in the Paβ and He I 10833 Å line. Only in three cases, namely two spectra of EV Lac (first two) and the last spectrum of StKM 2-809, we are confident that a blue asymmetry is present in the He I 10833 Å line. These correspond also to blue shifts in Hα.

7. Conclusions

We present the most comprehensive high-resolution spectral survey of wings and asymmetries in the profiles of Hα and other chromospheric lines in M dwarfs to date. We found 67 asymmetries in 473 spectra of 28 emission-line M dwarf stars. Line wing asymmetries in the Hα line, therefore, appear to be a wide-spread phenomenon in active M dwarfs, which we find in about 15% of the analysed spectra. Only eight stars do not show any wings or asymmetries.

In contrast to that, asymmetries in other spectral lines seem to occur less frequently. In particular, only 4% of the spectra with detected Hα asymmetry show also an asymmetry in the optical Na I D and He I D₃ lines. In the He I 10 833 Å line, we find broad wings for 34% of the cases. Excess emission in the Paα line was found only in a few cases, but we considered a meaningful analysis of its asymmetry unfeasible.

While the occurrence rate of the asymmetries varies widely between stars, we find a relation with the stellar activity level. In particular, more active stars (as measured by rotational velocity or median(I _{H α} )) also show a higher fraction of spectra with asymmetric Hα line profiles. Nevertheless, we find that only 24% of the asymmetries are associated with a flare, as defined by our flare criterion, and we conjecture that either asymmetries are not necessarily coupled to (large) flares or they can persist to the very end of the decay phase.

We find our results to be consistent with a scenario in which red asymmetries are associated with coronal rain or chromospheric condensations, two phenomena well known from the Sun. Unfortunately, they cannot be distinguished on the basis of the occurring velocities or line width, and we lack the timing information of when (and sometimes if) during a flare the asymmetry occurs. Lacatus et al. (2017) explain the width by Alfvénic turbulence, which may also cause the broadening in our case. Because of the relatively long exposure times for M dwarfs, however, we cannot rule out that the width is due to an evolution in the velocity field.

For the blue wing enhancements, we propose chromospheric evaporation as the mechanism responsible, which explains why we do not find substantially blue shifted broad components in combination with strong narrow core components. Supposedly, the chromospheric evaporation occurs during the early impulsive stage of a flare, while the largest amplitudes in chromospheric lines are typically observed at flare peak or early decay phase. While also symmetric line profiles may be explained by coronal rain with low (projected) velocities or time average effects, we cannot exclude Stark broadening as an alternative explanation. One exception here is the case of OT Ser, which exhibits asymmetrically broadened Hα line along with broadened Na I D lines, which is not expected for the Stark effect; in fact, Stark broadening affects higher Balmer lines more strongly than Hα itself. While CARMENES does not cover these lines, a dedicated study of the effect may take advantage of this fact.

While the data presented here are well suited for a statistical study of broadening and asymmetry in the Hα line, there is a clear need for further observations. Any detailed modelling attempt would greatly benefit from dedicated observations that clarify whether asymmetries are coupled to flares in all cases and if so, which sort of asymmetry (red or blue) is associated to which phase of the flare. Therefore, to better understand the phenomenon of asymmetric line profiles, continuous spectral time series with a higher temporal cadence (or simultaneous photometry) and spectral coverage of the end of the Balmer series are definitely needed.

Acknowledgments

B. F. acknowledges funding by the DFG under Cz 222/1- 1 and thanks E. N. Johnson and L. Tal-Or for helpful remarks. CARMENES is an instrument of 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, Insitut 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.

Appendix A: Detected asymmetries

We present here all Hα spectra with detected asymmetries in Figs. A.1–A.21. The quiescent spectrum is already subtracted. Moreover, we plot a velocity scale in Fig. A.1 for reference. If the star shows an asymmetry in more than one spectrum, the spectra are plotted with an offset for better comparison and in cycling colours.

Appendix B: Detected asymmetries in Na I D and He I D₃

We present here all Na I D and He I D₃ spectra with detected asymmetries with the quiescent spectrum subtracted and the best fit overlaid in Figs. B.1–B.3.

Appendix C: Detected asymmetries in He I 10833 Å and corresponding excess fluxes in Paβ

Here we present all quiescent flux density subtracted spectra with a He i10833Å broadwing in Figs.C.1–C.8. We searched in all spectra exhibiting an Hα asymmetry. The problem of the strong air glow and telluric lines in the region is apparent. Besides the broad wing spectra we also always present a quiescent spectrum. In theright panel we show the same for the corresponding Paβ spectra. It is quite apparent that the line reacts in a much less sensitive manner. For both spectral lines we mark the reference central wavelength with a blue vertical line.

Appendix D: Examples of the Hα profile fit for the weakest and strongest asymmetries

Here we present examples of our fits of the Hα line profile. For each of the categories (i) red asymmetry, (ii) blue asymmetry, and (iii) symmetric broadening, we show the strongest and the weakest asymmetry and its fit.

References

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