High-resolution spectroscopy of flares and CMEs on AD Leo^††thanks: Based on observations obtained at the Thüringer Landessternwarte Tautenburg, Germany

AD Leo shows a very high level of chromospheric activity, especially in the Balmer lines ($\rm H_{\alpha}$ and $\rm H_{\beta}$) and the $\rm He\,I\,D_{3}$ , and we therefore studied the behaviour of these three lines. In order to detect flares in AD Leo, we measured the fluxes in the $\rm H_{\alpha}$, $\rm H_{\beta}$ , and $\rm He\,I\,D_{3}$ lines and used them to construct light curves.

Examples of the relative flux variation in $\rm H_{\alpha}$ of the flares are shown in Fig. 2. As is typical for flares, not all the events show the classical light curve (panel 2) of a sudden increase and slow decrease, but often a more complex structure (panel 1). Figure  2 shows nights in which multiple events occured (e.g. panels 5-8).
The enhancement in the He I 5876 emission line (see Fig. 3) shows that a plasma that is much hotter than the photosphere is present during these events. The He I 5876 emission line occurs at about 20000 K (Giampapa et al. 1978). However, we did not detect the He II 4686 line, which requires a temperature of 30000 K to be excited (Lamzin 1989). This means that the plasma was not hot enough to excite this line.

In addition to the unfavourable weather conditions that interrupted the observations especially in 2016, the activity seems to be lower in 2016 and 2017 than in 2018 and 2019. There is an increase in the activity levels beginning in February 2018 (see Table 1).

We obtained an average flare rate of $\approx 0.092$ flares per hour, ignoring nights with fewer than six spectra. However, as we explain in section 3.2, flares have a power-law distribution, which means that the number of flares that are detected depends on the sensitivity of the measurements. The flare rates of solar observations are much higher than those of stellar observations because the Sun is much brighter and we cannot spatially resolve the stellar disc for stellar observations. When we consider only 2018 and 2019, we obtain a slightly higher rate of $\approx 0.107$ flares per hour. Generally, the activity levels are much lower than those obtained in other studies e.g., f = 0.57 (Pettersen et al. 1984), $\rm f\,>0.71$ (Crespo-Chacón et al. 2006) and $\rm f\sim 0.1$ (Hunt-Walker et al. 2012), where f is the frequency of flares per hour.

Buccino et al. (2014) obtained two possible activity cycles for AD Leo: one of seven years, and another less significant cycle of two years. The seven-year cycle reached a minimum in 2007, and the authors predicted that the next minimum would be in 2015 and that the stellar activity would be even lower. This might explain why the activity levels were low in 2016 to 2017 and have started to increase beginning in 2018.

In order to estimate the energy released during a flare, we integrated the luminosity over the flare duration. The absolute line fluxes were computed from the flux of each line and its nearby continuum. The continuum flux near the emission lines was determined using direct scaling of the flux-calibrated spectrum of AD Leo from Cincunegui & Mauas (2004), assuming the same brightness of the star over time because AD Leo has very small photometric variations of $\approx$ 0.04 mag (Buccino et al. 2014). If the continuum were to increase during the flare, the relative strength of the line would decrease. By assuming the continuum is constant, we therefore obtain a lower limit for the line flux and thus the flares might be more energetic than estimated. To obtain the luminosities, we used the distance to the star of $4.9660\pm 0.0017$ pc from Gaia (Gaia Collaboration et al. 2018). The estimated values of the energy released in each observed flare are also shown in Table 1. The energies given in Table 1 are for $\rm H_{\alpha}$, $\rm H_{\beta}$ , and He I 5876. The smallest flare we detected had an energy of $\rm 3.19\pm 0.01\times 10^{31}\,erg$ in $\rm H_{\alpha}$, $\rm 8.40\pm 0.01\times 10^{30}$ erg in $\mbox{H}_{\beta}$ and $9.93\pm 0.05\times 10^{29}$ erg in He I 5876.

Fig.4 shows the cumulative frequency distribution diagram for the observed flares.

The cumulative frequency distribution of flares follows a Pareto distribution and can be fitted by a linear relation,

where $\nu$ is the cumulative frequency of flares with an energy E or greater and $\beta$ is the power-law exponent. The more energetic flares occur less frequently, as shown by several photometric studies (e.g. Lacy et al. 1976; Pettersen et al. 1984; Hunt-Walker et al. 2012). The lines in Fig. 4 are the formal fits of a straight line (Eqn. 1) to the data to give a scale.

We obtained a value of $\beta=-0.98\pm 0.21$ for the flares in $\rm H_{\alpha}$ and $\beta=-0.97\pm 0.06$ in $\rm H_{\beta}$. This is close to what has previously been obtained for AD Leo, for instance, $-0.82\pm 0.27$ (Lacy et al. 1976), 0.85 (Audard et al. 2000), and $-0.68\pm 0.16$ (Hunt-Walker et al. 2012). However, our fit is steeper probably because we sample low-energy events better. Figure 4 shows that the last five points bend over. The cumulative frequency distribution bends over probably because we miss some flares close to the sensitivity limit. When we ignore these points in the fitting, the slope changes by $\sim 0.58$ for the flares in $\rm H_{\alpha}$.

In Fig. 4 we also show the flare frequency distributions for the flares in $\rm H_{\beta}$ for this work and that of Crespo-Chacón et al. (2006). Crespo-Chacón et al. (2006) observed AD Leo for 16.2 h in $\rm H_{\beta}$ , and despite the longer period of observation for this work, the two data sets show substantial agreement in the distribution of flares on AD Leo. We obtained a value of $\beta=-0.96\pm 0.14$ for the data obtained from Crespo-Chacón et al. (2006), which is similar to the value we obtained for the flares in $\rm H_{\beta}$ for this work. AD Leo was on average more active during our observation time than on April 2-5, 2001 when Crespo-Chacón et al. (2006) observed it. Because the last maximum as observed by Buccino et al. (2014) was in 2011, it is expected that there also was a maximum in about 2018, which falls in our time of observations.

According to Gizis et al. (2017), the slope of the fit is greatly influenced by the energy range of the flares. A maximum likelihood estimation gives a better prediction of the value of $\alpha,$ especially for heavy tailed power-law distributions. The value of $\alpha$ is obtained from the equation

From  $\beta=1-\alpha$ (Hawley et al. 2014), we obtained values of $\beta$ = $-1.45\pm 0.26$ for the flares in $\rm H_{\alpha}$, $-1.12\pm 0.35$ in $\rm H_{\beta}$ , and $-1.01\pm 0.44$ for data from Crespo-Chacón et al. (2006). The discrepancy in the values to those obtained from the least-squares fitting especially for $\rm H_{\alpha}$ is probably due to the fact that it has a heavy tailed distribution. This may be attributed not only to the closeness to the sensitivity limit, but also to the fact that some values of the energy were a lower limit when only the impulsive phase was observed. When we account for the bias caused by the smallness of the samples, as in Gizis et al. (2017), we obtain new values of $\beta=-1.23\pm 0.33,\leavevmode\nobreak\ -0.92\pm 0.26,\leavevmode\nobreak\ \rm and\leavevmode\nobreak\ -0.57\pm 0.33,$ respectively. Within the error ranges, these values are rather similar to those obtained from the least-squares fitting. Table 2 gives a summary of the $\beta$ values obtained using the different techniques.

The ratio of the energy in $\rm H_{\alpha}$ to the energy in $\rm H_{\beta}$ does not depend on the energy of the events. We obtained an average flux ratio of $3.36\pm 0.26$. With this ratio, we are able to correlate the energy in the Balmer lines to that in the X-ray also using the ratio of the energy in $\rm H_{\beta}$ to that in $\rm H_{\gamma}$ ($1.82\pm 0.18$,  Crespo-Chacón et al. 2006). The luminosity in X-ray can be related to the luminosity in $\rm H_{\gamma}$ from the relation $\rm L_{x}(0.04\leavevmode\nobreak\ to\leavevmode\nobreak\ 2.0\leavevmode\nobreak\ keV)=31.6L_{\rm H_{\gamma}}$ (Butler 1993). We also calculated the average flux ratios of the He I 5876/$\rm H_{\alpha}$ as 0.0445$\pm$0.022 and He I 5876/$\rm H_{\beta}$ as 0.145$\pm$0.085. There is no correlation observed between the total line flux and these ratios. The largest flare was observed in the night of February 14, 2018. In that night, we monitored AD Leo continuously from 18:39 UT to 03:14 UT. During that time, we obtained 49 spectra with an exposure time of 600 s.

The total emission during the flare was $2.9\times 10^{31}$ erg in $\rm H_{\beta}$ and $2.12\times 10^{32}$ erg in $\rm H\alpha$. As we discuss below, flares of this size certainly affect planetary atmospheres. During the decay phase of the flare, two events that we may classify as weak events were observed. The first, marked as A in Fig. 5, lasted about $7.2\times 10^{3}$ s, and event B lasted about $3\times 10^{3}$ s. These weak post-flare events tend to occur during large CMEs on the Sun as a result of the movement of magnetic loop footpoints that form current sheets and in this way trigger other smaller events (Kovári et al. 2007). Pre-flare dips are also observed before the impulsive phase of almost all the flares that were observed, including this large flare. The dips last for about 10–30 min. The duration of these dips is consistent with those presented in literature (e.g. Ventura et al. 1995; Leitzinger et al. 2014). These dips might be a result of variations in the $\rm H_{\alpha}$ flux due to pre-flare stellar activity (Leitzinger et al. 2014). CMEs on the Sun are commonly associated with very energetic flares (Yashiro & Gopalswamy 2009).

In order to detect CMEs, we searched for line asymmetries by visual inspection of the average subtracted spectra. We also measured the position of the line centre at each intensity, thus obtaining accurate radial velocities at each intensity level. We observed line asymmetries (in red and in blue) and broadening of wings in several spectra during flares. Table 3 gives a summary of the asymmetries observed and the velocities determined.

We found 75 spectra with line asymmetries. Three large events were found, and these corresponded to nights with large flare events. However, there were nights with weak or no flares, but the spectra showed some asymmetry. This asymmetry could be interpreted as multiple chromospheric condensations that may result from unresolved low-energy flares (Crespo-Chacón et al. 2006). To determine the velocities of the events, we subtracted the spectra for each night from the spectrum in quiescence (an average of the spectra without enhancement in $\rm H_{\alpha}$) and calculated the Doppler shift in the red and blue of the $\rm H_{\alpha}$ emission line. The maximum velocity is determined at the point where the continuum of the residual spectrum merges with the continuum of the spectrum in quiescence. In searching for CMEs, we looked for asymmetries in the blue wings of emission lines because they are often used as a possible signature. The escape velocity of AD Leo is $\approx 590\pm 11\leavevmode\nobreak\ \rm km\,s^{-1}$ , and a sign of a CME would be a blue-shifted component with a velocity greater than this value. Fig. 6 shows the evolution of the different emission line profiles during the strongest flare after subtracting the spectra in quiescence.

There is an increase in the flux at the impulsive phase, however, the core of the lines increases faster than the wings. The emission lines also broaden during the impulsive phase of the flare and decrease with flare evolution. The broadening of the lines might be a result of the Stark broadening effect (Švestka 1972; Gizis et al. 2013) and turbulent motions in the chromosphere of the star (Kowalski et al. 2017). In the impulsive phase, the blue wing is more strongly enhanced, but as the flare decays, more enhancement is observed in the red wing. We also note that the continuum does not change much in quiescence and during the flares. These flares, known as non-white flares, are common on the Sun and have previously been observed on AD Leo (e.g. Crespo-Chacón et al. 2006). However, we may not completely rule out the fact that the continuum changed because there was no simultaneous photometry.

In Fig. 7 we show the temporal evolution of the bulk velocity (using a bisector) of the helium line during the largest flare. This line is an indicator of a very hot plasma, and the asymmetry was more pronounced in this line than in the $\rm H_{\alpha}$ and $\rm H_{\beta}$ lines. The bulk velocities of the plasma in the impulsive phase ranged between $8-10\,\rm km\,s^{-1}$.

In general, asymmetries can be interpreted as a signature of chromospheric plasma motions. Blue asymmetry is usually interpreted as upward-moving material, whereas a red asymmetry can be associated with downward motions (chromospheric condensation) (Canfield et al. 1990; Heinzel et al. 1994; Crespo-Chacón et al. 2006; Kuridze et al. 2016; Fuhrmeister et al. 2018). During the impulsive phase, the broad component appears blue-shifted up to $\sim 260\,\rm km\,s^{-1}$ and is then red-shifted up to $\sim 190\,\rm km\,s^{-1}$ during the gradual decay phase (see Fig.6). These asymmetries have been observed in this and other M stars by several authors (e.g.  Houdebine et al. 1990, 1993; Gunn et al. 1994; Guenther & Emerson 1997; Montes et al. 1999; Fuhrmeister & Schmitt 2004; Fuhrmeister et al. 2005; Crespo-Chacón et al. 2006; Leitzinger et al. 2014; Vida et al. 2016; Fuhrmeister et al. 2018). We found that the observed velocities of the blue asymmetry events were between $80-260\leavevmode\nobreak\ \rm km\,s^{-1}$ , which is far below the escape velocity of the star. This implies that none of these are CME events. The slow events can be attributed to three origins that we describe below.

1. (i)

   Chromospheric evaporation may be one origin, as discussed by Fuhrmeister et al. (2018). During flare onset, material rises with a different velocity, producing the broad component of the line, and as the flare decays, the material flows downwards, leading to the red asymmetry that is observed (Fuhrmeister et al. 2008). The authors interpreted this scenario as a chromospheric prominence that is lifted during flare onset and then rains down during decay. During solar flares, the velocities of chromospheric evaporation reach several tens of $\rm km\,s^{-1}$ and in extremes, even to a few hundred $\rm km\,s^{-1}$.

2. (ii)

   The velocities we obtained are projected velocities because the propagation angle of the CMEs is unknown (Leitzinger et al. 2010).

3. (iii)

   Magnetic field confinement of CMEs in very active stars is another cause (Drake et al. 2016; Alvarado-Gómez et al. 2018). Alvarado-Gómez et al. (2018) suggested that the strong magnetic fields on active stars do not allow material to leave the stellar surface. Only monster CMEs with energies greater than $3\times 10^{32}$ erg may escape a strong field of 75 G. Previous studies showed that AD Leo has a magnetic field of strength $\rm B\sim 3300\,G$ (Cranmer & Saar 2011, and references therein) and an average magnetic field of $\sim 300-330\,\rm G$ (Lavail et al. 2018), which is stronger than the field (75 G) used in the model of Alvarado-Gómez et al. (2018). This implies that CMEs on AD Leo require vast energy to escape this magnetic field. The authors further stated that eruptions following the solar flare–CME relation can only occur during flare events with energies higher than $6\times 10^{32}$ erg (e.g. Guenther & Emerson 1997), but the energy in the largest event we observed was one-third of this in $\rm H_{\alpha}$. The overlying field in active stars reduces the CME speeds in comparison with the solar observations and their extrapolations. In addition to this, Chen et al. (2006) found in their CME velocity distribution study on the Sun that CMEs that were associated with non-active region filaments had higher eruption speeds than those with active region filaments. This shows that the magnetic field configuration plays an important role in CME propagation.

Red asymmetries usually occur at the impulsive phase of flares on the Sun and are driven by non–thermal downward electron beams (e.g.  Ichimoto & Kurokawa 1984; Canfield et al. 1990; Heinzel et al. 1994). These red-shifted downflows in the cool lines on the Sun with velocities in the order of $\rm\sim 100\leavevmode\nobreak\ km\,s^{-1}$ have been interpreted as solar chromospheric condensations. This condensation is often associated with explosive evaporation. During explosive evaporation, the chromosphere is unable to radiate the flare energy away, and this results in excess pressure that causes plasma to move downwards (Milligan et al. 2006).

On the other hand, these asymmetries may not solely be attributed to chromospheric flows, but also to opacity changes occuring at different wavelengths because the velocity gradients in the chromosphere are very steep. This leads to the formation of blue and red asymmetries (Kuridze et al. 2015).

The low bulk velocities obtained from the bisector of the largest event might also be an indication that material may not be rising or falling. Rather, there is a movement in the flare footpoints that causes the red and blue asymmetries. During flare reconnection, the flare footpoints mostly appear to move away from one another (Asai et al. 2004; Temmer et al. 2007). To understand this better, we need photometric observations. Thus, there is need for simultaneous photometry and spectroscopy to fully understand the processes taking place in the photosphere and the chromosphere on this star during flare events.

Vida et al. (2019) studied 21 high-resolution spectra of AD Leo in their search for CMEs in late-type stars. In the 21 spectra, they found 9 events with low velocities with a maximum of $195\leavevmode\nobreak\ \rm km\,s^{-1}$ in the blue and $296\leavevmode\nobreak\ \rm km\,s^{-1}$ in the red, which is far below the escape velocity of AD Leo. Although their sample is smaller, their findings are in agreement with our findings. This might imply that fast events are rare on this and other M stars, and solar flare–CME relations may therefore not be extended to M stars.

Coronal mass ejections are commonly associated with flares that release energy in $10^{32}$ erg and last $\approx\leavevmode\nobreak\ 10^{4}$ s. The total emission during the largest flare that we observed was $2.9\times 10^{31}$ erg in $\rm H_{\beta}$ and $2.12\times 10^{32}$ erg in $\rm H\alpha$. In the case of solar flares, the energy released in soft X-rays and UV is one order of magnitude higher than that in $\rm H_{\alpha}$ (see reviews by  Mirzoian 1984; Haisch 1999; Garcia Alvarez 2000; Benz & Güdel 2010). Because the largest flare had $2.12\times 10^{32}$ erg in $\rm H_{\alpha}$, the flux in the X-ray and UV is expected to be $\approx 2.12\times 10^{33}$ erg. According to Somov (1992), the largest solar flares have $3\times 10^{30}$ erg in $\rm H\alpha$, which means that this flare was 70 times more energetic. From the flare frequency distribution we obtained for flares on this star, about one event with an energy of $3\times 10^{30}$ erg occurs per hour. On the Sun, many X class flares occur during solar maximum, but only a few or none during minimum. The average number of X class flares per year given in Aschwanden & Freeland (2012) is $\approx 6.7,$ which translates into 0.000765 events per hour. This implies that the flare activity of AD Leo is 1 000 times higher than that of the Sun for very large flares.

Using the parallax of AD Leo from Gaia, we obtain a distance of $4.9660\pm 0.0017$ pc, radius of 0.444$\mbox{R}_{\odot}$ , and luminosity of 0.024$\mbox{L}_{\odot}$. Following the method of determining the habitable zone boundaries in Whitmire & Reynolds (1996), we estimated its habitable zone to be at about 0.2 AU. Considering the largest flare, its intensity would be 2 000 times higher for a planet in the habitable zone. This means that an Earth-size planet in the habitable zone of AD Leo would receive more than $10^{6}$ times as much energy than the Earth does from solar flares. The total energy of the observed flares is $\approx 1.77\times 10^{33}$ erg during our observation time. In a year, the star would emit 35 times as much energy, which means the star would emit $\approx 6.2\times 10^{34}$ erg. When we consider a planet with the radius of the Earth in the habitable zone, the planet would receive at least $\approx 2.6\times 10^{28}$ erg per year in soft X-rays and XUV radiation.

Segura et al. (2010) analysed the effect of one flare with a total energy of $\sim 10^{34}$ erg that was observed on AD Leo in 1985. They found that the event did not necessarily present a problem for life on the surface of an Earth-like planet through the UV radiation. However, a substantial decrement in the ozone ($\sim 94\%$) was noted, caused by protons that would be produced if there were a CME. The authors estimated that the recovery time for the effects of such a flare is about 50 years. Venot et al. (2016) studied the effect of the same flare on the chemical composition of two hypothetical sub-Neptune and super-Earth-like planets orbiting AD Leo. They found that a single flare event could irreversibly alter the chemical composition of warm or hot planetary atmospheres, with the final steady-state being significantly different from the initial steady-state in both cases. Tilley et al. (2017) modelled the effects of frequent flaring of an M dwarf on the atmosphere of an unmagnetised Earth-like planet in the habitable zone. They found that the impact of one flare (equivalent to the size of flares on AD Leo) per month is sufficient to drive a loss of $99.99\%$ of the ozone column within eight years, with an unlikely recovery and thus further destruction. The surface of the planet would experience a UV flux of $\sim 0.18-1\,\rm W\,m^{-2}$. The authors suggested further experiments to establish the impact of these fluxes on the onset of complex organic chemistry and life. Howard et al. (2018) discussed the impact of flares on the habitability of planets around Proxima Centauri. They simulated flares with energies in the range of $10^{29.5}-10^{32.9}$ erg in the U band. They found that such events deplete the ozone by $90\%$ and the system hardly reaches a steady state with increasing time. This may seriously question the possibility of the existence of complex life forms around these active stars because the planetary systems seem to experience a high loss of ozone during high-energy events, which leaves the planetary surfaces largely unprotected from UV light. Only organisms capable of tolerating extreme conditions can survive such an activity.