Detection of Flare-induced Plasma Flows in the Corona of EV Lac with X-ray Spectroscopy

The Chandra X-ray Observatory was launched on 1999-Jul-23 (Weisskopf et al., 2000). As one of the two high-resolution grating systems on the Chandra, the High Energy Transmission Grating (HETG) consists of two sets of transmission gratings, i.e., the Medium Energy Grating (MEG) and the High Energy Grating (HEG), which simultaneously collect X-ray spectral signals in the wavelength ranges of 2.5$-$31 Å and 1.2$-$15 Å, respectively. In conjunction with a spectroscopic array of the Advanced CCD Imaging Spectrometer (ACIS-S) detector (Garmire et al., 2003), the HETG forms the High-Energy Transmission Grating Spectrometer (HETGS) (Canizares et al., 2005). The Chandra/HETGS provides a very high spectral resolving power ($\lambda$/$\Delta\lambda\sim$100$-$1000) and the high-accuracy wavelength calibration allows velocity measurements down to $\sim$10$-$20 km s^-1 (see Ishibashi et al., 2006; Argiroffi et al., 2017).

The Chandra Transmission Grating Data Archive and Catalog (TGCat, Huenemoerder et al., 2011) provides easy access to observations of a particular object or type of object, and its web search interface also supports a quick review on the quality and potential scientific usefulness of the spectra products. In order to search for flare-induced coronal plasma flows and possible stellar CMEs, we checked the spectra products of strong X-ray flare events that occur on single stars with the aid of TGCat, focusing on the Chandra category “Stars and WD”. Finally, we found observations of two single stars, including HR 9024 and EV Lac, with obvious Doppler shifts of spectral lines. The former has been investigated by Argiroffi et al. (2019). Here, we investigated the plasma flow pattern during several flares on EV Lac and tried to explain their physical origins.

EV Lac (EV Lacertae or Gl 873) is a nearby (5 pc) dM3.5e flare star in the constellation Lacerta, which emits strong X-rays and is known to frequently produce flares (with frequency up to 0.48 hr^-1) (e.g., Ambruster et al., 1984; Leto et al., 1997; Osten et al., 2005; Paudel et al., 2021; Muheki et al., 2020b). The quiescent coronal temperature of EV Lac appears to be 3$-$20 MK, since its differential emission measure (DEM) distribution derived from the Extreme Ultraviolet Explorer (EUVE, Bowyer & Malina, 1991) and Chandra observations peaks at log T/K $\sim$6.4 and does not decrease too much till log T/K = 7.2 (Osten et al., 2006). Due to its rapid spinning ($\sim$4.3 days), EV Lac hosts stronger magnetic activities and can produce many more powerful flares (with energy up to 10³⁴ erg) compared to our Sun (Favata et al., 2000; Osten et al., 2010). With time-resolved high-resolution H$\alpha$ spectroscopy of a flare on EV Lac, Honda et al. (2018) recently reported a blue wing enhancement during the whole duration of the flare (more than 1.5 hr) and an absorption component in the red wing during the early and later phases of the flare. They attributed the latter to chromospheric downflows in the post-flare loops, while tentatively ascribed the former to evaporation or filament activation/activity. Muheki et al. (2020b) monitored EV Lac spectroscopically at a high resolution for 127 hours. They found a significant blue shift ($\sim$ 220 km s^-1) in one of 27 H$\alpha$ flares and ascribed it to an erupting filament.

EV Lac was observed by the Chandra/HETGS twice in September 2001 for 100 ks (ObsID 1885) and March 2009 for 97 ks (ObsID 10679). Using these observations, Huenemoerder et al. (2010) previously conducted a survey of all short- and long-duration flares on EV Lac, focusing on their photometric parameters (amplitude, shape, and scale), temperature, emission measure, and Fe K fluorescence. With these two observations, our current work aims to probe flare-associated plasma flows and plasma parameter variations. For brevity, we hereafter refer to these two observations as Obs1 and Obs2, respectively. We used the analysis-ready Chandra/HETGS X-ray count spectra products obtained from the TGCat.

Figure 1 presents the X-ray spectra and total light curves of EV Lac observed in Obs1 and Obs2. The total 200-ks-long observation of EV Lac includes at least 12 flares (as labeled by No.1$-$12), indicating a high level of flaring activity. In order to study the coronal dynamics of these flares with time-resolved spectroscopy, we extracted both HEG and MEG spectra as a function of time during Obs1 and Obs2. As pre-study test cases, we tried to integrate the HEG and MEG spectra over many different time periods to obtain composite spectra using the Chandra’s data analysis system (CIAO version 4.12; Fruscione et al., 2006). As a result, we concluded that: (1) the MEG composite spectra with a higher SNR are suitable for our current study, while the HEG spectra are too weak to generate time-resolved composite spectra with enough counts for a line fit (on the time scale of several tens of ks); (2) Even for the strong spectral lines, the higher-SNR MEG composite spectra can only reflect the averaged coronal plasma dynamics over a time period of at least several tens of ks.

Therefore, we mainly investigated four time intervals with strong flare activities that we respectively labeled as “D1”, “D2”, “D3”, and “D4” (see Figure 1) and two relatively quiescent time intervals flare activities that we labeled as “reference” ones, using time-resolved MEG composite spectra. Despite that the reference interval (60$-$100 ks) in Obs1 includes a small short-duration flare (No.5), we confirmed that it still appears to be a good reference as compared to the flaring intervals D1 and D2 (Section 4.1). The average X-ray luminosity of these two reference time intervals in the wavelength range of 1.8–26 Å  is around 1.3 $\times$ 10²⁸ erg s^-1 and 1.7 $\times$ 10²⁸ erg s^-1, respectively. For each time intervals of our interest, we extracted composite spectra from the MEG spectra and their integration time ranges were manually selected based on our pre-study tests. The time range selection first ensures that each of the analyzed spectral lines has enough counts for a line fit (with a flux of at least $\sim$ 10 count bin^-1), and then should divide flare events into more different evolution phases from the light curves. According to these selection criteria, the number of composite spectra for each of the analyzed spectral lines could be different (see Section 4). In this integrating process, count errors of composite spectra were recomputed using the default methods provided by CIAO. For bins with sufficiently large counts (N $>20-$30), Gaussian statistics are appropriate, so that the 1-$\sigma$ error is given by $\rm\sqrt{N}$; for bins with lower counts, the Gehrels approximation (Gehrels, 1986) to confidence limits for a Poisson distribution was used, so that the 1-$\sigma$ error is given by $\rm 1+\sqrt{(N+0.75)}$.

The observed line profiles of these composite spectra can be well characterized by a modified Lorentzian function (see the Chandra Proposers’ Observatory Guide¹¹1https://cxc.cfa.harvard.edu/proposer/POG/html/ and Testa et al., 2004). This function is described by the relation

where $a$ is line intensity, $\lambda_{0}$ is line center, $\beta$ is the exponent, and $\Gamma$ is line width. This modified Lorentzian function will be used for further spectral analysis in Section 3.2 and 3.3.

We selected three strong and isolated Lyman $\alpha$ doublet lines: O viii (18.97 Å, T_peak$\sim$3 MK), Mg xii (8.42 Å, T_peak$\sim$10 MK), and Si xiv (6.18 Å, T_peak$\sim$16 MK), as well as one strong coronal emission line: Fe xvii (15.01 Å, T_peak$\sim$6 MK), for Doppler shift measurements. Each of these three Lyman $\alpha$ doublet lines have a known theoretical wavelength difference and an intensity ratio of 2:1 in the optically thin stellar coronae. We applied a two-component Lorentzian function with a fixed wavelength difference, intensity ratio, and line width plus a background to fit these observed Lyman $\alpha$ doublet lines (see Section 4). For the isolated Fe xvii line, a Lorentzian function was applied. With the aid of a Markov chain Monte Carlo (MCMC) analysis method (see Appendix A), the position of each selected line was determined. Considering that the coronal temperature of EV Lac is 3$-$20 MK, Doppler shifts of these selected lines can characterize plasma motions of the cool ($\sim$3 MK), warm (5$-$10 MK), and hot ($\sim$16 MK) components of EV Lac’s corona, respectively. Meanwhile, due to the negligible radial velocity of EV Lac (1.5 km s^-1) and the low satellite velocity (1-2 km s^-1), the observed Doppler shift of each analyzed spectral line should represent the plasma velocity on the star.

The variable line intensities of the He-like triplets of Si xiii (6.7 Å, T_peak$\sim$10 MK) and O vii (22 Å, $\sim$2 MK) and the line pair of Fe xvii (17.05/17.10 Å, T_peak$\sim$5 MK) were used to estimate the electron density and temperature variations during the flares on EV Lac. The relevant triplets of Si xiii and O vii are each formed by radiative decays from the upper to the ground state, including the resonance transition ($r$: $1s^{2}{~{}}^{1}S_{0}-1s2p{~{}}^{1}P_{1}$), the intercombination transition ($i$: $1s^{2}{~{}}^{1}S_{0}-1s2p{~{}}^{3}P_{1,2}$), and the forbidden transition ($f$: $1s^{2}{~{}}^{1}S_{0}-1s2s{~{}}^{3}S_{1}$). The flux ratio G = $(f+i)/r$ is mainly sensitive to temperature, while the flux ratio R = $f/i$ is sensitive to electron density because increased electron collisions excite the transition from the $3S_{1}$ to the $3P$ state before the former’s radiative decays (Gabriel & Jordan, 1969; Pradhan & Shull, 1981). Although other He-like triplets of Ne ix and Mg xi in Chandra X-ray spectra had occasionally been used for coronal plasma diagnostics on stars (e.g., Ness et al., 2002), here we did not undertake an analysis of them, since they were found to be heavily blended with other lines (e.g., Güdel et al., 2002; Testa et al., 2004).

For the relevant triplet, line parameters were determined through a three-component Lorentzian function. Assuming each component of the triplet has the same line width and a fixed wavelength difference, this function can be expressed as the following

where the subscripts, i.e., $\rm r$, $\rm i$, and $\rm f$, respectively represent the three components of the triplet, and B₀ is the background flux. Based on the known wavelength differences between different components of the triplet and the definitions of line ratios, this relation can be rewritten as the following

where the R and G ratios are the density- and temperature-sensitive line ratios of our interest, respectively. Similarly, line ratios and other parameters of the line pair of Fe xvii were also determined through a two-component Lorentzian function. The MCMC analysis method was also used to constrain and estimate each fitting result (see Appendix A). Composite spectra at different time intervals and their best fitting results are shown in Section 4. Meanwhile, the Doppler shifts measured from the Si xiii triplet and the line pair of Fe xvii were also provided as a complement to the Doppler shift measurements in Section 3.3.

The theoretical curves of R- and G-ratios of the Si xiii and O vii lines, as well as the line ratio of the Fe xvii line pair that we used for the order-of-magnitude estimation of plasma density and temperature are shown in Figure 2, which were obtained from the CHIANTI atomic database V.9.0.1 (Dere et al., 2019). The line pair of Fe xvii are density sensitive when log(n${}_{e})$ is larger than $10^{13}$ cm^-3 and their line ratio can well constrain the density as it is below 0.9. The Si xiii triplet are density sensitive when log(n${}_{e})>10^{12}$ cm^-3 and the R ratios we measured are mostly near 2.3, so that only an upper limit of density can be given in some time intervals. From Figure 2(b), we can see that the G ratio of the Si xiii triplet only slightly changes with the electron density. So in this work we used the theoretical G-ratio curve computed at the density of 10¹³ cm^-3 for temperature estimations, because this density is similar to previous density measurement results of the X-ray coronae on many stars from the Si xiii triplet (Ness et al., 2002; Testa et al., 2004). For the much weaker O vii triplet, reliable measurements of line ratios and Doppler shifts in different time intervals are impossible. But its R ratio (around 1.51$\pm$0.28) measured in the total observed MEG spectra reveals a characteristic coronal density of 5.5$\times$10¹⁰ cm^-3, consistent with other previous measurement results (e.g., Güdel et al., 2002; Testa et al., 2004; Liefke et al., 2010). Considering the potential model inaccuracies, we would emphasize as much as possible trends in the observed line ratios in this study, rather than the exact density/temperature values derived from the theoretical models.

In the 200-ks-long observation, we detected significant Doppler shifts during four flaring durations: D1, D2, D3, and D4. Their Doppler velocities in the range of 30$-$110 km s^-1 can not be explained by the spinning motion of coronal structures fixed on the stellar surface, because the velocity of EV Lac is low (4.5 km s^-1). The detected Doppler shifts in multi-temperature coronal emission lines result from flare-induced motions of X-ray emitting plasma, since each of their detections is temporally correlated with a flare activity. By comparison, Doppler shifts measured in the reference intervals (60$-$100 ks in Obs1 and 0$-$40 ks in Obs2) are almost all below $\pm$ 20 km s^-1, which confirms the accuracy and reliability of the wavelength calibration of the Chandra/HETGS.

In general, the densities we measured from the line ratios of Si xiii are compatible with the low-density limit of 10¹³ cm^-3 that reported for many stars by Testa et al. (2004). Moreover, the variable line ratios of the He-like Si xiii triplet in each flaring durations indicate a significant variation of plasma density and temperature with respect to that of the quiescent state. Variable ratios of the Fe xvii line pair generally indicate an average electron density near $10^{13}$ cm^-3, but their relevance to the flare activity seems to be more complex. Relatively high densities were found for medium flares, whereas lower densities were found for both the quiescent intervals and strong flares. (see Figure 4(h) and Figure 6(h)). Possibly, this is because this line pair have a formation temperature (5 MK) that is close to the background coronal temperature (peaks at log T/K $\sim$6.4) and thus are less sensitive to the high-temperature flaring plasma. So in the following discussion, we will focus on the more illustrative density/temperature diagnostics of high-temperature flaring plasma from the He-like Si xiii triplet.

The flaring duration D1 includes the decay phase of a long-duration flare (No.1) and another medium flare (No.2) detected in Obs1 (time range of 0$-$40 ks, see Figure 1(c) and Figure 3). The total X-ray energy radiated during D1 is around 7.7$\times$10³² erg and its maximum luminosity is about 9.4 $\times$10²⁸ erg s^-1. During D1, the measured R- and G- ratios of Si xiii display an increasing trend, along with the decrease of the X-ray flux (Figure 4 (a) and (c)). In other words, the characteristic coronal density and temperature during F1 are gradually decreasing to a quiescent state (Figure 4 (b) and (d)). The coronal density in flare No.1 was estimated as around 10^13.5 cm^-3 (see Figure 4 (b) (even with its lower limit unconstrained), which is significantly higher than that of the quiescent state in Obs1 (about 10¹² cm^-3) and thus indicates a significant density increase in the flaring coronal loops.

The Doppler shift measurements of D1 in Figure 3 and Figure 4 reveal the following behaviors: in the cool O viii line at 18.98 Å, a blueshift first increases from 28 $\pm$ 10 km s^-1 to 70 $\pm$ 7 km s^-1 in the 0$-$25-ks time interval and then decreases down to a near-zero velocity in the 25$-$35-ks time interval; obvious blueshifts of 50$-$130 km s^-1 simultaneously appear in many warm lines, including the Mg xii line, the Fe xvii lines, and the Si xiii triplet; by contrast, in the hot Si xiv line, a redshift decreases from 83 $\pm$ 44 km s^-1 to 48 $\pm$ 77 km s^-1. This Doppler shift pattern suggests simultaneous hot plasma downflows and cool/warm upflows. We will discuss the possible origin of such plasma flow pattern in Section 5.

The flaring duration D2 includes two short-duration but relatively strong flares (No.3 and 4) occurring in the 35$-$60-ks time interval of Obs1 (see Figure 1(c) and Figure 3). These two flares have peak luminosities of about 6.1 $\times$10²⁸ erg s^-1 and 5.5 $\times$10²⁸ erg s^-1, respectively. The total X-ray flare energy during D2 is about 2.0 $\times$10³² erg. During these two flares, the measured R- and G-ratio values of Si xiii are 2.05$\pm^{0.461}_{0.339}$ and 0.70$\pm^{0.053}_{0.052}$, respectively (Figure 4 (a) and (c)). Compared to the quiescent state in 60$-$100 ks, these line ratios indicate a significant increase of the coronal density up to 10^13.4 cm^-3 and a temperature rise (Figure 4 (b) and (d)). Note that the density measurement of D2 only gives the best and upper limit values, with the lower limit unconstrained (see Figure 4 (b)).

For D2, only one composite spectrum was obtained for each of the analyzed spectral lines. Our Doppler shift measurements of D2 in Figure 3 and Figure 4 demonstrate no obvious Doppler shift at the cool O viii line, but simultaneous blueshifts in other warm and hot lines with a velocity of 40$-$80 km s^-1. The Doppler shift pattern suggests the presence of hot and warm coronal upflows without cool downflows. Interestingly, the blue shift appears to increase with the line formation temperature, i.e., 40$-$50 km s^-1 in warm lines and 76 km s^-1 in the hot Si xiv line, despite the large uncertainty in the latter. Such features are quite similar to the observational characteristics of the gentle chromospheric evaporation observed in some solar flares with a relatively low energy injection rate (e.g., Fisher et al., 1985a; Zhang & Ji, 2013; Li et al., 2019b). In this case, the absence of blueshifts in the cool O viii can be ascribed to a low injection rate of nonthermal electrons and insufficient dissipation of energy in the lower atmosphere.

The flaring duration D3 occurs in the 40$-$60-ks time interval of Obs2 (see Figure 1(c) and Figure 5), which includes two relatively long-duration flares (No. 6 and 8), and a very short-duration flare (No.7). The total X-ray flare energy of D3 is about 2.6 $\times$10³² erg and its maximum peak luminosity is about 1.1 $\times$10²⁹ erg s^-1. The plasma flow pattern of D3 and its associated plasma parameter variation measured from the Si xiii triplet are also suggestive of gentle evaporation. Our Doppler shift measurements in Figure 5 and Figure 6 (e2) demonstrate that during D3, blueshifts of several tens km s^-1 appear in all cool, warm, and hot spectral lines. Their Doppler velocities also appear to increase with the line formation temperature, i.e., around 40 $\pm$ 10 km s^-1 in the O viii line, 43 $\pm$ 4 km s^-1 in the Fe xvii line pair, 44 $\pm$ 16 km s^-1 in the Fe xvii 15.01 Å line, 50 $\pm$ 20 km s^-1 in the Mg xii line, 62 $\pm$ 7 km s^-1 in the Si xiii triplet, and 69 $\pm$ 36 km s^-1 in the Si xiv line. Moreover, during D3, the measured R- and G-ratio values of Si xiii, as presented in Figure 6, are 2.03$\pm^{0.191}_{0.165}$ and 1.11$\pm^{0.030}_{0.033}$, respectively. Compared to the quiescent state in 0$-$40 ks, these line ratios also indicate an increase of the coronal density up to 10^13.0 cm^-3. However, its temperature appears to show no obvious change (Figure 6 (b) and (d)).

The flaring duration D4 includes two long-duration flares (No.11 and 12) occurring in 75$-$105 ks of Obs2 (see Figure 1(f) and Figure 5). During D2, the peak luminosity of is about 9.1 $\times$10²⁸ erg s^-1 and the total X-ray flare energy is about 6.7 $\times$10³² erg. Similarly, the plasma density and temperature diagnosed in D4 from the Si xiii triplet also reveal a significant increase compared to the quiescent state (Figure 6). In particular, the highest plasma density (10^13.8±0.1 cm^-3) measured in Obs2 is temporally correlated with the flare peak of the event No.11, which is also accompanied with a rise in temperature from the pre-flare level of log T/K = 6.5 to log T/K = 6.8.

For D4, one composite spectral profile was obtained for the warm Mg xii line, and two for the other selected spectral lines. Different from the smaller Doppler shift detected in the pre-flare state (see the time intervals 0$-$18 ks and 18$-$36 ks in Figure 5), our Doppler shift measurements in Figure 5 and Figure 6 indicate a simultaneous presence of cool/warm coronal downflows and hot coronal upflows in D4. The hot upflows appear as a significant blueshift at the 16-MK Si xiv line, which shows a possible velocity increase from 71 $\pm$ 44 km s^-1 in the 76$-$90-ks period to 95 $\pm$ 72 km s^-1 in the 90$-$105-ks period. For the warm downflows, their Doppler velocities are 54 $\pm$ 11 km s^-1 at the Si xii triplet and 105 $\pm$ 27 km s^-1 at the Mg xii line, respectively. Cooler downflows are simultaneously detected at the O viii line and the Fe xvii lines, with Doppler velocities in the range of 30$-$45 km s^-1.

Such a unique plasma flow pattern is highly analogous to that of the explosive chromospheric evaporation process observed in many large solar flares (e.g., Milligan & Dennis, 2009; Tian et al., 2015; Li et al., 2015a). In this case, the blueshift in the Si xiv line can be ascribed to the high-speed evaporating flows at a temperature of $\sim$16 MK, and the redshift detected in the Mg xii line and the Si xiii triplet most likely results from on-going cooling in post-flare loops. Such downward cooling flows in the 10-MK warm lines likely correspond to the “warm rain” phenomena, which have been reported in the explosive evaporation of solar flares with a formation temperature higher than the background coronal temperature but lower than that of the flaring loops (e.g., Brosius, 2003; Li & Ding, 2011). The redshifts of 30$-$45 km s^-1 detected in the cooler O viii line and the Fe xvii lines may be caused by cold rains (e.g., Tian et al., 2015; Antolin, 2020; Li et al., 2021a; Chen et al., 2022) in post-flare loops and/or chromospheric condensation driven by continuing nonthermal heating. As revealed by many solar flare cases, the appearance of “warm rain” and possible chromospheric condensation both can be regarded as supportive signatures of explosive injections of non-thermal electrons during flares (e.g., Ichimoto & Kurokawa, 1984; Fisher et al., 1985a; Brosius, 2003). In particular, the peak characteristic coronal density of D4 is found to rise up to 10^13.8 cm^-3, which indicates that a huge amount of heated chromospheric plasma is continuously replenished into the flare loops. Compared to D2 and D3, D4 indeed includes more powerful flare activities with X-ray energy up to 6.7$\times$10³² erg, which implies that a higher energy injection rate may be responsible for the observed explosive evaporation process.