(Namekata et al. 2022d), indicating that a similar phenomenon is occurring except for their radiation signature. As for flare E2, the deceleration rate comes out as $0.12 \pm 0.20 \text{ km s}^{-2}$. Although the error is large due to the time resolution of the spectral fit and the weakness of the signal, the order of magnitude matches the surface gravity.

What are other possible causes for the observed blueshift emission profile? First, the active regions/quiescent prominences moving in LOS because of stellar rotation (see Jardine et al. 2020) can potentially contribute to the blueshift, but given that the stellar rotational velocity (vsini) is $16.4 \pm 0.1 \text{ km s}^{-1}$, a possibility of the sudden appearance of active regions/quiescent prominences due to stellar rotation can be rejected. For instance, the co-rotation radius at a velocity of $500 \text{ km s}^{-1}$ is 30 stellar radius. Given the sudden occurrence of blueshift associated with the WLF originating from the stellar surface, events at 30 stellar radii are likely negligible. Second, the presence of a cool plasma above the chromospheric evaporation flows can cause blueshifts as discussed in flare studies from M-type stars (Honda et al. 2018). Very rarely in solar flares, blueshifted emission line profiles of $<100 \text{ km s}^{-1}$ are observed in spatially resolved flare ribbon Hα spectra (Švestka et al. 1962; Tei et al. 2018). The solar observations are interpreted by a process where high-energy particles penetrate deep into the chromosphere, causing evaporation, and cool plasma in the upper chromosphere is accelerated before being heated (Tei et al. 2018). However, it is difficult to explain the phenomena we observed in EK Dra (especially E1) with this process. The occurrence of evaporation implies simultaneous chromospheric heating and condensation flows, with chromospheric radiation from denser plasma expected in the Hα core or redshifted components. However, in flare E1, initially almost all Hα emission components are blueshifted, and even when it decelerates and overlaps with the line core, the blueshifted component’s EW is a dominant feature, which contradicts the expected time evolution. Therefore, it is difficult to explain the observations (especially E1) caused by evaporated flows.

Furthermore, as mentioned in Section 4.2, for flare E1, the total radiation energy of the Hα line (including the blueshifted component and line center component) is exceptionally large, around ~30% relative to the WL energy, which is unusual considering the values of other EK Dra flares E2 ~ E5 (~1%). This suggests that most of the Hα radiation for flare E1 comes from a source spatially different from the WLF source, i.e., an erupted prominence.

Based on the above discussion, we concluded that we discovered prominence eruptions on a solar-type star for the first time (undoubtedly for flare E1). Like the Sun, our study has made it clear that on solar-type stars, it is possible to determine whether the prominence/filament has erupted beyond/within the stellar visible disk based on whether it appears as an emission/absorption (see summary in Section 6.3). In the following, we will conduct a more detailed analysis of the prominence eruptions observed in this study.

## 5.2. Properties of Prominence Eruptions

### 5.2.1. Velocity, Velocity Dispersion, and Their Time Evolution

The observational properties of the blueshifted component are estimated in Sections 3.3.1 and 3.3.2. Here, we review the obtained results in terms of the blueshifted velocity, the velocity dispersion, and their time evolution.

<figure><img src="image_24.png" /><figcaption>**Figure 20.** Velocity of solar and stellar prominence/filament eruptions (blueshift events) as a function of flare GOES flux (bottom axis) or bolometric WLF energy (top axis). Data for filament/prominence eruptions on the G-dwarf EK Dra are derived from this study and Namekata et al. (2022d). Data for solar filament eruptions are taken from Seki et al. (2021). Data for M-dwarfs, RS CVn, and young stellar objects are taken from Moschou et al. (2019), Inoue et al. (2023), and Maehara et al. (2021). The cyan solid line is a power-law fitting line for all the solar and stellar data. The black dashed line is a line with a power-law index of 1/6, which represents the upper edge of the solar and stellar data (Takahashi et al. 2016).</figcaption></figure>

(E1) This flare was the most remarkable, fastest, and long-lived prominence eruption. The ΔEW of the blueshifted component was 0.45–0.70 Å. The duration was $34_{-2}^{+8}$ minutes, appearing at the start of the white-light flare or possibly earlier (the duration of the white light was 20 minutes). The maximum blueshifted velocity is $330_{-35}^{+690} \pm 92 \text{ km s}^{-1}$ for one-component fit ($490_{-33}^{+690} \pm 93 \text{ km s}^{-1}$ for two-component). No significant acceleration time was observed; instead, it showed an exponential decay of velocity, with an initial deceleration rate of $0.34_{-0.15}^{+0.15} \text{ km s}^{-2}$ (already discussed in Section 5.1 in comparison with surface gravity). The velocity eventually approach to zero velocity, and emission component disappeared without showing significant redshifts. The typical velocity dispersion was $300 \text{ km s}^{-2}$, exhibiting a pattern of decay synchronous with the velocity.

(E2) This flare was the weak, slow, short-lived prominence eruption. The ΔEW of the blueshifted emission component was 0.034 Å. The duration was $10_{-5}^{+5}$ minutes, appearing at the peak of the WLF. The maximum velocity is $430_{-19}^{+19} \text{ km s}^{-1}$. No significant acceleration and deceleration phases were observed, although possible deceleration was estimated as $0.12_{-0.20}^{+0.20} \text{ km s}^{-2}$. The typical velocity dispersion was $55 \text{ km s}^{-2}$.

How can we understand the velocity in the relation of solar flares and blueshift events on other types of stars? Figure 20 shows the velocity of prominence/filament eruptions (blueshift events) as a function of flare’s GOES-band flux (bottom axis) or bolometric WLF energy (top axis) for solar and stellar flares. The velocity of prominence/filament eruptions on EK Dra is comparable to the largest values of solar prominence eruptions, while some stellar prominence eruptions from “megaflares”
(Namekata et al. 2022d), indicating that a similar phenomenon is occurring except for their radiation signature. As for flare E2, the deceleration rate comes out as $0.12 \pm 0.20 \text{ km s}^{-2}$. Although the error is large due to the time resolution of the spectral fit and the weakness of the signal, the order of magnitude matches the surface gravity.

What are other possible causes for the observed blueshift emission profile? First, the active regions/quiescent prominences moving in LOS because of stellar rotation (see Jardine et al. 2020) can potentially contribute to the blueshift, but given that the stellar rotational velocity (vsini) is $16.4 \pm 0.1 \text{ km s}^{-1}$, a possibility of the sudden appearance of active regions/quiescent prominences due to stellar rotation can be rejected. For instance, the co-rotation radius at a velocity of $500 \text{ km s}^{-1}$ is 30 stellar radius. Given the sudden occurrence of blueshift associated with the WLF originating from the stellar surface, events at 30 stellar radii are likely negligible. Second, the presence of a cool plasma above the chromospheric evaporation flows can cause blueshifts as discussed in flare studies from M-type stars (Honda et al. 2018). Very rarely in solar flares, blueshifted emission line profiles of $<100 \text{ km s}^{-1}$ are observed in spatially resolved flare ribbon Hα spectra (Švestka et al. 1962; Tei et al. 2018). The solar observations are interpreted by a process where high-energy particles penetrate deep into the chromosphere, causing evaporation, and cool plasma in the upper chromosphere is accelerated before being heated (Tei et al. 2018). However, it is difficult to explain the phenomena we observed in EK Dra (especially E1) with this process. The occurrence of evaporation implies simultaneous chromospheric heating and condensation flows, with chromospheric radiation from denser plasma expected in the Hα core or redshifted components. However, in flare E1, initially almost all Hα emission components are blueshifted, and even when it decelerates and overlaps with the line core, the blueshifted component’s EW is a dominant feature, which contradicts the expected time evolution. Therefore, it is difficult to explain the observations (especially E1) caused by evaporated flows.

Furthermore, as mentioned in Section 4.2, for flare E1, the total radiation energy of the Hα line (including the blueshifted component and line center component) is exceptionally large, around ~30% relative to the WL energy, which is unusual considering the values of other EK Dra flares E2 ~ E5 (~1%). This suggests that most of the Hα radiation for flare E1 comes from a source spatially different from the WLF source, i.e., an erupted prominence.

Based on the above discussion, we concluded that we discovered prominence eruptions on a solar-type star for the first time (undoubtedly for flare E1). Like the Sun, our study has made it clear that on solar-type stars, it is possible to determine whether the prominence/filament has erupted beyond/within the stellar visible disk based on whether it appears as an emission/absorption (see summary in Section 6.3). In the following, we will conduct a more detailed analysis of the prominence eruptions observed in this study.

## 5.2. Properties of Prominence Eruptions

### 5.2.1. Velocity, Velocity Dispersion, and Their Time Evolution

The observational properties of the blueshifted component are estimated in Sections 3.3.1 and 3.3.2. Here, we review the obtained results in terms of the blueshifted velocity, the velocity dispersion, and their time evolution.

<figure><img src="image_25.png" /><figcaption>**Figure 20.** Velocity of solar and stellar prominence/filament eruptions (blueshift events) as a function of flare GOES flux (bottom axis) or bolometric WLF energy (top axis). Data for filament/prominence eruptions on the G-dwarf EK Dra are derived from this study and Namekata et al. (2022d). Data for solar filament eruptions are taken from Seki et al. (2021). Data for M-dwarfs, RS CVn, and young stellar objects are taken from Moschou et al. (2019), Inoue et al. (2023), and Maehara et al. (2021). The cyan solid line is a power-law fitting line for all the solar and stellar data. The black dashed line is a line with a power-law index of 1/6, which represents the upper edge of the solar and stellar data (Takahashi et al. 2016).</figcaption></figure>

(E1) This flare was the most remarkable, fastest, and long-lived prominence eruption. The ΔEW of the blueshifted component was 0.45–0.70 Å. The duration was $34_{-2}^{+8}$ minutes, appearing at the start of the white-light flare or possibly earlier (the duration of the white light was 20 minutes). The maximum blueshifted velocity is $330_{-35}^{+690} \pm 92 \text{ km s}^{-1}$ for one-component fit ($490_{-33}^{+690} \pm 93 \text{ km s}^{-1}$ for two-component). No significant acceleration time was observed; instead, it showed an exponential decay of velocity, with an initial deceleration rate of $0.34_{-0.15}^{+0.15} \text{ km s}^{-2}$ (already discussed in Section 5.1 in comparison with surface gravity). The velocity eventually approach to zero velocity, and emission component disappeared without showing significant redshifts. The typical velocity dispersion was $300 \text{ km s}^{-2}$, exhibiting a pattern of decay synchronous with the velocity.

(E2) This flare was the weak, slow, short-lived prominence eruption. The ΔEW of the blueshifted emission component was 0.034 Å. The duration was $10_{-5}^{+5}$ minutes, appearing at the peak of the WLF. The maximum velocity is $430_{-19}^{+19} \text{ km s}^{-1}$. No significant acceleration and deceleration phases were observed, although possible deceleration was estimated as $0.12_{-0.20}^{+0.20} \text{ km s}^{-2}$. The typical velocity dispersion was $55 \text{ km s}^{-2}$.

How can we understand the velocity in the relation of solar flares and blueshift events on other types of stars? Figure 20 shows the velocity of prominence/filament eruptions (blueshift events) as a function of flare’s GOES-band flux (bottom axis) or bolometric WLF energy (top axis) for solar and stellar flares. The velocity of prominence/filament eruptions on EK Dra is comparable to the largest values of solar prominence eruptions, while some stellar prominence eruptions from “megaflares”
(10$^{35-36}$ erg) on RS CVn-type stars/M-dwarfs seems to have a much larger velocity than solar flares (Houdebine et al. 1990; Inoue et al. 2023). It appears that there is a weak positive trend if we include solar and stellar data as

$$V = 590 \cdot (F_{\text{GOES}})^{0.10 \pm 0.02}. \qquad (10)$$

Note that this correlation may be influenced by observational bias because it is likely that only those with sufficiently high velocities are being detected for stellar flares (due to spectral resolution, flare contamination, and LOS uncertainty). Therefore, this trend may be an apparent one, and there can be a large diversity in velocity.

Because some stellar superflares exhibit prominence eruptions at much higher velocities than the Sun, it can be anticipated that the upper limits of stellar observational data are of significance. Takahashi et al. (2016) suggested that the upper limit of the CME speed can be theoretically described by the scaling law of $V_{\text{CME,upper}} = V_0 \cdot (F_{\text{GOES}})^{1/6}$, based on the assumption that the flare radiation energy $E_{\text{WL,bol}} \sim 10^{35} F_{\text{GOES}}$ should be roughly less than CME kinetic energy $0.5 \cdot M_{\text{CME}} \cdot V_{\text{CME,upper}}^2$. Recently, Kotani et al. (2023) suggested that the power-law index for the relation between erupted mass and flare energy scale is the same for CMEs and prominence eruptions, i.e., $M \propto F_{\text{GOES}}^{2/3}$; therefore, a similar scaling law for the upper limit of the prominence velocity $V_p$ can be also derived by following Takahashi et al. (2016):

$$F_{\text{GOES}} \propto \frac{1}{2} M_p V_{\text{p,upper}}^2 \propto F_{\text{GOES}}^{2/3} V_{\text{p,upper}}^2, \qquad (11)$$

$$V_{\text{p,upper}} = V_0 \cdot (F_{\text{GOES}})^{1/6}. \qquad (12)$$

Where $F_{\text{GOES}}$ can be replaced with $10^{-35} E_{\text{WL,bol}}$, $V_0 \sim 5200 \text{ km s}^{-1}$ is roughly determined by observational upper limits for solar flares/filament eruptions. In stellar flares, there have been no observed events exceeding this empirical scaling in velocity (Equation (12)), implying that this established solar scaling law poses no contradictions in describing the upper limits of velocities for filament/prominence eruptions observed in the case of superflares.

Lastly, we would like to focus on a new aspect, the velocity dispersion of the blueshifted components. For flare E1, we discovered a clear decay in velocity dispersion (Figure 11). Furthermore, it was found to have a positive correlation with the absolute value of the velocity (Figure 12). Given that the spatial distribution of thermal and turbulent velocities of prominences are on the order of several tens of km s$^{-1}$, similar to the Sun (e.g., Sakaue et al. 2018; Namekata et al. 2022d), we cannot explain a velocity dispersion of approximately 300 km s$^{-1}$ of flares E1 and E4, even considering the velocity dispersion of the instrumental broadenings (~75 km s$^{-1}$; Matsubayashi et al. 2019). Actually, this broad velocity dispersion has also been detected in M-dwarf flares (Vida et al. 2016; Leitzinger et al. 2022). Here, by assuming that prominence eruptions are a phenomenon in which loop structures expand self-similarly, we propose that this velocity dispersion may be observing components from spatially different regions. In other words, the slower parts could be near the foot of the loop-like prominence, and the faster parts near the top. Considering this self-similarly expanding loop structure, the fact that velocity dispersion has a positive correlation with the average speed is also reasonable. If this is true, the obtained central velocity of the prominence could be

just an average one, with the velocity dispersion indicating the existence of both faster and slower plasma. Therefore, we suggest that the maximum speed of flare E1 could reach up to 630–990 km s$^{-1}$ (or even up to 880–1080 km s$^{-1}$), considering the velocity dispersion.

These larger velocities exceed the escape velocity of EK Dra, ~670 km s$^{-1}$, and it can be suggested from the Hα line observation alone that flare E1 (and even flare E2) could be connected to a CME. The possibility that these are connected to CMEs will be discussed in further detail combined with another indicator in X-ray in Section 6.1.

### 5.2.2. Area and Length Scale

Here, we estimate the area and length scale of the prominence. We basically follow the method described by Inoue et al. (2023), but the assumption of optical depth and electron density is original based on the discussion in Section 5.2.4. The luminosity of the blueshift component ($L_{\text{Hα,blue}}$) at the time of maximum EW is derived as $16.6_{\pm 1.7} \times 10^{28} \text{ erg s}^{-1}$ for flare E1 and $0.47_{\pm 1.6} \times 10^{28} \text{ erg s}^{-1}$ for flare E2 as shown in Table 3, based on the results of the Gaussian spectral fit. Assuming an optical depth $\tau = 10 \sim 1000$ for our prominences (see Section 5.2.4 for the assumption), we derive the area, length scale, mass, and kinetic energy based on the theoretical correlations between prominence plasma parameters and the emitted radiation derived by Heinzel et al. (1994). Note that Heinzel et al. (1994)'s work is based on the model of solar quiescent prominence, and the parameters in eruptive prominences on active stars could be different, although further radiative transfer modeling is beyond the scope of this paper. The assumption of the optical depth $\tau = 1 \sim 100$ gives the theoretical value of surface flux of the prominence $F_{\text{blue}}$ as

$$F_{\text{blue}} = \begin{cases} 10^{\log_{10}(\tau)+5} & (\log_{10}(\tau) < -0.22) \\ 10^{0.55 \cdot \log_{10}(\tau)+4.9} & (\log_{10}(\tau) > -0.22) \end{cases} \qquad (13)$$

$$= \begin{cases} 2.8 \times 10^5 & (\tau = 10) \\ 3.5 \times 10^6 & (\tau = 1000) \end{cases} [\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}]. \qquad (14)$$

Using these values, the projected surface area of the prominence $A_p$ can be expressed as

$$A_p = L_{\text{Hα,blue}}/(2\pi F_{\text{blue}}). \qquad (15)$$

This equation gives the surface area of the prominence as $1.8 \times 10^{22}–6.3 \times 10^{22} \text{ cm}^2$ for flare E1 and $5.3 \times 10^{20}–1.9 \times 10^{21} \text{ cm}^2$ for flare E2. Furthermore, the length scale of the prominence $L_p$ is derived as follows, assuming a simple hypothesis that the prominence is roughly square ($A_p = L_p^2$, the assumption of “cubic” erupted prominences) for the lower limit, and an aspect ratio of the length and width of the prominence of 1:10 for the upper limit ($A_p = L_p \cdot L_p/10$, the assumption of “cylinder”-like erupted prominences):

$$L_p = (A_p)^{0.5} \sim 10 \cdot (A_p)^{0.5}. \qquad (16)$$

The estimated length scale of the prominence is $(8.3–30) \times 10^{10} \text{ cm}$ $(1.3–4.5 R_{\text{star}}) \sim (83–300) \times 10^{10} \text{ cm}$ $(13–45 R_{\text{star}})$ for flare E1 and $(1.4–5.1) \times 10^{10} \text{ cm}$ $(0.2–0.8 R_{\text{star}}) \sim (14–51) \times 10^{10} \text{ cm}$ $(2.2–7.8 R_{\text{star}})$ for flare E2. Because we used the maximum EW value for calculations, the observed length scale would be the one after the prominence is erupted and expands, so it would be possible
(10$^{35-36}$ erg) on RS CVn-type stars/M-dwarfs seems to have a much larger velocity than solar flares (Houdebine et al. 1990; Inoue et al. 2023). It appears that there is a weak positive trend if we include solar and stellar data as

$$V = 590 \cdot (F_{\text{GOES}})^{0.10 \pm 0.02}. \qquad (10)$$

Note that this correlation may be influenced by observational bias because it is likely that only those with sufficiently high velocities are being detected for stellar flares (due to spectral resolution, flare contamination, and LOS uncertainty). Therefore, this trend may be an apparent one, and there can be a large diversity in velocity.

Because some stellar superflares exhibit prominence eruptions at much higher velocities than the Sun, it can be anticipated that the upper limits of stellar observational data are of significance. Takahashi et al. (2016) suggested that the upper limit of the CME speed can be theoretically described by the scaling law of $V_{\text{CME,upper}} = V_0 \cdot (F_{\text{GOES}})^{1/6}$, based on the assumption that the flare radiation energy $E_{\text{WL,bol}} \sim 10^{35} F_{\text{GOES}}$ should be roughly less than CME kinetic energy $0.5 \cdot M_{\text{CME}} \cdot V_{\text{CME,upper}}^2$. Recently, Kotani et al. (2023) suggested that the power-law index for the relation between erupted mass and flare energy scale is the same for CMEs and prominence eruptions, i.e., $M \propto F_{\text{GOES}}^{2/3}$; therefore, a similar scaling law for the upper limit of the prominence velocity $V_p$ can be also derived by following Takahashi et al. (2016):

$$F_{\text{GOES}} \propto \frac{1}{2} M_p V_{\text{p,upper}}^2 \propto F_{\text{GOES}}^{2/3} V_{\text{p,upper}}^2, \qquad (11)$$

$$V_{\text{p,upper}} = V_0 \cdot (F_{\text{GOES}})^{1/6}. \qquad (12)$$

Where $F_{\text{GOES}}$ can be replaced with $10^{-35} E_{\text{WL,bol}}$, $V_0 \sim 5200 \text{ km s}^{-1}$ is roughly determined by observational upper limits for solar flares/filament eruptions. In stellar flares, there have been no observed events exceeding this empirical scaling in velocity (Equation (12)), implying that this established solar scaling law poses no contradictions in describing the upper limits of velocities for filament/prominence eruptions observed in the case of superflares.

Lastly, we would like to focus on a new aspect, the velocity dispersion of the blueshifted components. For flare E1, we discovered a clear decay in velocity dispersion (Figure 11). Furthermore, it was found to have a positive correlation with the absolute value of the velocity (Figure 12). Given that the spatial distribution of thermal and turbulent velocities of prominences are on the order of several tens of km s$^{-1}$, similar to the Sun (e.g., Sakaue et al. 2018; Namekata et al. 2022d), we cannot explain a velocity dispersion of approximately 300 km s$^{-1}$ of flares E1 and E4, even considering the velocity dispersion of the instrumental broadenings (~75 km s$^{-1}$; Matsubayashi et al. 2019). Actually, this broad velocity dispersion has also been detected in M-dwarf flares (Vida et al. 2016; Leitzinger et al. 2022). Here, by assuming that prominence eruptions are a phenomenon in which loop structures expand self-similarly, we propose that this velocity dispersion may be observing components from spatially different regions. In other words, the slower parts could be near the foot of the loop-like prominence, and the faster parts near the top. Considering this self-similarly expanding loop structure, the fact that velocity dispersion has a positive correlation with the average speed is also reasonable. If this is true, the obtained central velocity of the prominence could be

just an average one, with the velocity dispersion indicating the existence of both faster and slower plasma. Therefore, we suggest that the maximum speed of flare E1 could reach up to 630–990 km s$^{-1}$ (or even up to 880–1080 km s$^{-1}$), considering the velocity dispersion.

These larger velocities exceed the escape velocity of EK Dra, ~670 km s$^{-1}$, and it can be suggested from the Hα line observation alone that flare E1 (and even flare E2) could be connected to a CME. The possibility that these are connected to CMEs will be discussed in further detail combined with another indicator in X-ray in Section 6.1.

### 5.2.2. Area and Length Scale

Here, we estimate the area and length scale of the prominence. We basically follow the method described by Inoue et al. (2023), but the assumption of optical depth and electron density is original based on the discussion in Section 5.2.4. The luminosity of the blueshift component ($L_{\text{Hα,blue}}$) at the time of maximum EW is derived as $16.6_{-1.7}^{+10} \times 10^{28} \text{ erg s}^{-1}$ for flare E1 and $0.47_{-1.6}^{+10} \times 10^{28} \text{ erg s}^{-1}$ for flare E2 as shown in Table 3, based on the results of the Gaussian spectral fit. Assuming an optical depth $\tau = 10 \sim 1000$ for our prominences (see Section 5.2.4 for the assumption), we derive the area, length scale, mass, and kinetic energy based on the theoretical correlations between prominence plasma parameters and the emitted radiation derived by Heinzel et al. (1994). Note that Heinzel et al. (1994)'s work is based on the model of solar quiescent prominence, and the parameters in eruptive prominences on active stars could be different, although further radiative transfer modeling is beyond the scope of this paper. The assumption of the optical depth $\tau = 1 \sim 100$ gives the theoretical value of surface flux of the prominence $F_{\text{blue}}$ as

$$F_{\text{blue}} = \begin{cases} 10^{\log_{10}(\tau)+5} & (\log_{10}(\tau) < -0.22) \\ 10^{0.55 \cdot \log_{10}(\tau)+4.9} & (\log_{10}(\tau) > -0.22) \end{cases} \qquad (13)$$

$$= \begin{cases} 2.8 \times 10^5 & (\tau = 10) \\ 3.5 \times 10^6 & (\tau = 1000) \end{cases} [\text{erg s}^{-1} \text{ cm}^{-2} \text{ sr}^{-1}]. \qquad (14)$$

Using these values, the projected surface area of the prominence $A_p$ can be expressed as

$$A_p = L_{\text{Hα,blue}}/(2\pi F_{\text{blue}}). \qquad (15)$$

This equation gives the surface area of the prominence as $1.8 \times 10^{22} - 6.3 \times 10^{22} \text{ cm}^2$ for flare E1 and $5.3 \times 10^{20} - 1.9 \times 10^{21} \text{ cm}^2$ for flare E2. Furthermore, the length scale of the prominence $L_p$ is derived as follows, assuming a simple hypothesis that the prominence is roughly square ($A_p = L_p^2$, the assumption of “cubic” erupted prominences) for the lower limit, and an aspect ratio of the length and width of the prominence of 1:10 for the upper limit ($A_p = L_p \cdot L_p/10$, the assumption of “cylinder”-like erupted prominences):

$$L_p = (A_p)^{0.5} \sim 10 \cdot (A_p)^{0.5}. \qquad (16)$$

The estimated length scale of the prominence is $(8.3 - 30) \times 10^{10} \text{ cm}$ ($1.3-4.5 R_{\text{star}}$) ~$(83 - 300) \times 10^{10} \text{ cm}$ ($13-45 R_{\text{star}}$) for flare E1 and $(1.4 - 5.1) \times 10^{10} \text{ cm}$ ($0.2-0.8 R_{\text{star}}$) ~$(14 - 51) \times 10^{10} \text{ cm}$ ($2.2-7.8 R_{\text{star}}$) for flare E2. Because we used the maximum EW value for calculations, the observed length scale would be the one after the prominence is erupted and expands, so it would be possible
<figure><img src="image_25.png" /><figcaption>**Figure 21.** Comparison between the velocity ($V_{r\_max}$) and length scale (L) of filament/prominence eruptions on the Sun and G-dwarf EK Dra. The blue circles and orange crosses indicate the solar filament eruptions with and without CMEs, respectively. The green and red points correspond to the stellar prominence and filament eruptions on EK Dra, respectively (this study, Namekata et al. 2022d). The stellar data are the maximum line-of-sight velocities while the solar data are maximum radial velocity. The solid black line indicates an empirical solar threshold that can roughly distinguish whether a filament eruption is associated with CMEs or not in the formula of $(V_{r\_max}/100 \text{ km s}^{-1})(L/100 \text{ Mm})^{0.96} = 0.8$ (Seki et al. 2021).</figcaption></figure>

that the estimated length scale of prominence is larger than the stellar radius.

How significant is the assumption of aspect ratio? The correction of the prominence aspect ratio with Equation (16) tends to give an extremely large length scale. This may indicate that the prominences could be not necessarily a filamentary structure after the eruptions and could look like halo-type prominence eruptions (see Parenti 2014). Anyway, we do not know the shape of the stellar prominence for now, so to include all the possibilities, we use the values including the aspect ratio correction as an upper limit of the prominence length scale, following the methods in Namekata et al. (2022d). Actually, this assumption does not significantly affect the following discussion of length scale because the lower limit value is important, but it will be revisited when we discuss the general picture of the relationship among flares, prominences, and starspots in Section 6.2.

Figure 21 shows the plot of the prominence length scale and the maximum radial velocity. In the figure, the prominence/ filament eruptions of EK Dra are compared with solar filament eruptions (Seki et al. 2021). Seki et al. (2021) proposed a criterion, namely

$$ (V_{r\_max}/100 \text{ km s}^{-1})(L_p/100 \text{ Mm})^{0.96} = 0.8, \quad (17) $$

to determine whether a solar prominence eruption is associated with a CME, where $V_{r\_max}$ is the maximum radial velocity of filament eruption. In other words, the longer the prominence and the higher the velocity (i.e., the larger the kinetic energy), the higher the likelihood of it leading to a CME. This threshold was first applied to stellar filament eruptions on EK Dra by Namekata et al. (2022d). While this threshold is fundamentally applicable to the Sun, EK Dra has similar surface gravity, surface temperature, and atmospheric stratification as the Sun, suggesting the potential applicability of this threshold. As can be seen in the figure, even the lower limit values of prominence

eruptions E1 and E2 are positioned well above this criterion. This supports the possibility that the prominence eruptions associated with flares E1 and E2 may ultimately lead to stellar CMEs. Note, however, that the different activity levels between the Sun and EK Dra could potentially affect relative change in this criterion. Future theoretical investigations are required for this threshold.

### 5.2.3. Mass and Kinetic Energy

Here, under the assumption mentioned above, with an optical depth of $\tau = 10 \sim 1000$ for the prominences, we determine the prominence mass $M_p$. The mass can generally be calculated as $M_p \sim A_p D n_H m_H$, with the spatial LOS depth of the prominence as D, the number density of hydrogen as $n_H$, and the mass of hydrogen as $m_H$. Here, based on the numerical calculations by Heinzel et al. (1994), a relationship has been derived between the optical depth of the prominence and the emission measure EM<sub>blue</sub>, as follows:

$$ \mathrm{EM}_{\mathrm{blue}} = D n_e^2 = \begin{cases} 8.1 \times 10^{29} & (\tau = 10) \\ 3.3 \times 10^{32} & (\tau = 1000) \end{cases} [\mathrm{cm}^{-5}] \quad (18) $$

Here, based on the assumption of “cubic” or “cylinder”-like structure introduced in Section 5.2.2, we assume that the depth of the prominence is approximately equal to $L_p$ (cubic) or $0.1 \times L_p$ (cylinder). By using the emission measure EM<sub>blue</sub> value under the assumed optical depth, we can describe the $M_p$ as

$$ M_p \sim A_p D n_H m_H \quad (19) $$

$$ = A_p D \left( \frac{\mathrm{EM}_{\mathrm{blue}}}{D} \right)^{0.5} \left( \frac{n_e}{n_H} \right)^{-1} m_H, \quad (20) $$

Here, we roughly assume the prominence ionization fraction $n_e/n_H = 0.17 \sim 0.47$ (see Table 1 of Labrosse et al. 2010). Note that this value is modified in Notsu et al. (2023) because the original values used in Inoue et al. (2023) was a mistake. As a result, the mass of prominence is $1.3_{-0.9}^{+2.9} \times 10^{20} g$ (i.e., $4.0 \times 10^{19} g-4.2 \times 10^{20} g$) and $1.7_{-1.1}^{+3.7} \times 10^{18} g$ (i.e., $5.2 \times 10^{17} g-5.3 \times 10^{18} g$) for flares E1 and E2, respectively. Here, the average of the upper and lower limits in the log scale is denoted as the representative value (the same applies to kinetic energy).

Also, the prominence kinetic energy can be derived from

$$ E_{\mathrm{kin}} = \frac{1}{2} M_p V_{\mathrm{typical}}^2, \quad (21) $$

where $V_{\mathrm{typical}}$ is the blueshifted velocity at the maximum Hα EW. As a result, the kinetic energy of prominence for E1 and E2 eruptive events is $5.8_{-4.0}^{+12.8} \times 10^{34} \text{ erg}$ (i.e., $1.8 \times 10^{34} \text{ erg} -1.9 \times 10^{35} \text{ erg}$) and $1.2_{-0.8}^{+2.7} \times 10^{33} \text{ erg}$ (i.e., $3.8 \times 10^{32} \text{ erg} -3.9 \times 10^{33} \text{ erg}$), respectively. Thus, the kinetic energy of the prominence is about three times larger for the E1 event ($E_{\mathrm{WL,bol}} = 1.5 \times 10^{33} \text{ erg}$) and about 50 times smaller for the E2 event ($E_{\mathrm{WL,bol}} = 12.2 \times 10^{33} \text{ erg}$) than the radiative energy of the WLF ($E_{\mathrm{WL,bol}}$ (see Figure 21(b)). This indicates a diversity depending on the flares; flare E1, which has a smaller energy scale for the WLF than flare E2, is larger in all aspects such as mass, speed, and kinetic energy (see the discussion of diversity in Section 6.3).
<figure><img src="image_26.png" /><figcaption>Figure 21. Comparison between the velocity ($V_{r_{max}}$) and length scale (L) of filament/prominence eruptions on the Sun and G-dwarf EK Dra. The blue circles and orange crosses indicate the solar filament eruptions with and without CMEs, respectively. The green and red points correspond to the stellar prominence and filament eruptions on EK Dra, respectively (this study, Namekata et al. 2022d). The stellar data are the maximum line-of-sight velocities while the solar data are maximum radial velocity. The solid black line indicates an empirical solar threshold that can roughly distinguish whether a filament eruption is associated with CMEs or not in the formula of $(V_{r_{max}}/100 \text{ km s}^{-1})(L/100 \text{ Mm})^{0.96} = 0.8$ (Seki et al. 2021).</figcaption></figure>

that the estimated length scale of prominence is larger than the stellar radius.

How significant is the assumption of aspect ratio? The correction of the prominence aspect ratio with Equation (16) tends to give an extremely large length scale. This may indicate that the prominences could be not necessarily a filamentary structure after the eruptions and could look like halo-type prominence eruptions (see Parenti 2014). Anyway, we do not know the shape of the stellar prominence for now, so to include all the possibilities, we use the values including the aspect ratio correction as an upper limit of the prominence length scale, following the methods in Namekata et al. (2022d). Actually, this assumption does not significantly affect the following discussion of length scale because the lower limit value is important, but it will be revisited when we discuss the general picture of the relationship among flares, prominences, and starspots in Section 6.2.

Figure 21 shows the plot of the prominence length scale and the maximum radial velocity. In the figure, the prominence/ filament eruptions of EK Dra are compared with solar filament eruptions (Seki et al. 2021). Seki et al. (2021) proposed a criterion, namely

$$ (V_{r_{max}}/100 \text{ km s}^{-1})(L_p/100 \text{ Mm})^{0.96} = 0.8, \quad (17) $$

to determine whether a solar prominence eruption is associated with a CME, where $V_{r_{max}}$ is the maximum radial velocity of filament eruption. In other words, the longer the prominence and the higher the velocity (i.e., the larger the kinetic energy), the higher the likelihood of it leading to a CME. This threshold was first applied to stellar filament eruptions on EK Dra by Namekata et al. (2022d). While this threshold is fundamentally applicable to the Sun, EK Dra has similar surface gravity, surface temperature, and atmospheric stratification as the Sun, suggesting the potential applicability of this threshold. As can be seen in the figure, even the lower limit values of prominence

eruptions E1 and E2 are positioned well above this criterion. This supports the possibility that the prominence eruptions associated with flares E1 and E2 may ultimately lead to stellar CMEs. Note, however, that the different activity levels between the Sun and EK Dra could potentially affect relative change in this criterion. Future theoretical investigations are required for this threshold.

### 5.2.3. Mass and Kinetic Energy

Here, under the assumption mentioned above, with an optical depth of $\tau = 10 \sim 1000$ for the prominences, we determine the prominence mass $M_p$. The mass can generally be calculated as $M_p \sim A_p D n_H m_H$, with the spatial LOS depth of the prominence as D, the number density of hydrogen as $n_H$, and the mass of hydrogen as $m_H$. Here, based on the numerical calculations by Heinzel et al. (1994), a relationship has been derived between the optical depth of the prominence and the emission measure EM<sub>blue</sub>, as follows:

$$ \mathrm{EM}_{\mathrm{blue}} = D n_e^2 = \begin{cases} 8.1 \times 10^{29} & (\tau = 10) \\ 3.3 \times 10^{32} & (\tau = 1000) \end{cases} [\mathrm{cm}^{-5}] \quad (18) $$

Here, based on the assumption of “cubic” or “cylinder”-like structure introduced in Section 5.2.2, we assume that the depth of the prominence is approximately equal to $L_p$ (cubic) or $0.1 \times L_p$ (cylinder). By using the emission measure EM<sub>blue</sub> value under the assumed optical depth, we can describe the $M_p$ as

$$ M_p \sim A_p D n_H m_H \quad (19) $$

$$ = A_p D \left( \frac{\mathrm{EM}_{\mathrm{blue}}}{D} \right)^{0.5} \left( \frac{n_e}{n_H} \right)^{-1} m_H, \quad (20) $$

Here, we roughly assume the prominence ionization fraction $n_e/n_H = 0.17 \sim 0.47$ (see Table 1 of Labrosse et al. 2010). Note that this value is modified in Notsu et al. (2023) because the original values used in Inoue et al. (2023) was a mistake. As a result, the mass of prominence is $1.3_{-0.9}^{+2.9} \times 10^{20} \text{g}$ (i.e., $4.0 \times 10^{19} \text{g}$—$4.2 \times 10^{20} \text{g}$) and $1.7_{-1.1}^{+3.7} \times 10^{18} \text{g}$ (i.e., $5.2 \times 10^{17} \text{g}$—$5.3 \times 10^{18} \text{g}$) for flares E1 and E2, respectively. Here, the average of the upper and lower limits in the log scale is denoted as the representative value (the same applies to kinetic energy).

Also, the prominence kinetic energy can be derived from

$$ E_{\mathrm{kin}} = \frac{1}{2} M_p V_{\mathrm{typical}}^2, \quad (21) $$

where $V_{\mathrm{typical}}$ is the blueshifted velocity at the maximum Hα EW. As a result, the kinetic energy of prominence for E1 and E2 eruptive events is $5.8_{-4.0}^{+12.8} \times 10^{34} \text{erg}$ (i.e., $1.8 \times 10^{34} \text{erg}$—$1.9 \times 10^{35} \text{erg}$) and $1.2_{-0.8}^{+2.7} \times 10^{33} \text{erg}$ (i.e., $3.8 \times 10^{32} \text{erg}$—$3.9 \times 10^{33} \text{erg}$), respectively. Thus, the kinetic energy of the prominence is about three times larger for the E1 event ($E_{\mathrm{WL,bol}} = 1.5 \times 10^{33} \text{erg}$) and about 50 times smaller for the E2 event ($E_{\mathrm{WL,bol}} = 12.2 \times 10^{33} \text{erg}$) than the radiative energy of the WLF ($E_{\mathrm{WL,bol}}$) (see Figure 21(b)). This indicates a diversity depending on the flares; flare E1, which has a smaller energy scale for the WLF than flare E2, is larger in all aspects such as mass, speed, and kinetic energy (see the discussion of diversity in Section 6.3).
<figure><img src="image_26.png" /><figcaption>**Figure 22.** Mass and kinetic energy of solar/stellar filament/prominence eruptions and CMEs as a function of bolometric WLF energy or GOES X-ray energy. The green and red points correspond to the stellar prominence and filament eruptions on EK Dra, respectively (this study, Namekata et al. 2022d). The black crosses are solar CME data (Yashiro & Gopalswamy 2009; Drake et al. 2013), while the green pluses are data for solar prominence/filament eruptions taken from Namekata et al. (2022d) and Kotani et al. (2023). The cyan dashed and magenta dotted lines are observational fits for solar CMEs expressed as $M_{CME} \propto E_{bol}^{0.59}$ and $E_{kin} \propto E_{bol}^{1.05}$ (cyan color; Drake et al. 2013) and $M_{CME} \propto E_{bol}^{0.7}$ (magenta color; Aarnio et al. 2012). The relations of $E_{kin} = E_{bol}$, $E_{kin} = E_{bol}/10$, and $E_{kin} = E_{bol}/100$ are also plotted in gray in the right panel. Here, GOES X-ray energy/flux is related to bolometric energy with the relations of $E_{bol}=100 E_{GOES}$ (Emslie et al. 2012) and $E_{bol}$ [erg] = $10^{35} F_{GOES}$ [W m$^{-2}$] (Shibata et al. 2013) to connect solar data to stellar data. Also, we assume bolometric energy ≈bolometric WLF energy (Kretzschmar et al. 2010; Kretzschmar 2011; Osten & Wolk 2015).</figcaption></figure>

Figure 22 shows the mass and kinetic energy as a function of flare-radiated energy for flares E1, E2, and E4 in comparison with solar filament eruptions/CMEs (Namekata et al. 2022d; Kotani et al. 2023) and their empirical scaling relations (Aarnio et al. 2012; Drake et al. 2013). Here, we focus comparisons among solar-type stars, the Sun and EK Dra, to show a solar-stellar comparison without many different factors, such as surface gravity, atmospheric density, etc., while other studies have already focused on the comparison among different spectral types. The original figures are taken from Namekata et al. (2022d), and here we added two newly discovered stellar prominence eruptions on EK Dra in green-filled symbols. In addition, small-scale solar filament eruptions/surges investigated by Kotani et al. (2023) were newly added for increasing samples in a small energy regime ($10^{28-30}$ erg).

We found that the mass of the gigantic prominence eruption in flare E1 exceeds the predictions of solar empirical scaling relations between flares and CMEs, while the measurements for E2 and E4 are consistent with these relations. Our results suggest that, like solar CMEs/filament eruptions, the ejected mass against a given flare energy scale exhibits considerable scattering in the case of young Sun-like stars, spanning one to two orders of magnitude. Kotani et al. 2023 theoretically suggested that the scattering may be explained by difference in magnetic field strength supporting the prominence. Hence, our findings in diversity in mass (and kinetic energy below) may be related to the diversity in the local magnetic field strength of the star.

Also, the kinetic energy of the E1 event aligns with or exceeds the solar scaling relation between flare energy and CME kinetic energy. In contrast, the kinetic energies of the E2 and E4 events and solar filament eruptions/surges are smaller by one to two orders of magnitude than the scaling relation.

The smaller kinetic energies associated with solar-stellar prominence/filament eruptions have been explained in the context of two scenarios, as discussed in Namekata et al. (2022d). The first explanation posits that the velocity of stellar CMEs and prominence/filament eruptions can be suppressed by an overlying robust magnetic field, leading to a smaller allocation of kinetic energy (Alvarado-Gómez et al. 2018). The second explanation attributes it to the different velocity between CMEs and prominence or filament eruptions (Maehara et al. 2021; Namekata et al. 2022d). Solar prominence or filament eruptions are represented by the expanding dense and cool lower portion of the self-similarly expanding flux rope. Consequently, the velocity of prominence or filament eruption is 4–8 times less than that of overlying CMEs (Gopalswamy et al. 2003). This perspective naturally accounts for the smaller kinetic energy observed in solar and stellar prominence or filament eruptions than the solar CME’s scaling relation. However, given the significant scattering in solar data, the broad range observed in the kinetic energy of stellar prominence/filament eruptions on EK Dra appears plausible by solar analogy. The cause of this wide variation of solar and stellar prominences/CMEs warrants further investigation in the future.

### 5.2.4. Optical Depth and Electron Density of Prominences

Then, is the assumption of optical depth $\tau = 10–1000$ appropriate? Table 10 summarizes the estimated prominence length scales for different values on the optical depth $\tau$ of 0.1, 1, 10, 100, 1000, and 10,000 as references. Solar prominence eruptions often show optical depth of $\tau \sim 1$ in $H\alpha$ line (e.g., Sakaue et al. 2018; Namekata et al. 2022d). The optical depth $\tau = 0.1$ and 1 gives an extremely large value of the length scale
<figure><img src="image_27.png" /><figcaption>**Figure 22.** Mass and kinetic energy of solar/stellar filament/prominence eruptions and CMEs as a function of bolometric WLF energy or GOES X-ray energy. The green and red points correspond to the stellar prominence and filament eruptions on EK Dra, respectively (this study, Namekata et al. 2022d). The black crosses are solar CME data (Yashiro & Gopalswamy 2009; Drake et al. 2013), while the green pluses are data for solar prominence/filament eruptions taken from Namekata et al. (2022d) and Kotani et al. (2023). The cyan dashed and magenta dotted lines are observational fits for solar CMEs expressed as $M_{CME} \propto E_{bol}^{0.59}$ and $E_{kin} \propto E_{bol}^{1.05}$ (cyan color; Drake et al. 2013) and $M_{CME} \propto E_{bol}^{0.7}$ (magenta color; Aarnio et al. 2012). The relations of $E_{kin} = E_{bol}$, $E_{kin} = E_{bol}/10$, and $E_{kin} = E_{bol}/100$ are also plotted in gray in the right panel. Here, GOES X-ray energy/flux is related to bolometric energy with the relations of $E_{bol}=100 E_{GOES}$ (Emslie et al. 2012) and $E_{bol}$ [erg] = $10^{35} F_{GOES}$ [W m$^{-2}$] (Shibata et al. 2013) to connect solar data to stellar data. Also, we assume bolometric energy ≈bolometric WLF energy (Kretzschmar et al. 2010; Kretzschmar 2011; Osten & Wolk 2015).</figcaption></figure>

Figure 22 shows the mass and kinetic energy as a function of flare-radiated energy for flares E1, E2, and E4 in comparison with solar filament eruptions/CMEs (Namekata et al. 2022d; Kotani et al. 2023) and their empirical scaling relations (Aarnio et al. 2012; Drake et al. 2013). Here, we focus comparisons among solar-type stars, the Sun and EK Dra, to show a solar-stellar comparison without many different factors, such as surface gravity, atmospheric density, etc., while other studies have already focused on the comparison among different spectral types. The original figures are taken from Namekata et al. (2022d), and here we added two newly discovered stellar prominence eruptions on EK Dra in green-filled symbols. In addition, small-scale solar filament eruptions/surges investigated by Kotani et al. (2023) were newly added for increasing samples in a small energy regime ($10^{28-30}$ erg).

We found that the mass of the gigantic prominence eruption in flare E1 exceeds the predictions of solar empirical scaling relations between flares and CMEs, while the measurements for E2 and E4 are consistent with these relations. Our results suggest that, like solar CMEs/filament eruptions, the ejected mass against a given flare energy scale exhibits considerable scattering in the case of young Sun-like stars, spanning one to two orders of magnitude. Kotani et al. 2023 theoretically suggested that the scattering may be explained by difference in magnetic field strength supporting the prominence. Hence, our findings in diversity in mass (and kinetic energy below) may be related to the diversity in the local magnetic field strength of the star.

Also, the kinetic energy of the E1 event aligns with or exceeds the solar scaling relation between flare energy and CME kinetic energy. In contrast, the kinetic energies of the E2 and E4 events and solar filament eruptions/surges are smaller by one to two orders of magnitude than the scaling relation.

The smaller kinetic energies associated with solar-stellar prominence/filament eruptions have been explained in the context of two scenarios, as discussed in Namekata et al. (2022d). The first explanation posits that the velocity of stellar CMEs and prominence/filament eruptions can be suppressed by an overlying robust magnetic field, leading to a smaller allocation of kinetic energy (Alvarado-Gómez et al. 2018). The second explanation attributes it to the different velocity between CMEs and prominence or filament eruptions (Maehara et al. 2021; Namekata et al. 2022d). Solar prominence or filament eruptions are represented by the expanding dense and cool lower portion of the self-similarly expanding flux rope. Consequently, the velocity of prominence or filament eruption is 4–8 times less than that of overlying CMEs (Gopalswamy et al. 2003). This perspective naturally accounts for the smaller kinetic energy observed in solar and stellar prominence or filament eruptions than the solar CME’s scaling relation. However, given the significant scattering in solar data, the broad range observed in the kinetic energy of stellar prominence/filament eruptions on EK Dra appears plausible by solar analogy. The cause of this wide variation of solar and stellar prominences/CMEs warrants further investigation in the future.

### 5.2.4. Optical Depth and Electron Density of Prominences

Then, is the assumption of optical depth $\tau = 10–1000$ appropriate? Table 10 summarizes the estimated prominence length scales for different values on the optical depth $\tau$ of 0.1, 1, 10, 100, 1000, and 10,000 as references. Solar prominence eruptions often show optical depth of $\tau \sim 1$ in $H\alpha$ line (e.g., Sakaue et al. 2018; Namekata et al. 2022d). The optical depth $\tau = 0.1$ and 1 gives an extremely large value of the length scale
<figure><img src="image_27.png" /><figcaption>**Figure 23.** Estimated electron density as a function of optical depth. The left y-axis is the case when the prominence is cubic structure, while right y-axis is the cause when the prominence is cylinder (i.e., filamentary structure). The blue colored region corresponds to the assumed optical depth.</figcaption></figure>

<table><caption>**Table 10**
Length Scale of Prominences in Different Prominence Parameters for Flares E1 and E2</caption><thead><tr><th rowspan="3">(optical depth)<br>τ = 0.1</th><th colspan="4">Prominence length</th></tr><tr><th colspan="2">E1</th><th colspan="2">E2</th></tr><tr><th>(R<sub>star</sub>)<br>24–240</th><th>(10<sup>10</sup> cm)<br>160–1600</th><th>(R<sub>star</sub>)<br>4.1–41</th><th>(10<sup>10</sup> cm)<br>27–270</th></tr></thead><tbody><tr><td>τ = 1</td><td>8.5–85</td><td>56–560</td><td>1.5–15</td><td>9.7–97</td></tr><tr><td>τ = 10</td><td>4.5–45</td><td>30–300</td><td>0.78–7.8</td><td>5.1–51</td></tr><tr><td>τ = 100</td><td>2.4–24</td><td>16–160</td><td>0.41–4.1</td><td>2.7–27</td></tr><tr><td>τ = 1000</td><td>1.3–13</td><td>8.3–83</td><td>0.22–2.2</td><td>1.4–14</td></tr><tr><td>τ = 10,000</td><td>0.67–6.7</td><td>4.4–44</td><td>0.12–1.2</td><td>0.77–7.7</td></tr></tbody></table>

**Note.** The lower value is not an assumption of the prominence's aspect ratio, while the upper value is derived with the assumption of the aspect ratio of the prominence.

of at least >24 $R_{\text{star}}$ and >8.5 $R_{\text{star}}$, respectively, for flare E1. These values look to be unrealistic considering that the prominence expanding velocity of ~500 km s⁻¹ can reach up to only 2.4 stellar radius within 1 hr (although plane-of-sky prominence velocities might be larger than the LOS velocities). Therefore, it would be reasonable to assume the optical depth of $\tau = 10$ as a lower limit.

Next, let us discuss the validity of the assumed optical depth from the consistency in the electron density. Figure 23 shows the estimated electron density as a function of assumed optical depth. The electron densities are estimated from Equation (18). As you can see, the optical depth of 10–1000 gives the electron densities of $1.7 \times 10^9–6.3 \times 10^{10} \text{ cm}^{-3}$. This is actually consistent with the solar prominence observations of $10^9–11 \text{ cm}^{-3}$ (Parenti 2014). This consistency in electron density supports the assumed range of the optical depth of this study.

Then, what about the electron densities of stellar erupting prominences on active stars? Past X-ray observations indicate that the electron density in the quiescent corona of EK Dra is at least $4 \times 10^{10} \text{ cm}^{-3}$ with a temperature of ~2 × 10⁶ K (Güdel et al. 1995). This means that the gas pressure in outside corona is ~40 times larger than in solar ones because solar coronal electron density is ~$10^9 \text{ cm}^{-3}$ with the similar temperature.

Considering the gas pressure balance between outside corona and prominences, we can estimate that the prominence density in EK Dra can be ~40 times larger than the solar values ($10^9–11 \text{ cm}^{-3}$), i.e., ~4 × $10^{10–12} \text{ cm}^{-3}$. The plasma $\beta$ of solar prominences are roughly ~1, so this could be the upper limit value of the quiescent prominence electron density. This value (~4 × $10^{10–12}$) could be a little bit larger than the estimated prominence electron density ($1.7 \times 10^9–6.3 \times 10^{10} \text{ cm}^{-3}$). However, because our prominence parameters are estimated from the $H\alpha$ luminosity of ~10 minutes after the prominence initiation for flare E1, the prominence could be more dilute than the original value. Under the assumption of the expansion velocity of 500 km s⁻¹ and the timescale of ~10 minutes, the prominence could be expanded into ~3 × $10^{10} \text{ cm}$, which is ~4 times larger than the flare loop size. If we assume that the prominence expands in a cubic way, the volume could expand into ~64 larger than the original volume, resulting in ~1/64 of the original electron density, i.e., ~6 × $10^8–10^9 \text{ cm}^{-3}$. This expanded prominence case in active stars is approximately consistent with the electron density estimated from the optical depth and cubic shape (Figure 23).

In summary, the optical depth of 0.1–1 (~solar values) is doubtful considering the unrealistically large prominence size. The upper limit of the optical depth could be difficult to be constrained only from the size, but the assumed optical depth of <1000 well covers the realistic prominence electron density. Table 10 includes estimates with much more extreme optical depth $\tau = 10,000$ as a reference. Because Equation (13) shows that the dependence of optical depth on the length scale $L_p \propto (\tau)^{-0.25}$ is not so strong, the discussion will not significantly change even though we assume $\tau = 10,000$.

### 5.3. Candidate of Possible X-Ray Dimming after Flares and Prominence Eruptions

We investigated whether the prominence eruptions in flares E1 and E2 are associated with X-ray dimmings, as other evidence of CMEs in multiwavelength (e.g., Veronig et al. 2021). Figures 24(b) and 25 show the ISS-orbital-binned X-ray light curves (see also Appendix A for more details on flare E1). We found that the X-ray count rates in the post-flare phase of flare E1 (i.e., blocks 5 and 6) decrease compared to the possible pre-flare level (block 3) by $-5.8_{-5.1}^{+5.1} \%$ and $-8.5_{-5.6}^{+5.6} \%$ for blocks 5 and 6, respectively (Figure 24(b)). The error bars are calculated by considering those in the pre-flare phase (block 3) and those in corresponding phases. The tiny X-ray enhancement in block 2 would be related to a simultaneous TESS WLF, and in block 4 can include the decay phase in flare E1, so we interpret block 3 (and possibly block 1) as representative of the pre-flare level. To remove the possible contamination of background X-ray flux (from the NICER's nonimaging field of view of 5' diameter<fnref n="29" />; Gendreau et al. 2016), we also calculated a background-subtracted X-ray count rate in Figure 24(b) using a 3C50 background model (nibackgen3c50; Remillard et al. 2022), which produced the dimming amplitude of $-8.8_{-6.2}^{+6.1} \%$ and $-14.7_{-7.1}^{+7.1} \%$ for each block. On the other hand, Figure 25 shows that there were no significant dimming events for flare E2 and E3.

Then, is this X-ray flux decrease a CME-related X-ray dimming? Indeed, the NICER X-ray data are not completely continuous, because NICER is on the ISS, so the full variation

<footnote n="29">²⁹ https://heasarc.gsfc.nasa.gov/docs/nicer/nicerAbout.html</footnote>
<figure><img src="image_28.png" /><figcaption>**Figure 23.** Estimated electron density as a function of optical depth. The left y-axis is the case when the prominence is cubic structure, while right y-axis is the cause when the prominence is cylinder (i.e., filamentary structure). The blue colored region corresponds to the assumed optical depth.</figcaption></figure>

<table><caption>**Table 10**
Length Scale of Prominences in Different Prominence Parameters for Flares E1 and E2</caption><thead><tr><th rowspan="3">(optical depth)<br>τ = 0.1</th><th colspan="4">Prominence length</th></tr><tr><th colspan="2">E1</th><th colspan="2">E2</th></tr><tr><th>(R<sub>star</sub>)<br>24–240</th><th>(10<sup>10</sup> cm)<br>160–1600</th><th>(R<sub>star</sub>)<br>4.1–41</th><th>(10<sup>10</sup> cm)<br>27–270</th></tr></thead><tbody><tr><td>τ = 1</td><td>8.5–85</td><td>56–560</td><td>1.5–15</td><td>9.7–97</td></tr><tr><td>τ = 10</td><td>4.5–45</td><td>30–300</td><td>0.78–7.8</td><td>5.1–51</td></tr><tr><td>τ = 100</td><td>2.4–24</td><td>16–160</td><td>0.41–4.1</td><td>2.7–27</td></tr><tr><td>τ = 1000</td><td>1.3–13</td><td>8.3–83</td><td>0.22–2.2</td><td>1.4–14</td></tr><tr><td>τ = 10,000</td><td>0.67–6.7</td><td>4.4–44</td><td>0.12–1.2</td><td>0.77–7.7</td></tr></tbody></table>

**Note.** The lower value is not an assumption of the prominence's aspect ratio, while the upper value is derived with the assumption of the aspect ratio of the prominence.

of at least >24 $R_{\text{star}}$ and >8.5 $R_{\text{star}}$, respectively, for flare E1. These values look to be unrealistic considering that the prominence expanding velocity of ~500 km s⁻¹ can reach up to only 2.4 stellar radius within 1 hr (although plane-of-sky prominence velocities might be larger than the LOS velocities). Therefore, it would be reasonable to assume the optical depth of $\tau = 10$ as a lower limit.

Next, let us discuss the validity of the assumed optical depth from the consistency in the electron density. Figure 23 shows the estimated electron density as a function of assumed optical depth. The electron densities are estimated from Equation (18). As you can see, the optical depth of 10–1000 gives the electron densities of $1.7 \times 10^9–6.3 \times 10^{10} \text{ cm}^{-3}$. This is actually consistent with the solar prominence observations of $10^9–11 \text{ cm}^{-3}$ (Parenti 2014). This consistency in electron density supports the assumed range of the optical depth of this study.

Then, what about the electron densities of stellar erupting prominences on active stars? Past X-ray observations indicate that the electron density in the quiescent corona of EK Dra is at least $4 \times 10^{10} \text{ cm}^{-3}$ with a temperature of ~2 × 10⁶ K (Güdel et al. 1995). This means that the gas pressure in outside corona is ~40 times larger than in solar ones because solar coronal electron density is ~$10^9 \text{ cm}^{-3}$ with the similar temperature.

Considering the gas pressure balance between outside corona and prominences, we can estimate that the prominence density in EK Dra can be ~40 times larger than the solar values ($10^9–11 \text{ cm}^{-3}$), i.e., ~4 × $10^{10–12} \text{ cm}^{-3}$. The plasma $\beta$ of solar prominences are roughly ~1, so this could be the upper limit value of the quiescent prominence electron density. This value (~4 × $10^{10–12}$) could be a little bit larger than the estimated prominence electron density ($1.7 \times 10^9–6.3 \times 10^{10} \text{ cm}^{-3}$). However, because our prominence parameters are estimated from the $H\alpha$ luminosity of ~10 minutes after the prominence initiation for flare E1, the prominence could be more dilute than the original value. Under the assumption of the expansion velocity of 500 km s⁻¹ and the timescale of ~10 minutes, the prominence could be expanded into ~3 × $10^{10} \text{ cm}$, which is ~4 times larger than the flare loop size. If we assume that the prominence expands in a cubic way, the volume could expand into ~64 larger than the original volume, resulting in ~1/64 of the original electron density, i.e., ~6 × $10^8–10^9 \text{ cm}^{-3}$. This expanded prominence case in active stars is approximately consistent with the electron density estimated from the optical depth and cubic shape (Figure 23).

In summary, the optical depth of 0.1–1 (~solar values) is doubtful considering the unrealistically large prominence size. The upper limit of the optical depth could be difficult to be constrained only from the size, but the assumed optical depth of <1000 well covers the realistic prominence electron density. Table 10 includes estimates with much more extreme optical depth $\tau = 10,000$ as a reference. Because Equation (13) shows that the dependence of optical depth on the length scale $L_p \propto (\tau)^{-0.25}$ is not so strong, the discussion will not significantly change even though we assume $\tau = 10,000$.

### 5.3. Candidate of Possible X-Ray Dimming after Flares and Prominence Eruptions

We investigated whether the prominence eruptions in flares E1 and E2 are associated with X-ray dimmings, as other evidence of CMEs in multiwavelength (e.g., Veronig et al. 2021). Figures 24(b) and 25 show the ISS-orbital-binned X-ray light curves (see also Appendix A for more details on flare E1). We found that the X-ray count rates in the post-flare phase of flare E1 (i.e., blocks 5 and 6) decrease compared to the possible pre-flare level (block 3) by −5.8$_{±5.1}$ % and −8.5$_{±5.6}$ % for blocks 5 and 6, respectively (Figure 24(b)). The error bars are calculated by considering those in the pre-flare phase (block 3) and those in corresponding phases. The tiny X-ray enhancement in block 2 would be related to a simultaneous TESS WLF, and in block 4 can include the decay phase in flare E1, so we interpret block 3 (and possibly block 1) as representative of the pre-flare level. To remove the possible contamination of background X-ray flux (from the NICER's nonimaging field of view of 5' diameter<fnref n="29" />; Gendreau et al. 2016), we also calculated a background-subtracted X-ray count rate in Figure 24(b) using a 3C50 background model (nibackgen3c50; Remillard et al. 2022), which produced the dimming amplitude of −8.8$_{±6.2}$ % and −14.7$_{±7.1}$ % for each block. On the other hand, Figure 25 shows that there were no significant dimming events for flare E2 and E3.

Then, is this X-ray flux decrease a CME-related X-ray dimming? Indeed, the NICER X-ray data are not completely continuous, because NICER is on the ISS, so the full variation

<footnote n="29">²⁹ https://heasarc.gsfc.nasa.gov/docs/nicer/nicerAbout.html</footnote>
<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /><figcaption>**Figure 24.** Possible X-ray (0.5–3 keV) dimming after the gigantic prominence eruptions associated with the superflare on 2022 April 10 (E1). (a) Reference TESS X-ray light curve. (b) The X-ray light curve. The blue points represent the average of the gray data with a 2-minute resolution for each orbital period. The red points denote the count rate after NICER’s background subtraction. The area filled in blue represents the time interval believed to show dimming relative to the pre-flare (block 3). The area filled with gray and red represents the pre-flare level, with error bars for blue and red points data, respectively. (c), (d) The temporal evolution of the temperature and emission measure of two components. The gray-shaded area in panel (d) represents the pre-flare level with error bars.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>**Figure 25.** X-ray (0.5–3 keV) light curves binned for each ISS orbit around superflares on 2022 April 16 (E2) and 2022 April 17 (E3). The gray points represent the data with a time resolution of 2 minutes, while the blue points correspond to the average of the gray data for each ISS orbit (~90-minute period). The horizontal lines denote the pre-flare values. For flare E3, the average value of the previous orbit and the pre-flare value just before the flare are plotted.</figcaption></figure>

of the X-ray light curve is not obtained. This is one of the difficulties of identifying whether it could be a dimming. Also, the net exposure time of this date is relatively short compared to other dates, and the data quality is lower than usual. In addition, the definitions of “pre-flare level” is very difficult for finding XUV dimming in active stars (Veronig et al. 2021; Loyd et al. 2022) because their “pre-flare levels” are essentially

a superposition of frequent small (but solar M/X-class) flares and therefore variable. Considering these, it may be not possible to conclusively suggest that an X-ray dimming is detected. However, simultaneous detection with Hα blueshifts in flare E1 supports the possible association of the X-ray dimming, which could indicate the occurrence of unknown CMEs. Therefore, in the following, we call this an X-ray
<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

<figure><img src="image_32.png" /></figure>

**Figure 24.** Possible X-ray (0.5–3 keV) dimming after the gigantic prominence eruptions associated with the superflare on 2022 April 10 (E1). (a) Reference TESS light curve. (b) The X-ray light curve. The blue points represent the average of the gray data with a 2-minute resolution for each orbital period. The red points denote the count rate after NICER’s background subtraction. The area filled in blue represents the time interval believed to show dimming relative to the pre-flare (block 3). The area filled with gray and red represents the pre-flare level, with error bars for blue and red points data, respectively. (c), (d) The temporal evolution of the temperature and emission measure of two components. The gray-shaded area in panel (d) represents the pre-flare level with error bars.

<figure><img src="image_33.png" /></figure>

(a)

<figure><img src="image_34.png" /></figure>

(b)

**Figure 25.** X-ray (0.5–3 keV) light curves binned for each ISS orbit around superflares on 2022 April 16 (E2) and 2022 April 17 (E3). The gray points represent the data with a time resolution of 2 minutes, while the blue points correspond to the average of the gray data for each ISS orbit (~90-minute period). The horizontal lines denote the pre-flare values. For flare E3, the average value of the previous orbit and the pre-flare value just before the flare are plotted.

of the X-ray light curve is not obtained. This is one of the difficulties of identifying whether it could be a dimming. Also, the net exposure time of this date is relatively short compared to other dates, and the data quality is lower than usual. In addition, the definitions of “pre-flare level” is very difficult for finding XUV dimming in active stars (Veronig et al. 2021; Loyd et al. 2022) because their “pre-flare levels” are essentially

a superposition of frequent small (but solar M/X-class) flares and therefore variable. Considering these, it may be not possible to conclusively suggest that an X-ray dimming is detected. However, simultaneous detection with Hα blueshifts in flare E1 supports the possible association of the X-ray dimming, which could indicate the occurrence of unknown CMEs. Therefore, in the following, we call this an X-ray
<figure><img src="image_31.png" /><figcaption>Figure 26. The same as Figure 13, but for the superflare on 2022 April 10 (E1).</figcaption></figure>

<table><caption>Table 11
Results of NICER X-Ray Spectral Fit for Flares E1 X-Ray Dimming</caption><thead><tr><th>Flare E1's block</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>T<sub>1</sub> (keV)</td><td>0.95<sub>±0.04</sub></td><td>1.11<sub>±0.04</sub></td><td>1.06<sub>±0.05</sub></td><td>1.08<sub>±0.08</sub></td><td>0.91<sub>±0.05</sub></td><td>0.99<sub>±0.05</sub></td></tr><tr><td>(T<sub>1</sub> [10<sup>7</sup> K])</td><td>(1.10<sub>±0.05</sub>)</td><td>(1.29<sub>±0.04</sub>)</td><td>(1.23<sub>±0.05</sub>)</td><td>(1.25<sub>±0.09</sub>)</td><td>(1.06<sub>±0.05</sub>)</td><td>(1.15<sub>±0.06</sub>)</td></tr><tr><td>T<sub>2</sub> (keV)</td><td>0.44<sub>±0.05</sub></td><td>0.54<sub>±0.05</sub></td><td>0.53<sub>±0.07</sub></td><td>0.65<sub>±0.09</sub></td><td>0.43<sub>±0.07</sub></td><td>0.51<sub>±0.07</sub></td></tr><tr><td>(T<sub>2</sub> [10<sup>7</sup> K])</td><td>(0.51<sub>±0.06</sub>)</td><td>(0.62<sub>±0.06</sub>)</td><td>(0.61<sub>±0.09</sub>)</td><td>(0.75<sub>±0.10</sub>)</td><td>(0.50<sub>±0.08</sub>)</td><td>(0.59<sub>±0.08</sub>)</td></tr><tr><td>EM<sub>1</sub> [10<sup>52</sup> cm<sup>-3</sup>]</td><td>5.34<sub>±0.47</sub></td><td>6.84<sub>±0.39</sub></td><td>6.05<sub>±0.48</sub></td><td>5.83<sub>±1.11</sub></td><td>5.68<sub>±0.59</sub></td><td>4.51<sub>±0.49</sub></td></tr><tr><td>EM<sub>2</sub> [10<sup>52</sup> cm<sup>-3</sup>]</td><td>3.69<sub>±0.49</sub></td><td>4.02<sub>±0.32</sub></td><td>3.16<sub>±0.42</sub></td><td>3.84<sub>±1.09</sub></td><td>2.81<sub>±0.63</sub></td><td>3.43<sub>±0.45</sub></td></tr><tr><td>χ<sup>2</sup>(dof)</td><td>81(83)</td><td>139(110)</td><td>110(81)</td><td>75(79)</td><td>48(51)</td><td>79(74)</td></tr><tr><td>reduced χ<sup>2</sup></td><td>0.98</td><td>1.26</td><td>1.36</td><td>0.95</td><td>0.94</td><td>1.07</td></tr></tbody></table>

Note. The hydrogen column density $N_H$ in TBAbs is fixed as $3 \times 10^{18} \text{ cm}^{-2}$. The abundance in apec is fixed as a typical value of 0.23.

decrease of flare E1 as “possible X-ray dimming” or just a “candidate” and investigate its properties and whether they are consistent with flare and prominence eruption sizes, following the previous studies on M/K-dwarfs (Veronig et al. 2021; Loyd et al. 2022).

For estimating the emission measure of the possible X-ray dimming, we performed the spectral fitting of a background-subtracted X-ray spectrum for each ISS orbit on 2022 April 10 with two-component apec models, which are emission spectra from collisionally ionized diffuse gas calculated from the AtomDB atomic database.<fnref n="30" /> The hydrogen column density is fixed as $N_H = 3 \times 10^{18} \text{ cm}^{-2}$, which was the same assumption made by Güdel et al. (1997a). Abundance relative to solar one is fixed as 0.23 in this analysis, which is a median value for two-component fitting results for all orbits in this campaign. Figure 26 shows the X-ray spectra for each orbit and the fitting results, whose parameters are summarized in Table 11. Figure 24(c) and (d) show the time evolution of the temperature and emission measure of two plasma components.

The decrease in total emission measure ($EM_{tot} = EM_1 + EM_2$) of blocks 5 and 6 compared to the pre-flare orbit (block 3) is $7.2_{±11.7} \times 10^{51} \text{ cm}^{-3}$ ($7.8_{±11.7} \%$) and $12.7_{±9.2} \times 10^{51} \text{ cm}^{-3}$ ($13.8_{±10.0} \%$), respectively. Here, the error bars are a bit large but this is because the EM was obtained by the spectral fitting while the error bars in the light curves were obtained by energy-integrated count rates. This is roughly consistent with the dimming amplitude in their light curve [$5.8_{±5.1} \text{ (block 5)}-8.5_{±5.6} \text{ (block 6)} \%$ for non-background-subtracted count rates or $8.8_{±6.2} \times 14.7_{±7.1} \%$ for background-subtracted count rates]. We can estimate the volume and the length scale of the corona from the equation of $\Delta EM_{tot} = n_e n_H V \approx n_e^2 V = n_e^2 L_{dim}^3$.

$$V \approx n_e^{-2} \Delta EM_{tot} = (7.2_{±11.7} - 12.7_{±9.2}) \times 10^{31} \cdot \left( \frac{n_e}{10^{10} \text{cm}^{-3}} \right)^{-2} \text{cm}^3 \quad (22)$$

$$L_{dim} \approx n_e^{-2/3} \Delta EM_{tot}^{1/3} = (4.2_{-4.2}^{+1.6} - 5.0_{-1.7}^{+1.0}) \times 10^{10} \cdot \left( \frac{n_e}{10^{10} \text{cm}^{-3}} \right)^{-2/3} \text{cm} \quad (23)$$

<footnote n="30">³⁰ https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node134.html</footnote>
<figure><img src="image_35.png" /><figcaption>Figure 26. The same as Figure 13, but for the superflare on 2022 April 10 (E1).</figcaption></figure>

<table><caption>Table 11
Results of NICER X-Ray Spectral Fit for Flares E1 X-Ray Dimming</caption><thead><tr><th>Flare E1's block</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>T<sub>1</sub> (keV)</td><td>0.95<sub>±0.04</sub></td><td>1.11<sub>±0.04</sub></td><td>1.06<sub>±0.05</sub></td><td>1.08<sub>±0.08</sub></td><td>0.91<sub>±0.05</sub></td><td>0.99<sub>±0.05</sub></td></tr><tr><td>(T<sub>1</sub> [10<sup>7</sup> K])</td><td>(1.10<sub>±0.05</sub>)</td><td>(1.29<sub>±0.04</sub>)</td><td>(1.23<sub>±0.05</sub>)</td><td>(1.25<sub>±0.09</sub>)</td><td>(1.06<sub>±0.05</sub>)</td><td>(1.15<sub>±0.06</sub>)</td></tr><tr><td>T<sub>2</sub> (keV)</td><td>0.44<sub>±0.05</sub></td><td>0.54<sub>±0.05</sub></td><td>0.53<sub>±0.07</sub></td><td>0.65<sub>±0.09</sub></td><td>0.43<sub>±0.07</sub></td><td>0.51<sub>±0.07</sub></td></tr><tr><td>(T<sub>2</sub> [10<sup>7</sup> K])</td><td>(0.51<sub>±0.06</sub>)</td><td>(0.62<sub>±0.06</sub>)</td><td>(0.61<sub>±0.09</sub>)</td><td>(0.75<sub>±0.10</sub>)</td><td>(0.50<sub>±0.08</sub>)</td><td>(0.59<sub>±0.08</sub>)</td></tr><tr><td>EM<sub>1</sub> [10<sup>52</sup> cm<sup>-3</sup>]</td><td>5.34<sub>±0.47</sub></td><td>6.84<sub>±0.39</sub></td><td>6.05<sub>±0.48</sub></td><td>5.83<sub>±1.11</sub></td><td>5.68<sub>±0.59</sub></td><td>4.51<sub>±0.49</sub></td></tr><tr><td>EM<sub>2</sub> [10<sup>52</sup> cm<sup>-3</sup>]</td><td>3.69<sub>±0.49</sub></td><td>4.02<sub>±0.32</sub></td><td>3.16<sub>±0.42</sub></td><td>3.84<sub>±1.09</sub></td><td>2.81<sub>±0.63</sub></td><td>3.43<sub>±0.45</sub></td></tr><tr><td>χ<sup>2</sup>(dof)</td><td>81(83)</td><td>139(110)</td><td>110(81)</td><td>75(79)</td><td>48(51)</td><td>79(74)</td></tr><tr><td>reduced χ<sup>2</sup></td><td>0.98</td><td>1.26</td><td>1.36</td><td>0.95</td><td>0.94</td><td>1.07</td></tr></tbody></table>

Note. The hydrogen column density $N_H$ in TBAbs is fixed as $3 \times 10^{18} \text{ cm}^{-2}$. The abundance in apec is fixed as a typical value of 0.23.

decrease of flare E1 as “possible X-ray dimming” or just a “candidate” and investigate its properties and whether they are consistent with flare and prominence eruption sizes, following the previous studies on M/K-dwarfs (Veronig et al. 2021; Loyd et al. 2022).

For estimating the emission measure of the possible X-ray dimming, we performed the spectral fitting of a background-subtracted X-ray spectrum for each ISS orbit on 2022 April 10 with two-component apec models, which are emission spectra from collisionally ionized diffuse gas calculated from the AtomDB atomic database.<fnref n="30" /> The hydrogen column density is fixed as $N_H = 3 \times 10^{18} \text{ cm}^{-2}$, which was the same assumption made by Güdel et al. (1997a). Abundance relative to solar one is fixed as 0.23 in this analysis, which is a median value for two-component fitting results for all orbits in this campaign. Figure 26 shows the X-ray spectra for each orbit and the fitting results, whose parameters are summarized in Table 11. Figure 24(c) and (d) show the time evolution of the temperature and emission measure of two plasma components.

The decrease in total emission measure ($EM_{tot} = EM_1 + EM_2$) of blocks 5 and 6 compared to the pre-flare orbit (block 3) is $7.2_{±11.7} \times 10^{51} \text{ cm}^{-3}$ (7.8_{±11.7} %) and $12.7_{±9.2} \times 10^{51} \text{ cm}^{-3}$ (13.8_{±10.0} %), respectively. Here, the error bars are a bit large but this is because the EM was obtained by the spectral fitting while the error bars in the light curves were obtained by energy-integrated count rates. This is roughly consistent with the dimming amplitude in their light curve [5.8_{±5.1} (block 5)–8.5_{±5.6} (block 6) % for non-background-subtracted count rates or 8.8_{±6.2}–14.7_{±7.1} % for background-subtracted count rates]. We can estimate the volume and the length scale of the corona from the equation of $\Delta EM_{tot} = n_e n_H V \approx n_e^2 V = n_e^2 L_{dim}^3$.

$$V \approx n_e^{-2} \Delta EM_{tot} = (7.2_{±11.7} - 12.7_{±9.2}) \times 10^{31} \cdot \left( \frac{n_e}{10^{10} \text{cm}^{-3}} \right)^{-2} \text{cm}^3 \quad (22)$$

$$L_{dim} \approx n_e^{-2/3} \Delta EM_{tot}^{1/3} = (4.2_{-4.2}^{+1.6} - 5.0_{-1.7}^{+1.0}) \times 10^{10} \cdot \left( \frac{n_e}{10^{10} \text{cm}^{-3}} \right)^{-2/3} \text{cm} \quad (23)$$

<footnote n="30">³⁰ https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node134.html</footnote>
The mass that escapes can be estimated in the formula of

$$M_{\text{dim}} = m_{\text{H}}n_{\text{H}}V \approx m_{\text{H}}n_{\text{e}}V = m_{\text{H}}n_{\text{e}}^{-1}\Delta\text{EM}_{\text{tot}} \quad (24)$$

$$= (1.67 \times 10^{-24} \text{ g}) \cdot (10^{10} \text{cm}^{-3})^{-1} \cdot \left( \frac{n_{\text{e}}}{10^{10} \text{cm}^{-3}} \right)^{-1} \cdot (7.2_{\pm 11.7} - 12.7_{\pm 9.2}) \times 10^{51} \text{cm}^{-3} \quad (25)$$

$$= (1.2_{\pm 2.0} - 2.1_{\pm 1.5}) \times 10^{18} \cdot \left( \frac{n_{\text{e}}}{10^{10} \text{cm}^{-3}} \right)^{-1} \text{g} \quad (26)$$

It is reasonable to assume that this dimming region possesses the typical density of the active regions, as numerical simulations by Shiota et al. (2005) show that the dimming region can be considered as the immediate adjacent space to the magnetic field lines undergoing reconnection. Therefore, the assumption of coronal density of $10^{10-11} \text{cm}^{-3}$ would be reasonable for EK Dra's active region (see Section 4.3; Güdel et al. 1995; Güdel 2004; Ness et al. 2004). The assumption of a coronal density $n_e$ of $10^{11} \text{cm}^{-3}$ gives the estimates of the volume $V = (7.2_{\pm 11.7} - 12.7_{\pm 9.2}) \times 10^{29} \text{cm}^3$, the length scale $L_{\text{dim}} = (0.90_{-0.9}^{+0.3} - 1.1_{-0.4}^{+0.2}) \times 10^{10} \text{cm}$, and the mass $M_{\text{dim}} = (1.2_{\pm 2.0} - 2.1_{\pm 1.5}) \times 10^{17} \text{g}$. Likewise, the assumption of a coronal density $n_e$ of $10^{10} \text{cm}^{-3}$ gives different estimations as $V = (7.2_{\pm 11.7} - 12.7_{\pm 9.2}) \times 10^{31} \text{cm}^3$, $L_{\text{dim}} = (4.2_{-4.2}^{+1.6} - 5.0_{-1.7}^{+1.0}) \times 10^{10} \text{cm}$, and $M_{\text{dim}} = (1.2_{\pm 2.0} - 2.1_{\pm 1.5}) \times 10^{18} \text{g}$.

The length scale of the coronal source of the possible X-ray dimming region ((0.90$_{-0.9}^{+0.3}$ - 1.1$_{-0.4}^{+0.2}$) × 10$^{10}$ cm or (4.2$_{-4.2}^{+1.6}$ - 5.0$_{-1.7}^{+1.0}$) × 10$^{10}$ cm) is roughly consistent with—or slightly larger than—the flaring loop length (0.73 × 10$^{10}$ cm) estimated in Section 4.3. This supports that the observed post-flare decrease in soft X-ray count rate can be related to the escape of hot coronal plasma associated with a CME. Now, if this X-ray dimming were indeed the so-called dimming, how would it be compared to the properties of the prominence? The length scale of the dimming region is actually much smaller by one to two orders of magnitude than the estimated length scale of prominence eruption ((8.3–300) × 10$^{10}$ cm). It is speculated that the prominence gradually expands and its area increases as it erupts, as in the case of solar prominence/filament eruptions. The length scale of the prominence estimated here corresponds to the value when its surface area (i.e., EW) was the largest. Therefore, it is reasonable that estimated prominence length scale is larger than the length scale of the flare region and dimming region. Moreover, the escaped coronal mass estimated from the possible X-ray dimming is smaller than the estimated mass of prominence (4.0 × 10$^{19}$g—4.2 × 10$^{20}$g). Therefore, it is not surprising even if an X-ray dimming associated with the gigantic prominence eruption in E1 is detected. These comparisons in length scale and mass, however, largely depend on the assumed physical quantities of stellar corona and prominences (see Section 5.2). More detailed comparisons to ensure that there is no inconsistency between the possible dimming and prominences require further models (see Leitzinger et al. 2022; Loyd et al. 2022).

## 6. Discussion and Conclusion

We report on three superflares (labeled as E1–E3) from the young solar-type star EK Dra, using our simultaneous optical and X-ray observations taken with Seimei, TESS, and NICER. The time-resolved $H\alpha$ spectra were characterized in the relation

with simultaneous WL and X-ray flares for the first time on solar-type stars. A short summary of the preceding sections is as follows: Section 4 describes the multiwavelength time evolution, energy partitions, and length scales of superflares. Section 4.1 suggests that occurrence mechanism of superflares on solar-type stars could be as common as those of solar and M-dwarf flares, as time delay of X-ray against WL and $H\alpha$ suggest chromospheric heating followed by chromospheric evaporation. Section 4.2 provides meaningful empirical laws for flare radiative energy partition into X-ray and WL, linking the well-established Kepler/TESS photometry to assessing their impact on the exoplanetary environment. Section 5 reports on the first discovery and properties of gigantic prominence eruptions (E1 and E2) on a solar-type star. Section 5.1 concludes that the detected blueshifted emissions are stellar prominence eruptions from several observational considerations. Section 5.3 reports and discusses a possible candidate of the associated post-flare X-ray dimming (E1), which enables the first simultaneous multiwavelength diagnostics of stellar CMEs on solar-type stars in different signatures (i.e., the Balmer line blueshifts and the possible candidate of X-ray dimming).

Here, bringing all the information together, we will discuss the following remaining topics entitled in Sections 6.1–6.3 and give a conclusion for each topic. In the following, we also mention previous studies reporting two $H\alpha$ superflares on the EK Dra, where one of them shows filament eruptions (labeled as “E4,” Namekata et al. 2022d) and the other does not (labeled as “E5,” Namekata et al. 2022c), as summarized in Tables 3, 4, and 9.

### 6.1. Can the Prominence Eruptions Be Associated with Stellar CMEs?

In Section 5, we report the discovery of gigantic stellar prominence eruptions associated with superflares (E1 and E2). The occurrence of the prominence eruption is conclusively suggested in Section 5.1. The maximum velocity of the prominence eruption in flare E1 was 690 km s$^{-1}$ (conservatively, 330–490 km s$^{-1}$), and 430 km s$^{-1}$ in flare E2 (Section 5.2.1). While the maximum velocity in E1 event is slightly larger than the escape velocity of EK Dra of ~670 km s$^{-1}$, it was gradually decelerated and eventually showed almost zero velocity. This may suggest that most of the emitting mass of the prominence stalled, and it is unclear if the prominence itself ultimately escaped. However, we consider that the following points indicate the occurrence of the associated CMEs which consist of outer coronal mass and fast prominence components, especially in flare E1:

1. The large velocity dispersion of a blueshifted $H\alpha$ component can be interpreted as spatial velocity distribution in the expanding 3D loop structure (Section 5.2.1), which is also apparent in the Sun-as-a-star analysis (Appendix B). Based on this interpretation, the maximum velocity component in the E1 event could reach 990–1080 km s$^{-1}$ (conservatively, 630–880 km s$^{-1}$), which is significantly greater than the escape velocity. In the case of the Sun, prominence eruptions represent the lower part of CMEs, and some solar events show that the majority of prominence falls back to the Sun, while the other part of fast prominence components and outer coronal masses actually leads to CMEs (e.g., Wood et al. 2016, Appendix B). These suggest
The mass that escapes can be estimated in the formula of

$$M_{\text{dim}} = m_{\text{H}}n_{\text{H}}V \approx m_{\text{H}}n_{\text{e}}V = m_{\text{H}}n_{\text{e}}^{-1}\Delta\text{EM}_{\text{tot}} \quad (24)$$

$$= (1.67 \times 10^{-24} \text{ g}) \cdot (10^{10} \text{cm}^{-3})^{-1} \cdot \left(\frac{n_{\text{e}}}{10^{10} \text{cm}^{-3}}\right)^{-1} \cdot (7.2_{\pm 11.7} - 12.7_{\pm 9.2}) \times 10^{51} \text{cm}^{-3} \quad (25)$$

$$= (1.2_{\pm 2.0} - 2.1_{\pm 1.5}) \times 10^{18} \cdot \left(\frac{n_{\text{e}}}{10^{10} \text{cm}^{-3}}\right)^{-1} \text{g} \quad (26)$$

It is reasonable to assume that this dimming region possesses the typical density of the active regions, as numerical simulations by Shiota et al. (2005) show that the dimming region can be considered as the immediate adjacent space to the magnetic field lines undergoing reconnection. Therefore, the assumption of coronal density of $10^{10-11} \text{cm}^{-3}$ would be reasonable for EK Dra's active region (see Section 4.3; Güdel et al. 1995; Güdel 2004; Ness et al. 2004). The assumption of a coronal density $n_e$ of $10^{11} \text{cm}^{-3}$ gives the estimates of the volume $V = (7.2_{\pm 11.7} - 12.7_{\pm 9.2}) \times 10^{29} \text{cm}^3$, the length scale $L_{\text{dim}} = (0.90_{-0.9}^{+0.3} - 1.1_{-0.4}^{+0.2}) \times 10^{10} \text{cm}$, and the mass $M_{\text{dim}} = (1.2_{\pm 2.0} - 2.1_{\pm 1.5}) \times 10^{17} \text{g}$. Likewise, the assumption of a coronal density $n_e$ of $10^{10} \text{cm}^{-3}$ gives different estimations as $V = (7.2_{\pm 11.7} - 12.7_{\pm 9.2}) \times 10^{31} \text{cm}^3$, $L_{\text{dim}} = (4.2_{-4.2}^{+1.6} - 5.0_{-1.7}^{+1.0}) \times 10^{10} \text{cm}$, and $M_{\text{dim}} = (1.2_{\pm 2.0} - 2.1_{\pm 1.5}) \times 10^{18} \text{g}$.

The length scale of the coronal source of the possible X-ray dimming region ($(0.90_{-0.9}^{+0.3} - 1.1_{-0.4}^{+0.2}) \times 10^{10} \text{cm}$ or $(4.2_{-4.2}^{+1.6} - 5.0_{-1.7}^{+1.0}) \times 10^{10} \text{cm}$) is roughly consistent with—or slightly larger than—the flaring loop length $(0.73 \times 10^{10} \text{cm})$ estimated in Section 4.3. This supports that the observed post-flare decrease in soft X-ray count rate can be related to the escape of hot coronal plasma associated with a CME. Now, if this X-ray dimming were indeed the so-called dimming, how would it be compared to the properties of the prominence? The length scale of the dimming region is actually much smaller by one to two orders of magnitude than the estimated length scale of prominence eruption ($(8.3-300) \times 10^{10} \text{cm}$). It is speculated that the prominence gradually expands and its area increases as it erupts, as in the case of solar prominence/filament eruptions. The length scale of the prominence estimated here corresponds to the value when its surface area (i.e., EW) was the largest. Therefore, it is reasonable that estimated prominence length scale is larger than the length scale of the flare region and dimming region. Moreover, the escaped coronal mass estimated from the possible X-ray dimming is smaller than the estimated mass of prominence $(4.0 \times 10^{19} \text{g}-4.2 \times 10^{20} \text{g})$. Therefore, it is not surprising even if an X-ray dimming associated with the gigantic prominence eruption in E1 is detected. These comparisons in length scale and mass, however, largely depend on the assumed physical quantities of stellar corona and prominences (see Section 5.2). More detailed comparisons to ensure that there is no inconsistency between the possible dimming and prominences require further models (see Leitzinger et al. 2022; Loyd et al. 2022).

## 6. Discussion and Conclusion

We report on three superflares (labeled as E1-E3) from the young solar-type star EK Dra, using our simultaneous optical and X-ray observations taken with Seimei, TESS, and NICER. The time-resolved $H\alpha$ spectra were characterized in the relation

with simultaneous WL and X-ray flares for the first time on solar-type stars. A short summary of the preceding sections is as follows: Section 4 describes the multiwavelength time evolution, energy partitions, and length scales of superflares. Section 4.1 suggests that occurrence mechanism of superflares on solar-type stars could be as common as those of solar and M-dwarf flares, as time delay of X-ray against WL and $H\alpha$ suggest chromospheric heating followed by chromospheric evaporation. Section 4.2 provides meaningful empirical laws for flare radiative energy partition into X-ray and WL, linking the well-established Kepler/TESS photometry to assessing their impact on the exoplanetary environment. Section 5 reports on the first discovery and properties of gigantic prominence eruptions (E1 and E2) on a solar-type star. Section 5.1 concludes that the detected blueshifted emissions are stellar prominence eruptions from several observational considerations. Section 5.3 reports and discusses a possible candidate of the associated post-flare X-ray dimming (E1), which enables the first simultaneous multiwavelength diagnostics of stellar CMEs on solar-type stars in different signatures (i.e., the Balmer line blueshifts and the possible candidate of X-ray dimming).

Here, bringing all the information together, we will discuss the following remaining topics entitled in Sections 6.1–6.3 and give a conclusion for each topic. In the following, we also mention previous studies reporting two $H\alpha$ superflares on the EK Dra, where one of them shows filament eruptions (labeled as “E4,” Namekata et al. 2022d) and the other does not (labeled as “E5,” Namekata et al. 2022c), as summarized in Tables 3, 4, and 9.

### 6.1. Can the Prominence Eruptions Be Associated with Stellar CMEs?

In Section 5, we report the discovery of gigantic stellar prominence eruptions associated with superflares (E1 and E2). The occurrence of the prominence eruption is conclusively suggested in Section 5.1. The maximum velocity of the prominence eruption in flare E1 was $690 \text{ km s}^{-1}$ (conservatively, $330-490 \text{ km s}^{-1}$), and $430 \text{ km s}^{-1}$ in flare E2 (Section 5.2.1). While the maximum velocity in E1 event is slightly larger than the escape velocity of EK Dra of ~$670 \text{ km s}^{-1}$, it was gradually decelerated and eventually showed almost zero velocity. This may suggest that most of the emitting mass of the prominence stalled, and it is unclear if the prominence itself ultimately escaped. However, we consider that the following points indicate the occurrence of the associated CMEs which consist of outer coronal mass and fast prominence components, especially in flare E1:

1. The large velocity dispersion of a blueshifted $H\alpha$ component can be interpreted as spatial velocity distribution in the expanding 3D loop structure (Section 5.2.1), which is also apparent in the Sun-as-a-star analysis (Appendix B). Based on this interpretation, the maximum velocity component in the E1 event could reach $990-1080 \text{ km s}^{-1}$ (conservatively, $630-880 \text{ km s}^{-1}$), which is significantly greater than the escape velocity. In the case of the Sun, prominence eruptions represent the lower part of CMEs, and some solar events show that the majority of prominence falls back to the Sun, while the other part of fast prominence components and outer coronal masses actually leads to CMEs (e.g., Wood et al. 2016, Appendix B). These suggest
that a part of the fast prominence components might have escaped.

2. Following the scheme suggested by Namekata et al. (2022d), comparing solar and stellar eruptions in terms of the length scale and velocity strongly suggests that the prominence eruptions in flares E1 and E2 could be associated with CMEs, considering their gigantic length scales and velocities (Section 5.2.2).

3. The numerical simulation by Alvarado-Gómez et al. (2018) suggests that the large-scale magnetic field could suppress CMEs under the average magnetic field strength of 75 G if the kinetic energy of CMEs is below a threshold around ~3 × 10³² erg. Because the EK Dra's averaged magnetic field strength of 66–89 G is similar to this numerical setup (e.g., Waite et al. 2017), we may be able to apply this threshold to our superflares (see Namekata et al. 2022d, Supplementary Information). The initial kinetic energy of the prominence eruptions from events E1 and E2 is 5.8±4.0 × 10³⁴ erg and 1.2±0.8 × 10³³ erg, respectively (Section 5.2.4), which is significantly larger than this threshold. This indicates that the magnetic suppression might not be an efficient process in these cases. Indeed, the mentioned model employs a dipolar magnetic field, while spectropolarimetric observations of this star show that large-scale magnetic fields have multipolar components (e.g., Rosén et al. 2016), and we will perform further numerical modelings with the observed data in the future (Section 6.4).

4. After flare E1, a possible candidate of X-ray dimming was detected, as an indication of escaping the surrounding hot coronal plasma associated with CMEs (Section 5.3). Although the determination of the pre-flare X-ray level is an issue in detecting stellar XUV dimming, the simultaneous detection with the Hα blueshift event supports the detection of X-ray dimming. The estimated upper limit of length scale of the dimming region of up to ~ (9–11) × 10⁹ cm is roughly consistent with the length scale of the flares ~7.3 × 10⁹ cm. The estimated mass of escaping coronal plasma of 1.2 × 10¹⁷–2.1 × 10¹⁸ g is enough small that the erupted prominence mass is 4.0 × 10¹⁹–4.2 × 10²⁰ g. Therefore, it is not surprising that the detected X-ray dimming amplitudes are likely to be interpreted as CME-related dimming (Section 5.3). However, again we should note that the NICER X-ray observation is usually sparse due to the ISS orbit, and we need to be careful with the treatment of these data (see also Appendix A). More convincing detections should be required for further discussions.

Given these without any suggestive evidence that is against the occurrence of CMEs in flare E1, we concluded that the flare E1 is associated with the occurrence a stellar CME. This conclusion is stronger than that drawn in Namekata et al. (2022d). Furthermore, solar studies indicate that velocities of outer CMEs are typically 4–8 times larger than the velocities of prominences (Gopalswamy et al. 2003), suggesting that the associated CME velocity from flare E1 could reach up to 2800–5500 km s⁻¹.

It is important to mention that the center-of-mass velocity of the giant prominence in E1 evolved from 690 km s⁻¹ to near zero in about 20 minutes, and then disappeared without showing a redshift. This means that the center-of-mass of the

prominence stopped midway and disappeared for some reason. The disappearance and terminal zero velocity are puzzling because solar prominence eruptions show redshifted spectra after impulsive blueshifts, as presented in Appendix B. By integrating the blueshift velocity over evolution time (up to t < 50 minutes), the line-of-sight displacement of the center-of-mass is calculated as 6.0±0.3 × 10¹⁰ cm (0.91±0.04 R<sub>star</sub>) for one-component fitting and 7.5±0.2 × 10¹⁰ cm (1.14±0.03 R<sub>star</sub>) for two-component fitting. The gravity is expected to be 3.6 times weaker at the height of 0.91 R<sub>star</sub> than the surface gravity. The timescale of plasma acceleration from rest to > 50 km s⁻¹ from this height is approximately 10 minutes. It is likely that before it began falling back to the star, the plasma was heated or became more diffuse and thus became invisible in the Hα line. Another possible explanation is that in the later phase, the emissions in line center come from flare ribbons. Also, one may speculate that this zero-velocity erupted prominence could be linked to “slingshot” prominences (e.g., Jardine & Collier Cameron 2019). Although there is no observation of slingshot prominences for EK Dra, the E1 event may provide a possibility that the flare-related prominence could be one source of the slingshot prominences seen in rapidly rotating stars.

The prominence eruption in flare E2 (this study) and filament eruptions in flare E4 (Namekata et al. 2022d) offer less robust evidence of CMEs than flare E1. The prominence eruption associated with the E2 flare event was relatively small and short-lived, and it did not exhibit any substantial X-ray dimming. The lack of significant X-ray dimming following the E2 event could be attributed to its small dimming amplitude, which could be caused by the relatively small prominence area, an order of magnitude smaller than that observed in the E1 flare event. The filament eruptions associated with the E4 flare event (Namekata et al. 2022d) exhibited a clear blueshifted absorption, but its maximum velocity of 510 km s⁻¹ was lower than the escape velocity, and it eventually showed redshifted absorption in Hα at velocities of a few tens of km s⁻¹. However, these low velocities associated with E2 and E4 flare events do not necessarily rule out the presence of CMEs. These values could represent a lower limit of velocity along the LOS. Also, large velocity dispersion in blueshifted components indicates the existence of faster components than the fitting center, which exceeds the escape velocity (see Section 5.2.1). Furthermore, solar observations show that the velocities of CMEs are typically 4–8 times larger than those of prominence eruptions (Gopalswamy et al. 2003), as also discussed in Section 5.2.1. Consequently, the low velocity (less than the escape velocity) blueshift plasma motions in E2 and E4 may suggest that the associated CME velocities could be as high as ~1700–3400 km s⁻¹ (E2) and 2000–4100 km s⁻¹ (E4), respectively. Therefore, following the solar analogy, we speculate that both E2 and E4 eruptive events are likely associated with fast CMEs, as suggested by Namekata et al. (2022d).

## 6.2. The Overall Picture: Relationship among Starspots, Superflares, and Prominences Eruptions/CMEs

In this section, we will present an overall picture of the eruptive phenomena observed in the young solar-type star EK Dra. This spans from the occurrence of starspots to the manifestation of superflares and prominence eruptions/CMEs, being compared in terms of length scale, energetics, time evolution, and rotational phase.
that a part of the fast prominence components might have
escaped.

2. Following the scheme suggested by Namekata et al. (2022d), comparing solar and stellar eruptions in terms of the length scale and velocity strongly suggests that the prominence eruptions in flares E1 and E2 could be associated with CMEs, considering their gigantic length scales and velocities (Section 5.2.2).

3. The numerical simulation by Alvarado-Gómez et al. (2018) suggests that the large-scale magnetic field could suppress CMEs under the average magnetic field strength of 75 G if the kinetic energy of CMEs is below a threshold around ~3 × 10³² erg. Because the EK Dra's averaged magnetic field strength of 66–89 G is similar to this numerical setup (e.g., Waite et al. 2017), we may be able to apply this threshold to our superflares (see Namekata et al. 2022d, Supplementary Information). The initial kinetic energy of the prominence eruptions from events E1 and E2 is 5.8±4.0 × 10³⁴ erg and 1.2±0.8 × 10³³ erg, respectively (Section 5.2.4), which is significantly larger than this threshold. This indicates that the magnetic suppression might not be an efficient process in these cases. Indeed, the mentioned model employs a dipolar magnetic field, while spectropolarimetric observations of this star show that large-scale magnetic fields have multipolar components (e.g., Rosén et al. 2016), and we will perform further numerical modelings with the observed data in the future (Section 6.4).

4. After flare E1, a possible candidate of X-ray dimming was detected, as an indication of escaping the surrounding hot coronal plasma associated with CMEs (Section 5.3). Although the determination of the pre-flare X-ray level is an issue in detecting stellar XUV dimming, the simultaneous detection with the Hα blueshift event supports the detection of X-ray dimming. The estimated upper limit of length scale of the dimming region of up to ~*(9–11) × 10⁹ cm is roughly consistent with the length scale of the flares ~7.3 × 10⁹ cm. The estimated mass of escaping coronal plasma of 1.2 × 10¹⁷–2.1 × 10¹⁸ g is enough small that the erupted prominence mass is 4.0 × 10¹⁹–4.2 × 10²⁰ g. Therefore, it is not surprising that the detected X-ray dimming amplitudes are likely to be interpreted as CME-related dimming (Section 5.3). However, again we should note that the NICER X-ray observation is usually sparse due to the ISS orbit, and we need to be careful with the treatment of these data (see also Appendix A). More convincing detections should be required for further discussions.

Given these without any suggestive evidence that is against the
occurrence of CMEs in flare E1, we concluded that the flare E1
is associated with the occurrence a stellar CME. This
conclusion is stronger than that drawn in Namekata et al.
(2022d). Furthermore, solar studies indicate that velocities of
outer CMEs are typically 4–8 times larger than the velocities of
prominences (Gopalswamy et al. 2003), suggesting that the
associated CME velocity from flare E1 could reach up to
2800–5500 km s⁻¹.

It is important to mention that the center-of-mass velocity of
the giant prominence in E1 evolved from 690 km s⁻¹ to near
zero in about 20 minutes, and then disappeared without
showing a redshift. This means that the center-of-mass of the

prominence stopped midway and disappeared for some reason. The disappearance and terminal zero velocity are puzzling because solar prominence eruptions show redshifted spectra after impulsive blueshifts, as presented in Appendix B. By integrating the blueshift velocity over evolution time (up to $t < 50$ minutes), the line-of-sight displacement of the center-of-mass is calculated as $6.0_{-0.3}^{+12.8} \times 10^{10}$ cm (0.91$_{+0.04}^{-.04}$ $R_{\text{star}}$) for one-component fitting and $7.5_{-0.2}^{+2.7} \times 10^{10}$ cm (1.14$_{+0.03}^{-.03}$ $R_{\text{star}}$) for two-component fitting. The gravity is expected to be 3.6 times weaker at the height of 0.91 $R_{\text{star}}$ than the surface gravity. The timescale of plasma acceleration from rest to $> 50$ km s⁻¹ from this height is approximately 10 minutes. It is likely that before it began falling back to the star, the plasma was heated or became more diffuse and thus became invisible in the Hα line. Another possible explanation is that in the later phase, the emissions in line center come from flare ribbons. Also, one may speculate that this zero-velocity erupted prominence could be linked to “slingshot” prominences (e.g., Jardine & Collier Cameron 2019). Although there is no observation of slingshot prominences for EK Dra, the E1 event may provide a possibility that the flare-related prominence could be one source of the slingshot prominences seen in rapidly rotating stars.

The prominence eruption in flare E2 (this study) and filament eruptions in flare E4 (Namekata et al. 2022d) offer less robust evidence of CMEs than flare E1. The prominence eruption associated with the E2 flare event was relatively small and short-lived, and it did not exhibit any substantial X-ray dimming. The lack of significant X-ray dimming following the E2 event could be attributed to its small dimming amplitude, which could be caused by the relatively small prominence area, an order of magnitude smaller than that observed in the E1 flare event. The filament eruptions associated with the E4 flare event (Namekata et al. 2022d) exhibited a clear blueshifted absorption, but its maximum velocity of 510 km s⁻¹ was lower than the escape velocity, and it eventually showed redshifted absorption in Hα at velocities of a few tens of km s⁻¹. However, these low velocities associated with E2 and E4 flare events do not necessarily rule out the presence of CMEs. These values could represent a lower limit of velocity along the LOS. Also, large velocity dispersion in blueshifted components indicates the existence of faster components than the fitting center, which exceeds the escape velocity (see Section 5.2.1). Furthermore, solar observations show that the velocities of CMEs are typically 4–8 times larger than those of prominence eruptions (Gopalswamy et al. 2003), as also discussed in Section 5.2.1. Consequently, the low velocity (less than the escape velocity) blueshift plasma motions in E2 and E4 may suggest that the associated CME velocities could be as high as ~1700–3400 km s⁻¹ (E2) and 2000–4100 km s⁻¹ (E4), respectively. Therefore, following the solar analogy, we speculate that both E2 and E4 eruptive events are likely associated with fast CMEs, as suggested by Namekata et al. (2022d).

## 6.2. The Overall Picture: Relationship among Starspots, Superflares, and Prominences Eruptions/CMEs

In this section, we will present an overall picture of the
eruptive phenomena observed in the young solar-type star EK
Dra. This spans from the occurrence of starspots to the
manifestation of superflares and prominence eruptions/CMEs,
being compared in terms of length scale, energetics, time
evolution, and rotational phase.
### 6.2.1. Length Scale

Table 9 compiles the length scale of starspots $L_{spot}$, superflares (coronal loop length) $L_{flare}$ (Section 4.3), and erupting prominences $L_p$ (Section 5.2.2). The size and area of the starspots are calculated from the brightness variation amplitude (BV Amp) of TESS light curves using the methods of Maehara et al. (2017). Table 4 also compiles the length scale of possible dimming regions ($L_{dim}$) for the E1 flare event (see Section 5.3). Consequently, the following summarizes the ratios of these length scales to flare loop length:

$$L_{spot}: L_{flare}: L_p: L_{dim} = \begin{cases} 2.9: 1: (11 \sim 410): (1.5 \sim 6.8), & \text{for (E1)} \\ 2.1: 1: (1.2 \sim 44): (-), & \text{for (E2)} \\ 5.0: 1: (2.9 \sim 260): (-), & \text{for (E4)} \end{cases} \quad (27)$$

Here we use the $L_{flare}$ estimated by the method of Namekata et al. (2017b) since all of these flares have white-light flare observations (see Section 4.3). Equation (27) data provide an initial picture of eruptive phenomena on young solar-type stars: superflares originating from active regions associated with starspots at length scale of at least 2–5 times larger than the flare loop length and producing eruptive prominences/filaments at greater scales (at least 1–10 times the flare loop length). This picture is not unique but looks different depending on events. These relations are useful when comparing observational data with numerical simulations and solar observations. The uncertainty in the length scale of prominences/filaments is currently high as we consider a wide conservative range of optical depths ($\tau = 10–1000$). The prominence length scale would change depending on the phase of the prominence/filament eruption, as it is expected to expand over time, so we assumed a conservative range of optical depth. Also, ionization equilibrium in moving plasma would be different from quiescent prominence (Heinzel & Rompolt 1987), which can significantly change the relation in Equations (13) and (18). Further constraints could be made by combining several spectral lines (e.g., $H\alpha$ and $H\beta$) in future observations or radiative transfer modeling (Okada et al. 2020; Leitzinger et al. 2022).

### 6.2.2. Energy Scales

Our observations provide an initial picture of flare energetics in eruptive superflares from a young solar-type star. The energetics of the eruptive E1, E2, and E4 events can be compiled as follows:

$$fE_{\text{mag}}: E_{\text{WL,bol}}: E_{\text{X,bol}}: E_{\text{kin}} = \begin{cases} 230: 1: (-): 39_{-27}^{+85}, & \text{for (E1)} \\ 44: 1: (1.2_{\pm 0.2}): 0.10_{-0.07}^{+0.22}, & \text{for (E2)} \\ 180: 1: (-): 0.17_{-0.02}^{+0.70}, & \text{for (E4)} \end{cases} \quad (28)$$

where $fE_{mag}$ is the available magnetic energy stored in active regions associated with starspots, $f$ is the fraction of the nonpotential magnetic energy (here, $f=0.1$), $E_{mag}$ is calculated as $B^2L_{spot}^3/8\pi$, and B is assumed as 1000 G. Both the kinetic and radiation energies are much smaller than the stored magnetic energy of the active regions/starspots. This aligns

well with our general expectations that giant starspots can produce superflares and prominence/filament eruptions. The kinetic energies of prominence/filament eruptions are much larger than X-rays and WL radiative energies for flare E1, but the relation is opposite for flares E2 and E4. This diversity may require some theoretical explanations, which are beyond the scope of this paper.

Our flare observations of EK Dra show that the energy partition into X-rays and WL appear to be roughly equal. However, when incorporating data from solar flares and flares from other stars, and deriving the energy distribution rule to white light and X-rays via $H\alpha$, we noticed a trend where higher-energy flares tend to be more dominated by X-rays (Section 4.2). The derived Equations (3) or (6) could be useful when estimating the total amount of X-rays irradiated onto the atmospheres of young exoplanets by superflares. Also, we found that the large prominence eruptions of flare E1 emit the $H\alpha$ flare radiation energy of ~30% of WLF energy, which is an extremely large portion compared to the usual EK Dra and M-dwarf superflares of 1% (see Section 5.1). Hence, E1 is one of the outliers in the derived flare energy-scaling relationship. This may indicate that the flare statistics based on WLFs with Kepler and TESS can be affected to some extent by the contribution of $H\alpha$ line emissions from prominence eruptions.

### 6.2.3. Time Evolution

Table 4 catalogs the timescales and timing of blueshift events and potential X-ray dimming events relative to WLFs. The E1 flare event offers a probable sequence of events, as discussed in Section 6.1, whereby a stellar prominence begins to erupt almost concurrently with the brightenings of WLFs, potentially leading to the appearance of X-ray dimming approximately 2 hr after WLFs. On the other hand, the E2 and E4 events have different timescales and timings for the emergence of blueshift events, as seen in Table 4, though they lack detections or observations of X-ray dimming. This suggests that the appearances and formation/acceleration processes of stellar prominences/filaments can have a diverse nature (see Section 6.3).

### 6.2.4. Rotational Phase

Additionally, all five detected superflares (E1–E5) on EK Dra have simultaneous TESS long-term photometric data, allowing us to explore the relationship between flares and the stellar rotational phase. The rotational phase at which the flares occur is summarized in Table 9. By assuming the existence of a single dominant active region causing the rotational variation, we can infer that the flare E1 with prominence eruptions occurred when the dominant active region was near the disk center due to rotation. This seems inconsistent with the occurrence of prominence eruptions outside the stellar limb, suggesting that the source of the prominence eruption is not the dominant active region or that there may be multiple sizable active regions forming the complex rotational modulation. The E2 flare occurred as the dominant active regions neared the limb, which aligns with the occurrence of a prominence eruption. Finally, the E4 flare event occurred when the dominant spots were on the opposite side of the star, suggesting that the associated filament eruption was produced over the relatively small active regions (Namekata et al. 2022d). These conclusions are not yet definitive, given that observations of
### 6.2.1. Length Scale

Table 9 compiles the length scale of starspots $L_{spot}$, superflares (coronal loop length) $L_{flare}$ (Section 4.3), and erupting prominences $L_p$ (Section 5.2.2). The size and area of the starspots are calculated from the brightness variation amplitude (BV Amp) of TESS light curves using the methods of Maehara et al. (2017). Table 4 also compiles the length scale of possible dimming regions ($L_{dim}$) for the E1 flare event (see Section 5.3). Consequently, the following summarizes the ratios of these length scales to flare loop length:

$$ L_{spot}: L_{flare}: L_p: L_{dim} = \begin{cases} 2.9: 1: (11 \sim 410): (1.5 \sim 6.8), & \text{for (E1)} \\ 2.1: 1: (1.2 \sim 44): (-), & \text{for (E2)} \\ 5.0: 1: (2.9 \sim 260): (-), & \text{for (E4)} \end{cases} \quad (27) $$

Here we use the $L_{flare}$ estimated by the method of Namekata et al. (2017b) since all of these flares have white-light flare observations (see Section 4.3). Equation (27) data provide an initial picture of eruptive phenomena on young solar-type stars: superflares originating from active regions associated with starspots at length scale of at least 2–5 times larger than the flare loop length and producing eruptive prominences/filaments at greater scales (at least 1–10 times the flare loop length). This picture is not unique but looks different depending on events. These relations are useful when comparing observational data with numerical simulations and solar observations. The uncertainty in the length scale of prominences/filaments is currently high as we consider a wide conservative range of optical depths ($\tau = 10–1000$). The prominence length scale would change depending on the phase of the prominence/filament eruption, as it is expected to expand over time, so we assumed a conservative range of optical depth. Also, ionization equilibrium in moving plasma would be different from quiescent prominence (Heinzel & Rompolt 1987), which can significantly change the relation in Equations (13) and (18). Further constraints could be made by combining several spectral lines (e.g., $H\alpha$ and $H\beta$) in future observations or radiative transfer modeling (Okada et al. 2020; Leitzinger et al. 2022).

### 6.2.2. Energy Scales

Our observations provide an initial picture of flare energetics in eruptive superflares from a young solar-type star. The energetics of the eruptive E1, E2, and E4 events can be compiled as follows:

$$ fE_{mag}: E_{WL,bol}: E_{X,bol}: E_{kin} = \begin{cases} 230: 1: (-): 39_{-27}^{+85}, & \text{for (E1)} \\ 44: 1: (1.2_{\pm 0.2}): 0.10_{-0.07}^{+0.22}, & \text{for (E2)} \\ 180: 1: (-): 0.17_{-0.02}^{+0.70}, & \text{for (E4)} \end{cases} \quad (28) $$

where $fE_{mag}$ is the available magnetic energy stored in active regions associated with starspots, $f$ is the fraction of the nonpotential magnetic energy (here, $f = 0.1$), $E_{mag}$ is calculated as $B^2L_{spot}^3/8\pi$, and B is assumed as 1000 G. Both the kinetic and radiation energies are much smaller than the stored magnetic energy of the active regions/starspots. This aligns

well with our general expectations that giant starspots can produce superflares and prominence/filament eruptions. The kinetic energies of prominence/filament eruptions are much larger than X-rays and WL radiative energies for flare E1, but the relation is opposite for flares E2 and E4. This diversity may require some theoretical explanations, which are beyond the scope of this paper.

Our flare observations of EK Dra show that the energy partition into X-rays and WL appear to be roughly equal. However, when incorporating data from solar flares and flares from other stars, and deriving the energy distribution rule to white light and X-rays via $H\alpha$, we noticed a trend where higher-energy flares tend to be more dominated by X-rays (Section 4.2). The derived Equations (3) or (6) could be useful when estimating the total amount of X-rays irradiated onto the atmospheres of young exoplanets by superflares. Also, we found that the large prominence eruptions of flare E1 emit the $H\alpha$ flare radiation energy of ~30% of WLF energy, which is an extremely large portion compared to the usual EK Dra and M-dwarf superflares of 1% (see Section 5.1). Hence, E1 is one of the outliers in the derived flare energy-scaling relationship. This may indicate that the flare statistics based on WLFs with Kepler and TESS can be affected to some extent by the contribution of $H\alpha$ line emissions from prominence eruptions.

### 6.2.3. Time Evolution

Table 4 catalogs the timescales and timing of blueshift events and potential X-ray dimming events relative to WLFs. The E1 flare event offers a probable sequence of events, as discussed in Section 6.1, whereby a stellar prominence begins to erupt almost concurrently with the brightenings of WLFs, potentially leading to the appearance of X-ray dimming approximately 2 hr after WLFs. On the other hand, the E2 and E4 events have different timescales and timings for the emergence of blueshift events, as seen in Table 4, though they lack detections or observations of X-ray dimming. This suggests that the appearances and formation/acceleration processes of stellar prominences/filaments can have a diverse nature (see Section 6.3).

### 6.2.4. Rotational Phase

Additionally, all five detected superflares (E1–E5) on EK Dra have simultaneous TESS long-term photometric data, allowing us to explore the relationship between flares and the stellar rotational phase. The rotational phase at which the flares occur is summarized in Table 9. By assuming the existence of a single dominant active region causing the rotational variation, we can infer that the flare E1 with prominence eruptions occurred when the dominant active region was near the disk center due to rotation. This seems inconsistent with the occurrence of prominence eruptions outside the stellar limb, suggesting that the source of the prominence eruption is not the dominant active region or that there may be multiple sizable active regions forming the complex rotational modulation. The E2 flare occurred as the dominant active regions neared the limb, which aligns with the occurrence of a prominence eruption. Finally, the E4 flare event occurred when the dominant spots were on the opposite side of the star, suggesting that the associated filament eruption was produced over the relatively small active regions (Namekata et al. 2022d). These conclusions are not yet definitive, given that observations of
other solar-type stars suggest there may be multiple starspots on the surface even in single-spot-like optical light curves (Morris et al. 2017; Basri 2018; Namekata et al. 2020a). The Doppler imaging of EK Dra, performed in a different epoch from our campaign, shows the gigantic starspots, changing its latitude in time ranging from the equator up to high latitude, close to the pole (e.g., Strassmeier & Rice 1998; Rosén et al. 2016; Waite et al. 2017; Järvinen et al. 2018). The near-pole spots usually do not appear in optical light curves but could be the sites of the filament/prominence eruptions. Furthermore, the dark spot causing photometric variability may not necessarily be co-located with regions of strong large-scale magnetic fields (Waite et al. 2017), so we also require a magnetic-field mapping for further understanding. In our future work, we plan further investigations into the origins of these eruptive phenomena by performing multispot and/or magnetic-field mapping using the same observing periods (see Section 6.4).

## 6.3. Diversity and Frequency of Prominence/Filament Eruptions from Young Solar-type Stars

Tables 3, 4, and 9 provide preliminary insights into the diversity and frequency of eruptive flares on young solar-type stars. First, we demonstrate that blueshifted $H\alpha$ components can appear both in emission and absorption from the young solar-type star EK Dra. This discovery reveals that the well-known signatures of filament (absorption) and prominence (emission) observed on the Sun can also hold true for young solar-type stars. While it might be expected that young solar-type stars emit intense UV radiation, including $Ly\alpha$, that can alter the excitation states of hydrogen within the prominence (Leitzinger et al. 2022), our observations indicate that the radiative signatures of filaments and prominences do not significantly change even in young, active stars. In other words, the $H\alpha$ source function, $S_\lambda$, of the prominence relative to the background intensity $I_\lambda$ seems to remain below unity ($S_\lambda/I_\lambda < 1$). This could be a very strong constraint in stellar prominence whose emissivity is unknown.

While the occurrence frequency of prominence/filament eruptions (and CMEs) is a crucial factor for habitability of (exo-)planetary environments, its value is poorly understood and is usually estimated based on flare frequency by assuming a one-to-one relationship between stellar flares and CMEs. For example, it is known that large M/X-class solar flares do not necessarily produce CMEs as they could be supressed by overlying coronal magnetic fields of active regions (Toriumi et al. 2017; Sun et al. 2022). Our limited sample of eruption events shows that the association rate of stellar prominence/filament eruptions against superflares is 3/5 (60%) on young solar-type stars. Blueshifts can be detected with our spectrograph ($R \sim 2000$, $\delta v \sim 150 \text{ km s}^{-1}$) only when the eruption has relatively high ($>150 \text{ km s}^{-1}$) LOS velocity. Considering this limitation on the LOS velocity, we note that the absence of blueshifts in flares E3 and E5 does not necessarily imply the absence of eruptions. Therefore, the expected association rate of prominence/filament eruptions (and possibly CMEs) could be higher than 3/5. This evidence indicates that the strong suppression by local magnetic fields of active regions may not play a significant role in the case of a gigantic eruption associated with the superflare releasing large portions of the magnetic energy stored in an active region (see Section 6.2).

Recent numerical simulations of large-scale photospheric motion driven magnetic flux rope energization suggest an ejection of a CME from a young solar-type star, $\kappa^{-1}$ Ceti (Lynch et al. 2019). Such scenarios can be applicable to global multipole magnetic-field environments of young solar-type stars. Indeed, the magnetic fields observed on EK Dra and other young solar-type stars are relatively nonaxisymmetric compared to active M-dwarfs (Donati & Landstreet 2009), and the magnetic fields on solar-type stars are organized on smaller spatial scales than fully convective M-dwarfs (See et al. 2019); therefore, the fall-off with radius is much faster. Thus, we speculate that young solar-type stars can be relatively more CME-productive, at least than M-dwarfs. On the other hand, it is expected that ejection of CMEs from M-dwarfs with a dipolar magnetic field could be suppressed by the strong global dipole magnetic fields of the star (Alvarado-Gómez et al. 2018). This may explain why a recent M-dwarf flare survey shows that M-dwarfs' blueshift association rate is not so high (e.g., seven events among 41 flares on M-dwarfs YZ CMi, EV Lac, and AD Leonis; Notsu et al. 2023), compared to our estimate of expected CMEs from EK Dra.

Presently, all flares E1-E5 exhibit different properties in prominence/filament properties in terms of the radiation signatures, mass, duration, timing, and X-ray counterpart, as summarized in Tables 3, 4, and 9, and also mentioned in Sections 6.1 and 6.2. This indicates that there could be even more diversity if we increase the sample size. We will present and discuss further observational results in our forthcoming papers (see Section 6.4).

## 6.4. Future Studies

Our series of studies, including Namekata et al. (2022c) and Namekata et al. (2022d), has offered numerous observational constraints on the eruptions of prominences and filaments from young solar-type stars. This section outlines our future research plans for refining our understanding of these eruptive phenomena.

First, we plan to determine the maps of starspots and large-scale magnetic fields to address questions such as “Where do prominence and filament eruptions originate?” (refer to Section 6.2). We will model the rotational modulation in the optical light curves from TESS using our previously established starspot-mapping method (Ikuta et al. 2020, 2023). Additionally, at the almost similar period of the campaign periods in 2022 April, we conducted high-dispersion optical spectroscopy of EK Dra using the High Dispersion Echelle Spectrograph (HIDES; Izumiura 1999) on board the 1.88 m reflector at Okayama Observatory in Japan. We have also utilized the high-resolution echelle spectropolarimeter NARVAL, fiber-fed from the Cassegrain focus of the 2 m Bernard Lyot Telescope at the Pic du Midi observatory in France. These data will be analyzed using Doppler imaging and Zeeman Doppler imaging (ZDI) techniques to estimate the surface maps on EK Dra. The resulting maps will be compared with each other, with the occurrence of prominence eruptions (discussed in paper II), and with multiwavelength rotational modulations observed in $H\alpha$, X-ray, and ground-based B-band photometric observations (K. Ikuta et al. 2023, in preparation).

We will also perform further modeling of the prominence eruptions from flare E1. Specifically, the $H\alpha$ data offer several key constraints on the locations and trajectories of the prominence eruptions (see Section 6.2). For instance, an
other solar-type stars suggest there may be multiple starspots on the surface even in single-spot-like optical light curves (Morris et al. 2017; Basri 2018; Namekata et al. 2020a). The Doppler imaging of EK Dra, performed in a different epoch from our campaign, shows the gigantic starspots, changing its latitude in time ranging from the equator up to high latitude, close to the pole (e.g., Strassmeier & Rice 1998; Rosén et al. 2016; Waite et al. 2017; Järvinen et al. 2018). The near-pole spots usually do not appear in optical light curves but could be the sites of the filament/prominence eruptions. Furthermore, the dark spot causing photometric variability may not necessarily be co-located with regions of strong large-scale magnetic fields (Waite et al. 2017), so we also require a magnetic-field mapping for further understanding. In our future work, we plan further investigations into the origins of these eruptive phenomena by performing multispot and/or magnetic-field mapping using the same observing periods (see Section 6.4).

## 6.3. Diversity and Frequency of Prominence/Filament Eruptions from Young Solar-type Stars

Tables 3, 4, and 9 provide preliminary insights into the diversity and frequency of eruptive flares on young solar-type stars. First, we demonstrate that blueshifted $H\alpha$ components can appear both in emission and absorption from the young solar-type star EK Dra. This discovery reveals that the well-known signatures of filament (absorption) and prominence (emission) observed on the Sun can also hold true for young solar-type stars. While it might be expected that young solar-type stars emit intense UV radiation, including $Ly\alpha$, that can alter the excitation states of hydrogen within the prominence (Leitzinger et al. 2022), our observations indicate that the radiative signatures of filaments and prominences do not significantly change even in young, active stars. In other words, the $H\alpha$ source function, $S_\lambda$, of the prominence relative to the background intensity $I_\lambda$ seems to remain below unity ($S_\lambda/I_\lambda < 1$). This could be a very strong constraint in stellar prominence whose emissivity is unknown.

While the occurrence frequency of prominence/filament eruptions (and CMEs) is a crucial factor for habitability of (exo-)planetary environments, its value is poorly understood and is usually estimated based on flare frequency by assuming a one-to-one relationship between stellar flares and CMEs. For example, it is known that large M/X-class solar flares do not necessarily produce CMEs as they could be supressed by overlying coronal magnetic fields of active regions (Toriumi et al. 2017; Sun et al. 2022). Our limited sample of eruption events shows that the association rate of stellar prominence/filament eruptions against superflares is 3/5 (60%) on young solar-type stars. Blueshifts can be detected with our spectrograph ($R \sim 2000$, $\delta v \sim 150 \text{ km s}^{-1}$) only when the eruption has relatively high ($>150 \text{ km s}^{-1}$) LOS velocity. Considering this limitation on the LOS velocity, we note that the absence of blueshifts in flares E3 and E5 does not necessarily imply the absence of eruptions. Therefore, the expected association rate of prominence/filament eruptions (and possibly CMEs) could be higher than 3/5. This evidence indicates that the strong suppression by local magnetic fields of active regions may not play a significant role in the case of a gigantic eruption associated with the superflare releasing large portions of the magnetic energy stored in an active region (see Section 6.2).

Recent numerical simulations of large-scale photospheric motion driven magnetic flux rope energization suggest an ejection of a CME from a young solar-type star, $\kappa^{-1}$ Ceti (Lynch et al. 2019). Such scenarios can be applicable to global multipole magnetic-field environments of young solar-type stars. Indeed, the magnetic fields observed on EK Dra and other young solar-type stars are relatively nonaxisymmetric compared to active M-dwarfs (Donati & Landstreet 2009), and the magnetic fields on solar-type stars are organized on smaller spatial scales than fully convective M-dwarfs (See et al. 2019); therefore, the fall-off with radius is much faster. Thus, we speculate that young solar-type stars can be relatively more CME-productive, at least than M-dwarfs. On the other hand, it is expected that ejection of CMEs from M-dwarfs with a dipolar magnetic field could be suppressed by the strong global dipole magnetic fields of the star (Alvarado-Gómez et al. 2018). This may explain why a recent M-dwarf flare survey shows that M-dwarfs' blueshift association rate is not so high (e.g., seven events among 41 flares on M-dwarfs YZ CMi, EV Lac, and AD Leonis; Notsu et al. 2023), compared to our estimate of expected CMEs from EK Dra.

Presently, all flares E1-E5 exhibit different properties in prominence/filament properties in terms of the radiation signatures, mass, duration, timing, and X-ray counterpart, as summarized in Tables 3, 4, and 9, and also mentioned in Sections 6.1 and 6.2. This indicates that there could be even more diversity if we increase the sample size. We will present and discuss further observational results in our forthcoming papers (see Section 6.4).

## 6.4. Future Studies

Our series of studies, including Namekata et al. (2022c) and Namekata et al. (2022d), has offered numerous observational constraints on the eruptions of prominences and filaments from young solar-type stars. This section outlines our future research plans for refining our understanding of these eruptive phenomena.

First, we plan to determine the maps of starspots and large-scale magnetic fields to address questions such as “Where do prominence and filament eruptions originate?” (refer to Section 6.2). We will model the rotational modulation in the optical light curves from TESS using our previously established starspot-mapping method (Ikuta et al. 2020, 2023). Additionally, at the almost similar period of the campaign periods in 2022 April, we conducted high-dispersion optical spectroscopy of EK Dra using the High Dispersion Echelle Spectrograph (HIDES; Izumiura 1999) on board the 1.88 m reflector at Okayama Observatory in Japan. We have also utilized the high-resolution echelle spectropolarimeter NARVAL, fiber-fed from the Cassegrain focus of the 2 m Bernard Lyot Telescope at the Pic du Midi observatory in France. These data will be analyzed using Doppler imaging and Zeeman Doppler imaging (ZDI) techniques to estimate the surface maps on EK Dra. The resulting maps will be compared with each other, with the occurrence of prominence eruptions (discussed in paper II), and with multiwavelength rotational modulations observed in $H\alpha$, X-ray, and ground-based B-band photometric observations (K. Ikuta et al. 2023, in preparation).

We will also perform further modeling of the prominence eruptions from flare E1. Specifically, the $H\alpha$ data offer several key constraints on the locations and trajectories of the prominence eruptions (see Section 6.2). For instance, an
emission $H\alpha$ profile without any absorption signal implies that a prominence's location is consistently outside the stellar limb from the beginning to the end of the event. The occurrence of a WLF indicates that the eruptive flare's footpoints are not—or at least not entirely—rooted behind the stellar disk. Moreover, the nearly consistent deceleration with surface gravity suggests the eruptions could occur in directions close to LOS. These constraints limit the conditions under which prominence eruptions can occur, thus enabling us to estimate the eruptions' kinematics and evolution. In paper II, we will model these processes using a simple model and reveal the probable inclination angle relative to the LoS and its physical mechanism. By using the model, we plan to apply the radiative transfer to estimate the changes in the surface emission of the prominence as its size/height increases (see Leitzinger et al. 2022). Ultimately, we will carry out 3D numerical simulations of prominence eruptions/CMEs, incorporating the data from surface starspots and ZDI maps (e.g., Lynch et al. 2019; Airapetian et al. 2021; Jin et al. 2022).

Moreover, our observational campaign of two nearby young solar-type stars, including EK Dra, has been in progress since 2020 with the 3.8 m Seimei telescope, 2 m Nayuta telescope, Okayama 1.88 m telescope, and Bulgarian 2 m RCC telescope at Rozhen National Astronomical Observatory. We aim to provide further statistical results of the $H\alpha$ eruptive phenomena by increasing the superflare sample size to more than 10. This expanded statistical study will further constrain the frequency and diversity discussed in Section 6.3. The likelihood of viewing the eruptive events as prominences or filaments will be modeled and compared with observed diversity with more samples. We will later extend this approach to solar-mass stars of various ages—from weak-line/classical T-tauri stars (see Getman & Feigelson 2021; Getman et al. 2021; Bouvier et al. 2023) to main sequences, e.g., DS Tuc A and $\kappa^1$ Ceti—to eventually understand the Sun.

## Acknowledgments

The authors thank Dr. Shin Toriumi for fruitful comments. We thank Dr. Kenji Hamaguchi, Dr. Teruaki Enoto, and the NICER team for the helpful suggestions and comments on the NICER data analysis. We thank Dr. Wataru Iwakiri for the helpful comments on the correction of the data of Guarcello et al. (2019). We thank Dr. Daisaku Nogami, Dr. Satoshi Honda, and the staff at Okayama Observatory for contributions to the Seimei telescope project. This work was supported by JSPS (Japan Society for the Promotion of Science) KAKENHI grant Nos. 21J00316 (K.N.), 20K04032, 20H05643 (H.M.), 21J00106 (Y.N.), and 21H01131 (H.M., K.I., and K.S.), and JST CREST grant No. JPMJCR1761 (K.I.). V.S.A. was supported by the GSFC Sellers Exoplanet Environments Collaboration (SEEC), which is funded by the NASA Planetary Science Divisions Internal Scientist Funding Model (ISFM), the NASA NNH21ZDA001N-XRP F.3 Exoplanets Research Program grants, NICER Cycle 2 project funds, and the NICER DDT program. Y.N. was supported from the NASA ADAP

award program Number 80NSSC21K0632. A.A.A. acknowledges Bulgarian NSF grant No. KP-06-N58/3 (2021). S.V.J. acknowledges the support of the DFG priority program SPP 1992 "Exploring the Diversity of Extrasolar Planets" (JE 701/5-1). A.A.V. acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 817540, ASTROFLOW). The spectroscopic data used in this paper were obtained through the program 22A-N-CN06 (PI: K. N.) with the 3.8 m Seimei telescope, which is located at Okayama Observatory at Kyoto University. This paper includes data collected with the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the TESS mission is provided by the NASA Explorer Program. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via 10.17909/xgds-j146. NICER analysis software and data calibration were provided by the NASA NICER mission and the Astrophysics Explorers Program.

**Facilities:** 3.8m Seimei telescope, TESS, NICER.

**Software:** astropy (Astropy Collaboration et al. 2018), IRAF (Tody 1986), PyRAF (Science Software Branch at STScI 2012), HEASoft 6.31 (HEASARC 2022), xspec (Arnaud 1996).

## Appendix A

### Detailed Light Curves of NICER X-Ray on 2022 April 10

Figure 27 presents the expanded X-ray count rates and exposure fractions of NICER for the ISS orbital blocks 3 to 6 before and after the flare E1. nicerl2, xspec, and lcurve in HEASoft was used for extracting the data in good time intervals of NICER observations, which results in the exposure fractions of each exposure bin not necessarily being in unity. The nicerl2 task functions screens out exposures under unfavorable conditions, notably in situations with a high level of particle background or optical light contamination. When NICER encounters these suboptimal conditions, the Good Time Intervals (GTI) are fragmented. Consequently, this fragmentation leads to a decrease in the fractional exposures of the corresponding light-curve bins. From an analysis of our data set mkf file, it is observed that the TOT_OVER_COUNT is relatively high, nearing a value of ~200. This raises the possibility that the nicerl2 task may have excised certain segments from the exposures in each light-curve bin, especially those not meeting the standard screening criteria. This implies that the relatively high noise level of NICER X-ray count rates in short time cadence for the data on 2022 April 10 is attributable to the shortened exposure time resulting from the bad time corrections.
emission Hα profile without any absorption signal implies that a prominence's location is consistently outside the stellar limb from the beginning to the end of the event. The occurrence of a WLF indicates that the eruptive flare's footpoints are not—or at least not entirely—rooted behind the stellar disk. Moreover, the nearly consistent deceleration with surface gravity suggests the eruptions could occur in directions close to LOS. These constraints limit the conditions under which prominence eruptions can occur, thus enabling us to estimate the eruptions' kinematics and evolution. In paper II, we will model these processes using a simple model and reveal the probable inclination angle relative to the LoS and its physical mechanism. By using the model, we plan to apply the radiative transfer to estimate the changes in the surface emission of the prominence as its size/height increases (see Leitzinger et al. 2022). Ultimately, we will carry out 3D numerical simulations of prominence eruptions/CMEs, incorporating the data from surface starspots and ZDI maps (e.g., Lynch et al. 2019; Airapetian et al. 2021; Jin et al. 2022).

Moreover, our observational campaign of two nearby young solar-type stars, including EK Dra, has been in progress since 2020 with the 3.8 m Seimei telescope, 2 m Nayuta telescope, Okayama 1.88 m telescope, and Bulgarian 2 m RCC telescope at Rozhen National Astronomical Observatory. We aim to provide further statistical results of the Hα eruptive phenomena by increasing the superflare sample size to more than 10. This expanded statistical study will further constrain the frequency and diversity discussed in Section 6.3. The likelihood of viewing the eruptive events as prominences or filaments will be modeled and compared with observed diversity with more samples. We will later extend this approach to solar-mass stars of various ages—from weak-line/classical T-tauri stars (see Getman & Feigelson 2021; Getman et al. 2021; Bouvier et al. 2023) to main sequences, e.g., DS Tuc A and $κ^1$ Ceti—to eventually understand the Sun.

## Acknowledgments

The authors thank Dr. Shin Toriumi for fruitful comments. We thank Dr. Kenji Hamaguchi, Dr. Teruaki Enoto, and the NICER team for the helpful suggestions and comments on the NICER data analysis. We thank Dr. Wataru Iwakiri for the helpful comments on the correction of the data of Guarcello et al. (2019). We thank Dr. Daisaku Nogami, Dr. Satoshi Honda, and the staff at Okayama Observatory for contributions to the Seimei telescope project. This work was supported by JSPS (Japan Society for the Promotion of Science) KAKENHI grant Nos. 21J00316 (K.N.), 20K04032, 20H05643 (H.M.), 21J00106 (Y.N.), and 21H01131 (H.M., K.I., and K.S.), and JST CREST grant No. JPMJCR1761 (K.I.). V.S.A. was supported by the GSFC Sellers Exoplanet Environments Collaboration (SEEC), which is funded by the NASA Planetary Science Divisions Internal Scientist Funding Model (ISFM), the NASA NNH21ZDA001N-XRP F.3 Exoplanets Research Program grants, NICER Cycle 2 project funds, and the NICER DDT program. Y.N. was supported from the NASA ADAP

award program Number 80NSSC21K0632. A.A.A. acknowledges Bulgarian NSF grant No. KP-06-N58/3 (2021). S.V.J. acknowledges the support of the DFG priority program SPP 1992 "Exploring the Diversity of Extrasolar Planets" (JE 701/5-1). A.A.V. acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement No. 817540, ASTROFLOW). The spectroscopic data used in this paper were obtained through the program 22A-N-CN06 (PI: K. N.) with the 3.8 m Seimei telescope, which is located at Okayama Observatory at Kyoto University. This paper includes data collected with the TESS mission, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the TESS mission is provided by the NASA Explorer Program. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations analyzed can be accessed via 10.17909/xgds-j146. NICER analysis software and data calibration were provided by the NASA NICER mission and the Astrophysics Explorers Program.

**Facilities:** 3.8m Seimei telescope, TESS, NICER.

**Software:** astropy (Astropy Collaboration et al. 2018), IRAF (Tody 1986), PyRAF (Science Software Branch at STScI 2012), HEASoft 6.31 (HEASARC 2022), xspec (Arnaud 1996).

## Appendix A

### Detailed Light Curves of NICER X-Ray on 2022 April 10

Figure 27 presents the expanded X-ray count rates and exposure fractions of NICER for the ISS orbital blocks 3 to 6 before and after the flare E1. nicerl2, xspec, and lcurve in HEASoft was used for extracting the data in good time intervals of NICER observations, which results in the exposure fractions of each exposure bin not necessarily being in unity. The nicerl2 task functions screens out exposures under unfavorable conditions, notably in situations with a high level of particle background or optical light contamination. When NICER encounters these suboptimal conditions, the Good Time Intervals (GTI) are fragmented. Consequently, this fragmentation leads to a decrease in the fractional exposures of the corresponding light-curve bins. From an analysis of our data set mkf file, it is observed that the TOT_OVER_COUNT is relatively high, nearing a value of ~200. This raises the possibility that the nicerl2 task may have excised certain segments from the exposures in each light-curve bin, especially those not meeting the standard screening criteria. This implies that the relatively high noise level of NICER X-ray count rates in short time cadence for the data on 2022 April 10 is attributable to the shortened exposure time resulting from the bad time corrections.
<figure><img src="image_32.png" /><figcaption>**Figure 27.** (upper) NICER 0.5–3 keV X-ray count rates and (lower) fractional exposure rates for each orbit of blocks 3–6 on 2022 April 10. Fractional exposure rate is the “FRACEXP” column of the *lcurve* outputs. The value is the live-time fraction for each time bin and takes values between zero and one after the deadtime correction with “LDEADTIME.” The corrected rate and errors in upper panels are calculated by dividing original values by “FRACEXP.”</figcaption></figure>

## Appendix B
### Sun-as-a-star Analysis

The main text includes some discussion of solar prominences, particularly in relation to CMEs. Here we show “Sun-as-a-star” data sets of $H\alpha$ emission during prominence eruptions that could be compared side-by-side with the data from EK Dra. The first Sun-as-a-star analysis of $H\alpha$ line from solar filament eruptions has been carried out by Namekata et al. (2022d) using the Solar Dynamics Doppler Imager (SDDI) on board the Solar Magnetic Activity Research Telescope (SMART) at Hida Observatory. Later, Otsu et al. (2022) extend the samples to two prominence eruptions outside the solar limb, but they did not perform the spectral analysis of the obtained Sun-as-a-star spectra. Then, we reanalyzed the two prominence eruptions shown in the paper by Otsu et al. (2022) for direct comparison with the EK Dra data.

Figure 28 shows the pre-flare-subtracted Sun-as-a-star spectra of $H\alpha$ line of the two prominence eruptions, which are taken from Otsu et al. (2022). Figure 28(a) is the data for a prominence eruption at around 04:30 UT on 2017 June 19 (event “S1”). Figure 28(b) is the data for a prominence eruption at around 22:25 UT on 2021 May 5 (event “S2”). The dynamic spectrum of both S1 and S2 shows that the blueshifted emission component of 100–400 km s⁻¹ is initially prominent, and its velocity decreases in time and finally becomes redshifts of 0–100 km s⁻¹. This represents that a significant portion of the erupted prominences fall down to the solar surface. However, we noticed that event S2 is associated with high-speed prominence eruption (>400 km s⁻¹), and a portion of it moved beyond the field of view of the SDDI, which potentially erupted much higher and longer than seen in the dynamic spectrum. Furthermore, Otsu et al. (2022) reported that both events are associated with CMEs. We can learn from this solar

data set that, even though prominence eruptions ultimately show zero or redshift velocity, they can lead to CMEs, as discussed in 6.1.

Let us qualitatively compare them with the E1 event on EK Dra. The speed of EK Dra’s prominence eventually approaches near 0 km s⁻¹. Its maximum velocity is up to 690 km s⁻¹ and its duration is about 30 minutes. On the other hand, the solar S1 and S2 events finally show a redshift after decelerating. Furthermore, their blueshift speeds range from 10 to 400 km s⁻¹, which are typical values for solar prominence eruptions, and the duration with blueshift speeds exceeding ~100 km s⁻¹, detectable in stellar observations, is also less than about 10 minutes. While there are differences between the Sun’s events and EK Dra’s event in terms of whether they ultimately show a redshift, it can be interpreted that the smaller scale and velocity of the solar prominence eruption compared to stellar events have led to the differences. At present, large-scale prominence eruptions like EK Dra’s eruption, which eventually reaches a velocity of 0 km s⁻¹, have not been observed with SDDI. However, by increasing the number of samples in the future, there is a possibility to observe similar events.

We fitted the $H\alpha$ line profiles of S1 and S2 events with Gaussian function, as performed in stellar data, and derived the velocity and velocity dispersion. Figure 29 is the relation between velocity and velocity dispersion of the $H\alpha$ line profile. As you can see, they exhibit velocity dispersion that scales with the velocity of the prominence eruption, and its relation is very consistent with stellar data. This support our suggestion in Section 5.2.1 that the velocity dispersion represents superposition of different velocity components from spatially different regions.
<figure><img src="image_36.png" /><figcaption>**Figure 27.** (upper) NICER 0.5–3 keV X-ray count rates and (lower) fractional exposure rates for each orbit of blocks 3–6 on 2022 April 10. Fractional exposure rate is the “FRACEXP” column of the *lcurve* outputs. The value is the live-time fraction for each time bin and takes values between zero and one after the deadtime correction with “LDEADTIME.” The corrected rate and errors in upper panels are calculated by dividing original values by “FRACEXP.”</figcaption></figure>

## Appendix B
### Sun-as-a-star Analysis

The main text includes some discussion of solar prominences, particularly in relation to CMEs. Here we show “Sun-as-a-star” data sets of $H\alpha$ emission during prominence eruptions that could be compared side-by-side with the data from EK Dra. The first Sun-as-a-star analysis of $H\alpha$ line from solar filament eruptions has been carried out by Namekata et al. (2022d) using the Solar Dynamics Doppler Imager (SDDI) on board the Solar Magnetic Activity Research Telescope (SMART) at Hida Observatory. Later, Otsu et al. (2022) extend the samples to two prominence eruptions outside the solar limb, but they did not perform the spectral analysis of the obtained Sun-as-a-star spectra. Then, we reanalyzed the two prominence eruptions shown in the paper by Otsu et al. (2022) for direct comparison with the EK Dra data.

Figure 28 shows the pre-flare-subtracted Sun-as-a-star spectra of $H\alpha$ line of the two prominence eruptions, which are taken from Otsu et al. (2022). Figure 28(a) is the data for a prominence eruption at around 04:30 UT on 2017 June 19 (event “S1”). Figure 28(b) is the data for a prominence eruption at around 22:25 UT on 2021 May 5 (event “S2”). The dynamic spectrum of both S1 and S2 shows that the blueshifted emission component of 100–400 km s⁻¹ is initially prominent, and its velocity decreases in time and finally becomes redshifts of 0–100 km s⁻¹. This represents that a significant portion of the erupted prominences fall down to the solar surface. However, we noticed that event S2 is associated with high-speed prominence eruption (>400 km s⁻¹), and a portion of it moved beyond the field of view of the SDDI, which potentially erupted much higher and longer than seen in the dynamic spectrum. Furthermore, Otsu et al. (2022) reported that both events are associated with CMEs. We can learn from this solar

data set that, even though prominence eruptions ultimately show zero or redshift velocity, they can lead to CMEs, as discussed in 6.1.

Let us qualitatively compare them with the E1 event on EK Dra. The speed of EK Dra’s prominence eventually approaches near 0 km s⁻¹. Its maximum velocity is up to 690 km s⁻¹ and its duration is about 30 minutes. On the other hand, the solar S1 and S2 events finally show a redshift after decelerating. Furthermore, their blueshift speeds range from 10 to 400 km s⁻¹, which are typical values for solar prominence eruptions, and the duration with blueshift speeds exceeding ~100 km s⁻¹, detectable in stellar observations, is also less than about 10 minutes. While there are differences between the Sun’s events and EK Dra’s event in terms of whether they ultimately show a redshift, it can be interpreted that the smaller scale and velocity of the solar prominence eruption compared to stellar events have led to the differences. At present, large-scale prominence eruptions like EK Dra’s eruption, which eventually reaches a velocity of 0 km s⁻¹, have not been observed with SDDI. However, by increasing the number of samples in the future, there is a possibility to observe similar events.

We fitted the $H\alpha$ line profiles of S1 and S2 events with Gaussian function, as performed in stellar data, and derived the velocity and velocity dispersion. Figure 29 is the relation between velocity and velocity dispersion of the $H\alpha$ line profile. As you can see, they exhibit velocity dispersion that scales with the velocity of the prominence eruption, and its relation is very consistent with stellar data. This support our suggestion in Section 5.2.1 that the velocity dispersion represents superposition of different velocity components from spatially different regions.
<figure><img src="image_33.png" /><figcaption>**Figure 28.** Dynamic spectra of the pre-flare-subtracted H-alpha spectra of the Sun-as-a-star prominence eruptions. (a) The prominence eruption on 2017 June 19 (event "S1"). (b) The prominence eruption on 2021 May 5 (event "S2"). The data of the dynamic spectra were taken from Otsu et al. (2022), and the spectral fitting is newly done in this paper. In both events, the emissions from flare ribbons are behind the limb and not visible from the Earth, so the emission almost comes from the erupted prominence. Some of the white-colored region is the unavailable wavelength at that time. The cyan points are the central wavelength of the emission component. For the event S1, the velocity evolution is fitted by a linear function, and the deceleration is derived as $0.1089 \pm 0.0002 \text{ km s}^{-2}$.</figcaption></figure>

<figure><img src="image_34.png" /><figcaption>**Figure 29.** The same as Figure 12. The Sun-as-a-star data for events S1 and S2 are added with orange pluses and purple circles, respectively. (a) The comparison between solar and stellar data. (b) Enlarged panel only for solar data.</figcaption></figure>

## ORCID iDs

Kosuke Namekata https://orcid.org/0000-0002-1297-9485

Vladimir S. Airapetian https://orcid.org/0000-0003-4452-0588

Pascal Petit https://orcid.org/0000-0001-7624-9222

Hiroyuki Maehara https://orcid.org/0000-0003-0332-0811

Kai Ikuta https://orcid.org/0000-0002-5978-057X

Shun Inoue https://orcid.org/0000-0003-3085-304X

Yuta Notsu https://orcid.org/0000-0002-0412-0849

Rishi R. Paudel https://orcid.org/0000-0002-8090-3570

Antoaneta A. Avramova-Boncheva https://orcid.org/0009-0001-5099-8070

Keith Gendreau https://orcid.org/0000-0001-7115-2819

Sandra V. Jeffers https://orcid.org/0000-0003-2490-4779

Stephen Marsden https://orcid.org/0000-0001-5522-8887

Julien Morin https://orcid.org/0000-0002-4996-6901

Coralie Neiner https://orcid.org/0000-0003-1978-9809

Aline A. Vidotto https://orcid.org/0000-0001-5371-2675

Kazunari Shibata https://orcid.org/0000-0003-1206-7889

## References

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<figure><img src="image_37.png" /><figcaption>**Figure 28.** Dynamic spectra of the pre-flare-subtracted H-alpha spectra of the Sun-as-a-star prominence eruptions. (a) The prominence eruption on 2017 June 19 (event "S1"). (b) The prominence eruption on 2021 May 5 (event "S2"). The data of the dynamic spectra were taken from Otsu et al. (2022), and the spectral fitting is newly done in this paper. In both events, the emissions from flare ribbons are behind the limb and not visible from the Earth, so the emission almost comes from the erupted prominence. Some of the white-colored region is the unavailable wavelength at that time. The cyan points are the central wavelength of the emission component. For the event S1, the velocity evolution is fitted by a linear function, and the deceleration is derived as $0.1089 \pm 0.0002 \text{ km s}^{-2}$.</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>**Figure 29.** The same as Figure 12. The Sun-as-a-star data for events S1 and S2 are added with orange pluses and purple circles, respectively. (a) The comparison between solar and stellar data. (b) Enlarged panel only for solar data.</figcaption></figure>

## ORCID iDs

Kosuke Namekata https://orcid.org/0000-0002-1297-9485

Vladimir S. Airapetian https://orcid.org/0000-0003-4452-0588

Pascal Petit https://orcid.org/0000-0001-7624-9222

Hiroyuki Maehara https://orcid.org/0000-0003-0332-0811

Kai Ikuta https://orcid.org/0000-0002-5978-057X

Shun Inoue https://orcid.org/0000-0003-3085-304X

Yuta Notsu https://orcid.org/0000-0002-0412-0849

Rishi R. Paudel https://orcid.org/0000-0002-8090-3570

Antoaneta A. Avramova-Boncheva https://orcid.org/0009-0001-5099-8070

Keith Gendreau https://orcid.org/0000-0001-7115-2819

Sandra V. Jeffers https://orcid.org/0000-0003-2490-4779

Stephen Marsden https://orcid.org/0000-0001-5522-8887

Julien Morin https://orcid.org/0000-0002-4996-6901

Coralie Neiner https://orcid.org/0000-0003-1978-9809

Aline A. Vidotto https://orcid.org/0000-0001-5371-2675

Kazunari Shibata https://orcid.org/0000-0003-1206-7889

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