Apache Point Observatory (APO)/SMARTS Flare Star Campaign Observations. I. Blue Wing Asymmetries in Chromospheric Lines during Mid-M-Dwarf Flares from Simultaneous Spectroscopic and Photometric Observation Data

During the 31 nights over 2 yr (2019 January–2021 February), we conducted time-resolved simultaneous optical spectroscopic and photometric observations of the three nearby mid-M-dwarf flare stars YZ CMi, EV Lac, and AD Leo. The basic parameters of these three target flare stars are listed in Table 1. The log of the observations is summarized in Table 2. These three stars have been known to flare frequently (e.g., Lacy et al. 1976; Hawley & Pettersen 1991; Kowalski et al. 2013; Muheki et al. 2020b; Namekata et al. 2020; Maehara et al. 2021; Paudel et al. 2021; Ikuta et al. 2023). Zeeman-broadening and Zeeman–Doppler Imaging observations of these stars have shown the existence of strong magnetic fields on the stellar surface (e.g., Saar & Linsky 1985; Johns-Krull & Valenti 2000; Reiners & Basri 2007; Morin et al. 2008; Kochukhov 2021).

Table 1. Target Star Basic Parameters

Star Name	Spectral Type a	Ua	ga	Va	dGaia b	Rstar a	Prot c	$v\sin i$ d	id
		(mag)	(mag)	(mag)	(pc)	(R⊙)	(days)	(km s−1)	(deg)
YZ CMi (Gl 285)	dM4.5e	13.77	11.76	11.19	5.99	0.30	2.77	5.0	60
EV Lac (Gl 873)	dM3.5e	12.96	10.99	10.28	5.05	0.36	4.30	4.0	60
AD Leo (Gl 388)	dM3e	11.91	10.12	9.32	4.97	0.43	2.24	3.0	20

Notes.

^a The Spectral type, U- and V-band magnitudes, and stellar radius (R_star) values are from Table 1 of Kowalski et al. (2013). The g-band magnitudes are from Zacharias et al. (2013). ^b Stellar distance from Gaia DR2 catalog (Gaia Collaboration et al. 2018). ^c Rotation Period values (P_rot). The values of YZ CMi and EV Lac are those estimated from TESS data in Maehara et al. (2021), Muheki et al. (2020b), respectively. The P_rot value of AD Leo is from Morin et al. (2008). ^d Projected rotational velocities $(v\sin i)$ and stellar inclination angle values (i), reported in Morin et al. (2008).

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Time-resolved spectroscopic observations were obtained at two facilities. For the 25 nights among the total 31 nights (Table 2), we conducted spectroscopic observations of the three target stars, using the ARC Echelle Spectrograph (ARCES; Wang et al. 2003) on the ARC 3.5 m telescope at Apache Point Observatory (APO). The wavelength resolution (R = λ/Δλ) is ∼32000, and the spectral coverage is 3800–10000 Å. This wavelength range includes Hα, Hβ, Hδ, Hγ, H, Ca ii H&K, Ca ii 8542 Å, He i D3 5876, and Na i D1 and D2 lines. The exposure times are listed in Table 2, which were determined to achieve signal-to-noise ratio (S/N) values ∼40–50 at the continuum level around the Hα 6563 Å line. We note that the APO/ARCES spectroscopic data have a relatively long overhead and read-out time: ∼180 s in total. The data reduction methods of APO 3.5 m/ARCES spectroscopic data are the same as in Notsu et al. (2019). We conducted standard image reduction procedures such as bias subtraction, flat-fielding, and scattered light subtraction, using the ECHELLE package in IRAF ¹⁷ and PyRAF ¹⁸ software. We used a Th/Ar lamp for wavelength calibration. We also applied the heliocentric radial velocity correction using the ECHELLE package.

For the 8 nights among the total 31 nights (Table 2), we conducted spectroscopic observations of one of the target stars YZ CMi, using the cross-dispersed, fiber-fed echelle CTIO HIgh ResolutiON (CHIRON) spectrogragh (Tokovinin et al. 2013) attached to the SMARTS 1.5 m telescope at CTIO. For the 2 among these 8 nights (Table 2), we also observed YZ CMi, using APO 3.5 m/ARCES. The wavelength range and wavelength resolution of our CHIRON data are 4500–8900 Å and R ∼ 25,000, respectively. This wavelength range includes Hα, Hβ, Ca ii 8542 Å, He i D3 5876, and Na i D1 and D2 lines. The exposure time was 600 s (Table 2), which was determined to achieve S/N values ∼40 at the continuum level around the Hα 6563 Å line. The spectra were reduced using the CHIRON pipeline described in Tokovinin et al. (2013).

Time-resolved photometric observations were done by using two ground-based facilities (ARCSAT and LCOGT) and TESS satellite. We conducted ground-based photometric observations using 0.5 m ARCSAT for the 24 nights (Table 2), simultaneously with the spectroscopic observations using APO 3.5 m/ARCES. We note that, among the 25 nights when we conducted APO 3.5 m/ARCES spectroscopic observations, we have no ARCSAT0.5m photometric data on 2019 December 8 because of the bad weather condition. We carried out u and g-band photometric observations using the Flarecam instrument of ARCSAT0.5m (Hilton 2011; Kowalski et al. 2013), which has enhanced UV sensitivity and rapid filter wheel rotation. The exposure times are listed in Table 2. Considering the filter wheel rotation time, the typical time cadence for each band is 50–60 s. Dark subtraction and flat-fielding were performed using PyRAF software in the standard manner before the photometry. Aperture photometry was performed using AstroimageJ (Collins et al. 2017). We used nearby stars as the magnitude references.

We also conducted ground-based photometric observations of one of the target stars YZ CMi, using the LCOGT network (Brown et al. 2013). These Las Cumbres Observatory (LCO) observations were conducted for 12 nights (Table 2) to support SMARTS 1.5 m/CHIRON spectroscopic observations. Using LCO 1 m telescopes with the Sinistro cameras, we carried out U-band photometric observations with exposure times of 10 and 25 s (Table 2). V-band photometric observations were conducted using LCO 0.4 m telescopes with the SBIG STL6303 cameras, and the exposure times are 6 s (Table 2). The data were reduced with the LCOGT automatic pipeline BANZAI, ¹⁹ which masks bad-pixels, applies an astrometric solution, and performs bias and dark subtraction. Aperture photometry was performed using AstroimageJ (Collins et al. 2017), and we used nearby stars as the magnitude references.

Among the 31 nights that we conducted the above ground-based spectroscopic and photomteric observations, the two terms observing one of the target star YZ CMi (2019 January 26–28 and 2021 January 31–February 4) were also covered with the observation window of TESS (Ricker et al. 2015; Table 2). We used the 120 s time cadence TESS Sectors 7 and 34 Pre-search Data Conditioned Simple Aperture Photometry (PDC-SAP) light-curve data (Vanderspek et al. 2018) of YZ CMi, retrieved from the Multimission Archive at the Space Telescope (MAST) Portal site, ²⁰ as we have done in Maehara et al. (2021). The data release (DR) numbers of Sectors 7 and 34 data that we used are DR9 (Fausnaugh et al. 2019) and DR50 (Fausnaugh et al. 2021), respectively.

The X-ray instrument NICER (Gendreau et al. 2016) on board the International Space Station (ISS) conducted monitoring observations of YZ CMi on 2021 January 26, 27, and 28 (Observation ID: 1200510101–1200510103). This was scheduled for simultaneously observations with the ARC 3.5 m/ARCES spectroscopy, ARCSAT 0.5 m photometry, and TESS photometry of YZ CMi (Table 2). NICER observed YZ CMi for about ∼2 ks for each ISS orbit (about 90 minutes) and 3–4 times every day (Table 2).

NICER X-ray Timing Instrument (XTI) is an array of aligned 56 X-ray modules, each of which consists of a set of an X-ray concentrator (XRC; Okajima et al. 2016) and a silicon drift detector (SDD; Prigozhin et al. 2016). Each XRC concentrates X-rays within a ∼3' radius field of view to the paired SDD, which detects each photon at accuracy at ∼84 ns. The XTI as a whole has one of the largest collecting areas among X-ray instruments between 0.2 and 12 keV (∼1900 cm⁻² at 1.5 keV). We use 50 XTI modules as the remaining six (ID: 11, 14, 20, 22, 34, 60) are inactive or noisy.

As also done in Hamaguchi et al. (2023), we reprocess the data sets with the NIC calibration ver. CALDB XTI(20210707) using nicerl2 in HEASoft ver. 6.29c and NICERDAS ver. V008c. Since NICER is not an imaging instrument, we evaluate particle background level using nibackgen3C50 ver. v7b with the parameters dtmin = 10.0, dtmax = 60.0, hbgcut = 0.1, s0cut = 30.0 (Remillard et al. 2022).

In the following sections, the flare luminosities and energies are calculated for continuum bands and the chromospheric emission lines. In this process, the distance of the target stars (Table 1), the quiescent luminosities of photometric bands (L_band,q), and the quiescent flux densities at the continuum levels around the lines $({F}_{\mathrm{line},{\rm{q}}}^{\mathrm{cont}})$ are used.

Quiescent luminosities of photometric bands (L_U,q, L_u,q, L_g,q, L_V,q, L_TESS,q) are estimated as in the following and are listed in Table 3. The U-band quiescent luminosities L_U,q are taken from Table 1 of Kowalski et al. (2013). The u-band quiescent luminosities L_u,q are converted from L_U,q, using the flux-calibrated quiescent spectroscopic data of the three target stars reported in Kowalski et al. (2013) ²¹ and the bandpass data of sdss u band (used in ARCSAT) and LCO U band. ²² As an example, the quiescent spectrum of YZ CMi taken from Kowalski et al. (2013) is shown with the u- and U-bands filter data in Figure 1(a). The g- and V-bands quiescent luminosities L_g,q and L_V,q are calculated from the same flux-calibrated quiescent spectroscopic data (Kowalski et al. 2013), the bandpass data of sdss g band (used in ARCSAT) and LCO V band, and the stellar distance d_Gaia (Table 1). In Figure 1(b), the g- and V-bands filter data are shown with the quiescent spectrum of YZ CMi as an example. The TESS-band quiescent luminosities L_TESS,q are also calculated by using the flux-calibrated quiescent spectra, the filter data, and and the stellar distance d_Gaia. In the case of YZ CMi, as shown in Figure 1(c), the filter curve is convolved with an M4 near-UV (NUV) to near-IR (NIR) spectral template from Davenport et al. (2012), which is normalized to the above flux-calibrated spectrum of YZ CMi from Kowalski et al. (2013). The normalization is done by using the wavelength regions of 7000–7500 and 8000–9000 Å.

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Table 3. Quiescent Luminosities of Continuum Bands and Quiescent Flux Densities Around Lines

Star Name	$\mathrm{log}{L}_{U,{\rm{q}}}$ a	$\mathrm{log}{L}_{u,{\rm{q}}}$ a	$\mathrm{log}{L}_{g,{\rm{q}}}$ a	$\mathrm{log}{L}_{V,{\rm{q}}}$ a	$\mathrm{log}{L}_{\mathrm{TESS},{\rm{q}}}$ a	${F}_{{\rm{H}}\alpha ,{\rm{q}}}^{\mathrm{cont}}$ b	${F}_{{\rm{H}}\beta ,{\rm{q}}}^{\mathrm{cont}}$ b
YZ CMi	28.6	28.5	29.57	29.65	30.99	25.2	8.3
EV Lac	28.8	28.7	29.80	29.87	31.11	57.0	20.3
AD Leo	29.2	29.1	30.17	30.23	31.37	128.5	48.1

Notes.

^a The quiescent luminosity values in U, u, g, V, and TESS bands (see Figure 1). Units are ergs per second. ^b Quiescent flux densities at the continuum levels around the lines (Hα, Hβ lines). Units are 10⁻¹⁴ erg s⁻¹ cm⁻² Å⁻¹. The continuum regions are determined by using the definitions in Table 3 of Kowalski et al. (2013).

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It is noted that, when calculating L_TESS,q, the actual data are used for calculation at the wavelength where the data exist (<9168 Å), while the templates are only used in the remaining redder part (>9168 Å).

This method is basically the same as that done for an M4-dwarf flare star GJ1243 in Davenport et al. (2020). As for the other target stars EV Lac and AD Leo, we estimated L_TESS,q values with the basically same method using the flux-calibrated quiescent spectra, the filter data, and the stellar distances. The data of flux-calibrated spectra of EV Lac and AD Leo were taken from Kowalski et al. (2013). The M3 spectral template from Davenport et al. (2012) is used for AD Leo instead of the M4 template for YZ CMi and EV Lac.

The flare luminosities in the photometric bands $({L}_{\mathrm{band},\mathrm{flare}}(t))$ are calculated from the quiescent luminosities L_band,q (Table 3) and the relative fluxes during the flares $({\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}(t))$:

$$\begin{eqnarray}&&{L}_{\mathrm{band},\mathrm{flare}}(t)={L}_{\mathrm{band},{\rm{q}}}\times {\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}(t).\end{eqnarray} \tag{ 1 }$$

The relative flux (see Figures 2–7 in Section 3.1) is here defined as Δf(t) = (f(t) − f_ave)/f_ave, where f(t) is flux, and f_ave is average flux of the nonflare phase. The flare energies in the photometric bands $({E}_{\mathrm{band},\mathrm{flare}})$ are calculated by integrating ${L}_{\mathrm{band},\mathrm{flare}}$ over the flare duration:

$$\begin{eqnarray}&&{E}_{\mathrm{band},\mathrm{flare}}=\int {L}_{\mathrm{band},\mathrm{flare}}(t){dt}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&={L}_{\mathrm{band},{\rm{q}}}\times \int {\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}(t){dt}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\equiv {L}_{\mathrm{band},{\rm{q}}}\times {\mathrm{ED}}_{\mathrm{band},\mathrm{flare}},\end{eqnarray} \tag{ 4 }$$

where ED_band are equivalent durations (see Hunt-Walker et al. 2012).

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In this study, we identified flares in the photometric bands when the relative flux ${\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}(t)$ is larger than 3 × σ_band at around the flare peak for multiple data points, and the light-curve shape looks consistent with stellar optical flares (i.e., rapid increase and gradual decay as in Davenport et al. 2014; Okamoto et al. 2021). σ_band is the standard deviation of the relative flux in each band on each night for the phases without flares.

If no clear flares are identified in the photometric bands during the flares in Hα and Hβ lines, the upper limit of flare peak luminosity (L_band in Table 4) is estimated by applying this detection threshold ${\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}\lt 3\times {\sigma }_{\mathrm{band}}$ to Equation (1). The upper limit of flare energy (E_band in Table 4) is calculated by assuming the light curve shows the linear decay with the peak amplitude 3 × σ_band and the decay time comparable to the Hα flare duration $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ in Table 4). Then, we apply ${\mathrm{ED}}_{\mathrm{band},\mathrm{flare}}=0.5\times (3\times {\sigma }_{\mathrm{band}})\times {\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ in Equation (4) for estimating the upper limit of flare energy.

Table 4. List of All Flares Detected in Hα/Hβ Lines

ID a	WLF b	UT Date	${t}_{\mathrm{start}}^{\mathrm{flare}}$ d	Peak Luminosity e , f							Energy g , h						${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ d , h
	Assym. c		(JD/BJD)	(1027 erg s−1)							(1031 erg)						(hr)
				LU	Lu	Lg	LTESS	LHα	LHβ		EU	Eu	Eg	ETESS	EHα	EHβ
							LV i							EV i
Y1	WL	2019 Jan 26	2458509.706	⋯	⋯	419	320	2.4–2.8	2.0–2.3		⋯	⋯	11	15	0.73–0.84	0.37–0.42	1.5
Y2	NEP	2019 Jan 27	before obs.	⋯	<8	<16	<33	1.3	1.0		⋯	<4.1	<8.9	<19	>0.74	>0.49	>3.2
Y3	NWL, (B)	2019 Jan 27	2458510.748	⋯	<8	<16	<33	2.8	1.8		⋯	<5.6	<12	<26	1.7	0.76	4.3
Y4	WL, (R)	2019 Jan 28	2458511.654	⋯	22	16	73	4.2–4.3	3.0–3.1		⋯	0.8	0.7	6.0	0.92–0.93	0.51–0.52	1.1
Y5	NWL	2019 Jan 28	2458511.819	⋯	<5	<9	<29	1.7–1.8	1.5–1.6		⋯	<1.0	<1.9	<6.5	0.38–0.40	0.26–0.27	1.3
Y6	NWL, (B)(R)	2019 Dec 12	2458829.841	⋯	<8	<1.8	⋯	3.6–3.8	1.8–1.9		⋯	<7.2	<16	⋯	>3.9	>1.8	>4.9
Y7	WL, (B?)	2020 Jan 14	2458862.830	⋯	15	19	⋯	1.8–2.1	1.4–1.6		⋯	4.9	3.9	⋯	1.1–1.2	0.76–0.82	2.9
Y8	WL	2020 Jan 14	2458862.951	⋯	1249	1492	⋯	10	9.6		⋯	12	13	⋯	>0.88	>0.71	>0.4
Y9	WL	2020 Jan 16	before obs.	103	⋯	⋯	202	3.4	3.3		3.7	⋯	⋯	6.0	>0.72	>0.66	>1.7
Y10	WL, (R)	2020 Jan 16	2458864.670	44	⋯	⋯	⋯	2.8	3.0		1.8	⋯	⋯	⋯	0.84	0.89	1.2
Y11	WL, (R)	2020 Jan 16	2458864.719	97	⋯	⋯	144	3.5–3.9	3.1–3.3		1.8	⋯	⋯	3.2	1.2–1.4	0.89–0.97	2.0
Y12	WL, (R)	2020 Jan 18	2458866.677	84	71	63	47	3.9–4.5	3.4–3.6		5.6	11	16	4.2	4.2–4.8	3.0–3.2	5.7
Y13	WL	2020 Jan 18	2458866.914	⋯	38	63	32	2.0	1.7		⋯	1.5	1.9	0.8	0.97	0.60	2.3
Y14	WL	2020 Jan 19	2458867.788	21	14	21	22	2.3–2.7	1.9–2.1		2.1	1.9	4.2	3.3	0.54–0.67	0.40-0.47	1.2
Y15	WL	2020 Jan 19	2458867.844	⋯	292	547	⋯	2.4–3.7	2.7–3.5		⋯	8.0	13	⋯	>0.24	>0.07	>0.3
Y16	WL, (R)	2020 Jan 20	before obs.	⋯	24	21	30	4.0	4.3		⋯	2.4	1.7	0.7	>2.4	>2.4	>2.5
Y17	WL, (R)	2020 Jan 20	2458868.707	⋯	29	25	34	4.2–5.0	5.2–5.7		⋯	15	6.3	9.8	3.4–3.7	4.2–4.3	6.0
Y18	WL, (B)	2020 Jan 21	2458869.591	41	⋯	⋯	41	2.6–2.8	1.9		4.6	⋯	⋯	2.4	1.5–1.6	1.3	3.4
Y19	WL, (R)	2020 Jan 21	2458869.738	59	⋯	⋯	41	4.8–5.1	4.5–4.9		11	⋯	⋯	4.4	>3.3	>2.5	>2.5
Y20	WL	2020 Jan 22	2458870.669	87	⋯	⋯	46	1.5–1.9	1.3–1.7		5.8	⋯	⋯	2.2	0.52–0.56	0.26–0.28	2.0
Y21	WL	2020 Jan 23	2458871.586	21	⋯	⋯	<17	1.6	1.6		3.8	⋯	⋯	<5.0	0.44	0.40	1.7
Y22	NEP	2020 Jan 23	2458871.656	⋯	⋯	⋯	⋯	1.9	1.9		⋯	⋯	⋯	⋯	0.74	0.59	3.2
Y23	WL, (B)	2020 Dec 6	before obs.	⋯	397	461	⋯	4.1–4.5	3.0–3.2		⋯	16	22	⋯	>1.1	>0.59	>1.3
Y24	WL	2020 Dec 6	2459189.892	⋯	23	16	⋯	1.7–1.8	1.4–1.5		⋯	0.5	0.6	⋯	0.25–0.26	0.17–0.18	0.7
Y25	WL	2020 Dec 7	before obs.	⋯	27	20	⋯	1.9–2.0	2.4–2.5		⋯	0.8	0.5	⋯	>0.43	>0.39	>0.8
Y26	NWL	2020 Dec 7	2459190.839	⋯	<8	<18	⋯	1.8	1.5		⋯	<7.2	<16	⋯	0.82–0.86	0.59–0.62	1.9
Y27	WL	2020 Dec 7	2459190.916	⋯	32	28	⋯	1.7	1.1		⋯	1.2	0.4	⋯	0.41–0.42	0.29–0.30	0.8
Y28	WL, (R)	2020 Dec 7	2459190.952	⋯	30	28	⋯	2.9–3.3	3.0–3.3		⋯	1.7	1.0	⋯	0.71	0.52	1.7
Y29	WL	2021 Jan 31	2459245.674	⋯	43	63	57	1.3–1.4	0.94–0.95		⋯	3.3	1.8	2.5	1.7	0.95	5.3
E1	NEP, (B)	2019 Dec 15	2458832.556	⋯	⋯	⋯	⋯	4.3	2.2		⋯	⋯	⋯	⋯	2.9	1.4	3.6
E2	WL, (B)	2019 Dec 15	2458832.705	⋯	23	37	⋯	2.8–2.9	1.3–1.4		⋯	1.1	0.7	⋯	0.58	0.16–0.17	0.9
E3	WL	2020 Aug 26	before obs.	⋯	13	<8	⋯	2.0–2.2	1.9–2.1		⋯	1.0	<3.3	⋯	>0.74	>0.55	>2.3
E4	WL	2020 Aug 26	2459087.906	⋯	16	29	⋯	1.5–1.9	2.2–2.5		⋯	1.4	2.0	⋯	>0.47	>0.47	>2.1
E5	WL, (R)	2020 Aug 27	2459088.846	⋯	1618	2708	⋯	22–47	21–35		⋯	84	106	⋯	7.3–10.4	6.7–9.1	3.5
E6	WL	2020 Aug 29	before obs.	⋯	10	14	⋯	1.3–1.9	0.70–0.74		⋯	0.3	0.7	⋯	>0.53	>0.35	>2.7
E7	NEP	2020 Sep 1	before obs.	⋯	⋯	⋯	⋯	3.0–3.2	2.3–2.4		⋯	⋯	⋯	⋯	>1.2	>0.88	>2.1
E8	WL	2020 Sep 2	2459094.811	⋯	24	<9	⋯	0.78–0.81	0.68–0.70		⋯	0.1	<2.4	⋯	0.17–0.19	0.12–0.13	1.4
E9	WL	2020 Sep 2	2459094.884	⋯	14	<9	⋯	1.2–1.3	1.4		⋯	0.9	<4.5	⋯	0.55–0.61	0.55–0.58	2.7
A1	NEP	2019 May 17	before obs.	⋯	⋯	⋯	⋯	3.7	1.9		⋯	⋯	⋯	⋯	>0.85	>0.35	>1.1
A2	WL, (R)	2019 May 18	2458621.676	⋯	61	72	⋯	4.5–4.9	4.8–5.0		⋯	3.0	1.6	⋯	0.52–0.58	0.55–0.57	1.0
A3	NEP, (B)	2019 May 19	before obs.	⋯	⋯	⋯	⋯	7.4	3.7		⋯	>2.7	>1.4	⋯	>5.3	>2.5	>3.1

Notes.

^a Flare ID. Flares Y1–Y29 are on YZ CMi, Flares E1–E9 are on EV Lac, and Flares A1–A3 are on AD Leo. ^b The 6 flares with the mark for not enough photometric data ("NEP") do not have enough photometric data to judge whether the flares are white-light (WL) or non-white-light (NWL) flares. The 31 flares with the mark "WL" are identified as WL flares. The 4 flares with the mark "NWL" are identified as candidate NWL flares. See Section 4.1 for the classification criteria. ^c Flares with "(B)" showed clear blue wing asymmetries in Hα line, while those with "(B?)" showed possible blue wing asymmetries but not so clear. Flares with "(R)" showed clear red wing asymmetries in Hα line. ^d The flare start time $({t}_{\mathrm{start}}^{\mathrm{flare}})$ and flare duration $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}})$ are measured from the Hα light curve. Flares Y1–Y5 and Y29 are shown with BJD. Other flares are shown with JD. ^e As for the peak luminosities in photometric bands (L_U , L_u , L_g , L_V , and L_TESS), we selected the peaks that are considered to be most physically associated with the flare peaks in the Hα and Hβ lines. This means that the largest flare peaks in photometric bands are not necessarily selected, but those most closest in time with the flare peaks in the Hα and Hβ lines are basically selected. ^f The upper limit marks "<" for the peak luminosities in photometric bands (L_U , L_u , L_g , L_V , and L_TESS) show that the clear flare emission is not identified in this band, and the detection threshold value "${\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}\lt 3\times {\sigma }_{\mathrm{band}}$" is shown (see Section 2.5 for the details). ^g The upper limit marks "<" for the flare energies in photometric bands (E_U , E_u , E_g , E_V , and E_TESS) show that the clear flare emission is not identified in this band, and the upper limit flare energies are shown (see Section 2.5 for the estimation method). As for Flare A3, the lower limit of flare energies are listed with the marks ">" to show the energy values from the available data, since only the late phase of this Flare A3 was observed in photometric bands, and it is highly possible that there are additional white-light emission (see also Section 3.7). Most of the LCO U- and V-band photometric data (except for Flare Y14) have some data gaps. Because of this, E_U and E_V values can be lower limit values except for Flare Y14. ^h The lower limit marks (">") for the E_Hα , E_Hβ , and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ show that the total flare phases were not observed in the Balmer lines, and only lower limit of these values are measured. In these cases, the flare energy values in photometric bands (E_U , E_u , E_g , E_V , E_TESS) can be larger than the listed values, but the lower limit marks (">") are not added for these photometric flare energy values, since it is not necessarily obvious whether there are additional (unobserved) white-light emissions even if the total flare phases were not observed in the Balmer lines (except for Flare A3 described in the footnote (g)). As for Flares Y2, Y6, and E3, the upper limit values of photometric flare energies (E_u , E_g , and E_TESS) with the marks "<" are shown (see footnote (g)), but the real upper limit values of E_u , E_g , and E_TESS could be larger than the listed values, as the total flare phases of these flares were not observed in the Balmer lines (see the lower limit marks are shown for the E_Hα , E_Hβ , and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ values of these flares). ⁱ As for Flares Y1–Y5 and Y29, TESS-band data are listed. As for Flares Y9–Y22, V-band data are listed.

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The quiescent flux densities at the continuum levels around the Hα and Hβ lines $({F}_{{\rm{H}}\alpha ,{\rm{q}}}^{\mathrm{cont}}$ and ${F}_{{\rm{H}}\beta ,{\rm{q}}}^{\mathrm{cont}}$ ) are calculated based on the flux-calibrated quiescent spectra of the target stars from Kowalski et al. (2013; see Figure 1), and the values are listed in Table 3. In this process, the continuum regions are determined by using the definitions in Table 3 of Kowalski et al. (2013). Flare luminosities in Hα and Hβ lines $({L}_{\mathrm{line},\mathrm{flare}}(t))$ can be calculated from the quiescent fluxes $({F}_{\mathrm{line},{\rm{q}}}^{\mathrm{cont}}$ in Table 3, and ${F}_{\mathrm{line}}^{\mathrm{cont}}(t)$ is the flux at the continuum level), relative fluxes at the continuum level around the lines ${\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)=({f}_{\mathrm{line}}^{\mathrm{cont}}(t)-{f}_{\mathrm{ave},\mathrm{line}}^{\mathrm{cont}})/{f}_{\mathrm{ave},\mathrm{line}}^{\mathrm{cont}}$, the stellar distance d_Gaia (Table 1), and the equivalent width (EW) of the flare component $({\mathrm{EW}}_{\mathrm{line},\mathrm{flare}}(t)$ = EW_line(t) − EW_line,q where ${\mathrm{EW}}_{\mathrm{line},\mathrm{flare}}(t)$ is the EW of the flare component, EW_line(t) is the total EW, and EW_line,q is the EW at the quiescent level; see also Figures 2–7 in Section 3.1) ²³ :

$$\begin{eqnarray}\begin{array}{rcl}{L}_{\mathrm{line},\mathrm{flare}}(t) & = & 4\pi {d}_{\mathrm{Gaia}}^{2}\times \left({F}_{\mathrm{line}}^{\mathrm{cont}}(t)\right.\\ & & \left.\times {\mathrm{EW}}_{\mathrm{line}}(t)-{F}_{\mathrm{line},{\rm{q}}}^{\mathrm{cont}}\times {\mathrm{EW}}_{\mathrm{line},{\rm{q}}}\right)\end{array}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&\begin{array}{l}=\ 4\pi {d}_{\mathrm{Gaia}}^{2}\times {F}_{\mathrm{line},{\rm{q}}}^{\mathrm{cont}}\times \left[\left(1.0+{\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)\right)\right.\\ \ \ \left.\times \ \left({\mathrm{EW}}_{\mathrm{line},\mathrm{flare}}(t)+{\mathrm{EW}}_{\mathrm{line},{\rm{q}}}\right)-{\mathrm{EW}}_{\mathrm{line},{\rm{q}}}\right]\end{array}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&\begin{array}{l}=\ 4\pi {d}_{\mathrm{Gaia}}^{2}\times {F}_{\mathrm{line},{\rm{q}}}^{\mathrm{cont}}\times \left[\left(1.0+{\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)\right)\right.\\ \ \ \left.\times \ {\mathrm{EW}}_{\mathrm{line},\mathrm{flare}}(t)+{\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)\times {\mathrm{EW}}_{\mathrm{line},{\rm{q}}}\right].\end{array}\end{eqnarray} \tag{ 7 }$$

Flare energies in Hα and Hβ lines $({E}_{\mathrm{line},\mathrm{flare}})$ can be calculated by integrating ${L}_{\mathrm{line},\mathrm{flare}}$ over the flare duration:

$$\begin{eqnarray}&&{E}_{\mathrm{line},\mathrm{flare}}=\int {L}_{\mathrm{line},\mathrm{flare}}(t){dt}\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&\begin{array}{l}=\ 4\pi {d}_{\mathrm{Gaia}}^{2}\times {F}_{\mathrm{line},{\rm{q}}}^{\mathrm{cont}}\times \displaystyle \int \left[(1.0+{\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t))\right.\\ \ \ \left.\times \ {\mathrm{EW}}_{\mathrm{line},\mathrm{flare}}(t)+{\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)\times {\mathrm{EW}}_{\mathrm{line},{\rm{q}}}\right]{dt}.\end{array}\end{eqnarray} \tag{ 9 }$$

In this study, g-band flux observations are mainly used for estimating ${\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)$ at the continuum level around the Hα and Hβ lines. Since the g-band flux changes can be larger than the changes of the real local continuum levels around Hα and Hβ lines considering the typical M-dwarf flare spectra (see Kowalski et al. 2013), the resultant values are shown with the ranges (e.g., L_Hβ = 2.0–2.3 × 10²⁷ erg s⁻¹ for Flare Y1): the lower values do not take into account any continuum flux changes $({\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)=0$ in Equations (7) and (9)), and the upper values correspond to the values incorporating g-band flux changes $({\rm{\Delta }}{f}_{\mathrm{line}}^{\mathrm{cont}}(t)$ taken from g-band light curves). We use the same method when we estimate the flare peak luminosities (L) and flare energies (E) in the Hα and Hβ lines of all the other flares listed in Table 4. The TESS-band continuum fluxes are not used in this process even for flares with TESS data (e.g., Flare Y1), since most of the flares in this study have no TESS data (Table 4).

In addition, as for the peak luminosities in photometric bands (U, u, g, V, and TESS bands) in Table 4, we selected the peaks that are considered to be most physically associated with the flare peaks in the Hα and Hβ lines. This means that the largest flare peaks in photometric bands are not necessarily selected, but those closest in time with the flare main peaks in the Hα and Hβ lines are basically selected. The detailed descriptions for the individual flares are in Sections 3.2–3.7 and Appendices A.1–A.18. In contrast, all changes (peaks) of the photometric-band luminosity (not only the highest peaks) during the whole flare duration in Hα line $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}})$ are taken into account for calculating the flare energies following Equation (9).

It is noted that some flares reported in this study seem to be superimposed on potential decay tails of previous flares, and this could affect the values of flare luminosities and energies. However, we do not correct for this issue, since it is difficult to correctly subtract the component of previous flares. The potential errors caused from this point should be kept in mind when discussing flare luminosities (see also descriptions for each flare in the following sections of this paper). Moreover, some flares show an extra blueshifted and/or redshifted component (see the discussions in the following sections), but the flare luminosity and energy values were not corrected for this. The emission contributions from the blueshifted and/or redshifted extra components are included in the resultant flare luminosity and energy values. The reason is that main discussions are not affected without any correction since the purpose of this paper is not discussing the detailed energy partition of flares, and the order-of-magnitude estimates of flare energies are sufficient for the purposes of this paper.

As described in Section 2, we conducted the time-resolved simultaneous optical spectroscopic and photometric observations of the three target stars YZ CMi, EV Lac, and AD Leo during the 31 nights in total (Table 2). YZ CMi was observed during the five campaign seasons: [i] 2019 January (3 nights), [ii] 2019 December (4 nights), [iii] 2020 January (9 nights), [iv] 2020 December (3 nights), and [v] 2021 January–February (2 nights). EV Lac was observed during the two campaign seasons: [vi] 2019 December (1 night) and [vii] 2020 August–September (6 nights). AD Leo was observed during the one campaign season [viii] 2019 May (3 nights). Figures 2–7 show the all light curves from the campaigns.

We note that flares are defined from the Hα and Hβ data since the main purpose of this paper is to investigate the blue and red asymmetries of Balmer lines during flares, as described in the Introduction section. It could be possible by definition that blue and red asymmetries occur with (i) flare emissions of Balmer lines below the detectable level, or (ii) in absence of flare-enhanced Balmer emission. For example, if the prominence eruption causes the line asymmetries (see the references in the Introduction section), the detectability of prominence eruption could be unrelated with that of the flare emission itself in Balmer lines. However, distinguishing among these alternative scenarios is beyond the scope of the current paper, since the main purpose of this paper is to report blue asymmetries of Balmer lines associated with clear flares, and to discuss the properties of blue asymmetries with flare properties. We note that there are no clear blue and/or red line asymmetries without clear flares in Balmer lines (see figures in the following part of this paper), and all line asymmetries in our observations are associated with flares in Balmer lines. Therefore, our approach does not ultimately cause any major ambiguities.

In total, 41 flares are detected as shown in Figures 2–7 and listed in Table 4. We label the 41 flares by the first character of each the target star: Flares Y1–Y29 on YZ CMi, Flares E1–E9 on EV Lac, and Flares A1–A3 on AD Leo. As can be seen in Figures 2–7, the Hα and Hβ light curves are almost always variable (e.g., Figure 3(c)) compared with the photometric data, and this makes it difficult to define nonflare or quiescent phases for many nights. Since the duration of flares in Balmer lines can be relatively long (e.g., up to a few hours) in many cases, there can be a lot of flares overlapping with other flares, or in other words, the other flare starts before the preceding flare emission completely decays (e.g., Flares Y16 and Y17 in Figure 3(c)). Moreover, there are also many partial flares (e.g., Flare A3 in Figure 7(a)), and their observed flare properties (e.g., flare energies) could include various uncertainties since only the portions of flare phases were observed. The main purpose of this paper is to understand the existence of various blue asymmetry events among various Balmer line flares, and some uncertainty of definitions of each flare could be left, as long as they are not expected to cause a serious problem for the main conclusion of this paper. Then, we defined flares with rough definition as a phase having clear emission increase: the EW amplitude of Hα ≳ +(0.5–1) Å, compared with nearby quiescent phase (or the phase having locally smaller emission compared with nearby data points). The threshold values are roughly determined for each observation period, considering the data S/N and quiescent level modulations (≳ + (0.5–1) Å for YZ CMi; ≳ + 0.5 Å for EV Lac and AD Leo), and the values are also described in the following paragraphs of this subsection. There are flares with multiple peaks (e.g., Flare Y3 in Figure 2(a)), but they are basically broadly classified into one long-timescale flare if the Hα EW amplitude of these multiple peaks are smaller than the threshold ≲ + (0.5–1) Å (e.g., Flare Y6). We briefly describe how each flare is defined in the following paragraphs of this section. All of the uncertainties of the flare definition described in this subsection should be kept in mind for the remainder of the analyses and discussions in this paper.

Figure 2 shows the light curves of YZ CMi during the campaign season [i] 2019 January 26–28. During this campaign season [i], YZ CMi was observed with APO 3.5 m optical high-dispersion spectroscopy, ARCSAT ground-based photometry (u and g bands), TESS space photometry Sector 7, and NICER X-ray spectroscopy. Five flares (Y1–Y5) were detected in the Hα and Hβ EW data in Figure 2(a). These five flares were defined as phases showing the Hα EW increase of ≳1 Å compared with nearby local quiescent phase on each night (EW of Hα ∼ 8.0–8.6 Å in the period of 2019 January 26–28). With this definition, a small amplitude increase after Flare Y1 at ∼0.4 day in Figure 2(a) was not counted as a flare. Flares Y2 and Y3 consist of multiple peaks, but we only broadly classified into two flares since the peaks during Flare Y2 and Y3 have Hα EW amplitudes smaller than ∼1 Å, and the light curve returned below the threshold only once at ∼1.25 days in Figure 2(a) during the observation on 2019 January 27th (see also Section 3.2). Flares Y4 and Y5 could be classified into one flare since there is a continuous decreasing trend over the observation period of this night (2019 January 28th), but we classified them into two flares since both peaks have amplitudes larger than ∼1 Å. It is then probable that independent flares can cause the time evolution of the EWs, and there can be some meanings to separately classify them (as Flares Y4 and Y5) and investigate whether each peak has line asymmetries, considering the main purpose of this paper. There is also a Hα emission increase at around the beginning of the observation data on 2019 January 28 before Flare Y4 (at ∼2.13 days in Figure 2(a)), but we do not define this as a flare since only three data points with relatively low S/N exist, and it is difficult to judge whether it showed line asymmetries for these data points (see also figures in Appendix A.2). In other words, this event cannot contribute to the main purpose of this paper even if it is counted as a flare, since it cannot be used for the line asymmetry classification.

Among these five flares, only Flare Y3 was observed with NICER X-ray data (Figures 2(d) and (e)). The parameters of these five flares are listed in Table 4, and these flares are described in detail in Section 3.2 and Appendices A.1–A.2.

Figure 3 shows the light curves of YZ CMi during the two campaign seasons [ii] 2019 December and [iii] 2020 January. During the campaign season [ii], YZ CMi was observed with APO 3.5 m optical high-dispersion spectroscopy and ARCSAT ground-based photometry (u and g bands; Table 2). During the latter season [iii], YZ CMi was observed with APO 3.5 m spectroscopy on 2020 January 14, 18, and 20, and with SMARTS 1.5 m spectroscopy on every night from 2020 January 16 to January 23 (Table 2). ARCSAT photometry (u and g bands) and LCO photometry (U and V bands) were conducted during the nights with APO 3.5 m spectroscopy and SMARTS 1.5 m spectroscopy, respectively. We note that LCO observations continued until January 27 after the SMARTS 1.5 m spectroscopic observations finished on 2020 January 27 (Table 2 and Figure 3(c)).

As a result, 17 flares (Flares Y6–Y22) were detected in Hα and Hβ data during these extensive campaign seasons (Figures 3(a) and (b)). These 17 flares were defined as phases showing the Hα EW increase of ≳1 Å compared with the nearby local quiescent phase on each night. During the campaign seasons [ii] and [iii], there are flare-like increases at ∼6.2–6.3 days in Figure 3(b) (2019 December 8) and at ∼3.2–3.3 days in Figure 3(c) (2020 January 17), but we did not classify them into flares since a few data points with low S/N only exist and it is not possible to discuss whether they showed line asymmetries. In other words, these events cannot contribute to the main purpose of this paper even if they are counted as flares. Flare Y6 has multiple peaks, but these peaks are not separated into multiple independent flares, since the amplitude of each peak is only ≲1 Å​​​​, and the Hα EW value was continuously much larger (>2.5–3.0 Å) than the local quiescent level (∼10.0–10.2 Å) (see also Section 3.3). Although Flare Y8 has only three data points after the flare start, this is counted as a flare since this has a very larger amplitude (∼9 Å) compared with other flares, and it is possible to discuss the line profiles (see also Appendix A.3). As for Flares Y10 and Y11, the Hα EW did not come back to the quiescent level between these two flares, and it was still at ∼9.7–9.8 Å, but we classified these two events into two flares (Y10 and Y11), since both of the two have duration of ≳1 hr, and the emission has a clear local minimum between the two whose amplitude is ≳1 Å (see also Appendix A.4). It is then probable that independent flares can cause these time evolution of the EWs, and there can be some meanings to separately classify them (as Flares Y10 and Y11) and investigate whether each peak has line asymmetries, considering the main purpose of this paper. Moreover, Flares Y14 and Y15, and Y16 and Y17 are classified into separated two flares, respectively, because of the same reason with the above Flares Y10 and Y11 (see also Appendices A.6 and A.7). In addition, Flares Y16 and Y17 are similar to Flares Y4 and Y5 mentioned above for the point that they showed a continuous decreasing trend over the whole observation period of this night (2019 January 20), but they are treated as two flares because of the same reason with Flares Y4 and Y5 in the above.

These 17 flares (Flares Y6–Y22) are listed in Table 4 and are described with more detailed figures in Sections 3.3–3.4 and Appendices A.3–A.9. Figures 3(a) and (b) also show that the Hα and Hβ EW values of the quiescent phase (nonflare phase) exhibit variability among the observation dates; this could be related with the rotational modulations, considering the rotation period of 2.77 days (Table 1).

Figure 4 shows the light curves of YZ CMi during the campaign season [iv] 2020 December 3–7. During this campaign season [iv], YZ CMi was observed with APO 3.5 m optical high-dispersion spectroscopy and ARCSAT ground-based photometry (u and g bands). Six flares (Y23–Y28) were detected in the Hα and Hβ EW data in Figure 4(a).

These six flares were defined as phases showing the Hα EW increase of ≳1 Å compared with nearby local quiescent phase on each night (Hα EW ∼ 6–7 Å). As for the data of 2020 December 7, three Hα emission increase peaks with smaller amplitude (EW amplitude of Hα ≳ 0.5 Å) were classified into separated flares (Flares Y25, Y26, and Y27). This is because there are peaks whose duration is ≳1 hr, and the emission of each peak clearly come back to local quiescent phase (see also figures in Appendix A.10). It is then probable that independent flares can cause the time evolution of the EWs, and there can be some meanings to separately classify them (as Flares Y25, Y26, and Y27) and investigate whether each peak has line asymmetries, for the main purpose of this paper. These flares are listed in Table 4 and are described with more detailed figures in Section 3.5 and Appendix A.10.

Figure 5 shows the light curves of YZ CMi during the campaign season [v] 2021 January 31–February 4. During this campaign season [v], YZ CMi was observed with APO 3.5 m optical high-dispersion spectroscopy, ARCSAT ground-based photometry (u and g bands), and TESS space photometry Sector 34. One flare (Y29) was detected in the Hα and Hβ equivalent width data in Figure 5(a). There could be a flare on February 4 as shown with the description "flare ?" in Figure 5(a), but the S/N was low due to bad weather. These flares are listed in Table 4 and are described with more detailed figures in Appendix A.11.

Figure 6 shows the light curves of EV Lac during the two campaign seasons [vi] 2019 December 15 and [vii] 2020 August 26–September 2. During these two campaign seasons [vi] and [vii], EV Lac was observed with APO 3.5 m optical high-dispersion spectroscopy and ARCSAT ground-based photometry (u and g bands). Nine flares (E1–E9) were detected in the Hα and Hβ EW data in Figures 6(a) and (b). These nine flares were defined as phases showing the Hα EW increase of ≳0.5 Å compared with nearby local quiescent phase on each night (Hα EW ∼ 5–7 Å). These flares are listed in Table 4 and are described with more detailed figures in Section 3.6 and Appendices A.12–A.16.

Figure 7 shows the light curves of AD Leo during the campaign season [viii] 2019 May 17–19. During this campaign season [viii], AD Leo was observed with APO 3.5 m optical high-dispersion spectroscopy and ARCSAT ground-based photometry (u and g bands). Three flares (A1–A3) were detected in the Hα and Hβ EW data in Figure 7(a). These three flares were defined as phases showing the Hα EW increase of ≳0.5 Å compared with nearby local quiescent phase on each night (Hα EW ∼ 5–7 Å). These flares are listed in Table 4 and are described with more detailed figures in Section 3.7 and Appendices A.17–A.18.

Next, we investigate whether blue wing asymmetries (enhancements of blue wings) are seen in the hydrogen Balmer Hα and Hβ lines. If the blue wing asymmetries are observed during a flare in Hα and Hβ lines, we also investigate whether other major chromospheric lines (Hγ, Hδ, Ca ii K, Ca ii 8542, He i D3, Na i D1 and D2, H + Ca ii H) also show blue wing asymmetries. As reported in the following subsections and listed in Tables 4 and 5, seven flares (Flares Y3, Y6, Y18, Y23, E1, E2, and A3) among all the 41 flares showed clear blue wing asymmetries in Hα and Hβ lines. These seven flares are also marked as "(B)" in Table 4. In Sections 3.2–3.7, we discuss the detailed flare light curves and flare chromospheric line spectra from the observation dates when blue wing asymmetries in Hα and Hβ lines were detected (YZCMi, 2019 January 27, 2019 December 12, 2020 January 18, and 2020 December 6; EVLac, 2019 December 15; ADLeo, 2019 May 19). The data of the observation dates when blue wing asymmetries were not detected are shown in Appendix. In this paper, we focus our analysis on the flares with blue wing asymmetries; the flares without blue asymmetries (e.g., flares only with red asymmetries and symmetric broadening) are briefly summarized in Section 4.5 and will be discussed in detail in our future papers.

On 2019 January 27, two flares (Flares Y2 and Y3) were detected in Hα and Hβ lines as shown in Figure 8(a). During Flare Y2, the Hα and Hβ EWs increased to 9.9 Å and 13.9 Å, respectively, and the flare duration in Hα $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}})$ is >3.2 hr (Table 4). We note that Flare Y2 was in progress when the observation was started. Flare Y3 has the larger amplitude than Flare Y2. During Flare Y3, the Hα and Hβ EWs increased to 11.2 Å and 16.1 Å, respectively, and the flare duration ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is 4.3 hr (Table 4). In addition to chromospheric lines, Flare Y3 is detected also in NICER X-ray data (Figure 8(d)). The white-light (WL) flux observed by ARCSAT u and g bands and TESS did not show clear enhancements above the photometric errors of the data (3σ_u = 22.9% , 3σ_g = 4.2%, and 3σ_TESS = 0.34%) during these two flares (Figures 8(b) and (c)). As described in Section 2.5, 3 × the standard deviation (3σ_u , 3σ_g , and 3σ_TESS) of the relative flux in the quiescent phase for each night is used for the detection threshold of the WL flare emission. There are very small suggestive increases in u and g bands and TESS data around time 6–8 hr in Figures 8(b) and (c), although this is still smaller than the threshold (3σ_TESS = 0.34%). We also note that these small increases could be caused by the emission lines (e.g., Balmer lines) included in u, g, and TESS bands.

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We estimated the upper limits to the flare component peak luminosities and flare energies in u, g, and TESS bands, following the method described in Section 2.5, and the resultant values (L_u , L_g , L_TESS, E_u , E_g , and E_TESS) are in Table 4. The flare component peak luminosities and flare energies of Hα and Hβ lines (L_Hα , L_Hβ , E_Hα , and E_Hβ ) are also estimated and listed in Table 4, following the method described in Section 2.5. Since Flare Y2 already started when the observation was started, the real flare energy values could be larger than the values listed here.

The Hα and Hβ line profiles during Flares Y2 and Y3 are shown in Figures 9 and 10. The clear Hα blue wing asymmetries with blue wing enhancements up to ∼−200 km s⁻¹ were seen twice at around the time [3] and [5] during Flare Y3 (Figures 8–10). The durations of these two blue wing asymmetries were both only ∼20 minutes. As for Hβ line, the blue wing asymmetry was not so clear at around the time [3], while the blue wing asymmetry with wing enhancements up to ∼−150 km s⁻¹ was clearly seen at around the time [5]. In addition to blue wing asymmetries, we note that red wing components of Hα and Hβ lines show some enhancemnents up to ∼+150 km s⁻¹ (e.g., see the time [3], [4], and [6] in Figures 9 and 10), and it can be interpreted that almost symmetric broadened wing components are seen at around these times.

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The EW light curves of Hγ, Hδ, Ca ii K, Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines are also shown in Figures 8(e), (f), and (g). ²⁴ The profiles of these lines and H + Ca ii H lines during Flare Y3 are shown in Figure 11. Since S/N of the spectroscopic data around these lines are smaller than those of Hα and Hβ lines, we integrate two or three temporally adjacent spectra into one spectra (see time resolution of the Hγ, Hδ, Ca ii K, Na i D1 and D2, and He i D3 5876 lightcurve data in Figure 8). In Figure 11, such time-integrated data are shown with the prime mark, and for example, the time [3'] in Figure 11 shows the time 6.79–7.00 hr, which include time [3] (Figures 8 and 9). The same way of using the prime mark is applied to all figures in the following of this paper.

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As for Hγ, Hδ, H, and Ca ii H&K lines, the blue wing asymmetries were not so clear at around the time [3'], while the blue asymmetries with wing enhancements of up to −50 to −100 km s⁻¹ were seen at around the time [5']. At around the time [3'], blue wing asymmetries are not clearly seen for these lines, but almost symmetric broadened wing components (±150 km s⁻¹) can be seen, and these symmetric wing components can be similar to those seen in Hα. In addition, the redshifted absorption components were seen especially in Ca ii H&K lines together with blue wing asymmetries at around the time [5'], and this component looks larger than the noise level. Similar redshifted components have been observed in the previous observation of Hα blue wing asymmetry (Honda et al. 2018), but currently, the physical origin of them is still unclear. It is also important to discuss the origin of the redshifted absorption in the future studies (see also Section 4.5 for future prospects of redshifts of lines).

The clear blue wing asymmetries were not seen in Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines, while Na i D1 and D2, and He i D3 5876 lines show slight (−10 to −20 km s⁻¹) blueshifts at around the time [5'] (Figure 11(j)). The EW light curves in Figures 8(e), (f), and (g) show that Hα and Ca ii K evolve similarly while other Balmer lines decrease faster during Flare Y3. We also note that Ca ii 8542 and Na D lines show relatively large responses in Flare Y2, while other lines show smaller responses compared to Flare Y3.

We generate a background-subtracted X-ray light curve between 0.5 and 2 keV for the NICER X-ray data. The light curve shows a count rate increase by a factor of 2 on the second day, which coincides with Flare Y3 in the Hα band (Figure 8). The photon count in the other intervals hovers around 6−7 cts s⁻¹ with a few small flare-like variations.

We applied an adaptive binning to the light curve with a Bayesian block algorithm (Scargle et al. 2013; see Figures 12(a) and (b)) and used those blocks for a spectral analysis of Flare Y3. We assume Block 5 just before the flare onset to represent the flare's nonflaring (quiescent) emission. The spectrum shows a hump between 0.5 and 1 keV, which originates from the Fe L and O K lines and the weak Mg and Si K lines. We reproduce the spectral shape by an optically thin thermal plasma emission (apec Smith et al. 2001) model with two temperature components at 0.26 and 0.97 keV (3.1 × 10⁶ and 1.1 × 10⁷ K) and an elemental abundance at 0.52 solar (see also temperature and emission measure, hereafter EM, values of the quiescent component shown in Figure 12(e)). However, the fit is not statistically acceptable at above 3σ due to the line-like excesses at 0.51 and 1.22 keV.

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Figure 13 shows time-resolved X-ray spectra during Flare Y3. The flare spectrum near the peak is significantly harder than the quiescent spectrum, with a strong oxygen K line at 0.64 keV. Since we measure the X-ray flux variation during the flare in this study, we fit each spectrum by a one-temperature apec model with independent oxygen and iron elemental abundances on top of the best-fit quiescent spectrum model.

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The resultant values of the temperatures (T) and EMs (EM = n² V) are shown in Figure 12(e). Here, n is the electron density, and V is the volume. Using the modeling results, the X-ray luminosities in the 0.5–2.0 keV band $({L}_{\mathrm{Xray},\mathrm{flare}}$(0.5–2.0 keV)) and the GOES band (1.5–12.4 keV= 1–8 Å , ${L}_{\mathrm{Xray},\mathrm{flare}}$(GOES band)) ²⁵ were calculated and shown in Figures 12(c) and (d) with Hα light curve. From this figure, we can see that Hα flare duration is longer than that of soft X-ray. The X-ray energy of Flare Y3 in the 0.5–2.0 keV band $({E}_{\mathrm{Xray},\mathrm{flare}}$(0.5–2.0 keV)) and the GOES band $({E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band)) are also calculated to be 2.6 × 10³² and 4.7 × 10³¹ erg. ${E}_{\mathrm{Xray},\mathrm{flare}}$(0.5–2.0 keV) is ∼15 times larger than the Hα flare energy (E_Hα = 1.7 × 10³¹ erg) and at least slightly larger than the upper-limit of TESS WL flare energy (E_TESS < 2.6 × 10³² erg).

On 2019 December 12, a flare (Flare Y6) was detected in Hα and Hβ lines as shown in Figure 14(a). During Flare Y6, the Hα and Hβ EWs increased to 13.5 Å and 16.8 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is >4.9 hr (Table 4). The observation ended in the decay of Flare Y6. The continuum flux observed by ARCSAT u and g bands shows (at least two) short (≲10 minutes each) enhancements during Flare Y6 (Figures 14(b) and (c)). The amplitudes of these short continuum enhancements in u band are ∼60% (around the time 10.3–10.4 hr) and ∼40% (around the time 12.2–12.3 hr), and those in g band are ∼4%–5% (around the time 10.3–10.4 hr) and ∼5%–6% (around the time 12.2–12.3 hr).

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Although there are continuum enhancements around the times 10.3–10.4 and 12.2–12.3 hr, there are no clear WL emissions that are considered to be physically associated with the early increasing phase of the Hα and Hβ flare emission (time before ∼10 hr). Considering this, the flare peak luminosities of Flare Y6 listed in Table 4 are upper limit values considering the photometric error values (3σ_u = 26%, and 3σ_g = 4.9%): L_u < 8 × 10²⁷ erg s⁻¹ and L_g < 1.8 × 10²⁸ erg s⁻¹ (see Section 2.5). As for flare energies, only the upper limit values are calculated from these upper limit peak luminosities following the method in Section 2.5: E_u < 7.2 × 10³¹ erg and E_g < 1.6 × 10³² erg. These upper limit values are larger than the values that can be estimated by only integrating the clear peaks around the times 10.3–10.4 and 12.2–12.3 hr (E_u = 6 × 10³⁰ erg, and E_g = 3 × 10³⁰ erg). We also estimated L_Hα , L_Hβ , E_Hα , and E_Hβ values, which are listed in Table 4. Since the observation ended before Flare Y6 ended, the real flare energy values can be larger than the values listed here.

The Hα and Hβ line profiles during Flare Y6 are shown in Figures 15 and 16. The clear Hα blue wing enhancement (blue wing asymmetry) up to ∼−200 km s⁻¹ was seen in early phase of the flare (e.g., time [1]), while the line profile gradually shifted to the red-wing enhancement (red wing asymmetry) up to ∼+200 km s⁻¹ (e.g., time [4]; Figures 14–16). The evolution of the Hα line from blueshifted to redshifted line wing asymmetry is particularly evident. Hβ line also shows the time evolution from the blue wing asymmetry to the red wing asymmetry (Figures 15 and 16), which is very similar to that of Hα line. The wing enhancements of these blue and red wing asymmetries in Hβ line are slightly smaller than those in Hα line: from ∼−200 to ∼+200 km s⁻¹ in Hα line, and from ∼−150 to ∼+150 km s⁻¹ in Hβ line.

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The EW light curves of Hγ, Hδ, Ca ii K, Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines are also shown in Figures 14(c), (d), and (e). The profiles of these lines and H + Ca ii H lines during Flare Y6 are shown in Figures 17 and 18. As for Hγ and Hδ lines, the blue wing asymmetries in the early phase of the flare are not so evident (time [1'], [2'], and [3'] in Figure 17) while the red wing asymmetries in the later phase are seen (time [4'] in Figure 17). Similar time evolution of red wing asymmetry was seen also in He i D3 5876 line, but the possible red wing asymmetry component at time [4'] was very small (≲50 km s⁻¹) (Figure 18(j)). As for Ca ii H&K, Ca ii 8542, Na i D1 and D2, and H lines, the line asymmetries are not readily detected (Figure 18).

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On 2020 January 21, two flares (Flares Y18 and Y19) were detected in Hα and Hβ lines as shown in Figure 19(a). As for Flare Y18, the Hα and Hβ EWs increased up to 10.5 Å and 15.8 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is 3.4 hr (Table 4). In addition to these enhancements in Balmer emission lines, the continuum flux from the LCO U- and V-band increase is at least ∼90%, and ∼5%, respectively, during Flare Y18 (Figure 19(b)). We note that the LCO photometric observation has gaps in the later phase of Flare Y18, and it could be possible that we missed the continuum flux increase during this time. As for Flare Y19, the Hα and Hβ EWs increased to 12.5 Å and 23.2 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is >2.5 hr (Table 4). We note that the observation finished before Flare Y19 ended. In addition to these enhancements in Balmer emission lines, the continuum flux observed with LCO U and V band increased at least by ∼130%–140%, and ∼5%–10%, respectively, during Flare Y19 (Figure 19(b)). The LCO photometric observation has gaps during Flare Y19, and it is possible that we missed the continuum brightness increase components during the gap time.

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We estimated the flare component peak luminosities and flare energies in U and V bands, and the resultant values (L_U , L_V , E_U , and E_V ) are in Table 4. The values listed here could be only the lower limit values, since the LCO observation has gaps during both Flares Y18 and Y19, (Figure 19(b)), and in the case of Flare Y19, the observation also finished before the flare ended. The L_Hα , L_Hβ , E_Hα , and E_Hβ values are also estimated and listed in Table 4. The Hα and Hβ energy values of Flare Y19 listed here are only the lower limit values, since the observation finished before Flare Y19 ended.

The Hα and Hβ line profiles during Flares Y18 and Y19 are shown in Figures 20–22. During Flare Y18, the blue wing asymmetry of Hα line was detected over about 1 hr around the flare peak (Figure 22). The enhancements of the blue wing of Hα line were the largest at around the beginning of the decay phase (time [3] and [4] in Figures 19(a), 20, and 22), and we can see the enhancements up to ∼−200 km s⁻¹ then. These blue wing enhancements up to ∼−150 km s⁻¹ were also possibly seen in Hβ line (time [3] and [4] in Figure 20(h)); though, the S/N of the data is relatively low. During Flare Y19, the Hα line showed the line wing broadenings (∼±150–200 km s⁻¹) twice during flares: one at around the time [5]–[7], and the other at around the time [8]–[10] (Figures 21 and 22). During these broadenings, the red wing of the Hα line was slightly enhanced. The Hβ line showed the similar line wing broadening (∼±150–200 km s⁻¹) at around the time [5]–[7], but the wing broadening in Hβ line was not seen in the later phase at around the time [8]–[10] (Figures 21 and 22).

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The EW light curves of Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines are also shown in Figure 19(c). The profiles of these lines during Flare Y19 are shown in Figure 23. Line asymmetries were not clearly seen in these lines.

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On 2020 December 6, two flares (Flares Y23 and Y24) were detected in Hα and Hβ lines as shown in Figure 24(a). Flare Y23 already started when the spectroscopic observation started. The Hα and Hβ EWs decreased from 10.5 Å and 17.8 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is >1.3 hr (Table 4). The photometric observation captured early phase of the flare since it started ∼1 hr before the spectroscopic observation started. During Flare Y23, the continuum brightness observed with ARCSAT u and g bands increased by ∼1260% and ∼125%, respectively (Figure 24(b)). As for Flare Y24, the Hα and Hβ EWs increased to 8.2 Å and 13.4 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is 0.7 hr (Table 4). In addition to these enhancements in Balmer emission lines, the continuum brightness observed with ARCSAT u and g bands increased by ∼70%–75% and ∼4%, respectively, during Flare Y24 (Figure 24(b)).

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We estimated L_u , L_g , E_u , E_g , L_Hα , L_Hβ , E_Hα , and E_Hβ values, and they are listed in Table 4. Since the initial phase of Flare Y23 was not observed in the spectroscopic observation, the Hα and Hβ luminosities and flare energies of Flare Y23 estimated here are only lower limit values.

The Hα and Hβ line profiles during Flares Y23 and Y24 are shown in Figures 25 and 26. The blue wing of Hα line was enhanced during Flare Y23 (time [1]–[4] in Figures 25(b), (f), and 26(a)). This blue wing asymmetry was the largest at time [1] (up to ∼−250 km s⁻¹) and continued until around the end of the flare (time [4]), while the velocity of blue wing enhancement decayed gradually. The similar time evolution with the blue wing asymmetry (up to ∼−200 km s⁻¹) was seen also in the Hβ line (time [1]–[4] in Figures 25(d), (h), and 26(b)), but the line wing asymmetries at around the time [1] and [2] were not as clear compared to those of Hα line (Figures 25(b), and 26(b)). During Flare Y24, there were no clear blue or red wing asymmetries in Hα and Hβ lines (time [5] and [6] in Figures 25 and 26), and the line profiles showed roughly symmetrical broadenings with ∼±100–200 km s⁻¹ at around the peak time of the flares.

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The EW light curves of Hγ, Hδ, Ca ii K, Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines are also shown in Figures 24(c), (d), and (e). The profiles of these lines and H + Ca ii H lines during Flare Y23 are shown in Figure 27. At around time [1] or [1'] (Figure 27), slight blue asymmetries (slight blue wing enhancements) were seen in all the lines except for Ca ii 8542, while the blue wing asymmetry velocities are different among the lines. For example, Ca ii K line shows blue asymmetry up to −100 to −50 km s⁻¹ while Hγ line shows up to −150 to −100 km s⁻¹.

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On 2019 December 15, two flares (Flares E1 and E2) were detected on EV Lac in Hα and Hβ lines as shown in Figure 28(a). As for Flare E1, the Hα and Hβ EWs increased to 9.0 Å and 11.0 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is 3.6 hr (Table 4). Only the late phase of Flare E1 was observed with ARCSAT u and g bands, and an increase of the continuum flux was observed in late phase at ∼4.3–4.4 hr (Figure 28(b)). It is possible there were increases of the continuum flux in the early phase of Flare E1. As for Flare E2, the Hα and Hβ EWs increased to 8.1 Å and 9.4 Å, respectively, and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is 0.9 hr (Table 4). In addition to these enhancements in Balmer emission lines, the continuum brightness observed with ARCSAT u and g bands increased by ∼60%–65% and ∼5%, respectively, during Flare E2 (Figure 28(b)).

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The L_u , L_g , E_u , E_g , L_Hα , L_Hβ , E_Hα , and E_Hβ values are listed in Table 4. As for Flare E1, we did not estimate L_u , L_g , E_u , and E_g values, since only the late phase of Flare E1 was observed with ARCSAT u and g bands, and no clear increases of the continuum brightness were observed in the late phase (Figure 28(b)).

The Hα and Hβ line profiles during Flares E1 and E2 are shown in Figures 29 and 30. The blue wing of Hα line was enhanced (up to −150–200 km s⁻¹) during the early phase of Flare E1 (time [1] in Figures 29(b) and 30(a)). The similar blue wing asymmetry (up to −150 km s⁻¹) was seen also in the Hβ line (time [1] in Figures 29(d) and 30(b)), but the duration of the blue wing asymmetry in Hβ line (∼0.5 hr) is shorter than that of Hα line (≳1 hr) (Figure 30). The blue wing asymmetry in Hα and Hβ lines (up to −150 km s⁻¹) were also seen at around the peak time of Flare E2 (time [1] in Figures 29(b) and 30(a)). The duration of the blue wing asymmetry in Hα and Hβ lines during Flare E2 were ∼20 and ∼10 minutes, respectively.

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The EW light curves of Hγ, Hδ, Ca ii K, Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines are also shown in Figures 28(c), (d), and (e). The profiles of these lines and H + Ca ii H lines during Flares E1 and E2 are shown in Figure 31. As for Hγ line, the blue wing asymmetries up to ∼−100 km s⁻¹ are seen during both Flares E1 and E2. As for Hδ and Ca ii H&K lines, possible blue wing enhancements (up to ∼−50 km s⁻¹) are seen during Flare E1, while line wing asymmetries of these lines are not clearly seen during Flare E2. The line asymmetries of H, Ca ii 8542, Na i D1 and D2, and He i D3 lines are not so clear during both E1 and E2. However, we also note that there could be some slight peak blueshifts in the lines, for which we do not see clear line wing enhancements (e.g., Ca H&K lines during Flare E2, He i D3 and Ca ii 8542 lines during Flare E1).

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On 2019 May 19, one flare (Flare A3) was detected on AD Leo in Hα and Hβ lines as shown in Figure 32(a). Flare A3 already started when the observation started. The Hα and Hβ EWs increased to 5.8 Å and 6.7 Å, respectively, and the ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ is >3.1 hr (Table 4). In addition to these enhancements in Balmer emission lines, the continuum flux observed with ARCSAT u and g bands increased by ∼40% and ∼3%–4%, respectively,

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at around time ∼3.9–4 hr during Flare A3 (Figure 32(b)), However, the photomeric observation covered only the latter portion of the flare, and the flare already had started when the observation started. Because of these, we cannot judge whether the main Hα and Hβ flare emission components are associated with WL flares or not. In these cases, we also do not list the flare peak luminosities in the continuum bands (u and g bands) in Table 4. The lower limits of flare energies in the continuum bands (u and g bands) are estimated to be E_u > 2.7 × 10³¹ erg, and E_g > 1.4 × 10³¹ erg from the existing data period. Since Flare A3 already started when the observation started, the L_Hα , L_Hβ , E_Hα , and E_Hβ , which are also listed in Table 4, are only lower limit values.

The Hα and Hβ line profiles during Flare A3 are shown in Figures 33 and 34. It is noted that the data on 2019 May 18 (see Figures 100(a)) are used for quiescent profiles in these figure, since the quiescent phase data are limited (or there could be no quiescent phase) on 2019 May 19 as seen in Figure 32. During Flare A3, the blue wings of Hα and Hβ lines were enhanced up to −150 to −200 km s⁻¹ (time [1]–[3] in Figures 33(b) and (d)). These blue wing asymmetries continued for more than 2 hr until the flare decayed (Figure 34).

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The EW light curves of Hγ, Hδ, Ca ii K, Ca ii 8542, Na i D1 and D2, and He i D3 5876 lines are also shown in Figures 32(c), (d), and (e). The profiles of these lines and Ca ii H and H lines during Flare A3 are shown in Figure 35. As for Hγ, Hδ, H, Ca ii H&K, Ca ii 8542, and He i D3 lines, the blue wing asymmetries similar to Hα and Hβ lines are seen during Flare A3; though, the velocities of peak wing enhancements are different.

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In this study, we observed flares in chromospheric lines (e.g., Hα line) and WL continuum emission bands (e.g., u and g bands), as summarized in Section 3.1 and Table 4.

Among the total 41 flares observed in this paper, 6 flares (Flares Y2, Y22, E1, E7, A1, and A3 marked with "NEP" in Table 4) do not have appropriate data sets for judging whether the flares showed corresponding WL continuum flux enhancements. As for the four (Flares Y2, E7, A1, and A3) among these six flares, the initial part of the flare time evolution was not observed both in the spectroscopic and photometric data, while the other two flares (Flares Y22 and E1) have large data gaps in the photomeric data. We classified the remaining 35 flares into WL flares and non-white-light (NWL) flares. The procedure is summarized as follows:

• (i)  
  As also described in Section 2.5, if the relative flux $({\rm{\Delta }}{f}_{\mathrm{band},\mathrm{flare}}(t))$ shows the increase whose peak amplitude is larger than the photometric error (3σ_band) and the associated flare decays over multiple data points, we judge that flare emission is identified in the photometric band.
• (ii)  
  The M-dwarf flare amplitudes are generally larger in blue bands as seen for Flare Y4 in Figure 52 as well as in previous studies (e.g., Hawley & Pettersen 1991; Namekata et al. 2020) since flare optical continuum spectra have much higher temperature than those in the quiescent phase (Kowalski et al. 2010; Kowalski et al. 2019; Howard et al. 2020). Considering this point, flares are classified as WL flares in this paper if the flare emissions in U or u bands are identified. One exception is Flare Y1, which showed clear WL emissions in g and TESS bands while there are no available u-band observation data (Figure 49). If there are no flare emissions identified in any photometric bands with the above threshold, the flare is identified as NWL flares.
• (iii)  
  It is noted that the threshold 3σ_band may depend on the data quality (S/N) of each night. The classification of WL flares and NWL flares could be somewhat affected from this point. Moreover, the flare colors in the optical band can include some variety among events (see Kowalski et al. 2019), and the WL or NWL classification based on one band (U or u band in this study) could leave us some bias. However, the purpose of the WL or NWL classification in this study is only to show that the blue wing asymmetries can exist both in clear WL flares and candidate NWL flares (see Section 4.2). In other words, it is sufficient to investigate whether each flare shows WL emissions within the available data set for each flare (whose data quality has some variety among each event). From this point of view, a detailed statistical classification of WL or NWL flares is beyond the scope of this paper, considering that most of the photometric data are from the ground-based observations with small ARCSAT and LCO telescopes including some data gaps. We note here that the future studies on the WL or NWL associations during Hα and Hβ flares are necessary with a more comprehensive and more well-observed data set (e.g., TESS-like high-precision space photometry, in blue optical wavelength band).

As a result, 31 flares showed corresponding WL continuum flux enhancements, and are classified here as WL flares (marked with "WL" in Table 4). The remaining 4 flares (Flares Y3, Y5, Y6, and Y26 marked with "NWL" in Table 4) are classified as candidate NWL flares in this study. It is noted three (Flares Y3, Y5, and Y26) among these 4 flares showed marginal WL increases comparable to photometric errors (see Figures 8, 52, and 76), while the other one Flare Y6 showed WL emission peaks in late phase of the Hα and Hβ flare; though, we judged that there are no clear WL emissions that are considered to be physically associated with the early main increasing phase of the the Hα and Hβ flare (see Figure 14).

The flare energy partition among different wavelengths is an important topic of stellar flares since this can have constraints on how flare energy release occur in the different layers of flaring atmosphere from photosphere to corona (e.g., Osten & Wolk 2015; Guarcello et al. 2019; Stelzer et al. 2022). We, here, briefly mention this topic on the basis of our observation data; though, the main topic of this paper is blue wing asymmetries of chromospheric lines, and detailed discussions on the flare energy partition are beyond the scope of this paper.

In Figure 36, we compare flare peak luminosities and energies in photometric bands (u and g bands) and Hα line.

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Figure 36(b) suggests a rough correlation between the flare energies especially between u band and Hα line, but detailed quantitative conclusions are beyond the scope of this paper considering some uncertainties of the observation data available in this study (e.g., there are some gaps in the photometric data and many flares only partially observed as shown with various symbols in this figure). We will come back to this point in our future paper, discussing in detail the differences of time evolution of various chromospheric lines during stellar flares (e.g., Kowalski et al. 2013). In addition, related with this topic, soft X-ray energy of Flare Y3 is mentioned in Section 4.4.

In this study, 41 flares were detected from the total 31 night observations, as summarized in Section 3.1 and Table 4. Among these, 7 flares (Flares Y3, Y6, Y18, Y23, E1, E2, and A3 in Sections 3.2–3.7) showed clear blue wing asymmetries in Hα line. Various notable properties, which are described in Sections 3.2–3.7, are summarized in Table 5. For reference, three flares with Hα blue wing asymmetries in Vida et al. (2016), Honda et al. (2018), and Maehara et al. (2021) are also listed in this Table 5 ("V2016," "H2018," and "M2021," respectively). In Table 5, we list ${v}_{\mathrm{blue},\max }^{{\rm{H}}\alpha }$ values, which are the maximum velocities of blue wing enhancements of Hα line measured by eye. The same velocity values for other lines showing blue asymmetries (e.g., ${v}_{\mathrm{blue},\max }^{{\rm{H}}\beta })$ are also listed in Table 6. We discuss blue wing asymmetry velocities more in detail by the line fitting method in Section 4.3. As summarized in Table 5 and described in the following, there are various correspondences in flare properties (e.g., durations of blue wing asymmetries, intensities of WL emissions, blue wing asymmetries in various chromospheric lines).

Table 5. Flares Showing Blue Wing Asymmetries

Flare	Star Name	UT Date	WLF	EHα	${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$	${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{blueasym}}$	${v}_{\mathrm{blue},\max }^{{\rm{H}}\alpha }$	Other Lines a
				(1031 erg)	(hr)	(minutes)	(km s−1)
Y3	YZ CMi	2019 Jan 27	NWL	1.7	4.3	∼20 × 2	−200	[B] Hβ, Hγ, Hδ, H, Ca ii H&K
								[NB] Ca ii 8542, Na D1 and D2, He D3
	(1) The clear short-lived Hα blue wing asymmetries up to ∼−200 km s−1 were seen twice (20 minutes × 2) during the Hα flare over 4 hr.
	(2) As for Hβ, Hγ, Hδ, H, and Ca ii H&K lines, blue wing asymmetries are not so clear at around the time of the first Hα blue asymmetry
	(time [3] in Figures 8–11), while they are clearly seen at around the second one (time [5] in Figures 8–11).
	(3) Some red-wing enhancements (or almost symmetric broadened wing components) were also seen for Hα, Hβ, Hγ, Hδ, H, and Ca ii H&K
	lines (e.g., ±150 km s−1 for Hα line).
	(4) Equivalent width light curves (Figure 8): Hα and Ca ii K evolve similarly while other Balmer lines, Ca ii 8542, Na i D1 and D2, and He i D3 lines
	decrease faster.
	(5) No clear white-light flux enhancements during the flare even in TESS high-precision photometric data, while there are very small suggestive
	increases (ETESS < 2.6 × 1032 erg).
	(6) Flare emission was observed also in NICER soft X-ray data (EX(0.5–2.0 keV) = 2.6 × 1032 erg, and ${E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band) = 4.7 × 1031 erg).
Y6	YZ CMi	2019 Dec 12	NWL	>4.1	>4.9	90–120	−200	[B] Hβ
								[NB] Hγ, Hδ, H, Ca ii H&K, Ca ii 8542, Na D1 and D2, He D3
	(1) The clear Hα blue wing enhancement up to ∼−200 km s−1 was seen in early phase of the flare, while the line profile gradually shifted to
	the red-wing enhancement up to ∼+200 km s−1, during the Hα flare over 4.9 hr.
	(2) Similar shift from blue to red wing asymmetry was also seen in Hβ line (from ∼−150 to ∼+150 km s−1).
	(3) Late-phase red wing asymmetries were also seen clearly in Hγ and Hδ lines, and possibly in He i D3 5876 line.
	(4) There are at least two short white-light continuum enhancements (≲10 minutes each) in the middle/late phase of the flare, but there are no
	other clear white-light enhancements that are considered to be physically associated with the early main increasing phase of
	the whole Hα flare.
Y18	YZ CMi	2020 Jan 21	WL	1.5–1.6	3.4	60	−200	[B] Hβ
								[NB] Ca ii 8542, Na D1 and D2, He D3
	(1) The blue wing enhancements up to ∼−200 and ∼−150 km s−1 were seen in Hα and Hβ lines, respectively, during the decay phase of the flare.
	(2) The multiple white-light continuum flux enhancements during the Hα flare.
Y23	YZ CMi	2020 Dec 6	WL	colorred >1.1	>1.3	>45	−250	[B] Hβ, Hγ, Hδ, H, Ca ii H&K, Na D1 and D2, He D3
								[NB] Ca ii 8542
	(1) The clear white-light continuum flux enhancements (∼1260% and ∼125% in u and g bands, respectively) observed before the start of
	the spectroscopic observation.
	(2) The Hα and Hβ blue wing enhancements up to ∼−250 and ∼−200 km s−1, respectively, were seen almost over the whole observed phase
	of the flare, while the velocities of blue wing enhancements decayed gradually.
	(3) Blue wing enhancements were seen in all the lines except for Ca ii 8542, while the velocities of blue wing enhancements are different
	among the lines.
E1	EV Lac	2019 Dec 15	NEP	2.9	3.6	≳60	−200	[B] Hβ, Hγ, Hδ, Ca ii H&K
								[NB] H, Ca ii 8542, Na D1 and D2, He D3
	(1) Only the late-phase of the flare was observed with ARCSAT photometry, so it is possible there were increases of the continuum white-light flux
	in the early phase of the flare.
	(2) The Hα and Hβ blue wing enhancements up to ∼−200 and ∼−150 km s−1, respectively, were seen, but the duration of the blue wing
	enhancement in Hβ line (∼0.5 hr) is shorter than that of Hα line (≳1 hr).
	(3) The blue wing enhancements were also seen for Hγ, Hδ, and Ca ii H&K lines, while possible slight blueshifts of the line peak were also seen
	in Ca ii 8542 and He i D3 lines.
E2	EV Lac	2019 Dec 15	WL	0.58	0.9	20	−150	[B] Hβ, Hγ
								[NB] Hδ, H, Ca ii H&K, Ca ii 8542, Na D1 and D2, He D3
	(1) The Hα and Hβ blue wing enhancements up to ∼−150 km s−1 were seen for the durations 20 and 10 minutes, respectively.
	(2) The clear white-light continuum flux increase was observed almost simultaneously with the Hα and Hβ blue wing enhancements.
	(3) The blue wing enhancements were also seen for Hγ lines, while possible slight line peak blueshifts were also seen in Ca ii H&K lines.
A3	AD Leo	2019 May 19	NEP	>5.3	>3.1	120–150		[B] Hβ, Hγ, Hδ, H, Ca ii K, Ca ii 8542, He D3
								[NB] Na D1 and D2
	(1) Flare already started when the observation started, so it is possible there were increases of the continuum white-light flux before the observation
	started.
	(2) The Hα and Hβ blue wing enhancements up to −150 to −200 km s−1 were seen, which continued for more than 2 hr until the flare decayed.
	(3) Blue wing enhancements were seen in all the lines except for Na i D1 and D2, while the velocities of blue wing enhancements are different among
	the lines.
V2016 b	V374 Peg	2005 Aug 20	⋯	∼102	∼3	15–40 minutes × 3	−675	[B] Hα, H β, Hγ
								[NB] He D3 (not clearly mentioned in Vida et al. 2016)
	(1) Three consecutive blue-wing enhancements in Balmer lines.
	All three blue-wing asymmetries occurred during a single flare with flaring energy ∼1033 erg (see Moschou et al. 2019), with
	the third event being the strongest, corresponding to projected velocity of −675 km s−1.
	This event showed not only blue wing asymmetries but also clearly separated additional emission components
	(see Figure 2 of Leitzinger et al. 2022).
H2018 b	EV Lac	2015 Aug 15	⋯	2.0	2.6	120	−200	⋯
	(1) A blue wing asymmetry in the Hα line has been observed for ≳2 hr (almost from flare start to end).
	(2) The possible existence of absorption components in the red wing of the Hα line was reported when the Hα line showed blue
	wing asymmetry.
M2021 b	YZ CMi	2019 Jan 18	no	0.47	1.2	80	−150	−-
	(1) A Hα flare without clear brightening in continuum, which exhibited blue wing asymmetry lasting for ∼1 hr.

Notes. WLF: this column describes whether the flare is identified as white-light flare (WL) or non-white-light flare (NWL), while stars with "NEP" do not have enough photometric data for the WL or NWL identification (from Table 4). ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$: flare duration in Hα line (from Table 4). E_Hα : flare energy in Hα line (from Table 4). ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{blueasym}}$: duration of Hα blue wing asymmetry (e.g., the double-headed arrow in Figure 10(a)). ${v}_{\mathrm{blue},\max }^{{\rm{H}}\alpha }$: the maximum velocity of blue wing enhancements estimated by eye. Other lines: [B] and [NB] show the lines with and without blue wing asymmetries, respectively.

^a There are no observation data of Hγ, Hδ, H, Ca ii H&K lines for Flare Y18, since these lines are not included in the wavelength range of SMARTS 1.5 m/CHIRON. ^b V2016, H2018, and M2021 are flares with clear blue wing asymmetries reported in Vida et al. (2016), Honda et al. (2018), and Maehara et al. (2021), respectively. They are listed here just for comparison. As for chromospheric lines, Hα line is only observed in Honda et al. (2018), Maehara et al. (2021). There were no white-light observation data in Vida et al. (2016), Honda et al. (2018). The flare energy value of V2016 is from Moschou et al. (2019).

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Table 6. Velocities and Masses of Blue Wing Asymmetry Flares

	Y3		Y6	Y18	Y23	E1	E2	A3
	[3] a	[5] a
${v}_{\mathrm{blue},\max }^{{\rm{H}}\alpha }$ [km s−1] b	−250	−250	−200	−200	−250	−200	−150	−200
${v}_{\mathrm{blue},\max }^{{\rm{H}}\beta }$ [km s−1] b	−200	−200	−150	−150	−200	−150	−150	−150
${v}_{\mathrm{blue},\max }^{{\rm{H}}\gamma }$ [km s−1] b	−100	−100	[NB]	⋯	−150	−100	−100	−150
${v}_{\mathrm{blue},\max }^{{\rm{H}}\delta }$ [km s−1] b	−100	−75	[NB]	⋯	−100	−50	[NB]	−150
${v}_{\mathrm{blue},\max }^{{\rm{H}}\epsilon }$ [km s−1] b	−50	−50	[NB]	⋯	−75	[NB]	[NB]	−100
${v}_{\mathrm{blue},\max }^{\mathrm{CaK}}$ [km s−1] b	−50	−50	[NB]	⋯	−100	−50	[NB]	−100
${v}_{\mathrm{blue},\max }^{\mathrm{CaH}}$ [km s−1] b	−50	−50	[NB]	⋯	−75	−50	[NB]	−100
${v}_{\mathrm{blue},\max }^{\mathrm{Ca}8542}$ [km s−1] b	[NB]	[NB]	[NB]	[NB]	[NB]	[NB]	[NB]	−50
${v}_{\mathrm{blue},\max }^{\mathrm{NaD}1\&{\rm{D}}2}$ [km s−1] b	[NB]	[NB]	[NB]	[NB]	−100	[NB]	[NB]	[NB]
${v}_{\mathrm{blue},\max }^{\mathrm{He}\ {\rm{D}}3}$ [km s−1] b	[NB]	[NB]	[NB]	[NB]	−100	[NB]	[NB]	−50
${v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ [km s−1]	−105 ${}_{-8}^{+11}$	−88 ${}_{-9}^{+8}$	−122 ${}_{-1}^{+1}$	−115 ${}_{-5}^{+2}$	−106 ${}_{-3}^{+1}$	−87 ${}_{-9}^{+7}$	−73 ${}_{-18}^{+11}$	−106 ${}_{-3}^{+0}$
${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ [Å]	${0.23}_{-0.03}^{+0.04}$	${0.45}_{-0.08}^{+0.08}$	${0.32}_{-0.01}^{+0.01}$	${0.27}_{-0.02}^{+0.01}$	${0.45}_{-0.03}^{+0.02}$	${0.39}_{-0.08}^{+0.07}$	${0.19}_{-0.04}^{+0.07}$	${0.16}_{-0.01}^{+0.00}$
${v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$ [km s−1]	−97 ${}_{-6}^{+1}$	−90 ${}_{-12}^{+10}$	−107 ${}_{-1}^{+1}$	−116 ${}_{-3}^{+11}$	−97 ${}_{-8}^{+7}$	−86 ${}_{-14}^{+11}$	−86 ${}_{-15}^{+18}$	−85 ${}_{-4}^{+1}$
${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$ [Å]	${0.40}_{-0.05}^{+0.01}$	${0.82}_{-0.13}^{+0.12}$	${0.29}_{-0.01}^{+0.01}$	${0.24}_{-0.01}^{+0.04}$	${0.94}_{-0.13}^{+0.13}$	${0.39}_{-0.09}^{+0.08}$	${0.28}_{-0.07}^{+0.08}$	${0.17}_{-0.02}^{+0.01}$
${L}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ [erg s−1]	${2.5}_{-0.3}^{+0.4}\times {10}^{26}$	${4.9}_{-0.9}^{+0.9}\times {10}^{26}$	${3.5}_{-0.1}^{+0.1}\times {10}^{26}$	${2.9}_{-0.2}^{+0.1}\times {10}^{26}$	${5.0}_{-0.3}^{+0.2}\times {10}^{26}$	${6.8}_{-1.4}^{+1.2}\times {10}^{26}$	${3.5}_{-0.7}^{+1.3}\times {10}^{26}$	${6.1}_{-0.4}^{+0.0}\times {10}^{26}$
${L}_{\mathrm{blue}}^{{\rm{H}}\beta }$ [erg s−1]	${1.4}_{-0.2}^{+0.1}\times {10}^{26}$	${2.9}_{-0.5}^{+0.4}\times {10}^{26}$	${1.0}_{-0.1}^{+0.1}\times {10}^{26}$	${8.6}_{-0.1}^{+0.1}\times {10}^{25}$	${3.5}_{-0.5}^{+0.5}\times {10}^{26}$	${2.4}_{-0.6}^{+0.5}\times {10}^{26}$	${1.8}_{-0.5}^{+0.5}\times {10}^{26}$	${2.4}_{-0.3}^{+0.1}\times {10}^{26}$
α (=${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$/${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\beta })$	1.75 ± 0.31	1.67 ± 0.39	3.35 ± 0.16	3.42 ± 0.46	1.45 ± 0.22	2.81 ± 0.82	1.91 ± 0.77	2.51 ± 0.26
$\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ [erg s−1 cm−2 sr−1]	6.4 ${}_{-0.2}^{+0.2}$	6.4 ${}_{-0.2}^{+0.2}$	${5.9}_{-0.1}^{+0.1}$	${5.9}_{-0.1}^{+0.1}$	${6.5}_{-0.1}^{+0.1}$	${6.0}_{-0.2}^{+0.3}$	${6.3}_{-0.3}^{+0.4}$	${6.1}_{-0.1}^{+0.1}$
${A}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ [1019 cm2]	1.6 ${}_{-0.7}^{+1.1}$	2.8 ${}_{-1.5}^{+2.3}$	6.9 ${}_{-1.6}^{+2.1}$	6.1 ${}_{-2.1}^{+2.6}$	2.3 ${}_{-0.8}^{+1.1}$	9.9 ${}_{-5.8}^{+9.6}$	2.5 ${}_{-1.8}^{+4.1}$	7.3 ${}_{-2.2}^{+2.4}$
(1) Upper limit ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ case (e.g., $\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$[erg s−1 cm−2 sr−1] = 6.0 for Flare Y6)
${\mathrm{logEM}}_{\mathrm{blue}}^{(1)}$ [cm−5]	32.6–33.0	32.7–33.1	30.9–31.2	30.9–31.2	32.8–33.2	31.5–32.1	32.3–32.7	31.5–32.1
$\mathrm{log}{n}_{e}^{(1)}$ [cm−3]	11.1–11.5	11.2–11.5	10.3–11.5	10.3–11.5	11.2–11.5	10.5–11.5	11.0–11.5	10.6–11.5
${D}_{\mathrm{blue},\mathrm{upp}}^{(1)}$ [cm] c	Rstar	Rstar	Rstar	Rstar	Rstar	Rstar	Rstar	Rstar
${D}_{\mathrm{blue},\mathrm{low}}^{(1)}$ [cm]	4.0 × 109	5.0 × 109	7.9 × 107	7.9 × 107	6.3 × 109	3.2 × 108	2.0 × 109	3.2 × 108
${M}_{\mathrm{blue},\mathrm{upp}}^{(1)}$ [g] (ne /nH = 0.17)	1.9 × 1018	4.2 × 1018	7.3 × 1017	7.0 × 1017	3.0 × 1018	7.5 × 1018	3.7 × 1018	3.5 × 1018
${M}_{\mathrm{blue},\mathrm{low}}^{(1)}$ [g] (ne /nH = 0.47)	4.1 × 1016	7.8 × 1016	4.9 × 1015	3.6 × 1015	1.1 × 1017	1.5 × 1016	1.8 × 1016	1.8 × 1016
(2) Lower limit ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ case (e.g., $\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$[erg s−1 cm−2 sr−1] = 5.8 for Flare Y6)
${\mathrm{logEM}}_{\mathrm{blue}}^{(2)}$ [cm−5]	31.7–32.1	31.8–32.2	30.5–30.7	30.5–30.7	32.2–32.6	30.6–31.0	30.9–31.2	30.8–31.2
$\mathrm{log}{n}_{e}^{(2)}$ [cm−3]	10.7–11.5	10.7–11.5	10.1–11.5	10.1–11.5	10.9–11.5	10.1–11.5	10.3–11.5	10.2–11.5
${D}_{\mathrm{blue},\mathrm{upp}}^{(2)}$ [cm] c	Rstar	Rstar	Rstar	Rstar	Rstar	Rstar	Rstar	Rstar
${D}_{\mathrm{blue},\mathrm{low}}^{(2)}$ [cm]	5.0 × 108	6.3 ×108	3.2 × 107	3.2 × 107	1.6 × 109	4.0 × 107	7.9 × 107	6.3 × 107
${M}_{\mathrm{blue},\mathrm{upp}}^{(2)}$ [g] (ne /nH = 0.17)	6.8 × 1017	1.5 × 1018	3.7 × 1017	3.5 × 1017	1.5 × 1018	1.7 × 1018	5.9 × 1017	9.7 × 1017
${M}_{\mathrm{blue},\mathrm{low}}^{(2)}$ [g] (ne /nH = 0.47)	5.1 × 1015	9.9 × 1015	1.9 × 1015	1.4 × 1015	2.7 × 1016	1.9 × 1015	7.1 × 1014	3.5 × 1015
Mblue,upp [g]	6.1 × 1018		7.3 × 1017	7.0 × 1017	3.0 × 1018	7.5 × 1018	3.7 × 1018	3.5 × 1018
Mblue,low [g]	1.5 × 1016		1.9 × 1015	1.4 × 1015	2.7 × 1016	1.9 × 1015	7.1 × 1014	3.5 × 1015
Ekin,upp [erg]	2.2 × 1032		5.4 × 1031	4.5 × 1031	1.7 × 1032	2.4 × 1032	7.2 × 1031	1.9 × 1032
Ekin,low [erg]	7.9 × 1029		1.5 × 1029	1.0 × 1029	1.6 × 1030	8.7 × 1028	2.9 × 1028	2.1 × 1029
${E}_{u,\mathrm{flare}}$ [erg] d	<5.6 × 1031		<7.2 × 1031	⋯	1.6 × 1032	⋯	1.1 × 1031	>2.7 × 1031
${E}_{U,\mathrm{flare}}$ [erg] d	⋯		⋯	4.6 × 1031	⋯	⋯	⋯	⋯
${E}_{g,\mathrm{flare}}$ [erg] d	<1.2 × 1032		<1.6 × 1032	⋯	2.2 × 1032	⋯	7 × 1030	>1.4 × 1031
${E}_{V,\mathrm{flare}}$ [erg] d	⋯		⋯	2.4 × 1031	⋯	⋯	⋯	⋯
${E}_{{TESS},\mathrm{flare}}$ [erg] d	<2.6 × 1032		⋯	⋯	⋯	⋯	⋯	⋯
${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ [erg] e	<6.2 × 1032		<8.0 × 1032	4.2 × 1032	1.8 × 1033	⋯	1.2 × 1032	>3.0 × 1032
${E}_{{\rm{H}}\alpha ,\mathrm{flare}}$ [erg] d	1.7 × 1031		>3.9 × 1031	(1.5–1.6) × 1031	>1.1 × 1031	2.9 × 1031	5.8 × 1030	>5.3 × 1031
${E}_{\mathrm{Xray},\mathrm{flare}}$(0.5–2.0 keV) [erg] d	2.6 × 1032		⋯	⋯	⋯	⋯	⋯	⋯
${E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band) [erg] d	4.7 × 1031		>3.6 × 1031	(1.4–1.5) × 1031	>1.0 × 1031	2.7 × 1031	5.4 × 1030	>4.9 × 1031
${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$ [erg] e	7.8 × 1032		>6.0 × 1032	(2.3–2.5) × 1032	>1.7 × 1032	4.5 × 1032	9.0 × 1031	>8.2 × 1032
${E}_{\mathrm{bol},\mathrm{flare}}$ [erg] e	7.8 × 1032		6.0 × 1032	2.3 × 1032	1.7 × 1032	4.5 × 1032	9.0 × 1031	3.0 × 1032
			−8.0 × 1032	−4.2 × 1032	−1.8 ×1033		−1.2 ×1032	−1.0 × 1034

Notes.

^a Blue wing asymmetries were seen twice (20 minutes × 2) during Flare Y3. The values for these two asymmetries, which occurred at around time [3] and [5] in Figure 8, are listed separately here. As for the mass and kinetic energy values, the sum of the two asymmetries are listed. ^b ${v}_{\mathrm{blue},\max }^{{\rm{H}}\alpha }$, ${v}_{\mathrm{blue},\max }^{{\rm{H}}\beta }$, ${v}_{\mathrm{blue},\max }^{{\rm{H}}\gamma }$, ${v}_{\mathrm{blue},\max }^{{\rm{H}}\delta }$, ${v}_{\mathrm{blue},\max }^{{\rm{H}}\epsilon }$, ${v}_{\mathrm{blue},\max }^{\mathrm{CaK}}$, ${v}_{\mathrm{blue},\max }^{\mathrm{CaH}}$, ${v}_{\mathrm{blue},\max }^{\mathrm{Ca}8542}$, ${v}_{\mathrm{blue},\max }^{\mathrm{NaD}1\&amp;{\rm{D}}2}$, ${v}_{\mathrm{blue},\max }^{\mathrm{HeD}3}$: the maximum velocity values of blue wing enhancements measured by eye, for Hα, Hβ, Hγ, Hδ, H, Ca ii K, Ca ii H, Ca ii 8542, Na i D1 and D2, and He i D3 lines. [NB] means this line does not show blue wing asymmetry (see Table 5). There are no observation data of Hγ, Hδ, H, Ca ii H&K lines for Flare Y18, which was observed with SMARTS 1.5 m/CHIRON. ^c Stellar radius (R_star) of YZ CMi, EV Lac, and AD Leo are 2.1 × 10¹⁰, 2.5 × 10¹⁰, and 3.0 × 10¹⁰ cm, respectively (see Table 1). ^d ${E}_{{\rm{H}}\alpha ,\mathrm{flare}}$, ${E}_{u,\mathrm{flare}}$, ${E}_{U,\mathrm{flare}}$, ${E}_{g,\mathrm{flare}}$, ${E}_{V,\mathrm{flare}}$, and ${E}_{{TESS},\mathrm{flare}}$ are flare energies in Hα line, u band, U band, g band, V band, and TESS band, respectively, which are taken from Table 4. As for Flare Y3, ${E}_{\mathrm{Xray},\mathrm{flare}}$(0.5–2.0 keV) and ${E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band) are the soft X-ray energies in 0.5–2.0 keV and the GOES band (1.5–12.4 keV) from the NICER X-ray spectra. As for other flares, ${E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band) are estimated from the flare energies in Hα line using the scaling law from Haisch (1989; see Section 4.3). ^e ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ and ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$ are the flare bolometric energy with the two different methods described in Section 4.3, respectively. ${E}_{\mathrm{bol},\mathrm{flare}}$ is the resultant bolometric flare energy used for Figure 47.

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Figure 37 shows the scatter plots of the Hα flare peak luminosity, energy, and duration values of the 7 flares with blue wing asymmetries and the remaining 34 flares observed in this study. Blue wing asymmetries could be seen both in relatively large and long, and small and short flares, although it would be difficult to statistically conclude this point only from the limited number of observed samples in this study.

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The duration of Hα blue wing asymmetries $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{blueasym}}$ in Table 5) ranges from 20 minutes to 2.5 hr (Figure 38). Comparing Figures 38(a) and (b), there is some variation among the relations of ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{flare}}$ and ${\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{blueasym}}$.

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As a notable example, Flare Y3 showed clear short-lived Hα blue wing asymmetries twice (20 minutes × 2 at the times [3] and [5]) during the entire Flare Y3 in Hα line lasting over 4 hr (Figures 8 and 10). Similarly, Vida et al. (2016) also reported three distinct blue wing enhancements spanning more than 3 hr ("V2016" in Table 5). In contrast, Flares Y23, E1, and A3 showed Hα blue wing asymmetries over almost all the observed phases of the flares (Figures 26, 30, and 34), although initial phases of the flares were not observed during Flares Y23 and A3. Similarly, Honda et al. (2018) also reported a continuous blue asymmetry of Hα line over all the phase of the flare (H2018 in Table 5). As another notable point, the blue wing asymmetry velocities showed gradual decays during Flares Y6 and Y23 (Figures 16 and 26). In particular, Flare Y6 showed clear Hα blue wing enhancement (blue wing asymmetry) up to ∼−200 km s⁻¹ in early phase of the flare, while the line profile gradually shifted to the red-wing enhancement (red wing asymmetry) up to ∼+200 km s⁻¹, during the Hα flare over 4.9 hr (Figure 16). In the middle time between blue wing asymmetry and red wing asymmetry, the Hα line profile showed almost symmetric broadening with ±150 km s⁻¹. These red wing asymmetries could be caused by the chromospheric condensation, flare-driven coronal rain or post-flare loop, as summarized in Section 4.5. This example (Flare Y6) may show that both blue and red wing asymmetries of Hα line can evidently occur during the same flare of a mid-M-dwarf, which suggests dynamic plasma motions upward and downward during the same flare.

It is noted that the possible change from blue wing enhancement to the red-wing enhancement during a flare was also reported in Muheki et al. (2020a).

However, it can be also possible that Flare Y6 consists of different consecutive flares showing blue wing asymmetries and red wing asymmetries, respectively, considering that the flare light curve showed multiple peaks (see Figure 14).

There is also a notable difference among the intensities of red wing of the Hα line when the blue wing shows an excess enhancement (blue wing asymmetry). As for Flares Y3, Y6, and A3, the red wing of the Hα line is broadened up to ∼+150 km s⁻¹ when the blue wing is more enhanced up to ∼−200 km s⁻¹ (Figures 10, 16, and 34). In contrast, during Flares Y18 and E2, the red wing of the Hα line is broadened only up to ∼+50–100 km s⁻¹ when the blue wing is enhanced up to ∼−200 km s⁻¹ (Figures 22 and 30). These differences might suggest that Hα line symmetric broadening or red-wing enhancements, which have been often observed during stellar flares (e.g., Namekata et al. 2020; Wollmann et al. 2023), could occur to some extent simultaneously with larger Hα blue wing enhancements (see also Section 4.5). In a relevant context, Honda et al. (2018) reported the possible existence of absorption components in the red wing of the Hα line when the Hα line showed blue wing asymmetry.

The intensities of WL continuum fluxes also showed various properties even among these 7 flares (the "WLF" column in Table 5). Flare Y3 did not show clear WL continuum flux enhancements, while flare emissions were observed for ≳4 hr in various chromospheric lines and NICER soft X-ray data (Figure 8; see also Section 4.4 for detailed discussions of NICER soft X-ray data). There were very small suggestive increases in u and g bands and TESS data around time 6–8 hr in Figures 8(b) and (c), although they are still a bit smaller than the WL flare detection thresholds (see Section 3.2). We can speculate that these small suggestive increases could be caused by the emission lines (e.g., Balmer lines) included in u, g, and TESS bands (see Figure 1). This flare could be possibly categorized to so-called NWL flares, which are often seen in the case of solar flares (e.g., Watanabe et al. 2017). Maehara et al. (2021) also reported the Hα blue wing asymmetry during an NWL flare ("M2021" in Table 5). As for Flare Y6, there are short WL continuum flux enhancements in the middle/late phase of the flare (around time 10.0–10.5 and 12.0–12.5 hr in Figure 14), but there are no other clear WL enhancements that are considered to be physically associated with the early increasing phase of the whole Hα flare, so this flare could be categorized into NWL flare as the whole flare event.

As described in Section 4.1, the 31 flares are classified as WL flares among the 35 flares with enough data sets to judge whether the flares are WL flares. The remaining 4 flares (Flares Y3, Y5, Y6, and Y26) are classified as NWL flares in this study, while three of them (Flares Y3, Y5, and Y26) showed slight possible WL increases almost comparable to the photometric errors, and Flare Y6 showed WL emissions in the middle/late phase of the Hα and Hβ flare emission. As a result, as for the 7 flares with clear blue wing asymmetries discussed here (Flares Y3, Y6, Y18, Y23, E1, E2, and A3), 5 flares (Flares Y3, Y6, Y18, Y23, and E2) have enough data sets for judging whether they are WL flares. Among these 5 flares, three flares (Flares Y18, Y23, and E2) are classified as WL flares, and two flares (Flares Y3 and Y6) are candidate NWL flares as described in the above. These results can suggest that blue wing asymmetries of chromospheric lines can be seen both during clear WL and candidate NWL flares. However, it should be noted the NWL flares in this study could actually be weak WL flares, since the ground-based photometry used for most of the flares in this study have relatively large photomeric errors, and high-precision TESS photometry is only available for six flares, and it only observes the red wavelength range (6000–10000 Å). This is not the best wavelength range for stellar flare observations compared with blue optical wavelength range (e.g., U and u bands), since the M-dwarf flares generally have larger amplitudes in the blue optical wavelangth range than in the red range (Hawley & Pettersen 1991; Kowalski et al. 2010; Brasseur et al. 2023).

In Table 5, we list which chromospheric lines showed blue wing asymmetries ([B] and [NB], as explained in a footnote of the table) in addition to Hα line. Large variety is seen also for this point. Among the seven flares with Hα blue wing asymmetries, all seven flares in this study showed blue wing asymmetries also in Hβ lines; though, the Hβ data of Flare Y18 was not so clear (Figure 20). Flares Y6 and E2 showed blue wing asymmetries in higher-order Balmer lines up to Hβ and Hγ lines, respectively, but they did not show blue wing asymmetries in chromospheric lines other than Balmer lines (e.g., Ca ii lines, Na i D1 and D2 lines, and He i D3 lines). Flares Y3 and E1 showed blue wing asymmetries not only in Balmer lines up to H and Hδ lines, respectively, but also in Ca ii H&K lines. Moreover, Flares Y23 and A3 showed blue wing asymmetries in almost all chromospheric lines we investigated, except for Ca ii 8542 and Na i D1 and D2, respectively. Blue wing asymmetries in multiple chromospheric lines have been investigated in several previous studies. Flare V2016 on M4 dwarf V374Peg from Vida et al. (2016; in Table 5) showed blue asymmetries in Hα, Hβ, and Hγ lines (see also the reanalysis results in Leitzinger et al. 2022), while it is not clearly mentioned whether He i line showed blue asymmetries or not in the discussions of Vida et al. (2016), Leitzinger et al. (2022). A flare on EV Lac in Figure 7 of Muheki et al. (2020b) also showed blue wing asymmetry only in Hα line but not in Hβ and He i lines. In contrast, a flare on AD Leo in Figure 6 of Muheki et al. (2020a) showed blue asymmetries both in Hα and Hβ lines.

The velocities of blue wing enhancements in these various chromospheric lines are listed in Table 6 $({v}_{\mathrm{blue},\max }$ in the table). The velocities are different among different lines, and the lower-order Balmer lines especially Hα line tend to show larger velocities of blue wing asymmetries or wider blue wing tails, while higher-order Balmer lines, Ca ii lines, Na i D1 and D2, and He i D3 lines show smaller velocities. ²⁶

We speculate that these differences can be caused by the differences of optical depth and line wing broadening physics among other chromospheric lines as described in the following. The differences of optical depth and line wing broadening physics (e.g., Stark effect) can affect these differences in the flaring atmosphere (e.g., Kowalski et al. 2022), while those of optical depth can also affect the emission from prominences (e.g., Okada et al. 2020).

These differences can be clues to investigate how blue wing asymmetries occur associated with flares on mid-M-dwarfs. For example, there is a difference of optical depth among different Balmer lines, and Hα line is more optically thick than other Balmer lines (e.g., Drake & Ulrich 1980; Heinzel et al. 1994a). Then, the visibility difference of Balmer lines could be a clue to constrain density and total emitting area values of the upward-moving plasma that caused the blue wing enhancements during flares. However, in order to interpret these differences more quantitatively in detail, it is necessary to conduct observation-based modeling studies incorporating radiative transfer physics of stellar (erupting) prominences and flaring atmospheres (e.g., Kowalski et al. 2022; Leitzinger et al. 2022). Comparisons with the multiwavelength Sun-as-a-star observation data of solar (erupting) prominences and solar flares are also very important for further quantitative discussions (e.g, Namekata et al. 2022a; Otsu et al. 2022; Lynch et al. 2023).

Using the line fitting method similar to Maehara et al. (2021), we estimated the velocities of blue wing excess components of Hα and Hβ lines (Figures 39–45).

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We note that, in this line fitting method (see Maehara et al. 2021; Inoue et al. 2023), there is an assumption that the flare emission other than the component causing the blue wing asymmetry shows completely symmetric emission, and the red wing is not affected by any flare-related processes. If the red wing is affected by the flare-related processes simultaneously, then the measured blue wing asymmetry properties could be somewhat overestimated or underestimated.

As shown with the line (3) in Figures 39(a) and (b), we first fitted the Hα and Hβ difference profiles (the quiescent component subtracted profiles) with the Voigt functions, assuming the line-of-sight velocity of 0 km s⁻¹ and only using the red part (>0 km s⁻¹) of the original spectra (line (2)). Next, we calculated the residuals between the fitted Voigt functions and the observed spectra, which are shown with lines (4) and (5) in Figures 39(a) and (b). Finally, the residual was fitted with the Gaussian function to estimate the blue wing excess component (line (6) in Figures 39(a) and (b)). In this Gaussian fitting process, the wavelength ranges shorter than the threshold velocities (−45 and −40 km s⁻¹ for Hα and Hβ profiles in Figures 39(a) and (b), respectively) were only used (line (4)). These threshold velocities were determined by trial-and-error and by eye, so that asymmetries at the line center components (line (5)) do not affect the fitting, and only the blue wing excess components are used for the Gaussian fitting (line (6)). Figures 39(a) and (b), which are described here, show the results of the first blue asymmetry component of Flare Y3. The fitting results of the second blue asymmetry component of Flare Y3 are shown in Figures 39(c) and (d). The fitting results of blue asymmetry components of other six flares (Flares Y6, Y18, Y23, E1, E2, and A3) are shown in Figures 40–45. As for Flare Y6 shown in Figure 40, the Gaussian fitting was conducted instead of the initial Voigt fitting (line (3)), considering the line profile of the original spectra (line (1)). The threshold velocities of the Gaussian fitting (6) (e.g., −45 and −40 km s⁻¹ for Hα and Hβ profiles in Figures 39(a) and (b)) are different among the events and lines, and the values are shown in the figures. The results of Gaussian fitting (6) (line-of-sight velocity and EW of blue wing enhancement components of Hα and Hβ lines) are shown with blue characters in Figures 39–45, and these values are listed in Table 6 $({v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$, ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$, ${v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$, ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta })$. The error values of these fitting results are roughly obtained by changing the threshold velocities by ±15 km s⁻¹. This range, ±15 km s⁻¹, is roughly assumed by considering the accuracy of the by-eye determination of the threshold velocity. For example, in the case of the first asymmetry component (time [3]) of Flare Y3, ${v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }=-{105}_{-8}^{+11}$ km s⁻¹, and ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ = 0.23 ${}_{-0.03}^{+0.04}$ Å, ${v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }=-{97}_{-6}^{+1}$ km s⁻¹, and ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$ = 0.40 ${}_{-0.05}^{+0.01}$ Å, by considering the threshold velocities of −45 ± 15 and −40 ± 15 km s⁻¹ for Hα and Hβ profiles in Figures 39(a) and (b). In addition, it is noted that the Hβ profile of Flare Y18 in Figure 41(b) is particularly noisy, the error values for this event can be larger than those estimated here, and we have to keep this in mind in the following analyses.

The estimated Doppler velocities of the 7 blueshift (blue wing asymmetry) events $({v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha })$ range from −73 to −122 km s⁻¹ (Table 6).

Since the asymmetries do not recur periodically both in the blue and red wings independently of flares, these 7 blue wing asymmetries should be more likely to be related to flares, and cannot be explained by the rotationally modulated emission from the corotating prominence (e.g., Jardine et al. 2020). These velocities (73–122 km s⁻¹) are also a bit larger than the upward velocities of blue asymmetries observed in Hα line mainly in the early phase of solar flares (e.g., Canfield et al. 1990; Heinzel et al. 1994b). For reference, such blue asymmetries of solar flares have been also observed in other chromospheric lines (e.g., Mg ii lines) mainly in the early phase (e.g., Tei et al. 2018; Huang et al. 2019; Li et al. 2019). The durations of these solar blue asymmetries (a few minutes) are 1 or 2 orders of magnitude shorter than those of the blue wing asymmetries in this study $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{blueasym}}=20$ minutes–2.5 hr in Table 5). In contrast, the velocities of the blue wing asymmetries in this study (73–122 km s⁻¹) are in the same range of solar prominence/filament eruptions (e.g., 10–400 km s⁻¹ according to Gopalswamy et al. 2003). The timescale of solar prominence/filament eruptions observed in Hα line is roughly 20 minutes–1 hr (Namekata et al. 2022c; Otsu et al. 2022), and this could be comparable or a bit shorter than the durations of the blue wing asymmetries in this study $({\rm{\Delta }}{t}_{{\rm{H}}\alpha }^{\mathrm{blueasym}}=$ 20 minutes–2.5 hr). In the case of stellar flares, since we cannot obtain spatial information of the stellar surface, such prominence/filament eruption may be a possible cause of the blue wing asymmetries in chromospheric lines associated with flares. We note that Leitzinger et al. (2022) suggested that, unlike the Sun, the "filament" can be visible in emission even on the stellar disk in the case of M-dwarfs, since the stellar background emission components are quite weak. In the following of this subsection, we discuss the blue wing asymmetries detected in this study, from the viewpoint of stellar prominence eruptions.

The estimated EW values of the Hα and Hβ emissions from blueshifted excess components $({\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ and ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$ in Table 6) can be converted to the luminosities of Hα and Hβ emissions $({L}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ and ${L}_{\mathrm{blue}}^{{\rm{H}}\beta }$ in Table 6), by applying ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ and ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$ values into Equation (7). As done in Maehara et al. (2021), Inoue et al. (2023), if we assume the simple slab NLTE emission model of solar prominences (e.g., Heinzel et al. 1994a) can be applied to the upward-moving plasma (possible prominence eruptions) showing the blueshifted excess components (blue wing asymmetries) on the M-dwarfs, the luminosities of Hα and Hβ emissions $({L}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ and ${L}_{\mathrm{blue}}^{{\rm{H}}\beta })$ can be calculated as

$$\begin{eqnarray}&&{L}_{\mathrm{blue}}^{{\rm{H}}\alpha }=\int \int {\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }{dAd}{\rm{\Omega }}=2\pi {A}_{\mathrm{blue}}^{{\rm{H}}\alpha }{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha },,\end{eqnarray} \tag{ 10 }$$

and

$$\begin{eqnarray}&&{L}_{\mathrm{blue}}^{{\rm{H}}\beta }=\int \int {\epsilon }_{\mathrm{blue}}^{{\rm{H}}\beta }{dAd}{\rm{\Omega }}=2\pi {A}_{\mathrm{blue}}^{{\rm{H}}\beta }{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\beta },\end{eqnarray} \tag{ 11 }$$

where ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ and ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\beta }$ are the Hα and Hβ line integrated intensities (see Table 1 of Heinzel et al. 1994a), ²⁷ and ${A}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ and ${A}_{\mathrm{blue}}^{{\rm{H}}\beta }$ are the area of the region emitting Hα and Hβ lines. If we assume Hα and Hβ emissions originate from the same area $({A}_{\mathrm{blue}}^{{\rm{H}}\alpha }={A}_{\mathrm{blue}}^{{\rm{H}}\beta })$, these two, Equations (10) and (11), are combined into one equation:

$$\begin{eqnarray}&&\displaystyle \frac{{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }}{{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\beta }}=\displaystyle \frac{{L}_{\mathrm{blue}}^{{\rm{H}}\alpha }}{{L}_{\mathrm{blue}}^{{\rm{H}}\beta }}\equiv \alpha .\end{eqnarray} \tag{ 12 }$$

The α values calculated from ${L}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ and ${L}_{\mathrm{blue}}^{{\rm{H}}\beta }$ values are listed in Table 6 (note the error values of ${L}_{\mathrm{blue}}^{{\rm{H}}\alpha }$, ${L}_{\mathrm{blue}}^{{\rm{H}}\beta }$, and α values in Table 6 are from those of ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ and ${\mathrm{EW}}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\beta }$ values). Then, we get linear relations between logarithms of Hα and Hβ line integrated intensities:

$$\begin{eqnarray}&&\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }=\mathrm{log}\alpha +\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\beta },\end{eqnarray} \tag{ 13 }$$

and these relations are plotted in Figure 46.

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Heinzel et al. (1994a) conducted the theoretical calculation of the NLTE slab model of solar prominence, and estimated the relation between Hα and Hβ line integrated intensities (Figure 1 therein). If we assume this relation can be applied to the upward-moving plasma showing the present blueshifted excess components, we can roughly determine the values of ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$, by comparing Equation (13) with the theoretical relation as in Figure 46. The resultant values of ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ are listed in Table 6. The error values of ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ listed in Table 6 are from the errors of α values and the scatter of the data points in Figure 1 of Heinzel et al. (1994a; ≈ the width of the gray shaded area in Figure 46).

By adapting Figure 5 of Heinzel et al. (1994a), these values of $\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ [erg s⁻¹ cm⁻² sr⁻¹] = 5.9–6.4 correspond to the optical thicknesses of the Hα line (τ_Hα ) roughly ranging from 10 to 300 $(\mathrm{log}{\tau }_{{\rm{H}}\alpha }\sim 1.0\mbox{--}2.5)$. Using the resultant ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ values and Equation (10), the ${A}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ values are obtained as listed in Table 6. The resultant values of ${A}_{\mathrm{blue}}^{{\rm{H}}\alpha }\sim {10}^{19}\mbox{--}{10}^{20}$ cm² roughly correspond to 0.5%–4% of the visible stellar surface of the target stars (YZ CMi, EV Lac, and AD Leo). This value can be a bit smaller than or comparable to the area of starspots estimated from the amplitude of rotational modulations (e.g., the total spot coverage ∼6%–17% for YZ CMi in Maehara et al. 2021).

In Figure 15 of Heinzel et al. (1994a), the correlation between Hα line integrated intensity $({\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha })$ and EM EM_blue = ${n}_{e}^{2}D$ is provided, where n_e and D are the electron density and geometrical thickness of the prominence, respectively. ²⁸ By adapting this correlation, the EM_blue values are obtained as listed in Table 6. In this table, the EM_blue values are separately listed for two cases (e.g., ${\mathrm{EM}}_{\mathrm{blue}}^{(1)}$ and ${\mathrm{EM}}_{\mathrm{blue}}^{(2)})$. These two cases correspond to upper and lower limit values of ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ values (e.g., $\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ = 6.0, and 5.8 [erg s⁻¹ cm⁻² sr⁻¹] for Flare Y6), respectively, which come from the error range of ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ in Table 6 (e.g., $\mathrm{log}{\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$[erg s⁻¹ cm⁻² sr⁻¹] = ${5.9}_{-0.1}^{+0.1}$ for Flare Y6). Assuming the observedelectron density range of solar prominences $(\mathrm{log}{n}_{{\rm{e}}}$[cm⁻³] = 10–11.5 from Hirayama 1986), the geometrical thickness D_blue $(={\mathrm{EM}}_{\mathrm{blue}}/{n}_{{\rm{e}}}^{2})$ can be estimated from the EM EM_blue. Since this assumed range of n_e could be wide, here, we have another rough constraint that the prominence geometrical thickness is no larger than the stellar radius (D_blue ≤ R_star). From this constraint, the lower limit of n_e can be determined as ${n}_{{\rm{e}}}\geqslant \sqrt{{\mathrm{EM}}_{\mathrm{blue}}/{R}_{\mathrm{star}}}$. The resultant estimated range of n_e and D_blue are listed in Table 6. For example, $\mathrm{log}{n}_{{\rm{e}}}^{(1)}$[cm⁻³] = 10.3–11.5, and ${D}_{\mathrm{blue}}^{(1)}=7.9\,\times {10}^{7}\mathrm{cm}-{R}_{\mathrm{star}}$ (=2.0 × 10¹⁰ cm) for the upper limit ${\epsilon }_{\mathrm{blue}}^{{\rm{H}}\alpha }$ case of Flare Y6.

With the estimated surface area $({A}_{\mathrm{blue}}^{{\rm{H}}\alpha })$ and geometrical thickness (D_blue) values, we can estimate the mass of the upward-moving plasma showing the blueshifted excess components (M_blue):

$$\begin{eqnarray}&&{M}_{\mathrm{blue}}\sim {A}_{\mathrm{blue}}^{{\rm{H}}\alpha }{D}_{\mathrm{blue}}{n}_{{\rm{H}}}{m}_{{\rm{H}}}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&={A}_{\mathrm{blue}}^{{\rm{H}}\alpha }\left(\displaystyle \frac{{\mathrm{EM}}_{\mathrm{blue}}}{{n}_{{\rm{e}}}^{2}}\right){n}_{{\rm{H}}}{m}_{{\rm{H}}}\end{eqnarray} \tag{ 15 }$$

$$\begin{eqnarray}&&={A}_{\mathrm{blue}}^{{\rm{H}}\alpha }\left(\displaystyle \frac{{\mathrm{EM}}_{\mathrm{blue}}}{{n}_{{\rm{e}}}}\right){\left(\displaystyle \frac{{n}_{{\rm{e}}}}{{n}_{{\rm{H}}}}\right)}^{-1}{m}_{{\rm{H}}},\end{eqnarray} \tag{ 16 }$$

where n_H is the total hydrogen density, and m_H is the mass of hydrogen atom. Here, we roughly assume the prominence ionization fraction from Table 1 of Labrosse et al. (2010), and i = n_e/n(H⁰) ≈ n(H⁺)/n(H⁰) = 0.2 − 0.9, where n(H⁺) and n(H⁰) are the proton density and neutral hydrogen density, respectively. From this,

$$\begin{eqnarray}&&\displaystyle \frac{{n}_{{\rm{e}}}}{{n}_{{\rm{H}}}}=\left(\displaystyle \frac{{n}_{{\rm{e}}}}{n({{\rm{H}}}^{0})}\right)\left(\displaystyle \frac{n({{\rm{H}}}^{0})}{{n}_{{\rm{H}}}}\right)\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&=\left(\displaystyle \frac{{n}_{{\rm{e}}}}{n({{\rm{H}}}^{0})}\right)\left(\displaystyle \frac{n({{\rm{H}}}^{0})}{n({{\rm{H}}}^{0})+n({{\rm{H}}}^{+})}\right)\end{eqnarray} \tag{ 18 }$$

$$\begin{eqnarray}&&\approx \left(\displaystyle \frac{{n}_{{\rm{e}}}}{n({{\rm{H}}}^{0})}\right)\left(\displaystyle \frac{n({{\rm{H}}}^{0})}{n({{\rm{H}}}^{0})+{n}_{{\rm{e}}}}\right)\end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray}&&=i/(i+1)\end{eqnarray} \tag{ 20 }$$

$$\begin{eqnarray}&&=0.17-0.47.\end{eqnarray} \tag{ 21 }$$

Then, for example, the upper and lower limit of the prominence mass in the case of Flare Y6 are estimated as follows:

$$\begin{eqnarray}&&{M}_{\mathrm{blue},\mathrm{upp}}\sim {A}_{\mathrm{blue},\mathrm{upp}}^{{\rm{H}}\alpha }\left(\displaystyle \frac{{\mathrm{EM}}_{\mathrm{blue},\mathrm{upp}}^{(1)}}{{n}_{{\rm{e}},\mathrm{low}}^{(1)}}\right){\left({\left(\displaystyle \frac{{n}_{{\rm{e}}}}{{n}_{{\rm{H}}}}\right)}_{\mathrm{low}}\right)}^{-1}{m}_{{\rm{H}}}\end{eqnarray} \tag{ 22 }$$

$$\begin{eqnarray}&&\sim {\left((,6.9,+,1.6,),\times ,{10}^{19},),\left(\displaystyle \frac{{10}^{31.2}}{{10}^{10.3}}\right),(,0.17\right)}^{-1}(1.7\times {10}^{-24})\end{eqnarray} \tag{ 23 }$$

$$\begin{eqnarray}&&\sim 7.3\times {10}^{17}\,{\rm{g}},\end{eqnarray} \tag{ 24 }$$

and

$$\begin{eqnarray}&&{M}_{\mathrm{blue},\mathrm{low}}\sim {A}_{\mathrm{blue},\mathrm{low}}^{{\rm{H}}\alpha }\left(\displaystyle \frac{{\mathrm{EM}}_{\mathrm{blue},\mathrm{low}}^{(2)}}{{n}_{{\rm{e}},\mathrm{upp}}^{(2)}}\right){\left({\left(\displaystyle \frac{{n}_{{\rm{e}}}}{{n}_{{\rm{H}}}}\right)}_{\mathrm{upp}}\right)}^{-1}{m}_{{\rm{H}}}\end{eqnarray} \tag{ 25 }$$

$$\begin{eqnarray}&&\sim {\left((,6.9,-,1.6,),\times ,{10}^{19},),\left(\displaystyle \frac{{10}^{30.5}}{{10}^{11.5}}\right),(,0.47\right)}^{-1}(1.7\times {10}^{-24})\end{eqnarray} \tag{ 26 }$$

$$\begin{eqnarray}&&\sim 1.9\times {10}^{15}\,{\rm{g}}.\end{eqnarray} \tag{ 27 }$$

It must be noted that there is an important assumption that we simply applied the solar prominence model of Heinzel et al. (1994a) for estimating the parameters (e.g., mass) of the upward-moving plasma (prominence eruptions) of M-dwarfs. It is assumed that the parameter space of the prominence plasma (e.g., density, temperature) is the same for the Sun and M-dwarfs. The models of Heinzel et al. (1994a) are computed for solar incident radiation (solar intensity and spectral energy distribution, and line profile shapes) and for a fixed height of 10,000 km above the solar surface. These model setups can be different between the Sun and M-dwarfs. The resulting prominence parameters can also depend crucially on the scattering of the incident radiation since the emission of solar prominence is dominated by this scattering process (see Section 2 of Heinzel et al. 1994a). Moreover, Heinzel et al. (1994a) do not calculate the models of erupting prominences but those of static prominences. This can also affect the calculation results because of the Doppler dimming and brightening effects (e.g., Heinzel & Rompolt 1987; Gontikakis et al. 1997). These effects affect different lines in different ways, and for example, the parameter α in Equation (12) can be affected.

It is then important to assess the reliability of the obtained values by conducting the calculation of erupting prominences of M-dwarfs. However, the discussions on prominence parameters (e.g., mass) in this study already include errors with 2 or 3 orders of magnitude with various other assumptions (e.g., prominence shapes), and we only conduct broad discussions over many orders of magnitude in the following (see Figure 47). So in this study, we only use the simple assumption of solar prominence model from Heinzel et al. (1994a), and the calculation of erupting prominences of M-dwarfs is beyond the scope of this study, considering the main focus of this paper is reporting the blue wing asymmetries from the huge campaign observations. We demonstrate that, as a next study, it is important to conduct the NLTE model calculations of eruption prominences in the M-dwarf stellar atmosphere (see Leitzinger et al. 2022) and reevaluate the prominence parameters (e.g., mass) more accurately.

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We also estimated the kinetic energy of the upward-moving plasma showing the blueshifted excess components (E_kin,upp and E_kin,low in Table 6) from the velocity values of Hα blue asymmetry components $({v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha })$ and these mass values (M_blue,upp and M_blue,low) listed in Table 6. When we estimate E_kin,upp and E_kin,low values here, we simply used the line-of-sight velocity value ${v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha }$ as we use the same method with our previous studies estimating kinetic energies using Doppler shift velocities (e.g., Maehara et al. 2021; Namekata et al. 2022c; Inoue et al. 2023). We must keep in mind the effects that the line-of-sight velocity is always smaller than or equal to the true velocity, and the E_kin,upp values here cannot be true upper limit values, when we discuss the kinetic energy values in the following.

As also done in the previous studies (e.g., Moschou et al. 2019; Maehara et al. 2021; Namekata et al. 2022c; Inoue et al. 2023), these estimated mass $({M}_{\mathrm{blue}}^{{\rm{H}}\alpha })$, velocity $({v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha })$, and kinetic energy (E_kin) of the upward-moving plasma (or prominence eruptions) showing blue wing enhancements (blue wing asymmetries) can be discussed as a function of flare energy (Figure 47). In Figure 47, we use flare bolometric energy $({E}_{\mathrm{bol},\mathrm{flare}}$, see Osten & Wolk 2015) for more general discussions, instead of GOES-band X-ray energy used in some previous studies (e.g., Moschou et al. 2019; Maehara et al. 2021).

We estimated the flare bolometric energies with the following two methods. We simply used both values to estimate the value ranges of bolometric energies. We note that both methods include several assumptions and/or ambiguities. For example, the earlier method relies on the ground-based (ARCSAT and LCO) photometric data including some data gaps in this study. The latter relies on the scaling law between Hα and GOES X-ray band flare energies from Haisch (1989), which only used a small number of stellar flares. Moreover, the Hα and GOES X-ray emission components consist of roughly up to a few percent of the total flare energy, and they are emitted in the upper part of the stellar atmosphere (chromosphere and corona) while the dominant part of bolometric energy is emitted as WL emission from the lower atmosphere (e.g., Emslie et al. 2012; Osten & Wolk 2015). For more precise and accurate estimations of flare bolometric energies, more comprehensive multiwavelength observation data to estimate flare energies from X-rays to optical are important. This point should be kept in mind when discussing flare bolometric energies in the following, while we only conduct the order-of-magnitude discussions for flare energy values in Figure 47.

In the first method, we convert the flare energies in the u and U bands into bolometric energies assuming the energy partitions of Osten & Wolk (2015), since most of the flares in this study were observed in either u or U bands, and the flare amplitude S/Ns in u or U bands are generally better than those in g or V bands in this study (see light-curve figures in Section 3). The fraction of U-band flare energy to the the bolometric energy is ${E}_{U,\ \mathrm{flare}}/{E}_{\mathrm{bol},\mathrm{flare}}\sim 0.11$ (Table 2 of Osten & Wolk 2015). Then, assuming the luminosity ratio of U and u bands in Table 3, the fraction of u band to the the bolometric energy is ${E}_{u,\ \mathrm{flare}}/{E}_{\mathrm{bol},\mathrm{flare}}\sim 0.09$.

The resultant energy values from this first method are listed as ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ in Table 6. ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ values of Flares Y23 and E2 were estimated to be ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ = 1.8 × 10³³ and 1.2 × 10³² erg, respectively, from the observed ${E}_{u,\ \mathrm{flare}}$ values, and that of Flare Y18 was to be ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ = 4.2 × 10³² erg from the observed ${E}_{U,\ \mathrm{flare}}$ value. As for Flares Y3 and Y6, the upper limit of bolometric energies could be estimated to be ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}\lt 6.2\,\times {10}^{32}$ and <8.0 × 10³² erg from the observed upper limit of ${E}_{u,\ \mathrm{flare}}$ value. As for Flare A3, only the lower limit of bolometric energy was estimated to be ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}\gt 3.0\times {10}^{32}$ erg from the observed lower limit of ${E}_{u,\ \mathrm{flare}}$, since the flare already started when the observation started. Flare E1 did not have simultaneous photometric data.

In the second method, we convert the GOES-band X-ray (1.5–12.4 keV = 1–8 Å range, ${E}_{\mathrm{Xray},\mathrm{flare}}$ (GOES band)) into bolometric energies $({E}_{\mathrm{bol},\mathrm{flare}})$ assuming the energy partitions of Osten & Wolk (2015) $({E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band) $=\,0.06{E}_{\mathrm{bol},\mathrm{flare}}$ in Table 2 therein). As for Flare Y3, the GOES-band X-ray energy estimated from NICER X-ray spectra in Section 3.2 is used here $({E}_{\mathrm{Xray},\mathrm{flare}}$(GOES band) = 4.7 × 10³¹ erg). As for the other flares without NICER X-ray data in this study, the GOES-band X-ray energy was converted from the Hα flare energy $({E}_{{\rm{H}}\alpha ,\mathrm{flare}})$, using the empirical relationship between Hα and GOES-band soft X-ray flare energies in Figure 2 and Equation (1) of Haisch (1989). The resultant energy values from this first method are listed as ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$ in Table 6.

Using the bolometric energies estimated with these two methods $({E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ and ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)})$, the resultant ${E}_{\mathrm{bol},\mathrm{flare}}$ values are estimated and shown in Table 6 and in Figure 47. As for Flares Y6, Y18, Y23, and E2, the ranges of ${E}_{\mathrm{bol},\mathrm{flare}}$ values are estimated by simply taking the value differences of ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ and ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$. As for Flare Y3, we only used ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$ for ${E}_{\mathrm{bol},\mathrm{flare}}$ value, since the estimated upper limit value of ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ is smaller than ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$. As for Flare E1, only ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}$ is used for ${E}_{\mathrm{bol},\mathrm{flare}}$ value since there were no photometric data. As for Flare A3, ${E}_{\mathrm{bol},\mathrm{flare}}^{(1)}$ is used for the lower limit of ${E}_{\mathrm{bol},\mathrm{flare}}$ value. The upper limit of ${E}_{\mathrm{bol},\mathrm{flare}}$ is set to be 10³⁴ erg, very roughly assuming that the total flare energy is not larger than 1 order of magnitude larger than the limit ${E}_{\mathrm{bol},\mathrm{flare}}^{(2)}\gt 8.2\times {10}^{32}$ erg in the second method from the available Hα observation data.

In Figure 47, the bolometric energies of solar events (the pink filled star marks and gray crosses) are plotted, assuming the energy conversion from GOES X-ray band to bolometric energy for solar flares: ${E}_{\mathrm{GOES}}=0.01{E}_{\mathrm{bol},\mathrm{flare}}$ (Emslie et al. 2012; Osten & Wolk 2015). As for the data from Namekata et al. (2022c), Inoue et al. (2023), the bolometric energy values estimated in these papers are used in Figure 47.

As for the event from Maehara et al. (2021; listed as "M2021" in Table 5), we estimated to be ${E}_{\mathrm{bol},\mathrm{flare}}=2.6\,\times {10}^{32}$ erg from their reported Hα flare energy (E_Hα = 4.7 × 10³⁰ erg) on the basis of the above second method using the scaling relation of Haisch (1989). ²⁹ It is noted Maehara et al. (2021) included the TESS data, but this event did not show clear WL emission and can be categorized as an NWL flare.

The bolometric energies of the stellar blueshift events from Moschou et al. (2019; including the event "V2016" in Table 5) are plotted in Figure 47, assuming the energy conversion relation from GOES X-ray band energy to bolometric energy ${E}_{\mathrm{GOES}}=0.06{E}_{\mathrm{bol},\mathrm{flare}}$, which is the scaling relation for active stars in Osten & Wolk (2015).

Moschou et al. (2019) originally included the events observed from X-ray absorptions, but only the events detected by blueshifts of chromospheric lines are plotted in Figure 47 for simple comparison with blueshift events reported in this study.

In addition, the mass value of the M-dwarf blueshift event of Maehara et al. (2021) is reestimated to be 2.2 × 10¹⁵–1.5 × 10¹⁸ g (blue filled diamonds in Figures 47(a) and (c)), by assuming the ${F}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ range from the 7 M-dwarf events in this study $(\mathrm{log}{F}_{\mathrm{blue}}^{{\rm{H}}\alpha }$[erg s⁻¹ cm⁻² sr⁻¹] = 5.9–6.4) and using the almost the same estimation method as in this study. Only the difference of the method with this study is that we assume the ${F}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ range, since Maehara et al. (2021) only had Hα data, and we cannot determine ${F}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ value from the relation of ${F}_{\mathrm{blue}}^{{\rm{H}}\alpha }$ and ${F}_{\mathrm{blue}}^{{\rm{H}}\beta }$ (see Figure 46). The mass value of the blueshift event of the RS Canum Venaticorum (CVn)-type star from our previous paper, Inoue et al. (2023), is also slightly revised from 9.5 × 10¹⁷–1.4 × 10²¹ to 1.1 × 10¹⁸–2.7 × 10²¹ g. This is because, in Inoue et al. (2023), although we used the same basic equations with this study (see Equation 16), we mistakenly assumed n_e/n_H = n_e/n(H⁰) = 0.2–0.9, which is incorrect. The correct value is n_e/n_H = 0.17–0.47 (see Equation (21)), and the resultant mass value range is slightly affected (the lower limit value becomes double). The overall discussions do not change since there were already a larger range of values.

As we can see in Figure 47(b), the maximum observed line-of-sight velocities of the 7 blueshift (blue wing asymmetry) events reported in this study $({v}_{\mathrm{blue},\mathrm{fit}}^{{\rm{H}}\alpha })$ range from 73 to 122 km s⁻¹. These values are in the same range of solar filament and prominence eruptions associated with CMEs (10–400 km s⁻¹ in Gopalswamy et al. 2003; see also the pink star marks in Figure 47(b)). These values are also roughly comparable to the M-dwarf blueshift event from Maehara et al. (2021; the green open diamond mark) and some of the events from Moschou et al. (2019; the green filled square marks). In addition, the velocities of M-dwarf blue wing asymmetries from the other papers (Vida et al. 2019; Muheki et al. 2020a; Muheki et al. 2020b) are also in the similar ranges (e.g., the observed maximum velocities of M-dwarf blue wing asymmetries are 100–300 km s⁻¹ in Vida et al. 2019).

It has been discussed whether blue wing asymmetries on M-dwarfs cause stellar CMEs (Vida et al. 2016; Moschou et al. 2019; Vida et al. 2019; Muheki et al. 2020b; Maehara et al. 2021).