# Multi-wavelength Campaign Observations of a Young Solar-type Star, EK Draconis I. Discovery of Prominence Eruptions Associated with Superflares

Kosuke Namekata, Vladimir Airapetian, Pascal Petit, Hiroyuki Maehara, Kai Ikuta, Shun Inoue, Yuta Notsu, Rishi Paudel, Zaven Arzoumanian, Antoaneta Avramova-Boncheva, et al.

► To cite this version:

Kosuke Namekata, Vladimir Airapetian, Pascal Petit, Hiroyuki Maehara, Kai Ikuta, et al. Multi-wavelength Campaign Observations of a Young Solar-type Star, EK Draconis I. Discovery of Prominence Eruptions Associated with Superflares. The Astrophysical Journal, 2023, 961 (1), pp.23. 10.3847/1538-4357/ad0b7c. hal-04286428

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# Multiwavelength Campaign Observations of a Young Solar-type Star, EK Draconis. I. Discovery of Prominence Eruptions Associated with Superflares

Kosuke Namekata¹, Vladimir S. Airapetian²,³, Pascal Petit⁴, Hiroyuki Maehara⁵, Kai Ikuta⁶, Shun Inoue⁷, Yuta Notsu⁸,⁹, Rishi R. Paudel¹⁰,¹¹, Zaven Arzoumanian¹², Antoaneta A. Avramova-Boncheva¹³, Keith Gendreau¹², Sandra V. Jeffers¹⁴, Stephen Marsden¹⁵, Julien Morin¹⁶, Coralie Neiner¹⁷, Aline A. Vidotto¹⁸, and Kazunari Shibata¹⁹,²⁰

¹ALMA Project, National Astronomical Observatory of Japan, NINS, Osawa, Mitaka, Tokyo, 181-8588, Japan; kosuke.namekata@astro.nao.ac.jp, namekata@kusastro.kyoto-u.ac.jp

²Sellers Exoplanetary Environments Collaboration, NASA Goddard Space Flight Center, Greenbelt, MD, USA

³Department of Physics, American University, Washington, DC, USA

⁴Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS, CNES, 14 avenue Édouard Belin, F-31400 Toulouse, France

⁵Okayama Branch Office, Subaru Telescope, National Astronomical Observatory of Japan, NINS, Kamogata, Asakuchi, Okayama 719-0232, Japan

⁶Department of Multidisciplinary Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan

⁷Department of Physics, Kyoto University, Sakyo, Kyoto 606-8502, Japan

⁸Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, 3665 Discovery Drive, Boulder, CO 80303, USA

⁹National Solar Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA

¹⁰NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA

¹¹University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

¹²NASA Goddard Space Flight Center, Greenbelt, MD, USA

¹³Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee Boulevard, 1784 Sofia, Bulgaria

¹⁴Max Planck Institute for Solar System Research, Justus-von-Liebig-weg 3, D-37077 Göttingen, Germany

¹⁵Centre for Astrophysics, University of Southern Queensland, Toowoomba, Queensland 4350, Australia

¹⁶LUPM, Université de Montpellier, CNRS, Place Eugène Bataillon, F-34095 Montpellier, France

¹⁷LESIA, Paris Observatory, PSL University, CNRS, Sorbonne University, Université Paris Cité, 5 place Jules Janssen, F-92195 Meudon, France

¹⁸Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands

¹⁹Kwasan Observatory, Kyoto University, Yamashina, Kyoto 607-8471, Japan

²⁰School of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan

Received 2023 August 29; revised 2023 November 4; accepted 2023 November 7; published 2024 January 11

## Abstract

Young solar-type stars frequently produce superflares, serving as a unique window into the young Sun-Earth environments. Large solar flares are closely linked to coronal mass ejections (CMEs) associated with filament/prominence eruptions, but observational evidence for stellar superflares remains scarce. Here, we present a 12-day, multiwavelength campaign observation of young solar-type star EK Draconis (G1.5V, 50–120 Myr age) utilizing the Transiting Exoplanet Survey Satellite, the Neutron star Interior Composition ExploreR, and the Seimei telescope. The star has previously exhibited blueshifted $H\alpha$ absorptions as evidence for a filament eruption associated with a superflare. Our simultaneous optical and X-ray observations identified three superflares of $1.5 \times 10^{33}–1.2 \times 10^{34}$ erg. We report the first discovery of two prominence eruptions on a solar-type star, observed as blueshifted $H\alpha$ emissions at speeds of 690 and 430 km s$^{-1}$ and masses of $1.1 \times 10^{19}$ and $3.2 \times 10^{17}$ g, respectively. The faster, massive event shows a candidate of post-flare X-ray dimming with the amplitude of up to ~10%. Several observational aspects consistently point to the occurrence of a fast CME associated with this event. The comparative analysis of the estimated length scales of flare loops, prominences, possible dimming region, and starspots provides the overall picture of the eruptive phenomena. Furthermore, the energy partition of the observed superflares in the optical and X-ray bands is consistent with flares from the Sun, M-dwarfs, and close binaries, yielding the unified empirical relations. These discoveries provide profound implications of the impact of these eruptive events on early Venus, Earth, and Mars and young exoplanets.

*Unified Astronomy Thesaurus concepts: Stellar flares (1603); Stellar coronal mass ejections (1881); Stellar coronal dimming (306); Solar prominences (1519); Solar filament eruptions (1981); Optical flares (1166); Stellar x-ray flares (1637); Flare stars (540); G dwarf stars (556); Solar analogs (1941)*

## 1. Introduction

Solar and stellar flares are the most powerful explosive phenomena in atmospheres of cool stars observed in the wide range of wavelengths, from radio to X-ray bands (see Shibata & Magara 2011; Benz 2017, for reviews). They are thought to

be caused by the conversion of magnetic energy stored in stellar coronae into kinetic and thermal energy via magnetic reconnection. These events on the Sun are frequently accompanied by coronal mass ejections (CMEs) of hundreds of millions of tons of hot coronal material propagating into the interplanetary space at a few hundreds to a few thousands of km s$^{-1}$. X-rays and extreme ultraviolet (EUV) emission from large solar flares and associated fast CMEs often have severe impacts on the planetary magnetospheres and ionospheres (see Airapetian et al. 2020; Temmer 2021; Cliver et al. 2022, for reviews).

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Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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# Multiwavelength Campaign Observations of a Young Solar-type Star, EK Draconis. I. Discovery of Prominence Eruptions Associated with Superflares

Kosuke Namekata¹, Vladimir S. Airapetian²,³, Pascal Petit⁴, Hiroyuki Maehara⁵, Kai Ikuta⁶, Shun Inoue⁷, Yuta Notsu⁸,⁹, Rishi R. Paudel¹⁰,¹¹, Zaven Arzoumanian¹², Antoaneta A. Avramova-Boncheva¹³, Keith Gendreau¹², Sandra V. Jeffers¹⁴, Stephen Marsden¹⁵, Julien Morin¹⁶, Coralie Neiner¹⁷, Aline A. Vidotto¹⁸, and Kazunari Shibata¹⁹,²⁰

¹ALMA Project, National Astronomical Observatory of Japan, NINS, Osawa, Mitaka, Tokyo, 181-8588, Japan; kosuke.namekata@astro.nao.ac.jp, namekata@kusastro.kyoto-u.ac.jp

²Sellers Exoplanetary Environments Collaboration, NASA Goddard Space Flight Center, Greenbelt, MD, USA

³Department of Physics, American University, Washington, DC, USA

⁴Institut de Recherche en Astrophysique et Planétologie, Université de Toulouse, CNRS, CNES, 14 avenue Édouard Belin, F-31400 Toulouse, France

⁵Okayama Branch Office, Subaru Telescope, National Astronomical Observatory of Japan, NINS, Kamogata, Asakuchi, Okayama 719-0232, Japan

⁶Department of Multidisciplinary Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan

⁷Department of Physics, Kyoto University, Sakyo, Kyoto 606-8502, Japan

⁸Laboratory for Atmospheric and Space Physics, University of Colorado Boulder, 3665 Discovery Drive, Boulder, CO 80303, USA

⁹National Solar Observatory, 3665 Discovery Drive, Boulder, CO 80303, USA

¹⁰NASA Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD 20771, USA

¹¹University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA

¹²NASA Goddard Space Flight Center, Greenbelt, MD, USA

¹³Institute of Astronomy and National Astronomical Observatory, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee Boulevard, 1784 Sofia, Bulgaria

¹⁴Max Planck Institute for Solar System Research, Justus-von-Liebig-weg 3, D-37077 Göttingen, Germany

¹⁵Centre for Astrophysics, University of Southern Queensland, Toowoomba, Queensland 4350, Australia

¹⁶LUPM, Université de Montpellier, CNRS, Place Eugène Bataillon, F-34095 Montpellier, France

¹⁷LESIA, Paris Observatory, PSL University, CNRS, Sorbonne University, Université Paris Cité, 5 place Jules Janssen, F-92195 Meudon, France

¹⁸Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands

¹⁹Kwasan Observatory, Kyoto University, Yamashina, Kyoto 607-8471, Japan

²⁰School of Science and Engineering, Doshisha University, Kyotanabe, Kyoto 610-0321, Japan

Received 2023 August 29; revised 2023 November 4; accepted 2023 November 7; published 2024 January 11

## Abstract

Young solar-type stars frequently produce superflares, serving as a unique window into the young Sun-Earth environments. Large solar flares are closely linked to coronal mass ejections (CMEs) associated with filament/prominence eruptions, but observational evidence for stellar superflares remains scarce. Here, we present a 12-day, multiwavelength campaign observation of young solar-type star EK Draconis (G1.5V, 50-120 Myr age) utilizing the Transiting Exoplanet Survey Satellite, the Neutron star Interior Composition ExploreR, and the Seimei telescope. The star has previously exhibited blueshifted Hα absorptions as evidence for a filament eruption associated with a superflare. Our simultaneous optical and X-ray observations identified three superflares of 1.5 × 10³³–1.2 × 10³⁴ erg. We report the first discovery of two prominence eruptions on a solar-type star, observed as blueshifted Hα emissions at speeds of 690 and 430 km s⁻¹ and masses of 1.1 × 10¹⁹ and 3.2 × 10¹⁷ g, respectively. The faster, massive event shows a candidate of post-flare X-ray dimming with the amplitude of up to ~10%. Several observational aspects consistently point to the occurrence of a fast CME associated with this event. The comparative analysis of the estimated length scales of flare loops, prominences, possible dimming region, and starspots provides the overall picture of the eruptive phenomena. Furthermore, the energy partition of the observed superflares in the optical and X-ray bands is consistent with flares from the Sun, M-dwarfs, and close binaries, yielding the unified empirical relations. These discoveries provide profound implications of the impact of these eruptive events on early Venus, Earth, and Mars and young exoplanets.

*Unified Astronomy Thesaurus concepts: Stellar flares (1603); Stellar coronal mass ejections (1881); Stellar coronal dimming (306); Solar prominences (1519); Solar filament eruptions (1981); Optical flares (1166); Stellar x-ray flares (1637); Flare stars (540); G dwarf stars (556); Solar analogs (1941)*

## 1. Introduction

Solar and stellar flares are the most powerful explosive phenomena in atmospheres of cool stars observed in the wide range of wavelengths, from radio to X-ray bands (see Shibata & Magara 2011; Benz 2017, for reviews). They are thought to

be caused by the conversion of magnetic energy stored in stellar coronae into kinetic and thermal energy via magnetic reconnection. These events on the Sun are frequently accompanied by coronal mass ejections (CMEs) of hundreds of millions of tons of hot coronal material propagating into the interplanetary space at a few hundreds to a few thousands of km s⁻¹. X-rays and extreme ultraviolet (EUV) emission from large solar flares and associated fast CMEs often have severe impacts on the planetary magnetospheres and ionospheres (see Airapetian et al. 2020; Temmer 2021; Cliver et al. 2022, for reviews).

<figure><img src="image_3.png" /></figure>

Original content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
The largest flare energy observed on our Sun is about $10^{32}$ erg (e.g., Emslie et al. 2012), while larger flares with the energy over $10^{33}$ erg, referred to as “superflares,” have never been reported in modern solar observations (e.g., Aulanier et al. 2013). However, recent studies have identified multiple possible extreme solar energetic events with energies up to $10^{34}$ erg that occurred in the past millennia using cosmogenic radionuclides ($^{14}$C, $^{10}$Be, $^{36}$Cl) recorded in tree rings and ice cores (e.g., Miyake et al. 2019; Usoskin 2023). Furthermore, recent observations of solar-type (G-type main-sequence) stars have provided important insights into the rate of occurrence of superflares from the young solar-type stars and the analogs of the present-day Sun. Vigorous observational studies of stellar flares over the last 30 yr revealed that young, rapidly rotating solar-type stars show frequent superflares at a rate of 1 event per day (age of ~100 Myr; Audard et al. 1999, 2000; Namekata et al. 2022c; Colombo et al. 2022; Yamashita et al. 2022), while mature, slowly rotating solar-type stars show superflares at much lower occurrence rates of about 1 event per a few thousand years (age of several Gyr; Maehara et al. 2012; Shibayama et al. 2013; Notsu et al. 2019; Okamoto et al. 2021). These data suggest that superflares from the young Sun could have had a significant impact on the magnetospheric and atmospheric environments of young Venus, Earth, and Mars, on a timescale of 300 Myr that is controlled the stellar rotation rate (Tu et al. 2015). Also, the detection of superflares on the slowly rotating stars imply a possibility that superflares can occur on the present-day, mature Sun. Such studies are critical for understanding the frequency and impact of these events on our civilization and its infrastructures. Thus, superflares on solar-type stars have been highlighted from the context of solar physics (e.g., Aulanier et al. 2013; Shibata et al. 2013; Cliver et al. 2022), planetary science (e.g., Fujii et al. 2018; Linsky 2019; Airapetian et al. 2020), biochemistry (e.g., Kobayashi et al. 2023), and historical and geophysical studies (e.g., Miyake et al. 2012; Hayakawa et al. 2017; Usoskin 2023).

High magnetic activity of young solar-type stars is characterized not only by stellar superflares but also by strong average surface magnetic fields (e.g., Vidotto et al. 2014; Kochukhov et al. 2020) and giant starspots covering a substantial portion of the hemisphere (up to tens of percent; e.g., Maehara et al. 2017; Waite et al. 2017; Namekata et al. 2019; Notsu et al. 2019; Namekata et al. 2020a; Herbst et al. 2021; Okamoto et al. 2021; Yamashita et al. 2022). The magnetic energy stored in active regions associated with starspots power X-ray and EUV bright (up to $10^{30}$ erg s$^{-1}$), hot (up to 10 MK), and dense ($10^{10-11}$ cm$^{-3}$) coronae and massive winds (e.g., Güdel et al. 1995, 1997a; Pevtsov et al. 2003; Güdel 2004; Wright et al. 2011; Takasao et al. 2020; Airapetian et al. 2021; Shoda & Takasao 2021; Toriumi & Airapetian 2022; Namekata et al. 2023). Observations of the nearby young solar-type stars in various phases of evolution have provided insights into the time history of our Sun and its heliosphere, which have had a profound influence on a young Earth over the span of millions to billions of years (e.g., Güdel et al. 1997b; Güdel 2007; Johnstone et al. 2019; Okamoto et al. 2021). According to recent geophysical and fossil data, life on Earth is thought to have originated between 4.4 and 3.8 billion years ago (Westall et al. 2023). This time period is known as the “Hadean Eon,” during which the Earth would have been subjected to intense X-ray and ultraviolet (XUV) radiation and

frequent solar flares and CMEs from the young Sun. The XUV radiation from the young Sun could have triggered photo-ionization processes and contributed to the atmospheric escape of the early Earth (Airapetian et al. 2017; Yoshida & Kuramoto 2021). Moreover, the powerful energetic particles associated with flares/CMEs could have induced chemical reactions, resulting in the formation of greenhouse gases and prebiotic chemistry in the Earth's primitive atmosphere (Airapetian et al. 2016; Kobayashi et al. 2023). These processes may intimately contribute to the formation and disruption of habitable worlds, conditions crucial for the emergence and sustainment of life. As there is little direct evidence of the strong XUV flare radiation and energetic CMEs of the young Sun from the present-day Solar system, we need to infer them from observations of young solar-type stars at ages of a few tens to hundreds of millions of years characteristic of the Hadean period.

Several nearby solar-type stars have been considered as likely proxies for the young Sun (e.g., Güdel et al. 1997b; Güdel 2007; Johnstone et al. 2019). These include $\kappa^1$ Ceti (G5V, ~600 Myr old), EK Draconis (EK Dra, G1.5V, ~125 Myr, Waite et al. 2017; Senavciet al. 2021), and DS Tucanae A (DS Tuc A, G6V, ~45 Myr old). Audard et al. (1999, 2000) reported on X-ray flare frequencies for $\kappa^1$ Ceti and EK Dra, using data from the Extreme Ultraviolet Explorer (EUVE). They examined the contribution of flares to coronal heating and investigated the relationship between flares and quiescent X-ray emissions. Later, Hamaguchi et al. (2023) reported X-ray superflares on $\kappa^1$ Ceti using the Neutron star Interior Composition ExploreR (NICER). Ayres (2015) detailed UV spectroscopic observations of the decay phase of a superflare on EK Dra, captured by the Hubble Space Telescope. They concluded that Si IV and O IV UV emission lines forming at $8 \times 10^5$ K redshifted at 30–40 km s$^{-1}$ are the signatures of the post-flare loop downflows. Guarcello et al. (2019) conducted multiwavelength observations of a superflare on the active solar-type star H II 345 (G8V), using the Kepler Space Telescope (K2 mission, 30 minutes cadence) and XMM-Newton. They estimated the energy partition between X-ray and white-light flares and derived the length scale of the flare loop from X-ray data analysis, although the time delay between the peaks in the optical and X-ray bands was not clearly resolved. More recently, Pillitteri et al. (2022) reported two superflares on DS Tuc A, an exoplanet-hosting star, in X-ray and Near-Ultraviolet (NUV) wavelengths using XMM-Newton. The X-ray emission peaks are notably delayed compared to NUV peaks, showing the relationship between heating processes associated with the Neupert effect as observed in solar flare events (Neupert 1968; Dennis & Zarro 1993). Specifically, these delays between peaks inform us about the impulsive sources that transport energetic particle energy flux from the solar/stellar coronae and deposit heating in lower chromospheric layers, which respond back in the form of evaporated flows filling coronal loops with hot and dense X-ray emitting plasma. While these studies have uncovered many critical aspects of flaring atmospheres of magnetically active stars, multiwavelength observations remain relatively scarce. The Kepler Space Telescope established a robust relationship between rotation (age) and the frequency of white-light flares (WLFs) for solar-type stars (Maehara et al. 2012; Shibayama et al. 2013; Notsu et al. 2019; Okamoto et al. 2021). Application of the extensive Kepler statistics to assess impact
The largest flare energy observed on our Sun is about $10^{32}$ erg (e.g., Emslie et al. 2012), while larger flares with the energy over $10^{33}$ erg, referred to as “superflares,” have never been reported in modern solar observations (e.g., Aulanier et al. 2013). However, recent studies have identified multiple possible extreme solar energetic events with energies up to $10^{34}$ erg that occurred in the past millennia using cosmogenic radionuclides ($^{14}$C, $^{10}$Be, $^{36}$Cl) recorded in tree rings and ice cores (e.g., Miyake et al. 2019; Usoskin 2023). Furthermore, recent observations of solar-type (G-type main-sequence) stars have provided important insights into the rate of occurrence of superflares from the young solar-type stars and the analogs of the present-day Sun. Vigorous observational studies of stellar flares over the last 30 yr revealed that young, rapidly rotating solar-type stars show frequent superflares at a rate of 1 event per day (age of ~100 Myr; Audard et al. 1999, 2000; Namekata et al. 2022c; Colombo et al. 2022; Yamashita et al. 2022), while mature, slowly rotating solar-type stars show superflares at much lower occurrence rates of about 1 event per a few thousand years (age of several Gyr; Maehara et al. 2012; Shibayama et al. 2013; Notsu et al. 2019; Okamoto et al. 2021). These data suggest that superflares from the young Sun could have had a significant impact on the magnetospheric and atmospheric environments of young Venus, Earth, and Mars, on a timescale of 300 Myr that is controlled the stellar rotation rate (Tu et al. 2015). Also, the detection of superflares on the slowly rotating stars imply a possibility that superflares can occur on the present-day, mature Sun. Such studies are critical for understanding the frequency and impact of these events on our civilization and its infrastructures. Thus, superflares on solar-type stars have been highlighted from the context of solar physics (e.g., Aulanier et al. 2013; Shibata et al. 2013; Cliver et al. 2022), planetary science (e.g., Fujii et al. 2018; Linsky 2019; Airapetian et al. 2020), biochemistry (e.g., Kobayashi et al. 2023), and historical and geophysical studies (e.g., Miyake et al. 2012; Hayakawa et al. 2017; Usoskin 2023).

High magnetic activity of young solar-type stars is characterized not only by stellar superflares but also by strong average surface magnetic fields (e.g., Vidotto et al. 2014; Kochukhov et al. 2020) and giant starspots covering a substantial portion of the hemisphere (up to tens of percent; e.g., Maehara et al. 2017; Waite et al. 2017; Namekata et al. 2019; Notsu et al. 2019; Namekata et al. 2020a; Herbst et al. 2021; Okamoto et al. 2021; Yamashita et al. 2022). The magnetic energy stored in active regions associated with starspots power X-ray and EUV bright (up to $10^{30}$ erg s$^{-1}$), hot (up to 10 MK), and dense ($10^{10-11}$ cm$^{-3}$) coronae and massive winds (e.g., Güdel et al. 1995, 1997a; Pevtsov et al. 2003; Güdel 2004; Wright et al. 2011; Takasao et al. 2020; Airapetian et al. 2021; Shoda & Takasao 2021; Toriumi & Airapetian 2022; Namekata et al. 2023). Observations of the nearby young solar-type stars in various phases of evolution have provided insights into the time history of our Sun and its heliosphere, which have had a profound influence on a young Earth over the span of millions to billions of years (e.g., Güdel et al. 1997b; Güdel 2007; Johnstone et al. 2019; Okamoto et al. 2021). According to recent geophysical and fossil data, life on Earth is thought to have originated between 4.4 and 3.8 billion years ago (Westall et al. 2023). This time period is known as the “Hadean Eon,” during which the Earth would have been subjected to intense X-ray and ultraviolet (XUV) radiation and

frequent solar flares and CMEs from the young Sun. The XUV radiation from the young Sun could have triggered photo-ionization processes and contributed to the atmospheric escape of the early Earth (Airapetian et al. 2017; Yoshida & Kuramoto 2021). Moreover, the powerful energetic particles associated with flares/CMEs could have induced chemical reactions, resulting in the formation of greenhouse gases and prebiotic chemistry in the Earth's primitive atmosphere (Airapetian et al. 2016; Kobayashi et al. 2023). These processes may intimately contribute to the formation and disruption of habitable worlds, conditions crucial for the emergence and sustainment of life. As there is little direct evidence of the strong XUV flare radiation and energetic CMEs of the young Sun from the present-day Solar system, we need to infer them from observations of young solar-type stars at ages of a few tens to hundreds of millions of years characteristic of the Hadean period.

Several nearby solar-type stars have been considered as likely proxies for the young Sun (e.g., Güdel et al. 1997b; Güdel 2007; Johnstone et al. 2019). These include $\kappa^1$ Ceti (G5V, ~600 Myr old), EK Draconis (EK Dra, G1.5V, ~125 Myr, Waite et al. 2017; Senavciet al. 2021), and DS Tucanae A (DS Tuc A, G6V, ~45 Myr old). Audard et al. (1999, 2000) reported on X-ray flare frequencies for $\kappa^1$ Ceti and EK Dra, using data from the Extreme Ultraviolet Explorer (EUVE). They examined the contribution of flares to coronal heating and investigated the relationship between flares and quiescent X-ray emissions. Later, Hamaguchi et al. (2023) reported X-ray superflares on $\kappa^1$ Ceti using the Neutron star Interior Composition ExploreR (NICER). Ayres (2015) detailed UV spectroscopic observations of the decay phase of a superflare on EK Dra, captured by the Hubble Space Telescope. They concluded that Si IV and O IV UV emission lines forming at $8 \times 10^5$ K redshifted at 30–40 km s$^{-1}$ are the signatures of the post-flare loop downflows. Guarcello et al. (2019) conducted multiwavelength observations of a superflare on the active solar-type star H II 345 (G8V), using the Kepler Space Telescope (K2 mission, 30 minutes cadence) and XMM-Newton. They estimated the energy partition between X-ray and white-light flares and derived the length scale of the flare loop from X-ray data analysis, although the time delay between the peaks in the optical and X-ray bands was not clearly resolved. More recently, Pillitteri et al. (2022) reported two superflares on DS Tuc A, an exoplanet-hosting star, in X-ray and Near-Ultraviolet (NUV) wavelengths using XMM-Newton. The X-ray emission peaks are notably delayed compared to NUV peaks, showing the relationship between heating processes associated with the Neupert effect as observed in solar flare events (Neupert 1968; Dennis & Zarro 1993). Specifically, these delays between peaks inform us about the impulsive sources that transport energetic particle energy flux from the solar/stellar coronae and deposit heating in lower chromospheric layers, which respond back in the form of evaporated flows filling coronal loops with hot and dense X-ray emitting plasma. While these studies have uncovered many critical aspects of flaring atmospheres of magnetically active stars, multiwavelength observations remain relatively scarce. The Kepler Space Telescope established a robust relationship between rotation (age) and the frequency of white-light flares (WLFs) for solar-type stars (Maehara et al. 2012; Shibayama et al. 2013; Notsu et al. 2019; Okamoto et al. 2021). Application of the extensive Kepler statistics to assess impact
of flares on exoplanetary environments requires characterization of the radiative flux from superflares on young solar-type stars in the wide range of wavelengths: from XUV to optical.

Recent optical spectroscopic observations of superflares on young solar-type stars provided indications of stellar CMEs. Namekata et al. (2022d) reported the first detection of the optical $H\alpha$ spectra of a superflare of ~$10^{33}$ erg on the young solar-type star EK Dra (the flare is labeled as “E4” in the following sections). The $H\alpha$ spectra show a blueshifted absorption as evidence of a gigantic stellar filament eruption ($10^4$ K plasma) with a velocity of 510 km s⁻¹ and mass of $10^{18}$ g (approximately 10 times larger than the largest solar CMEs). In the standard solar flare model, photospheric motions produce a stressed magnetic flux rope connected to a filament, which becomes unstable and is ejected into the solar corona, initiating a flare through magnetic reconnection (Shibata & Magara 2011; Lynch et al. 2019). These prominence signatures relate to the formation of magnetic flux ropes in the solar and stellar corona, a phenomenon widely researched in solar studies. On the Sun, filament or prominence eruptions (cores of CMEs) are often associated with interplanetary CMEs, the sources of space weather (Cliver et al. 2022). By directly comparing with solar and Sun-as-a-star observations, Namekata et al. (2022d) suggested that a massive high-energy stellar CME is probably associated with the eruption of an extended filament, affecting the young planetary systems and stellar mass loss. On the other hand, Namekata et al. (2022c) discovered another $10^{34}$ erg -class superflare on EK Dra (labeled as “E5”) that did not show significant blueshifted $H\alpha$ spectra, casting a doubt in the one-to-one relationship between filament eruptions/CMEs and superflares. Alternatively, Namekata et al. (2022c) suggested that the superflare could have occurred near the stellar limb and possibly is radiated from flare loops (Heinzel & Shibata 2018), resulting in no blue/redshifts due to the location. The above observational studies demonstrate that time-resolved optical spectroscopic observations are the promising—and currently the only—approach to studying CMEs on young solar-type stars, which are also beneficial for understanding other chromospheric heating phenomena (see Švestka et al. 1962; Ichimoto & Kurokawa 1984; Canfield & Gayley 1987; Kowalski et al. 2013; Namekata et al. 2020b; Graham et al. 2020; Namekata et al. 2022a; Otsu et al. 2022; Namizaki et al. 2023, for solar and M-dwarf flares). However, to date, only two such observational events have been reported in the literature. To further our understanding of the impact on young planetary environments, we need to significantly increase the number of samples.

The search for signatures of stellar CMEs on other types of stars, such as M/K-dwarfs and active close binaries, has been relatively successful, by using the strategy based on solar CME observations (see recent reviews by Osten & Wolk 2017; Namekata et al. 2022b; Leitzinger & Odert 2022). This is thanks to the long history of ground- and space-based observations, which is a result of their frequent flares and faint stellar quiescent background (e.g., Pettersen et al. 1984; Pettersen 1989; Hawley & Fisher 1992). Representatively, spectroscopic observations revealed many flare events associated with blueshifted emission line profiles, called “blue asymmetries,” in optical Hydrogen Balmer lines (Houdebine et al. 1990; Eason et al. 1992; Gunn et al. 1994; Crespo-Chacón et al. 2006; Fuhrmeister et al. 2008, 2011; Vida et al. 2016; Flores Soriano & Strassmeier 2017; Fuhrmeister et al. 2018; Honda et al. 2018; Vida et al. 2019;

Muheki et al. 2020a; Muheki et al. 2020b; Koller et al. 2021; Maehara et al. 2021; Inoue et al. 2023), UV lines (Hawley et al. 2007; Leitzinger et al. 2014), and low-temperature X-ray lines (Argiroffi et al. 2019) during flares on M-dwarfs, close binaries, and subgiant/giant stars. These signatures represent the direct evidence of plasma motions in line-of-sight (LOS) direction, and the detected number is very large (>100). Although their relatively low velocities of 100–300 km s⁻¹ in most cases make it difficult to distinguish whether they originate from prominence eruptions/CMEs or flare-related surface phenomena, some of them are characterized as prominence eruptions leading to CMEs by faster velocities than the stellar surface escape velocities (Houdebine et al. 1990; Vida et al. 2016, 2019; Inoue et al. 2023). Another promising method to identify stellar CMEs is based on the detection of the XUV dimming observed during solar CMEs forming as a direct result of evacuation and outward propagation of materials from the solar corona, which can last for hours (Mason et al. 2016; Jin et al. 2022). Veronig et al. (2021) reported on possible post-flare X-ray and EUV dimming in cool dwarfs by using an archive data set, and later Loyd et al. (2022) found post-flare dimming in coronal far ultraviolet (FUV) lines from $\epsilon$ Eridani (K2V). Furthermore, Zic et al. (2020) reported on a possible type-IV radio burst after a flare on Proxima Centauri (M5.5V), although no detections of type-II burst have been reported to date (Crosley & Osten 2018a, 2018b; Villadsen & Hallinan 2019). These eruptive events on cool dwarfs have been in general highlighted as a possible driver of mass and angular momentum loss evolution of the low-mass stars (e.g., Osten & Wolk 2015; Cranmer 2017; Wood et al. 2021) and as a threat to the exoplanet habitability (e.g., Segura et al. 2010; Tilley et al. 2019; Yamashiki et al. 2019; Airapetian et al. 2020; Chen et al. 2021). Although there is still a lack of conclusive observational evidence, these observations provide a hint for potential approaches that could further be extended to the search of eruptions from solar-type stars, as discussed in our study.

Given the above context, the aim of this study is threefold: (1) to understand the radiative energy distribution and evolution of flares among white-light, $H\alpha$, and X-ray wavelength; (2) to study the diversity of $H\alpha$ spectra from superflares on young solar-type stars by increasing the sample size; and (3) to provide a comprehensive understanding of stellar CMEs through multiwavelength observations. To achieve these goals, we conducted the optical and X-ray monitoring observations of the young solar-type star EK Dra over a 12-day period from 2022 April 10 to 2022 April 21 (refer to Table 1). This period coincides with the optical photometric observations performed by the Transiting Exoplanet Survey Satellite (TESS, Ricker et al. (2015), Section 2.2). The high-time-cadence optical spectroscopic observations were conducted with the 3.8 m Seimei telescope in Okayama Observatory, Japan (Section 2.3). The X-ray monitoring observations were also performed by NICER on board the International Space Station (ISS; Section 2.4). This paper is organized as follows. Section 2 outlines the observational details, while Section 3 describes the analyses and results. In Section 4, we investigate the radiative properties of superflares and their length scales. Section 5 examines the characteristics of prominence eruptions and a potential X-ray dimming. Section 6 integrates the information from Sections 4 and 5 to address our main questions and present our conclusions. In Section 6.4, we outline our future studies, which include
of flares on exoplanetary environments requires characterization of the radiative flux from superflares on young solar-type stars in the wide range of wavelengths: from XUV to optical.

Recent optical spectroscopic observations of superflares on young solar-type stars provided indications of stellar CMEs. Namekata et al. (2022d) reported the first detection of the optical $H\alpha$ spectra of a superflare of ~$10^{33}$ erg on the young solar-type star EK Dra (the flare is labeled as “E4” in the following sections). The $H\alpha$ spectra show a blueshifted absorption as evidence of a gigantic stellar filament eruption ($10^4$ K plasma) with a velocity of 510 km s⁻¹ and mass of $10^{18}$ g (approximately 10 times larger than the largest solar CMEs). In the standard solar flare model, photospheric motions produce a stressed magnetic flux rope connected to a filament, which becomes unstable and is ejected into the solar corona, initiating a flare through magnetic reconnection (Shibata & Magara 2011; Lynch et al. 2019). These prominence signatures relate to the formation of magnetic flux ropes in the solar and stellar corona, a phenomenon widely researched in solar studies. On the Sun, filament or prominence eruptions (cores of CMEs) are often associated with interplanetary CMEs, the sources of space weather (Cliver et al. 2022). By directly comparing with solar and Sun-as-a-star observations, Namekata et al. (2022d) suggested that a massive high-energy stellar CME is probably associated with the eruption of an extended filament, affecting the young planetary systems and stellar mass loss. On the other hand, Namekata et al. (2022c) discovered another $10^{34}$ erg -class superflare on EK Dra (labeled as “E5”) that did not show significant blueshifted $H\alpha$ spectra, casting a doubt in the one-to-one relationship between filament eruptions/CMEs and superflares. Alternatively, Namekata et al. (2022c) suggested that the superflare could have occurred near the stellar limb and possibly is radiated from flare loops (Heinzel & Shibata 2018), resulting in no blue/redshifts due to the location. The above observational studies demonstrate that time-resolved optical spectroscopic observations are the promising—and currently the only—approach to studying CMEs on young solar-type stars, which are also beneficial for understanding other chromospheric heating phenomena (see Švestka et al. 1962; Ichimoto & Kurokawa 1984; Canfield & Gayley 1987; Kowalski et al. 2013; Namekata et al. 2020b; Graham et al. 2020; Namekata et al. 2022a; Otsu et al. 2022; Namizaki et al. 2023, for solar and M-dwarf flares). However, to date, only two such observational events have been reported in the literature. To further our understanding of the impact on young planetary environments, we need to significantly increase the number of samples.

The search for signatures of stellar CMEs on other types of stars, such as M/K-dwarfs and active close binaries, has been relatively successful, by using the strategy based on solar CME observations (see recent reviews by Osten & Wolk 2017; Namekata et al. 2022b; Leitzinger & Odert 2022). This is thanks to the long history of ground- and space-based observations, which is a result of their frequent flares and faint stellar quiescent background (e.g., Pettersen et al. 1984; Pettersen 1989; Hawley & Fisher 1992). Representatively, spectroscopic observations revealed many flare events associated with blueshifted emission line profiles, called “blue asymmetries,” in optical Hydrogen Balmer lines (Houdebine et al. 1990; Eason et al. 1992; Gunn et al. 1994; Crespo-Chacón et al. 2006; Fuhrmeister et al. 2008, 2011; Vida et al. 2016; Flores Soriano & Strassmeier 2017; Fuhrmeister et al. 2018; Honda et al. 2018; Vida et al. 2019;

Muheki et al. 2020a; Muheki et al. 2020b; Koller et al. 2021; Maehara et al. 2021; Inoue et al. 2023), UV lines (Hawley et al. 2007; Leitzinger et al. 2014), and low-temperature X-ray lines (Argiroffi et al. 2019) during flares on M-dwarfs, close binaries, and subgiant/giant stars. These signatures represent the direct evidence of plasma motions in line-of-sight (LOS) direction, and the detected number is very large (>100). Although their relatively low velocities of 100–300 km s⁻¹ in most cases make it difficult to distinguish whether they originate from prominence eruptions/CMEs or flare-related surface phenomena, some of them are characterized as prominence eruptions leading to CMEs by faster velocities than the stellar surface escape velocities (Houdebine et al. 1990; Vida et al. 2016, 2019; Inoue et al. 2023). Another promising method to identify stellar CMEs is based on the detection of the XUV dimming observed during solar CMEs forming as a direct result of evacuation and outward propagation of materials from the solar corona, which can last for hours (Mason et al. 2016; Jin et al. 2022). Veronig et al. (2021) reported on possible post-flare X-ray and EUV dimming in cool dwarfs by using an archive data set, and later Loyd et al. (2022) found post-flare dimming in coronal far ultraviolet (FUV) lines from $\epsilon$ Eridani (K2V). Furthermore, Zic et al. (2020) reported on a possible type-IV radio burst after a flare on Proxima Centauri (M5.5V), although no detections of type-II burst have been reported to date (Crosley & Osten 2018a, 2018b; Villadsen & Hallinan 2019). These eruptive events on cool dwarfs have been in general highlighted as a possible driver of mass and angular momentum loss evolution of the low-mass stars (e.g., Osten & Wolk 2015; Cranmer 2017; Wood et al. 2021) and as a threat to the exoplanet habitability (e.g., Segura et al. 2010; Tilley et al. 2019; Yamashiki et al. 2019; Airapetian et al. 2020; Chen et al. 2021). Although there is still a lack of conclusive observational evidence, these observations provide a hint for potential approaches that could further be extended to the search of eruptions from solar-type stars, as discussed in our study.

Given the above context, the aim of this study is threefold: (1) to understand the radiative energy distribution and evolution of flares among white-light, $H\alpha$, and X-ray wavelength; (2) to study the diversity of $H\alpha$ spectra from superflares on young solar-type stars by increasing the sample size; and (3) to provide a comprehensive understanding of stellar CMEs through multiwavelength observations. To achieve these goals, we conducted the optical and X-ray monitoring observations of the young solar-type star EK Dra over a 12-day period from 2022 April 10 to 2022 April 21 (refer to Table 1). This period coincides with the optical photometric observations performed by the Transiting Exoplanet Survey Satellite (TESS, Ricker et al. (2015), Section 2.2). The high-time-cadence optical spectroscopic observations were conducted with the 3.8 m Seimei telescope in Okayama Observatory, Japan (Section 2.3). The X-ray monitoring observations were also performed by NICER on board the International Space Station (ISS; Section 2.4). This paper is organized as follows. Section 2 outlines the observational details, while Section 3 describes the analyses and results. In Section 4, we investigate the radiative properties of superflares and their length scales. Section 5 examines the characteristics of prominence eruptions and a potential X-ray dimming. Section 6 integrates the information from Sections 4 and 5 to address our main questions and present our conclusions. In Section 6.4, we outline our future studies, which include
<table><caption>**Table 1**
Observation Log</caption><thead><tr><th>Telescope<br>(Data type)</th><th>UT date</th><th>Total Obs.</th><th>Exp. time<br>(s)</th></tr></thead><tbody><tr><td rowspan="10">3.8 m Seimei<br>(Optical spec.)</td><td>2022 Apr 10</td><td>8.0 (hr)<sup>a</sup></td><td>60,120</td></tr><tr><td>2022 Apr 11</td><td>3.0 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 12</td><td>4.2 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 15</td><td>2.6 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 16</td><td>9.6 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 17</td><td>9.2 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 18</td><td>4.8 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 19</td><td>8.1</td><td>60,120</td></tr><tr><td>2022 Apr 20</td><td>7.3 (hr)</td><td>60,120</td></tr><tr><td>TESS<br>(Optical photo.)</td><td colspan="3">2022 Mar 26–Apr 22<br>(Sector 50)</td></tr><tr><td rowspan="12">NICER<sup>b</sup><br>(Soft X-ray)</td><td>2022 Apr 10</td><td>2192 (s)<sup>c</sup></td><td>...</td></tr><tr><td>2022 Apr 11</td><td>1361 (s)</td><td>...</td></tr><tr><td>2022 Apr 12</td><td>687 (s)</td><td>...</td></tr><tr><td>2022 Apr 13</td><td>3989 (s)</td><td>...</td></tr><tr><td>2022 Apr 14</td><td>2666 (s)</td><td>...</td></tr><tr><td>2022 Apr 15</td><td>3311 (s)</td><td>...</td></tr><tr><td>2022 Apr 16</td><td>8355 (s)</td><td>...</td></tr><tr><td>2022 Apr 17</td><td>9948 (s)</td><td>...</td></tr><tr><td>2022 Apr 18</td><td>560 (s)</td><td>...</td></tr><tr><td>2022 Apr 20</td><td>4436 (s)</td><td>...</td></tr><tr><td>2022 Apr 21</td><td>3357 (s)</td><td>...</td></tr></tbody></table>

**Notes.**

<sup>a</sup> These are calculated by multiplying the number of frames by each exposure time (plus readout time ~17 s).

<sup>b</sup> The Observation ID is 5202490102–5202490113.

<sup>c</sup> The exposure was obtained from https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3table.pl?tablehead=name%3Dnicermastr&Action=More+Options.

modeling prominence eruptions and starspots, as discussed in our forthcoming paper II (K. Namekata et al. 2023, in preparation).

## 2. Observation and Data Reduction

### 2.1. EK Draconis

EK Dra (HD 129333, G1.5V) is a young solar-type star at an age of 50–125 Myr. Its effective temperature of 5560–5700 K, radius of 0.94 $R_⊙$, and mass of 0.95 $M_⊙$ make this star one of the best proxies for an infant Sun at the time of the Hadean period on Earth (Waite et al. 2017; Senavciet al. 2021). It is a rapidly rotating star, with a rotation period of 2.77 days (Audard et al. 1999; Ayres 2015; Namekata et al. 2022d), and it exhibits a high level of magnetic activity in the form of a hot and dense corona (e.g., Scelsi et al. 2005; Linsky et al. 2012; Namekata et al. 2023), strong surface magnetic field and large starspots (e.g., Berdyugina & Järvinen 2005; Waite et al. 2017; Järvinen et al. 2018), and frequent superflares (e.g., Audard et al. 1999, 2000; Ayres 2015; Namekata et al. 2022c; Namekata et al. 2022d). Although a faint low-mass companion is reported ~20 au away in the projected distance from the G-type primary star (here we call the primary G-dwarf EK Dra), these two stars are not believed to be magnetically connected (Waite et al. 2017), and the G-dwarf is the main source of stellar superflares and associated eruptive events

(see Section “Low mass companion” in Supplementary Information of Namekata et al. 2022d).

### 2.2. TESS

TESS observed EK Dra (TIC 159613900) in its Sector 50 from 2022 March 26 to 2022 April 22.<sup>21</sup> TESS conducts photometric observations using four cameras with the TESS filter in the optical band of 6000–10000 Å. Each sector is observed for approximately 27 days (Ricker et al. 2015). During this period, EK Dra was observed with a 10-minute time cadence mode. The data were obtained from the Multimission Archive at the Space Telescope (MAST) archive.<sup>22</sup> We used *eleanor* for photometric analysis to extract light curves from TESS full-frame image (FFI) data (Feinstein et al. 2019). *Eleanor* yields “raw” flux; “corrected” flux, which is regressed against instrumental effects; and “principal component analysis” (“PCA”) flux, which has common systematics between targets on the same camera removed. We employed the “raw” flux for flare analysis due to the relatively high noise level of the “corrected” and “PCA” fluxes. For the analysis of rotational modulations, only the long-term rotational modulations in the “raw” flux were calibrated using a smoothed “PCA” flux.

### 2.3. 3.8 m Seimei Telescope

We conducted optical spectroscopic monitoring observations using the Kyoto Okayama Optical Low-dispersion Spectrograph with optical-fiber Integral Field Unit (KOOLS-IFU; Matsubayashi et al. 2019), installed on the 3.8 m Seimei Telescope (Kurita et al. 2020) at Okayama Observatory of Kyoto University. The KOOLS-IFU is an optical spectrograph that provides a spectral resolution of $R \sim 2000$ and covers a wavelength range from 5800 to 8000 Å. The campaign ran from 2022 April 10 to 2022 April 20, with the exposure time set at either 60 or 120 s, depending on weather conditions. We followed the data reduction procedure outlined in Namekata et al. (2020b), Namekata et al. (2022c), Namekata et al. (2022d) using IRAF<sup>23</sup> and PyRAF<sup>24</sup> packages. This produced a wavelength-calibrated and continuum-normalized 1D spectrum for each frame. The wavelength of the spectra was calibrated to account for the radial velocity shift caused by Earth’s motion and the radial velocity of EK Dra ($-20.7 \text{ km s}^{-1}$; Lindegren et al. 2018). Figure 1 shows examples of the obtained $H\alpha$ spectrum of EK Dra, which is typical G-dwarf spectra with absorption (even during flares). We computed the $H\alpha$ equivalent width (hereafter “EW,” which refers to $H\alpha$ emission integrated for 6562.8–10 Å ~6562.8 +10 Å), and used this value to plot the $H\alpha$ light curves. Note that we defined an EW in terms of an emission profile to be negative. In this literature, on the other hand, we often refer to pre-flare subtracted equivalent width as $\Delta EW = -(EW - EW_{\text{preflare}})$, where an emission is a positive value.

<footnote n="21"><sup>21</sup> https://archive.stsci.edu/missions/tess/doc/tess_drn/tess sector 50_drn72 v02.pdf</footnote>

<footnote n="22"><sup>22</sup> https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html</footnote>

<footnote n="23"><sup>23</sup> IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.</footnote>

<footnote n="24"><sup>24</sup> PyRAF is part of the stscipython package of astronomical data analysis tools and is a product of the Science Software Branch at the Space Telescope Science Institute.</footnote>
<table><caption>**Table 1**
Observation Log</caption><thead><tr><th>Telescope<br>(Data type)</th><th>UT date</th><th>Total Obs.</th><th>Exp. time<br>(s)</th></tr></thead><tbody><tr><td rowspan="10">3.8 m Seimei<br>(Optical spec.)</td><td>2022 Apr 10</td><td>8.0 (hr)<sup>a</sup></td><td>60,120</td></tr><tr><td>2022 Apr 11</td><td>3.0 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 12</td><td>4.2 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 15</td><td>2.6 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 16</td><td>9.6 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 17</td><td>9.2 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 18</td><td>4.8 (hr)</td><td>60,120</td></tr><tr><td>2022 Apr 19</td><td>8.1</td><td>60,120</td></tr><tr><td>2022 Apr 20</td><td>7.3 (hr)</td><td>60,120</td></tr><tr><td>TESS<br>(Optical photo.)</td><td colspan="3">2022 Mar 26–Apr 22<br>(Sector 50)</td></tr><tr><td rowspan="12">NICER<sup>b</sup><br>(Soft X-ray)</td><td>2022 Apr 10</td><td>2192 (s)<sup>c</sup></td><td>...</td></tr><tr><td>2022 Apr 11</td><td>1361 (s)</td><td>...</td></tr><tr><td>2022 Apr 12</td><td>687 (s)</td><td>...</td></tr><tr><td>2022 Apr 13</td><td>3989 (s)</td><td>...</td></tr><tr><td>2022 Apr 14</td><td>2666 (s)</td><td>...</td></tr><tr><td>2022 Apr 15</td><td>3311 (s)</td><td>...</td></tr><tr><td>2022 Apr 16</td><td>8355 (s)</td><td>...</td></tr><tr><td>2022 Apr 17</td><td>9948 (s)</td><td>...</td></tr><tr><td>2022 Apr 18</td><td>560 (s)</td><td>...</td></tr><tr><td>2022 Apr 20</td><td>4436 (s)</td><td>...</td></tr><tr><td>2022 Apr 21</td><td>3357 (s)</td><td>...</td></tr></tbody></table>

**Notes.**

<sup>a</sup> These are calculated by multiplying the number of frames by each exposure time (plus readout time ~17 s).

<sup>b</sup> The Observation ID is 5202490102–5202490113.

<sup>c</sup> The exposure was obtained from https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3table.pl?tablehead=name%3Dnicermastr&Action=More+Options.

modeling prominence eruptions and starspots, as discussed in our forthcoming paper II (K. Namekata et al. 2023, in preparation).

## 2. Observation and Data Reduction

### 2.1. EK Draconis

EK Dra (HD 129333, G1.5V) is a young solar-type star at an age of 50–125 Myr. Its effective temperature of 5560–5700 K, radius of 0.94 $R_⊙$, and mass of 0.95 $M_⊙$ make this star one of the best proxies for an infant Sun at the time of the Hadean period on Earth (Waite et al. 2017; Senavciet al. 2021). It is a rapidly rotating star, with a rotation period of 2.77 days (Audard et al. 1999; Ayres 2015; Namekata et al. 2022d), and it exhibits a high level of magnetic activity in the form of a hot and dense corona (e.g., Scelsi et al. 2005; Linsky et al. 2012; Namekata et al. 2023), strong surface magnetic field and large starspots (e.g., Berdyugina & Järvinen 2005; Waite et al. 2017; Järvinen et al. 2018), and frequent superflares (e.g., Audard et al. 1999, 2000; Ayres 2015; Namekata et al. 2022c; Namekata et al. 2022d). Although a faint low-mass companion is reported ~20 au away in the projected distance from the G-type primary star (here we call the primary G-dwarf EK Dra), these two stars are not believed to be magnetically connected (Waite et al. 2017), and the G-dwarf is the main source of stellar superflares and associated eruptive events

(see Section “Low mass companion” in Supplementary Information of Namekata et al. 2022d).

### 2.2. TESS

TESS observed EK Dra (TIC 159613900) in its Sector 50 from 2022 March 26 to 2022 April 22.<sup>21</sup> TESS conducts photometric observations using four cameras with the TESS filter in the optical band of 6000–10000 Å. Each sector is observed for approximately 27 days (Ricker et al. 2015). During this period, EK Dra was observed with a 10-minute time cadence mode. The data were obtained from the Multimission Archive at the Space Telescope (MAST) archive.<sup>22</sup> We used *eleanor* for photometric analysis to extract light curves from TESS full-frame image (FFI) data (Feinstein et al. 2019). *Eleanor* yields “raw” flux; “corrected” flux, which is regressed against instrumental effects; and “principal component analysis” (“PCA”) flux, which has common systematics between targets on the same camera removed. We employed the “raw” flux for flare analysis due to the relatively high noise level of the “corrected” and “PCA” fluxes. For the analysis of rotational modulations, only the long-term rotational modulations in the “raw” flux were calibrated using a smoothed “PCA” flux.

### 2.3. 3.8 m Seimei Telescope

We conducted optical spectroscopic monitoring observations using the Kyoto Okayama Optical Low-dispersion Spectrograph with optical-fiber Integral Field Unit (KOOLS-IFU; Matsubayashi et al. 2019), installed on the 3.8 m Seimei Telescope (Kurita et al. 2020) at Okayama Observatory of Kyoto University. The KOOLS-IFU is an optical spectrograph that provides a spectral resolution of $R \sim 2000$ and covers a wavelength range from 5800 to 8000 Å. The campaign ran from 2022 April 10 to 2022 April 20, with the exposure time set at either 60 or 120 s, depending on weather conditions. We followed the data reduction procedure outlined in Namekata et al. (2020b), Namekata et al. (2022c), Namekata et al. (2022d) using IRAF<sup>23</sup> and PyRAF<sup>24</sup> packages. This produced a wavelength-calibrated and continuum-normalized 1D spectrum for each frame. The wavelength of the spectra was calibrated to account for the radial velocity shift caused by Earth’s motion and the radial velocity of EK Dra ($-20.7 \text{ km s}^{-1}$; Lindegren et al. 2018). Figure 1 shows examples of the obtained $H\alpha$ spectrum of EK Dra, which is typical G-dwarf spectra with absorption (even during flares). We computed the $H\alpha$ equivalent width (hereafter “EW,” which refers to $H\alpha$ emission integrated for 6562.8–10 Å ~6562.8 +10 Å), and used this value to plot the $H\alpha$ light curves. Note that we defined an EW in terms of an emission profile to be negative. In this literature, on the other hand, we often refer to pre-flare subtracted equivalent width as $\Delta EW = -(EW - EW_{\text{preflare}})$, where an emission is a positive value.

<footnote n="21"><sup>21</sup> https://archive.stsci.edu/missions/tess/doc/tess_drn/tessSector_50_drn72_v02.pdf</footnote>

<footnote n="22"><sup>22</sup> https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html</footnote>

<footnote n="23"><sup>23</sup> IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.</footnote>

<footnote n="24"><sup>24</sup> PyRAF is part of the stscipython package of astronomical data analysis tools and is a product of the Science Software Branch at the Space Telescope Science Institute.</footnote>
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Examples of Hα spectra of EK Dra on 10 Apr 2022. A black solid line is the pre-flare template for flare E1, and a red dashed line is the flaring spectrum of flare E1.</figcaption></figure>

## 2.4. NICER

NICER is a soft X-ray instrument (0.2–12 keV) on board the ISS (Gendreau et al. 2016). NICER monitored EK Dra from 2022 April 10 to 2022 April 21 (Observation ID: 5202490102–5202490113).<fnref n="25" /> These observations were scheduled concurrently with those from the 3.8 m Seimei telescope and TESS. We downloaded the data from NASA’s website.<fnref n="26" /> The exposure time for each ISS orbit (about 90 minutes) varied from a few minutes to a few tens of minutes, depending on the dates.

We processed the data sets using the NICER calibration version CALDB XTI(20221001) and the *nicer2* tool within HEASoft version 6.31 (and NICERDAS version V010c). NICER’s X-ray Timing Instrument (XTI) consists of 56 X-ray modules. In our data processing with *nicer2*, we eliminated 6 modules (id = 11, 14, 20, 22, 34, 60) that were either inactive or noisy. We performed barycentric correction for each event file using *barycor*.

The XTI has a large collection area between 0.2 and 12 keV (approximately 1900 $cm^{-2}$ at 1.5 keV). We used *xselect* and *lcurve* to produce a light curve with a 2-minute time cadence and an energy band of 0.5–3 keV. As NICER is not an imaging instrument, there is some background contamination in the higher and lower energy bands. Thus, we chose 0.5–3 keV as a conservative energy range where the variation in background is relatively negligible.

We extracted the time-resolved X-ray spectra using *xselect*. The background files were created with *nibackgen3c50* (Remillard et al. 2022). We performed spectral model fitting with *xspec*. We will explain the details of the model in Section 3.4.

# 3. Analysis and Results

## 3.1. Light Curves

Figure 2 overviews the observed multiwavelength light curves of EK Dra. As shown in the figure, we have labeled the

superflares, targeted in this paper, as “E1” to “E3” (Table 2). We are targeting the events where there is an increase in Hα or X-ray that occurs simultaneously with the flares from TESS. Figures 3 to 5 show the enlarged light curves of flares E1 to E3. Flare E1 has shown the largest Hα emission increase (ΔEW of ~0.7 Å) ever reported for solar-type stars, and an increase has been confirmed in both Hα and white light (WL). Simultaneous observation data in X-rays do not exist for flare E1 due to the observation gap of the ISS, but data before and after the flare do exist also in X-ray. Flare E2 shows a simultaneous increase in Hα and WL, and an increase during its decay phase has been detected in X-ray. Furthermore, for Flare E3, an increase has been detected in Hα, WL, and X-rays altogether. We will describe the TESS data analyses and results in Section 3.2, Hα spectral analyses and results in Section 3.3, and X-ray, light-curve, and spectral analyses and results in Section 3.4.

## 3.2. TESS White-light Flare Analysis

We quantified the white-light flare (WLF) emission in the TESS band, following the procedures as taken in Namekata et al. (2022c) and Namekata et al. (2022d). The detection of flares first requires the removal of background rotational brightness variations. We removed them by using the fast Fourier transform ` numpy.fft.fft` and a low-pass filter with the cutoff frequency at 3.0 $day^{-1}$. The detrended light curves are shown in panels (a) of Figures 3, 4, and 5. This study did not perform an automatic flare detection, but simply identified the presence of significant WLFs in the TESS light curve, specifically those occurring simultaneously with Hα and X-ray flares. In this context, a “significant” flare refers to an event where more than two consecutive data points exceed the photometric error (approximately 100 ppm) as computed by *eleanor*. As noted in Section 3.1, we confirmed the presence of significant flare increases corresponding to each of the Hα and X-ray flares E1, E2, and E3, as in the vertical lines in panels (a) of Figures 3, 4, and 5, respectively. Throughout this paper, we define the first flare point in TESS light curve as the flare standard time (BJD-2459680.0329, 2459685.9980, 2459687.0119 for flares E1, E2, and E3, respectively).

The calculation of bolometric WL flare energy follows the conventional technique proposed by Shibayama et al. 2013. We assumed a 10,000 K blackbody radiation spectrum for the flares and computed the bolometric radiation energy. As a result, we derived the WLF energy ($E_{WL,bol}$) of flare E1 to be $1.5_{-0.1}^{+0.3}$ erg, flare E2 to be $1.22_{-0.02}^{+0.02}$ erg, and flare E3 to be $3.4_{-0.1}^{+0.1}$ erg; hence, all of these are classified as “superflares.” Namekata et al. 2022c reported that the largest energy scale of superflares on EK Dra is ~5 × $10^{34}$ erg, so these are relatively smaller than the upper limit. Also, we derived the FWHM duration ($\tau_{WL}$) and e-folding decay time of WLFs ($\tau_{WL}$). The e-folding decay times ($\tau_{WL}$) were obtained by fitting the decay phase of WLFs with an exponential function and `scipy.optimize.curve_fit`. These values are presented in Table 2.

To better constrain the white-light flare energy, we need to discuss the assumption of 10,000 K blackbody temperature. Most solar flare studies that employ spatially resolved data reported the emission temperature of 5,000–7,000 K (e.g., Watanabe et al. 2013; Kerr & Fletcher 2014; Kleint et al. 2016; Namekata et al. 2017b), while only Sun-as-a-star observations suggest the hotter temperature of the blackbody spectrum ~9000 K (Kretzschmar et al. 2010; Kretzschmar 2011). On the other hand, a historically well-known stellar superflare on an M-dwarf, AD Leonis, shows the broadband stellar spectra with the effective temperature of 9000–10,000 K (e.g., Hawley & Fisher 1992), and thus many

<footnote n="25">²⁵ Observations also took place on 2022 April 9 (ID: 5202490101) and 2022 April 19 (ID: 5202490111), but with exposure times of 9 and 0 s respectively, they were not included in our analysis.</footnote>

<footnote n="26">²⁶ https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3table.pl?tablehead=name%3Dnicermastr&Action=More+Options</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Examples of Hα spectra of EK Dra on 10 Apr 2022. A black solid line is the pre-flare template for flare E1, and a red dashed line is the flaring spectrum of flare E1.</figcaption></figure>

## 2.4. NICER

NICER is a soft X-ray instrument (0.2–12 keV) on board the ISS (Gendreau et al. 2016). NICER monitored EK Dra from 2022 April 10 to 2022 April 21 (Observation ID: 5202490102–5202490113).<fnref n="25" /> These observations were scheduled concurrently with those from the 3.8 m Seimei telescope and TESS. We downloaded the data from NASA’s website.<fnref n="26" /> The exposure time for each ISS orbit (about 90 minutes) varied from a few minutes to a few tens of minutes, depending on the dates.

We processed the data sets using the NICER calibration version CALDB XTI(20221001) and the *nicer2* tool within HEASoft version 6.31 (and NICERDAS version V010c). NICER’s X-ray Timing Instrument (XTI) consists of 56 X-ray modules. In our data processing with *nicer2*, we eliminated 6 modules (id = 11, 14, 20, 22, 34, 60) that were either inactive or noisy. We performed barycentric correction for each event file using *barycor*.

The XTI has a large collection area between 0.2 and 12 keV (approximately $1900 \text{ cm}^{-2}$ at 1.5 keV). We used *xselect* and *lcurve* to produce a light curve with a 2-minute time cadence and an energy band of 0.5–3 keV. As NICER is not an imaging instrument, there is some background contamination in the higher and lower energy bands. Thus, we chose 0.5–3 keV as a conservative energy range where the variation in background is relatively negligible.

We extracted the time-resolved X-ray spectra using *xselect*. The background files were created with *nibackgen3c50* (Remillard et al. 2022). We performed spectral model fitting with *xspec*. We will explain the details of the model in Section 3.4.

# 3. Analysis and Results

## 3.1. Light Curves

Figure 2 overviews the observed multiwavelength light curves of EK Dra. As shown in the figure, we have labeled the

superflares, targeted in this paper, as “E1” to “E3” (Table 2). We are targeting the events where there is an increase in Hα or X-ray that occurs simultaneously with the flares from TESS. Figures 3 to 5 show the enlarged light curves of flares E1 to E3. Flare E1 has shown the largest Hα emission increase (ΔEW of ~0.7 Å) ever reported for solar-type stars, and an increase has been confirmed in both Hα and white light (WL). Simultaneous observation data in X-rays do not exist for flare E1 due to the observation gap of the ISS, but data before and after the flare do exist also in X-ray. Flare E2 shows a simultaneous increase in Hα and WL, and an increase during its decay phase has been detected in X-ray. Furthermore, for Flare E3, an increase has been detected in Hα, WL, and X-rays altogether. We will describe the TESS data analyses and results in Section 3.2, Hα spectral analyses and results in Section 3.3, and X-ray, light-curve, and spectral analyses and results in Section 3.4.

## 3.2. TESS White-light Flare Analysis

We quantified the white-light flare (WLF) emission in the TESS band, following the procedures as taken in Namekata et al. (2022c) and Namekata et al. (2022d). The detection of flares first requires the removal of background rotational brightness variations. We removed them by using the fast Fourier transform ` numpy.fft.fft` and a low-pass filter with the cutoff frequency at 3.0 day⁻¹. The detrended light curves are shown in panels (a) of Figures 3, 4, and 5. This study did not perform an automatic flare detection, but simply identified the presence of significant WLFs in the TESS light curve, specifically those occurring simultaneously with Hα and X-ray flares. In this context, a “significant” flare refers to an event where more than two consecutive data points exceed the photometric error (approximately 100 ppm) as computed by *eleanor*. As noted in Section 3.1, we confirmed the presence of significant flare increases corresponding to each of the Hα and X-ray flares E1, E2, and E3, as in the vertical lines in panels (a) of Figures 3, 4, and 5, respectively. Throughout this paper, we define the first flare point in TESS light curve as the flare standard time (BJD-2459680.0329, 2459685.9980, 2459687.0119 for flares E1, E2, and E3, respectively).

The calculation of bolometric WL flare energy follows the conventional technique proposed by Shibayama et al. 2013. We assumed a 10,000 K blackbody radiation spectrum for the flares and computed the bolometric radiation energy. As a result, we derived the WLF energy ($E_{WL,bol}$) of flare E1 to be $1.5_{-0.1}^{+0.3}$ erg, flare E2 to be $1.22_{-0.02}^{+0.02}$ × 10³⁴ erg, and flare E3 to be $3.4_{-0.1}^{+0.1}$ × 10³³ erg; hence, all of these are classified as “superflares.” Namekata et al. 2022c reported that the largest energy scale of superflares on EK Dra is ~5 × 10³⁴ erg, so these are relatively smaller than the upper limit. Also, we derived the FWHM duration ($\tau_{WL}$) and e-folding decay time of WLFs ($\tau_{WL}$). The e-folding decay times ($\tau_{WL}$) were obtained by fitting the decay phase of WLFs with an exponential function and `scipy.optimize.curve_fit`. These values are presented in Table 2.

To better constrain the white-light flare energy, we need to discuss the assumption of 10,000 K blackbody temperature. Most solar flare studies that employ spatially resolved data reported the emission temperature of 5,000–7,000 K (e.g., Watanabe et al. 2013; Kerr & Fletcher 2014; Kleint et al. 2016; Namekata et al. 2017b), while only Sun-as-a-star observations suggest the hotter temperature of the blackbody spectrum ~9000 K (Kretzschmar et al. 2010; Kretzschmar 2011). On the other hand, a historically well-known stellar superflare on an M-dwarf, AD Leonis, shows the broadband stellar spectra with the effective temperature of 9000–10,000 K (e.g., Hawley & Fisher 1992), and thus many

<footnote n="25">²⁵ Observations also took place on 2022 April 9 (ID: 5202490101) and 2022 April 19 (ID: 5202490111), but with exposure times of 9 and 0 s respectively, they were not included in our analysis.</footnote>

<footnote n="26">²⁶ https://heasarc.gsfc.nasa.gov/db-perl/W3Browse/w3table.pl?tablehead=name%3Dnicermastr>Action=More+Options</footnote>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Overall light curves of EK Dra for (a) Hα EW, (b) TESS's optical white light, and (c) NICER's X-ray count rate (0.5–3 keV), taken from 2022 April 9 to 2022 April 21. Hα EW is calculated within the wavelength range of 6562.8 ± 10 Å. Note that a negative (or negative-direction) EW value corresponds to emission by definition. TESS's optical white-light fluxes are normalized to the average flux. The vertical dashed lines represent detected superflares, labeled as “E1,” “E2,” and “E3.”</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 3.** Light curves for the superflare observed on 2022 April 10 (E1). (a) The red line is pre-flare subtracted Hα equivalent width (ΔEW = − (EW-EW<sub>preflare</sub>)) with the grayed error bars. Note that positive ΔEW values correspond to emissions. The Hα EW is calculated within a range of 6562.8 ± 20 Å, which differs from the definition applied to flares E2 and E3 (i.e., 6562.8 ± 10 Å). (b) Background-subtracted TESS WL (=($F_{bkg}$/F<sub>av</sub>). (c) Soft X-ray count rate (0.5–3 keV). In panel (c), each ISS orbit on this day is labeled as block 1–6. (d) Hα ΔEW and WL, each normalized by their respective peak values. In each panel, the vertical dashed line marks the TESS flare onset time, and the horizontal dashed line depicts the basal level for each wavelength (Hα: median value of −80 to −20 minutes; soft X-ray: mean value of block 3).</figcaption></figure>

<table><caption>**Table 2**
The List of Superflares on EK Dra in This Study and Past Observations</caption><thead><tr><th></th><th>GOES</th><th>E<sub>X,bol</sub><br>(0.1–100 keV)<br>[10<sup>33</sup> erg]</th><th>E<sub>WL,bol</sub><br>[10<sup>33</sup> erg]</th><th>E<sub>Hα</sub><br>[10<sup>31</sup> erg]</th><th>t<sub>WL</sub><br>(FWHM)<br>(min)</th><th>τ<sub>WL</sub><br>(e-decay)<br>(min)</th><th>t<sub>Hα</sub><br>(FWHM)<br>(min)</th><th>Ref.</th></tr></thead><tbody><tr><td>2022 Apr 10 (E1)</td><td>...</td><td>...</td><td>1.5<sub>±0.1</sub></td><td>48.7<sub>±1.7</sub>(9.1<sub>±2.6</sub>)<sup>a</sup></td><td>20</td><td>18</td><td>48</td><td>(1)</td></tr><tr><td>2022 Apr 16 (E2)</td><td>X4000–5400<sup>b</sup></td><td>12.3<sup>+0.3</sup><sub>-0.5</sub>–16.7<sup>+0.4</sup><sub>-0.7</sub></td><td>12.2<sub>±0.2</sub></td><td>17.7<sub>±0.7</sub></td><td>40</td><td>20</td><td>54</td><td>(1)</td></tr><tr><td>2022 Apr 17 (E3)</td><td>X3200</td><td>1.14<sup>+0.06</sup><sub>-0.05</sub></td><td>3.4<sub>±0.1</sub></td><td>2.9<sub>±0.3</sub></td><td>30</td><td>9.6</td><td>23</td><td>(1)</td></tr><tr><td>2020 Apr 05 (E4)</td><td>...</td><td>...</td><td>2.0<sub>±0.1</sub></td><td>1.7<sub>±0.1</sub><sup>c</sup></td><td>6.0</td><td>5.4</td><td>7.8<sup>c</sup></td><td>(2)</td></tr><tr><td>2020 Mar 14 (E5)</td><td>...</td><td>...</td><td>26<sub>±3</sub></td><td>40<sub>±4</sub></td><td>130</td><td>26</td><td>130</td><td>(3)</td></tr></tbody></table>

Notes. “GOES” is the goes X-ray class. E<sub>X,bol</sub> is the bolometric X-ray flare energy in 0.1–100 keV. Note that the value of “GOES” and E<sub>X,bol</sub> are calibrated for the light-curve extrapolation. t<sub>WL</sub> and t<sub>Hα</sub> are the FWHM duration of the WL and Hα flare. τ<sub>WL</sub> is the e-folding decay time of the flare.

<sup>a</sup> The value in bracket is the radiation energy of the central component without the blueshifted component.

<sup>b</sup> The energy and flux values are already corrected for light-curve extrapolations.

<sup>c</sup> The flare emission on April 5 in Namekata et al. (2022d) is very short-lived, and its light curve is a combination of blueshift absorption and flaring emission, so the Hα flare duration is expected to be underestimated. References: (1) This study, (2) Namekata et al. (2022d), (3) Namekata et al. (2022c).
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Overall light curves of EK Dra for (a) Hα EW, (b) TESS's optical white light, and (c) NICER's X-ray count rate (0.5–3 keV), taken from 2022 April 9 to 2022 April 21. Hα EW is calculated within the wavelength range of 6562.8 ± 10 Å. Note that a negative (or negative-direction) EW value corresponds to emission by definition. TESS's optical white-light fluxes are normalized to the average flux. The vertical dashed lines represent detected superflares, labeled as “E1,” “E2,” and “E3.”</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 3.** Light curves for the superflare observed on 2022 April 10 (E1). (a) The red line is pre-flare subtracted Hα equivalent width (ΔEW = − (EW-EW<sub>preflare</sub>)) with the grayed error bars. Note that positive ΔEW values correspond to emissions. The Hα EW is calculated within a range of 6562.8 ± 20 Å, which differs from the definition applied to flares E2 and E3 (i.e., 6562.8 ± 10 Å). (b) Background-subtracted TESS WL (=($F_{bkg}$/F<sub>av</sub>). (c) Soft X-ray count rate (0.5–3 keV). In panel (c), each ISS orbit on this day is labeled as block 1–6. (d) Hα ΔEW and WL, each normalized by their respective peak values. In each panel, the vertical dashed line marks the TESS flare onset time, and the horizontal dashed line depicts the basal level for each wavelength (Hα: median value of −80 to −20 minutes; soft X-ray: mean value of block 3).</figcaption></figure>

<table><caption>**Table 2**
The List of Superflares on EK Dra in This Study and Past Observations</caption><thead><tr><th></th><th>GOES</th><th>E<sub>X,bol</sub><br>(0.1–100 keV)<br>[10<sup>33</sup> erg]</th><th>E<sub>WL,bol</sub><br>[10<sup>33</sup> erg]</th><th>E<sub>Hα</sub><br>[10<sup>31</sup> erg]</th><th>t<sub>WL</sub><br>(FWHM)<br>(min)</th><th>τ<sub>WL</sub><br>(e-decay)<br>(min)</th><th>t<sub>Hα</sub><br>(FWHM)<br>(min)</th><th>Ref.</th></tr></thead><tbody><tr><td>2022 Apr 10 (E1)</td><td>...</td><td>...</td><td>1.5<sub>±0.1</sub></td><td>48.7<sub>±1.7</sub>(9.1<sub>±2.6</sub>)<sup>a</sup></td><td>20</td><td>18</td><td>48</td><td>(1)</td></tr><tr><td>2022 Apr 16 (E2)</td><td>X4000–5400<sup>b</sup></td><td>12.3<sup>+0.3</sup><sub>-0.5</sub>–16.7<sup>+0.4</sup><sub>-0.7</sub></td><td>12.2<sub>±0.2</sub></td><td>17.7<sub>±0.7</sub></td><td>40</td><td>20</td><td>54</td><td>(1)</td></tr><tr><td>2022 Apr 17 (E3)</td><td>X3200</td><td>1.14<sup>+0.06</sup><sub>-0.05</sub></td><td>3.4<sub>±0.1</sub></td><td>2.9<sub>±0.3</sub></td><td>30</td><td>9.6</td><td>23</td><td>(1)</td></tr><tr><td>2020 Apr 05 (E4)</td><td>...</td><td>...</td><td>2.0<sub>±0.1</sub></td><td>1.7<sub>±0.1</sub><sup>c</sup></td><td>6.0</td><td>5.4</td><td>7.8<sup>c</sup></td><td>(2)</td></tr><tr><td>2020 Mar 14 (E5)</td><td>...</td><td>...</td><td>26<sub>±3</sub></td><td>40<sub>±4</sub></td><td>130</td><td>26</td><td>130</td><td>(3)</td></tr></tbody></table>

Notes. “GOES” is the goes X-ray class. E<sub>X,bol</sub> is the bolometric X-ray flare energy in 0.1–100 keV. Note that the value of “GOES” and E<sub>X,bol</sub> are calibrated for the light-curve extrapolation. t<sub>WL</sub> and t<sub>Hα</sub> are the FWHM duration of the WL and Hα flare. τ<sub>WL</sub> is the e-folding decay time of the flare.

<sup>a</sup> The value in bracket is the radiation energy of the central component without the blueshifted component.

<sup>b</sup> The energy and flux values are already corrected for light-curve extrapolations.

<sup>c</sup> The flare emission on April 5 in Namekata et al. (2022d) is very short-lived, and its light curve is a combination of blueshift absorption and flaring emission, so the Hα flare duration is expected to be underestimated. References: (1) This study, (2) Namekata et al. (2022d), (3) Namekata et al. (2022c).
<figure><img src="image_6.png" /><figcaption>**Figure 4.** The same as Figure 3, but for the superflare observed on 2022 April 16 (E2). In panel (a), the Hα EW is calculated within a range of 6562.8 ± 10 Å. Panel (d) displays Hα ΔEW, WL, and soft X-ray, each normalized by their respective peak values. The basal level of Hα ΔEW is a median value of −45 to −15 minutes, while the basal level of the soft X-ray is the mean value of block 2.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Figure 5.** The same as Figures 3 and 4, but for the superflare observed on 2022 April 17 (E3). The basal level of Hα EW is a median value of −25 to −5 minutes, while the basal level of soft X-ray is a mean value of block 1.</figcaption></figure>

stellar flare studies use this temperature as a template. A recent statistical survey shows that the flare temperatures vary depending on flare energies for M-dwarf flares (Howard et al. 2020). More recently, COROT's two-band photometric observations constrained the temperatures of G-dwarfs superflares as 3570–24,300 K (Rabello Soares et al. 2022). Hence, no unified model for radiation temperature of solar and stellar WLFs is currently available. Namekata et al. 2017b concluded that the uncertainty in the emission temperature does not largely affect the estimation of the WLF energy because the decrease in the temperature leads to the decrease in surface luminosity ($\propto T^4$) and the increase in emission area ($A \propto T^{-4}$), both of which are canceled by each other when using Equation (1) of Shibayama et al. (2013; i.e., $E = \sigma T^4 A$). Therefore, our assumption may provide an uncertainty of the flare energy by a factor of few. We need to perform multiband observations of superflares in U, B, V, and near-UV bands to derive better constraints on the flare energy (Brasseur et al. 2023).

## 3.3. Hα Flare Analysis

### 3.3.1. Overview of Hα Flare Spectra

Figures 6, 7, and 8 shows pre-flare subtracted Hα spectra of flares E1, E2, and E3. Each flare show different flare spectra as follows:

(E1) The flare E1 exhibits significant blueshifted emission profiles during the flare. During the impulsive phase of WLF, it does not demonstrate strong emission in the Hα line center and most of the radiation comes from the blueshifted component (see Section 3.3.3). Following the noticeable blueshift profiles, the blueshift wavelength gradually reverts to the Hα central wavelength, disappearing within approximately 34 minutes (see Section 3.3.2).

(E2) The superflare E2 primarily manifests emission in the Hα line center. However, the period spanning roughly 10 to 15 minutes from the TESS flare onset displays significant blueshifted emission profiles that exceed the 3σ noise level of the far-wing continuum.

(E3) The superflare E3 exhibits the weakest Hα EW enhancement and does not display any significant Hα line asymmetry.

### 3.3.2. Spectral Fitting

In regard to flares E1 and E2, which demonstrated explicit blueshift phenomena, we performed a spectral fit using Gaussian functions to derive the velocity, velocity dispersion, and EW of the blueshifted component. In this process, we conducted two types of fits based on whether or not to isolate and fit the central flare component. Method (1) simply fits the
<figure><img src="image_7.png" /><figcaption>**Figure 4.** The same as Figure 3, but for the superflare observed on 2022 April 16 (E2). In panel (a), the Hα EW is calculated within a range of 6562.8 ± 10 Å. Panel (d) displays Hα ΔEW, WL, and soft X-ray, each normalized by their respective peak values. The basal level of Hα ΔEW is a median value of −45 to −15 minutes, while the basal level of the soft X-ray is the mean value of block 2.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 5.** The same as Figures 3 and 4, but for the superflare observed on 2022 April 17 (E3). The basal level of Hα EW is a median value of −25 to −5 minutes, while the basal level of soft X-ray is a mean value of block 1.</figcaption></figure>

stellar flare studies use this temperature as a template. A recent statistical survey shows that the flare temperatures vary depending on flare energies for M-dwarf flares (Howard et al. 2020). More recently, COROT's two-band photometric observations constrained the temperatures of G-dwarfs superflares as 3570–24,300 K (Rabello Soares et al. 2022). Hence, no unified model for radiation temperature of solar and stellar WLFs is currently available. Namekata et al. 2017b concluded that the uncertainty in the emission temperature does not largely affect the estimation of the WLF energy because the decrease in the temperature leads to the decrease in surface luminosity ($\propto T^4$) and the increase in emission area ($A \propto T^{-4}$), both of which are canceled by each other when using Equation (1) of Shibayama et al. (2013; i.e., $E = \sigma T^4 A$). Therefore, our assumption may provide an uncertainty of the flare energy by a factor of few. We need to perform multiband observations of superflares in U, B, V, and near-UV bands to derive better constraints on the flare energy (Brasseur et al. 2023).

## 3.3. Hα Flare Analysis

### 3.3.1. Overview of Hα Flare Spectra

Figures 6, 7, and 8 shows pre-flare subtracted Hα spectra of flares E1, E2, and E3. Each flare show different flare spectra as follows:

(E1) The flare E1 exhibits significant blueshifted emission profiles during the flare. During the impulsive phase of WLF, it does not demonstrate strong emission in the Hα line center and most of the radiation comes from the blueshifted component (see Section 3.3.3). Following the noticeable blueshift profiles, the blueshift wavelength gradually reverts to the Hα central wavelength, disappearing within approximately 34 minutes (see Section 3.3.2).

(E2) The superflare E2 primarily manifests emission in the Hα line center. However, the period spanning roughly 10 to 15 minutes from the TESS flare onset displays significant blueshifted emission profiles that exceed the 3σ noise level of the far-wing continuum.

(E3) The superflare E3 exhibits the weakest Hα EW enhancement and does not display any significant Hα line asymmetry.

### 3.3.2. Spectral Fitting

In regard to flares E1 and E2, which demonstrated explicit blueshift phenomena, we performed a spectral fit using Gaussian functions to derive the velocity, velocity dispersion, and EW of the blueshifted component. In this process, we conducted two types of fits based on whether or not to isolate and fit the central flare component. Method (1) simply fits the
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Time evolution of pre-flare subtracted Hα spectra of the superflare observed on 2022 April 10 (E1). (a) Reference light curves in Hα ΔEW (scaled on the left vertical axis) and white light (scaled on the right vertical axis). (b) A dynamic spectrum of the pre-flare subtracted Hα spectrum, plotted on the time-wavelength plane. The red (blue) color represents emission (absorption) signals, with the upper part indicating shorter wavelengths (i.e., blueshift), following the unified format used in our series of papers (Namekata et al. 2022c; Namekata et al. 2022d). The color bar shows the nondimensional intensity, which is normalized by the continuum level. The dashed lines indicate the stellar surface gravity ($g_*$) and half of the surface gravity ($0.5 \cdot g_*$). (c) Time-binned, pre-flare subtracted Hα spectra during the superflare. Detailed spectra can be seen in Figure 9. The 1σ errors in the continuum level are plotted as error bars for reference.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>**Figure 7.** The same as Figure 6, but for the superflare on 2022 April 16 (E2).</figcaption></figure>

emission component with a single Gaussian function (referred to as “one component” fit). Method (2) first fits the central component by using the spectra only the longer wavelength of Hα line center (>6562.8 Å) with a Gaussian function to obtain the central Hα component. Following that, we subtracted this fit function from the original spectrum and then fitted the residual spectrum again with a Gaussian function, which we defined as the blueshifted component (referred to as “two components” fit). In both methods, we evaluated the errors on the y-axis based on the data scattering of the far-wing continuum level and performed the fitting using `scipy CURVE FITTING` `optimize.least_squares`. Method (2) has also been employed in studies such as Maehara et al. (2021) and Namizaki et al. (2023). We use a Gaussian function, which involves fewer

parameters than a Voigt function, because of the low signal-to-noise ratio (S/N) of our data. Figures 9 and 10 show the fitting results for the flares E1 and E2, respectively. The following is the summary of the obtained results of fitting:

(E1) For flare E1, we utilized both methods (1) and (2). This is because the profile seems to be totally blueshifted in its initial phase. Figure 9 displays the fitting results up to $t = 63$ minutes, where method 1 fits successfully. Regarding method (2), we show the fitting results up to $t = 25$ minutes, where the significant blueshifted component still remained after removing the central component. The maximum blueshifted velocity $V_{max}$, defined as $|\max\{V(t)\}|$, was 690$_{−}$$_{+}$$62$ km s$^{-1}$ at $t = -4.8$ minutes
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Time evolution of pre-flare subtracted Hα spectra of the superflare observed on 2022 April 10 (E1). (a) Reference light curves in Hα ΔEW (scaled on the left vertical axis) and white light (scaled on the right vertical axis). (b) A dynamic spectrum of the pre-flare subtracted Hα spectrum, plotted on the time-wavelength plane. The red (blue) color represents emission (absorption) signals, with the upper part indicating shorter wavelengths (i.e., blueshift), following the unified format used in our series of papers (Namekata et al. 2022c; Namekata et al. 2022d). The color bar shows the nondimensional intensity, which is normalized by the continuum level. The dashed lines indicate the stellar surface gravity ($g_*$) and half of the surface gravity ($0.5 \cdot g_*$). (c) Time-binned, pre-flare subtracted Hα spectra during the superflare. Detailed spectra can be seen in Figure 9. The 1σ errors in the continuum level are plotted as error bars for reference.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 7.** The same as Figure 6, but for the superflare on 2022 April 16 (E2).</figcaption></figure>

emission component with a single Gaussian function (referred to as “one component” fit). Method (2) first fits the central component by using the spectra only the longer wavelength of Hα line center (>6562.8 Å) with a Gaussian function to obtain the central Hα component. Following that, we subtracted this fit function from the original spectrum and then fitted the residual spectrum again with a Gaussian function, which we defined as the blueshifted component (referred to as “two components” fit). In both methods, we evaluated the errors on the y-axis based on the data scattering of the far-wing continuum level and performed the fitting using `scipyfit`. **optimize.least_squares.** Method (2) has also been employed in studies such as Maehara et al. (2021) and Namizaki et al. (2023). We use a Gaussian function, which involves fewer

parameters than a Voigt function, because of the low signal-to-noise ratio (S/N) of our data. Figures 9 and 10 show the fitting results for the flares E1 and E2, respectively. The following is the summary of the obtained results of fitting:

(E1) For flare E1, we utilized both methods (1) and (2). This is because the profile seems to be totally blueshifted in its initial phase. Figure 9 displays the fitting results up to $t = 63$ minutes, where method 1 fits successfully. Regarding method (2), we show the fitting results up to $t = 25$ minutes, where the significant blueshifted component still remained after removing the central component. The maximum blueshifted velocity $V_{max}$, defined as $|\max\{V(t)\}|$, was 690$_{−}$$_{+}$$62 \text{ km s}^{-1}$ at $t = -4.8$ minutes
<figure><img src="image_10.png" /><figcaption>Figure 8. The same as Figure 7, but for the superflare on 2022 April 10 (E3).</figcaption></figure>

for both methods. However, the period from $t = -9.3$ minutes to $-4.8$ minutes, where relatively high velocities are present, does not yet have a high signal compared to noise. We therefore sometimes describe the maximum velocity as $V_{max}=330_{-35}^{+69}_{-92}$ km s⁻¹ (one-component) and $490_{-33}^{+69}_{-93}$ km s⁻¹ (two-component) to include a conservative estimate (where the conservative value is the maximum velocity after $t > -2.5$ minutes).

(E2) For superflare E2, considering that the blueshifted component is clearly separated from the central component, we only applied method (2). The maximum velocity $V_{max}$ is $430_{-19}^{+1}$ km s⁻¹.

These values are summarized in Tables 3 and 4.

Figure 11 shows the temporal evolution of the EW, velocity, and velocity dispersion of the fitted parameters for the superflares E1 and E2. For flare E1, both results for one-component and two-component fitting are plotted. The flare E1 shows clear temporal decrease in the blueshifted EW, velocity, and velocity dispersion for both fitting results. The superflare E2 shows a weak decreasing trend of the blueshifted velocity, but no clear evolution for blueshifted EW and velocity dispersion.

Figure 12 shows the relation between velocity and velocity dispersion for blueshifted velocity of the flares E1 and E2. As a reference, the filament eruption event on EK Dra reported by Namekata et al. (2022d; “E4” events) is added in Figure 12. The superflare E2 and E4 show clear positive correlation between these two parameters.

Based on the temporal evolution of the blueshifted velocity, some basic values of blueshifted components are estimated and summarized in Tables 3 and 4. We estimated the typical blueshifted velocity $V_{typical}$ and velocity dispersion $V_{disp,typ}$ as follows: For flare E1, the values are estimated when the EWs of the blueshifted component are most prominent, while for flare E2, the values are estimated as a median value. The deceleration of the blueshifted components $-dV/dt (-A/τ)$ are obtained by fitting the time evolution of velocity with an exponential function=$Ae^{-(t-t_0)/τ}$. Also, the duration and

timing of the appearance of the blueshifted components are summarized in Table 4.

### 3.3.3. Estimation of Energy and Timescale

The Hα radiated energy is estimated from the light curve of ΔEW, whose emission is larger than one-fifth of the peak values. It is calculated by multiplying the enhanced Hα ΔEW by the continuum flux and integrating in time. The continuum flux of EK Dra around Hα is derived as $1.57$ W m⁻² nm⁻¹ at 1 au (Namekata et al. 2022d) from flux-calibrated EK Dra's spectrum and the stellar distance given by Gaia Data Release 2 (Lindegren et al. 2018). As a result, the Hα flare radiation energy was estimated as $4.9_{-0.2}^{+32}$ erg, $1.8_{-0.1}^{+0.1}$ × 10³² erg, and $2.9_{-0.3}^{+0.3}$ × 10³¹ erg for flares E1, E2, and E3, respectively (Table 2).

Note that the above radiation energies of the flares E1 and E2 include blueshifted components. For the flare E1, the radiation energy of the possible central component is estimated as $9.1 \times 10^{31}$ erg, which is only 19% of the total radiation energy, meaning that most of the radiation comes from the blueshifted component. Unlike the flare E1, for the flare E2, the radiation energy of the possible central component is estimated as $1.7 \times 10^{31}$ erg, which is 97% of the total radiation energy, meaning that most of the radiation comes from the central component.

The duration of the Hα flares are estimated as the one at FWHM of the smoothed flaring light curves of Hα ΔEW, summarized in Table 2. Note that most of the radiation of the flare E1 comes from the blueshifted component, so the duration of the flaring emission from footpoints or flare loops would be different from that obtained here.

## 3.4. X-Ray Flare Analysis

### 3.4.1. Spectral Fitting for X-Ray Spectra

For the flares E2 and E3, an increase in intensity was detected in NICER's X-ray data, simultaneously with TESS WL and Hα flares. We performed a spectral analysis on the
<figure><img src="image_11.png" /><figcaption>**Figure 8.** The same as Figure 7, but for the superflare on 2022 April 10 (E3).</figcaption></figure>

for both methods. However, the period from $t = -9.3$ minutes to $-4.8$ minutes, where relatively high velocities are present, does not yet have a high signal compared to noise. We therefore sometimes describe the maximum velocity as $V_{max}=330_{-35}^{+69}_{-92}$ km s⁻¹ (one-component) and $490_{-33}^{+69}_{-93}$ km s⁻¹ (two-component) to include a conservative estimate (where the conservative value is the maximum velocity after $t > -2.5$ minutes).

(E2) For superflare E2, considering that the blueshifted component is clearly separated from the central component, we only applied method (2). The maximum velocity $V_{max}$ is $430_{-19}^{+1}$ km s⁻¹.

These values are summarized in Tables 3 and 4.

Figure 11 shows the temporal evolution of the EW, velocity, and velocity dispersion of the fitted parameters for the superflares E1 and E2. For flare E1, both results for one-component and two-component fitting are plotted. The flare E1 shows clear temporal decrease in the blueshifted EW, velocity, and velocity dispersion for both fitting results. The superflare E2 shows a weak decreasing trend of the blueshifted velocity, but no clear evolution for blueshifted EW and velocity dispersion.

Figure 12 shows the relation between velocity and velocity dispersion for blueshifted velocity of the flares E1 and E2. As a reference, the filament eruption event on EK Dra reported by Namekata et al. (2022d; “E4” events) is added in Figure 12. The superflare E2 and E4 show clear positive correlation between these two parameters.

Based on the temporal evolution of the blueshifted velocity, some basic values of blueshifted components are estimated and summarized in Tables 3 and 4. We estimated the typical blueshifted velocity $V_{typical}$ and velocity dispersion $V_{disp,typ}$ as follows: For flare E1, the values are estimated when the EWs of the blueshifted component are most prominent, while for flare E2, the values are estimated as a median value. The deceleration of the blueshifted components $-dV/dt (-A/τ)$ are obtained by fitting the time evolution of velocity with an exponential function=$Ae^{-(t-t_0)/τ}$. Also, the duration and

timing of the appearance of the blueshifted components are summarized in Table 4.

### 3.3.3. Estimation of Energy and Timescale

The Hα radiated energy is estimated from the light curve of ΔEW, whose emission is larger than one-fifth of the peak values. It is calculated by multiplying the enhanced Hα ΔEW by the continuum flux and integrating in time. The continuum flux of EK Dra around Hα is derived as $1.57$ W m⁻² nm⁻¹ at 1 au (Namekata et al. 2022d) from flux-calibrated EK Dra's spectrum and the stellar distance given by Gaia Data Release 2 (Lindegren et al. 2018). As a result, the Hα flare radiation energy was estimated as $4.9_{-0.2}^{+32}$ erg, $1.8_{-0.1}^{+0.1}$ × 10³² erg, and $2.9_{-0.3}^{+0.3}$ × 10³¹ erg for flares E1, E2, and E3, respectively (Table 2).

Note that the above radiation energies of the flares E1 and E2 include blueshifted components. For the flare E1, the radiation energy of the possible central component is estimated as $9.1 \times 10^{31}$ erg, which is only 19% of the total radiation energy, meaning that most of the radiation comes from the blueshifted component. Unlike the flare E1, for the flare E2, the radiation energy of the possible central component is estimated as $1.7 \times 10^{31}$ erg, which is 97% of the total radiation energy, meaning that most of the radiation comes from the central component.

The duration of the Hα flares are estimated as the one at FWHM of the smoothed flaring light curves of Hα ΔEW, summarized in Table 2. Note that most of the radiation of the flare E1 comes from the blueshifted component, so the duration of the flaring emission from footpoints or flare loops would be different from that obtained here.

## 3.4. X-Ray Flare Analysis

### 3.4.1. Spectral Fitting for X-Ray Spectra

For the flares E2 and E3, an increase in intensity was detected in NICER's X-ray data, simultaneously with TESS WL and Hα flares. We performed a spectral analysis on the
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Temporal evolution of pre-flare-subtracted spectra during the superflare on 2022 April 10 (E1). Observations were carried out with an exposure time of 2 (or 1) minute(s) and a readout time of 17 s. The 1σ continuum-level scattering in each spectrum is represented by error bars. The blue line corresponds to the results of fitting with a single-component Gaussian, while the red and green lines denote the results of fitting with a two-component Gaussian. The fitting process was conducted using `scipyannya.least_squares`, taking into account the error bars.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Temporal evolution of pre-flare-subtracted spectra during the superflare on 2022 April 16 (E2). To improve the signal-to-noise ratio for fitting, the data have been binned into 5-minute intervals. The magenta and green lines represent the results of fitting with a two-component Gaussian, and the dashed lines correspond to the sum of the two Gaussians. Please see Figure 7 for the other spectra of flare E2 without significant blueshifted components.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure 9.** Temporal evolution of pre-flare-subtracted spectra during the superflare on 2022 April 10 (E1). Observations were carried out with an exposure time of 2 (or 1) minute(s) and a readout time of 17 s. The 1σ continuum-level scattering in each spectrum is represented by error bars. The blue line corresponds to the results of fitting with a single-component Gaussian, while the red and green lines denote the results of fitting with a two-component Gaussian. The fitting process was conducted using `scipyannya.least_squares`, taking into account the error bars.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 10.** Temporal evolution of pre-flare-subtracted spectra during the superflare on 2022 April 16 (E2). To improve the signal-to-noise ratio for fitting, the data have been binned into 5-minute intervals. The magenta and green lines represent the results of fitting with a two-component Gaussian, and the dashed lines correspond to the sum of the two Gaussians. Please see Figure 7 for the other spectra of flare E2 without significant blueshifted components.</figcaption></figure>
<table><caption>**Table 3**

Properties of the Prominence and Filament Eruptions on EK Dra</caption><thead><tr><th></th><th>Hα asymmetry</th><th>V<sub>max</sub><br>(km s<sup>-1</sup>)</th><th>V<sub>typical</sub><br>(km s<sup>-1</sup>)</th><th>V<sub>disp.typ</sub><br>(km s<sup>-1</sup>)</th><th>-dV/dt<br>[km s<sup>-2</sup>]</th><th>L<sub>Hα,blue</sub><br>[10<sup>28</sup> erg s<sup>-1</sup>]</th><th>M<sub>p</sub><br>[10<sup>18</sup> g]</th><th>E<sub>kin</sub><br>[10<sup>32</sup> erg]</th><th>Ref.</th></tr></thead><tbody><tr><td>2022 Apr 10 (E1)</td><td>Blue emission<br>(two comp.)<sup>a</sup></td><td>330-690<br>(490-690)</td><td>300<br>(390)</td><td>300<br>(230)</td><td>0.34<sup>±0.15</sup><br>(0.23<sup>±0.14</sup>)</td><td>16.6<sup>±1.7</sup><br>(9.8<sup>±1.3</sup>)</td><td>130<sup>+290</sup><sub>-90</sub><br>(-)</td><td>580<sup>+1280</sup><sub>-400</sub><br>(-)</td><td>(1)</td></tr><tr><td>2022 Apr 16 (E2)</td><td>Blue emission</td><td>430</td><td>380</td><td>55</td><td>0.12<sup>±0.20</sup></td><td>0.47<sup>±0.16</sup></td><td>1.7<sup>+3.7</sup><sub>-1.1</sub></td><td>12<sup>+27</sup><sub>-8</sub></td><td>(1)</td></tr><tr><td>2022 Apr 17 (E3)</td><td>No</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>(1)</td></tr><tr><td>2020 Apr 05 (E4)</td><td>Blue absorption</td><td>510</td><td>260</td><td>220</td><td>0.34<sup>±0.04</sup></td><td>...</td><td>1.1<sup>+4.2</sup><sub>-0.9</sub></td><td>3.5<sup>+14.0</sup><sub>-3.0</sub></td><td>(2)</td></tr><tr><td>2020 Mar 14 (E5)</td><td>No (Red?)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>(3)</td></tr></tbody></table>

**Note.** $V_{max}$ is the maximum blueshifted velocity ($\max(-V)$). $V_{typical}$ is the typical blueshifted velocity around when the EW takes a maximum value. $V_{typical}$ is the typical velocity dispersion ($\sigma$) in the fitted Gaussian function. $-dV/dt$ is the deceleration of the blueshifted component. EK Dra's surface gravity is $0.30_{-0.05}^{+0.05} \text{ km s}^{-2}$. $L_{H\alpha,blue}$ is the luminosity of the blueshifted component. $M_p$ is the mass of the erupted prominences/filament. $E_{kin}$ is the kinetic energy of the prominence/filament eruptions.

<sup>a</sup> The values in parentheses “()” are the values of the two-component fitting of the flare E1. References: (1) This study, (2) Namekata et al. (2022d), (3) Namekata et al. (2022c).

<table><caption>**Table 4**

Properties of the Prominence and Filament Eruptions (continued from Table 3) and the Possible X-Ray Dimming</caption><thead><tr><th></th><th>t<sub>WLF</sub><br>(min)</th><th>t<sub>blue</sub><br>(min)</th><th>Timing<sub>Blue asym.</sub></th><th>X-ray dimming</th><th>Timing<sub>X dim.</sub></th><th>t<sub>X dim.</sub><br>(min)</th><th>amp<sub>X dim.</sub><br>(%)</th><th>ΔEM<sub>X dim.</sub><br>(10<sup>51</sup> cm<sup>-3</sup>)</th><th>L<sub>X dim.</sub><br>(10<sup>10</sup> cm)</th></tr></thead><tbody><tr><td>(E1)</td><td>20<br>(-)</td><td>34<sub>±2</sub><br>(-)</td><td>~start of WLF<br>(-)</td><td>Yes?(block5,6)<br>(bkg subtracted)</td><td>133 minutes After WLF<br>(-)</td><td>&gt;91<br>(-)</td><td>5.8-8.5<br>8.8-14.7</td><td>(-)<br>7.2-12.7</td><td>(-)<br>0.90-5.0</td></tr><tr><td>(E2)</td><td>40</td><td>10<sub>±5</sub><br>...</td><td>~peak of WLF<br>No</td><td>No</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(E3)</td><td>30</td><td>...</td><td>...</td><td>No</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(E4)</td><td>6.0</td><td>58-86</td><td>~end of WLF<br>(No obs.)</td><td>(No obs.)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(E5)</td><td>130</td><td>...</td><td>...</td><td>(No obs.)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

**Note.** $t_{WLF}$ is the FWHM duration of WLFs as a reference. $t_{blue}$ is the duration of blueshifted components. For E1, the duration from $t = -7.1$ minutes to $t = 25.0$ minutes. For E2, the duration from $t = 15 \pm 2.5$ minutes to $t = 25 \pm 2.5$ minutes. For E3, the lower limit is the duration where the velocity $< 0 \text{ km s}^{-1}$, and the upper limit is the duration where the velocity is $< -100 \text{ km s}^{-1}$. “Timing<sub>Blue Asym.</sub>” is the timing when the blueshift components appear relative to WLFs. “Timing<sub>X dim.</sub>” is the timing when the possible X-ray dimming appears relative to WLFs. $t_{X dim.}$ is the duration of the possible X-ray dimming. $amp_{X dim.}$ is the X-ray dimming amplitude for the X-ray count rates (0.5–3 keV). The value in parentheses “()” is the dimming amplitude for the background-subtracted X-ray count rates. $\Delta EM_{X dim.}$ is the change of emission measure due to the possible X-ray dimming. $L_{X dim.}$ is the length scale of the possible X-ray dimming region.

increased intensity during the flares using an emission spectrum from collisionally ionized diffuse gas calculated from the AtomDB atomic database (apec)<sup>27</sup> and the Tuebingen-Boulder ISM absorption model (TBAbs)<sup>28</sup> in xspec. First, we defined the data from the ISS orbit prior to the flares as “pre-flare orbits” (block 2 for flare E2 in Figure 4(c), block 3 for flare E3 in Figure 5(c)) and carried out a spectral fit of the pre-flare spectra. The objective is to remove the pre-flare component from the flare component, thus we utilized as many as four apec models and TBAbs. Three apec models did not adequately reproduce the overall spectral shape. Only the ISM hydrogen column density $N_H$ is fixed as $3 \times 10^{18} \text{ cm}^{-2}$ based on the previous study (Güdel et al. 1995) because it is too small to consistently determine for each frame. Linsky et al. (2022) reported a similar $N_H$ value of $1.7 \times 10^{18} \text{ cm}^{-2}$. In each case, the $N_H$ value is so small that the factor 2 difference does not significantly affect the fitting results. The fitted spectra are presented in Figures 13(a) and 14(a), while the parameters are summarized in Table 5. The error bars are obtained as a result of the xspec fitting.

We fixed the parameters of the obtained pre-flare spectrum and added a new apec model to perform a spectral fit of the

flare component. The flare duration was divided into either two or five segments (named “block”). Initially, a 1-sec-cadence light curve was created in 0.5–3 keV. Based on this, time bins were generated to divide the total count value of the orbit during the flare by half or into fifths. For flare E2 (or E3), the two segmented bins are labeled as blocks 2A–2B (or blocks 3A–3B for flare E3) and the five segmented bins are labeled as blocks 2a–2e (or blocks 3a–3e for flare E3). See Figure 15 for more details of the time bins. A spectral fit was conducted for all these bins. We estimated temperature (T) and emission measure (EM) as free parameters. The coronal abundance was fixed as the pre-flare values because it was not determined consistently when it was set as a free parameter. The results of the spectral fits are summarized in Figures 13 and 14, while the fitting parameters are compiled in Table 6. The time-resolved temperature (T) and emission measure (EM) are plotted in Figure 15. Because the procedure “nicerarf” does not work for the barycentric corrected event data, the above spectral fit was performed for non-barycentric-corrected event data. After the spectral analysis, we corrected the times for a barycentric correction.

The flare radiation fluxes and energies are estimated in the energy band of 0.5–3 keV (an observed band), 0.1–100 keV (referred to as a “bolometric X-ray” in this study; Kawai et al. 2022), 0.5–7.9 keV (Guarcello et al. 2019), 0.2–12 keV

<footnote n="27"><sup>27</sup> https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node134.html</footnote>

<footnote n="28"><sup>28</sup> https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node268.html</footnote>
<table><caption>**Table 3**
Properties of the Prominence and Filament Eruptions on EK Dra</caption><thead><tr><th></th><th>Hα asymmetry</th><th>V<sub>max</sub><br>(km s<sup>-1</sup>)</th><th>V<sub>typical</sub><br>(km s<sup>-1</sup>)</th><th>V<sub>disp.typ</sub><br>(km s<sup>-1</sup>)</th><th>-dV/dt<br>[km s<sup>-2</sup>]</th><th>L<sub>Hα,blue</sub><br>[10<sup>28</sup> erg s<sup>-1</sup>]</th><th>M<sub>p</sub><br>[10<sup>18</sup> g]</th><th>E<sub>kin</sub><br>[10<sup>32</sup> erg]</th><th>Ref.</th></tr></thead><tbody><tr><td>2022 Apr 10 (E1)</td><td>Blue emission<br>(two comp.)<sup>a</sup></td><td>330-690<br>(490-690)</td><td>300<br>(390)</td><td>300<br>(230)</td><td>0.34<sup>±0.15</sup><br>(0.23<sup>±0.14</sup>)</td><td>16.6<sup>±1.7</sup><br>(9.8<sup>±1.3</sup>)</td><td>130<sup>+290</sup><sub>-90</sub><br>(-)</td><td>580<sup>+1280</sup><sub>-400</sub><br>(-)</td><td>(1)</td></tr><tr><td>2022 Apr 16 (E2)</td><td>Blue emission</td><td>430</td><td>380</td><td>55</td><td>0.12<sup>±0.20</sup></td><td>0.47<sup>±0.16</sup></td><td>1.7<sup>+3.7</sup><sub>-1.1</sub></td><td>12<sup>+27</sup><sub>-8</sub></td><td>(1)</td></tr><tr><td>2022 Apr 17 (E3)</td><td>No</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>(1)</td></tr><tr><td>2020 Apr 05 (E4)</td><td>Blue absorption</td><td>510</td><td>260</td><td>220</td><td>0.34<sup>±0.04</sup></td><td>...</td><td>1.1<sup>+4.2</sup><sub>-0.9</sub></td><td>3.5<sup>+14.0</sup><sub>-3.0</sub></td><td>(2)</td></tr><tr><td>2020 Mar 14 (E5)</td><td>No (Red?)</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>(3)</td></tr></tbody></table>

**Note.** $V_{max}$ is the maximum blueshifted velocity (max($-V$)). $V_{typical}$ is the typical blueshifted velocity around when the EW takes a maximum value. $V_{typical}$ is the typical velocity dispersion ($\sigma$) in the fitted Gaussian function. $-dV/dt$ is the deceleration of the blueshifted component. EK Dra's surface gravity is $0.30_{-0.05}^{+0.05} \text{ km s}^{-2}$. $L_{H\alpha,blue}$ is the luminosity of the blueshifted component. $M_p$ is the mass of the erupted prominences/filament. $E_{kin}$ is the kinetic energy of the prominence/filament eruptions.

<sup>a</sup> The values in parentheses “()” are the values of the two-component fitting of the flare E1. References: (1) This study, (2) Namekata et al. (2022d), (3) Namekata et al. (2022c).

<table><caption>**Table 4**
Properties of the Prominence and Filament Eruptions (continued from Table 3) and the Possible X-Ray Dimming</caption><thead><tr><th></th><th>t<sub>WLF</sub><br>(min)</th><th>t<sub>blue</sub><br>(min)</th><th>Timing<sub>Blue asym.</sub></th><th>X-ray dimming</th><th>Timing<sub>X dim.</sub></th><th>t<sub>X dim.</sub><br>(min)</th><th>amp<sub>X dim.</sub><br>(%)</th><th>ΔEM<sub>X dim.</sub><br>(10<sup>51</sup> cm<sup>-3</sup>)</th><th>L<sub>X dim.</sub><br>(10<sup>10</sup> cm)</th></tr></thead><tbody><tr><td>(E1)</td><td>20<br>(-)</td><td>34<sub>±2</sub><br>(-)</td><td>~start of WLF<br>(-)</td><td>Yes?(block5,6)<br>(bkg subtracted)</td><td>133 minutes After WLF<br>(-)</td><td>&gt;91<br>(-)</td><td>5.8-8.5<br>8.8-14.7</td><td>(-)<br>7.2-12.7</td><td>(-)<br>0.90-5.0</td></tr><tr><td>(E2)</td><td>40</td><td>10<sub>±5</sub><br>...</td><td>~peak of WLF<br>No</td><td>No</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(E3)</td><td>30</td><td>...</td><td>...</td><td>No</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(E4)</td><td>6.0</td><td>58-86</td><td>~end of WLF<br>(No obs.)</td><td>No obs.</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(E5)</td><td>130</td><td>...</td><td>...</td><td>No obs.</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

**Note.** $t_{WLF}$ is the FWHM duration of WLFs as a reference. $t_{blue}$ is the duration of blueshifted components. For E1, the duration from $t = -7.1$ minutes to $t = 25.0$ minutes. For E2, the duration from $t = 15 \pm 2.5$ minutes to $t = 25 \pm 2.5$ minutes. For E3, the lower limit is the duration where the velocity $< 0 \text{ km s}^{-1}$, and the upper limit is the duration where the velocity is $< -100 \text{ km s}^{-1}$. “Timing<sub>Blue Asym.</sub>” is the timing when the blueshift components appear relative to WLFs. “Timing<sub>X dim.</sub>” is the timing when the possible X-ray dimming appears relative to WLFs. $t_{X dim.}$ is the duration of the possible X-ray dimming. $amp_{X dim.}$ is the X-ray dimming amplitude for the X-ray count rates (0.5–3 keV). The value in parentheses “()” is the dimming amplitude for the background-subtracted X-ray count rates. $\Delta EM_{X dim.}$ is the change of emission measure due to the possible X-ray dimming. $L_{X dim.}$ is the length scale of the possible X-ray dimming region.

increased intensity during the flares using an emission spectrum from collisionally ionized diffuse gas calculated from the AtomDB atomic database (apec)<sup>27</sup> and the Tuebingen-Boulder ISM absorption model (TBAbs)<sup>28</sup> in xspec. First, we defined the data from the ISS orbit prior to the flares as “pre-flare orbits” (block 2 for flare E2 in Figure 4(c), block 3 for flare E3 in Figure 5(c)) and carried out a spectral fit of the pre-flare spectra. The objective is to remove the pre-flare component from the flare component, thus we utilized as many as four apec models and TBAbs. Three apec models did not adequately reproduce the overall spectral shape. Only the ISM hydrogen column density $N_H$ is fixed as $3 \times 10^{18} \text{ cm}^{-2}$ based on the previous study (Güdel et al. 1995) because it is too small to consistently determine for each frame. Linsky et al. (2022) reported a similar $N_H$ value of $1.7 \times 10^{18} \text{ cm}^{-2}$. In each case, the $N_H$ value is so small that the factor 2 difference does not significantly affect the fitting results. The fitted spectra are presented in Figures 13(a) and 14(a), while the parameters are summarized in Table 5. The error bars are obtained as a result of the xspec fitting.

We fixed the parameters of the obtained pre-flare spectrum and added a new apec model to perform a spectral fit of the

flare component. The flare duration was divided into either two or five segments (named “block”). Initially, a 1-sec-cadence light curve was created in 0.5–3 keV. Based on this, time bins were generated to divide the total count value of the orbit during the flare by half or into fifths. For flare E2 (or E3), the two segmented bins are labeled as blocks 2A–2B (or blocks 3A–3B for flare E3) and the five segmented bins are labeled as blocks 2a–2e (or blocks 3a–3e for flare E3). See Figure 15 for more details of the time bins. A spectral fit was conducted for all these bins. We estimated temperature (T) and emission measure (EM) as free parameters. The coronal abundance was fixed as the pre-flare values because it was not determined consistently when it was set as a free parameter. The results of the spectral fits are summarized in Figures 13 and 14, while the fitting parameters are compiled in Table 6. The time-resolved temperature (T) and emission measure (EM) are plotted in Figure 15. Because the procedure “nicerarf” does not work for the barycentric corrected event data, the above spectral fit was performed for non-barycentric-corrected event data. After the spectral analysis, we corrected the times for a barycentric correction.

The flare radiation fluxes and energies are estimated in the energy band of 0.5–3 keV (an observed band), 0.1–100 keV (referred to as a “bolometric X-ray” in this study; Kawai et al. 2022), 0.5–7.9 keV (Guarcello et al. 2019), 0.2–12 keV

<footnote n="27"><sup>27</sup> https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node134.html</footnote>

<footnote n="28"><sup>28</sup> https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/node268.html</footnote>
<figure><img src="image_13.png" /><figcaption>**Figure 11.** Temporal evolution of the blueshifted emission line components for (upper) flare E1 on 2022 April 10 and (lower) superlare E2 on 2022 April 16. Left: Temporal variation in EW (note that positive values mean emissions); middle: temporal variation in velocity; right: temporal variation in velocity dispersion (Gaussian's standard deviation σ). The blue squares represent the result of fitting with a one-component Gaussian, while the red and green lines represent the blueshifted component and the central component, respectively, from the two-component Gaussian fit.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Figure 12.** Relationship between the velocity and velocity dispersion of the blueshifted component. The data for E1 and E2 are from Figure 11. The filament eruption (blueshifted absorptions) on EK Dra on 2020 April 5 (labeled as "E4") was taken from Namekata et al. (2022d; labeled as "N22a").</figcaption></figure>

(Kuznetsov & Kolotkov 2021; Stelzer et al. 2022), and 1.55–12.4 keV (=$1–8$ Å, GOES band, Stelzer et al. 2022) by using *flux* command in *xspec*. We calculated the flare energies in these different bands to compare with previous studies. Table 7 shows the peak X-ray flux and total X-ray energy in each band.

### 3.4.2. *Light-curve Fitting*

NICER's orbit did not cover the total flare evolution enough, so we have extrapolated the light curve by fitting the

decay phase with exponential function and fitting the rise phase with linear function (see Figure 16). The rise time and decay time are summarized in Table 7. For flare E2, the flare rise phase was not observed, so the rise timescale is just an upper limit. By assuming that the flare peak time is 0 minutes or 10 minutes later than the peak time of the TESS's WLF, we extrapolated the possible peak X-ray flux. As a result of the extrapolation, the X-ray peak of flare E2 is possibly higher by a factor of 4.2–5.7 than the observed peak. The X-ray energy of flare E2 is possibly higher by a factor of 2.7–3.2 than the energy calculated from the observed light curve. In this study, we use the possible X-ray flare peak value of flare E2 as the flux when the flare peak time is 10 minutes later than the peak time of TESS's WLF. For flare E3, we did not perform any extrapolation for the flux and energy because most of the flare evolution was covered by the one NICER orbit.

## 4. Time Evolution, Energetics, and Length Scales of Superflares

### 4.1. *Time Evolution of Optical and X-Ray Flares*

Here we discuss the time evolution of flaring emissions in multiwavelength, particularly focusing on flare E3. Figures 5 reveals that the rise of the soft X-rays appears to be clearly delayed in comparison to the white-light and $H\alpha$ emissions. We used the method employed by Mitra-Kraev et al. (2005; later, Tristan et al. 2023) to estimate the most likely delay time of soft X-ray flare $L_X(t)$ and time-derivative soft X-ray $dL_X(t)/dt$ (>0). Figure 17 shows the cross-correlation coefficient as a function of time lags. The time lags of maximum of the Pearson's correlation coefficients, $r_{max}$, is defined as the most likely value. The time delay of X-ray against $H\alpha$ is
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Temporal evolution of the blueshifted emission line components for (upper) flare E1 on 2022 April 10 and (lower) superlare E2 on 2022 April 16. Left: Temporal variation in EW (note that positive values mean emissions); middle: temporal variation in velocity; right: temporal variation in velocity dispersion (Gaussian's standard deviation σ). The blue squares represent the result of fitting with a one-component Gaussian, while the red and green lines represent the blueshifted component and the central component, respectively, from the two-component Gaussian fit.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Figure 12.** Relationship between the velocity and velocity dispersion of the blueshifted component. The data for E1 and E2 are from Figure 11. The filament eruption (blueshifted absorptions) on EK Dra on 2020 April 5 (labeled as "E4") was taken from Namekata et al. (2022d; labeled as "N22a").</figcaption></figure>

(Kuznetsov & Kolotkov 2021; Stelzer et al. 2022), and 1.55–12.4 keV (=$1–8$ Å, GOES band, Stelzer et al. 2022) by using *flux* command in *xspec*. We calculated the flare energies in these different bands to compare with previous studies. Table 7 shows the peak X-ray flux and total X-ray energy in each band.

### 3.4.2. *Light-curve Fitting*

NICER's orbit did not cover the total flare evolution enough, so we have extrapolated the light curve by fitting the

decay phase with exponential function and fitting the rise phase with linear function (see Figure 16). The rise time and decay time are summarized in Table 7. For flare E2, the flare rise phase was not observed, so the rise timescale is just an upper limit. By assuming that the flare peak time is 0 minutes or 10 minutes later than the peak time of the TESS's WLF, we extrapolated the possible peak X-ray flux. As a result of the extrapolation, the X-ray peak of flare E2 is possibly higher by a factor of 4.2–5.7 than the observed peak. The X-ray energy of flare E2 is possibly higher by a factor of 2.7–3.2 than the energy calculated from the observed light curve. In this study, we use the possible X-ray flare peak value of flare E2 as the flux when the flare peak time is 10 minutes later than the peak time of TESS's WLF. For flare E3, we did not perform any extrapolation for the flux and energy because most of the flare evolution was covered by the one NICER orbit.

## 4. Time Evolution, Energetics, and Length Scales of Superflares

### 4.1. *Time Evolution of Optical and X-Ray Flares*

Here we discuss the time evolution of flaring emissions in multiwavelength, particularly focusing on flare E3. Figures 5 reveals that the rise of the soft X-rays appears to be clearly delayed in comparison to the white-light and $H\alpha$ emissions. We used the method employed by Mitra-Kraev et al. (2005; later, Tristan et al. 2023) to estimate the most likely delay time of soft X-ray flare $L_X(t)$ and time-derivative soft X-ray $dL_X(t)/dt$ (>0). Figure 17 shows the cross-correlation coefficient as a function of time lags. The time lags of maximum of the Pearson's correlation coefficients, $r_{max}$, is defined as the most likely value. The time delay of X-ray against $H\alpha$ is
<figure><img src="image_15.png" /><figcaption>**Figure 13.** NICER X-ray spectrum of the superflare on 2022 April 16 (E2) and the corresponding fitting results (applied to the range of 0.3–8.0 keV). (a) Fitting results for the pre-flare spectrum of block 2 of E2, fitted with four *SPEC* components (each represented by a black line). The blue line represents the total model spectrum, which is used as the pre-flare spectrum in panels (b) through (f). (b–f) Observed and model spectra when flare block 3 is divided into blocks 3a through 3e. Refer to Figure 15 for the division times and Tables 5 and 6 for the fitting parameters.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Figure 14.** The same as Figure 13, but for the superflare on 2022 April 17 (E3).</figcaption></figure>

6+3/2 minutes, and the time delay of X-ray against WL is
7+3/2 minutes. The error bar is obtained the same way as Tristan
et al. (2023). Also, we calculated the time-derivative soft X-ray
light curve, as a good proxy of the nonthermal radiation
(dL<sub>X</sub>/dt, Veronig et al. 2002). The time delay of time-
derivative X-ray against Hα is -3+1/2 minutes, and the time
delay of differential X-ray against WL is -3+2/4 minutes. The

time-derivative soft X-ray light curve (dL<sub>X</sub>/dt) shows an
increase almost simultaneous with the WL and Hα, with an
overall delay of a few minutes for the entire light curve, but
peaking at nearly the same time.

The close correspondence between the impulsive phase of WL
and Hα with the time-derivative X-ray light curve may be an
indication of the Neupert effect (Neupert 1968; Tristan et al. 2023).
<figure><img src="image_16.png" /><figcaption>**Figure 13.** NICER X-ray spectrum of the superflare on 2022 April 16 (E2) and the corresponding fitting results (applied to the range of 0.3–8.0 keV). (a) Fitting results for the pre-flare spectrum of block 2 of E2, fitted with four *SPEC* components (each represented by a black line). The blue line represents the total model spectrum, which is used as the pre-flare spectrum in panels (b) through (f). (b–f) Observed and model spectra when flare block 3 is divided into blocks 3a through 3e. Refer to Figure 15 for the division times and Tables 5 and 6 for the fitting parameters.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 14.** The same as Figure 13, but for the superflare on 2022 April 17 (E3).</figcaption></figure>

6+3/2 minutes, and the time delay of X-ray against WL is
7+3/2 minutes. The error bar is obtained the same way as Tristan
et al. (2023). Also, we calculated the time-derivative soft X-ray
light curve, as a good proxy of the nonthermal radiation
(dL<sub>X</sub>/dt, Veronig et al. 2002). The time delay of time-
derivative X-ray against Hα is -3+1/2 minutes, and the time
delay of differential X-ray against WL is -3+2/4 minutes. The

time-derivative soft X-ray light curve (dL<sub>X</sub>/dt) shows an
increase almost simultaneous with the WL and Hα, with an
overall delay of a few minutes for the entire light curve, but
peaking at nearly the same time.

The close correspondence between the impulsive phase of WL
and Hα with the time-derivative X-ray light curve may be an
indication of the Neupert effect (Neupert 1968; Tristan et al. 2023).
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 15.** Temporal evolution of the X-ray spectral fitting results for superflares E2 (A) and E3 (B). (a) Light curves of X-ray count rates with a time resolution of 2 minutes in the 0.5–3 keV range. (b) Hardness ratio, which is obtained by dividing the flux in the 0.5–1 keV range by the flux in the 1–3 keV range. (c) Temporal change in temperature, with different colors indicating different time resolutions. (d) Temporal change in the emission measure (EM).</figcaption></figure>

<table><caption>**Table 5**
Best-fit Values of the Pre-flare NICER X-Ray Spectra for E2 and E3</caption><thead><tr><th rowspan="2">Component</th><th colspan="4">Flare E2 (block 2)</th><th colspan="4">Flare E3 (block 1)</th></tr><tr><th>T (keV)</th><th>(T [10<sup>7</sup> K])</th><th>EM (10<sup>52</sup> cm<sup>-3</sup>)</th><th>Abund.</th><th>T (keV)</th><th>(T [10<sup>7</sup> K])</th><th>EM (10<sup>52</sup> cm<sup>-3</sup>)</th><th>Abund.</th></tr></thead><tbody><tr><td>1</td><td>2.06<sub>&plusmn;0.53</sub></td><td>(2.39<sub>&plusmn;0.62</sub>)</td><td>1.58<sub>&plusmn;0.52</sub></td><td>0.28<sub>&plusmn;0.04</sub></td><td>2.77<sub>&plusmn;0.62</sub></td><td>(3.21<sub>&plusmn;0.71</sub>)</td><td>2.12<sub>&plusmn;0.38</sub></td><td>0.38<sub>&plusmn;0.06</sub></td></tr><tr><td>2</td><td>0.94<sub>&plusmn;0.02</sub></td><td>(1.09<sub>&plusmn;0.03</sub>)</td><td>5.28<sub>&plusmn;0.74</sub></td><td>...</td><td>0.96<sub>&plusmn;0.04</sub></td><td>(1.11<sub>&plusmn;0.05</sub>)</td><td>3.30<sub>&plusmn;0.42</sub></td><td>...</td></tr><tr><td>3</td><td>0.40<sub>&plusmn;0.08</sub></td><td>(0.47<sub>&plusmn;0.09</sub>)</td><td>2.63<sub>&plusmn;0.77</sub></td><td>...</td><td>0.50<sub>&plusmn;0.09</sub></td><td>(0.58<sub>&plusmn;0.10</sub>)</td><td>1.94<sub>&plusmn;0.33</sub></td><td>...</td></tr><tr><td>4</td><td>0.19<sub>&plusmn;0.38</sub></td><td>(0.22<sub>&plusmn;0.44</sub>)</td><td>0.18<sub>&plusmn;0.62</sub></td><td>...</td><td>0.17<sub>&plusmn;0.03</sub></td><td>(0.20<sub>&plusmn;0.04</sub>)</td><td>0.99<sub>&plusmn;0.15</sub></td><td>...</td></tr><tr><td>&chi;<sup>2</sup>(dof)</td><td colspan="4">184(168)</td><td colspan="4">190(177)</td></tr><tr><td>reduced &chi;<sup>2</sup></td><td colspan="4">1.10</td><td colspan="4">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 theoretical Neupert effect is usually expressed as a delay of soft X-rays (thermal emission) against hard X-rays (nonthermal radiation; see Veronig et al. 2002), which is the evidence of the heating by nonthermal electrons followed by the chromospheric evaporation increasing the coronal density of the flaring loops (Shibata & Magara 2011). Because the WL emissions (and some of the $H\alpha$ emissions) are known to be a good proxy of hard X-ray emission in the Sun (Krucker et al. 2011; Namekata et al. 2017b),

the time delay of soft X-ray against WL (and possibly $H\alpha$) for flare E3 is interpreted as the “empirical” Neupert effect (e.g., Tristan et al. 2023). This interpretation suggests that flare E3 occurs through the same physical mechanism as solar flares (the same conclusion has been obtained for M-dwarf flares; Hawley et al. 1995; Tristan et al. 2023). Pillitteri et al. (2022) found a clear signature of the “empirical” Neupert effect in 200–300 nm near-UV band and soft X-ray relation for superflares on a young
<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>**Figure 15.** Temporal evolution of the X-ray spectral fitting results for superflares E2 (A) and E3 (B). (a) Light curves of X-ray count rates with a time resolution of 2 minutes in the 0.5–3 keV range. (b) Hardness ratio, which is obtained by dividing the flux in the 0.5–1 keV range by the flux in the 1–3 keV range. (c) Temporal change in temperature, with different colors indicating different time resolutions. (d) Temporal change in the emission measure (EM).</figcaption></figure>

<table><caption>**Table 5**
Best-fit Values of the Pre-flare NICER X-Ray Spectra for E2 and E3</caption><thead><tr><th rowspan="2">Component</th><th colspan="4">Flare E2 (block 2)</th><th colspan="4">Flare E3 (block 1)</th></tr><tr><th>T (keV)</th><th>(T [10<sup>7</sup> K])</th><th>EM (10<sup>52</sup> cm<sup>-3</sup>)</th><th>Abund.</th><th>T (keV)</th><th>(T [10<sup>7</sup> K])</th><th>EM (10<sup>52</sup> cm<sup>-3</sup>)</th><th>Abund.</th></tr></thead><tbody><tr><td>1</td><td>2.06<sub>&plusmn;0.53</sub></td><td>(2.39<sub>&plusmn;0.62</sub>)</td><td>1.58<sub>&plusmn;0.52</sub></td><td>0.28<sub>&plusmn;0.04</sub></td><td>2.77<sub>&plusmn;0.62</sub></td><td>(3.21<sub>&plusmn;0.71</sub>)</td><td>2.12<sub>&plusmn;0.38</sub></td><td>0.38<sub>&plusmn;0.06</sub></td></tr><tr><td>2</td><td>0.94<sub>&plusmn;0.02</sub></td><td>(1.09<sub>&plusmn;0.03</sub>)</td><td>5.28<sub>&plusmn;0.74</sub></td><td>...</td><td>0.96<sub>&plusmn;0.04</sub></td><td>(1.11<sub>&plusmn;0.05</sub>)</td><td>3.30<sub>&plusmn;0.42</sub></td><td>...</td></tr><tr><td>3</td><td>0.40<sub>&plusmn;0.08</sub></td><td>(0.47<sub>&plusmn;0.09</sub>)</td><td>2.63<sub>&plusmn;0.77</sub></td><td>...</td><td>0.50<sub>&plusmn;0.09</sub></td><td>(0.58<sub>&plusmn;0.10</sub>)</td><td>1.94<sub>&plusmn;0.33</sub></td><td>...</td></tr><tr><td>4</td><td>0.19<sub>&plusmn;0.38</sub></td><td>(0.22<sub>&plusmn;0.44</sub>)</td><td>0.18<sub>&plusmn;0.62</sub></td><td>...</td><td>0.17<sub>&plusmn;0.03</sub></td><td>(0.20<sub>&plusmn;0.04</sub>)</td><td>0.99<sub>&plusmn;0.15</sub></td><td>...</td></tr><tr><td>&chi;<sup>2</sup>(dof)</td><td colspan="4">184(168)</td><td colspan="4">190(177)</td></tr><tr><td>reduced &chi;<sup>2</sup></td><td colspan="4">1.10</td><td colspan="4">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 theoretical Neupert effect is usually expressed as a delay of soft X-rays (thermal emission) against hard X-rays (nonthermal radiation; see Veronig et al. 2002), which is the evidence of the heating by nonthermal electrons followed by the chromospheric evaporation increasing the coronal density of the flaring loops (Shibata & Magara 2011). Because the WL emissions (and some of the $H\alpha$ emissions) are known to be a good proxy of hard X-ray emission in the Sun (Krucker et al. 2011; Namekata et al. 2017b),

the time delay of soft X-ray against WL (and possibly $H\alpha$) for flare E3 is interpreted as the “empirical” Neupert effect (e.g., Tristan et al. 2023). This interpretation suggests that flare E3 occurs through the same physical mechanism as solar flares (the same conclusion has been obtained for M-dwarf flares; Hawley et al. 1995; Tristan et al. 2023). Pillitteri et al. (2022) found a clear signature of the “empirical” Neupert effect in 200–300 nm near-UV band and soft X-ray relation for superflares on a young
<table><caption>**Table 6**
Results of NICER X-Ray Spectral Fit for Flares E2 and E3</caption><thead><tr><th>Flare E2's block</th><th>3</th><th>3A</th><th>3B</th><th>3a</th><th>3b</th><th>3c</th><th>3d</th><th>3e</th><th>-</th></tr></thead><tbody><tr><td>T (keV)</td><td>1.14±0.01</td><td>1.27±0.02</td><td>1.01±0.02</td><td>1.35±0.03</td><td>1.19±0.03</td><td>1.20±0.03</td><td>1.05±0.03</td><td>0.96±0.03</td><td>...</td></tr><tr><td>(T [10<sup>7</sup> K])</td><td>1.32±0.01</td><td>1.48±0.02</td><td>1.17±0.02</td><td>1.57±0.04</td><td>1.38±0.03</td><td>1.39±0.03</td><td>1.22±0.04</td><td>1.11±0.03</td><td>...</td></tr><tr><td>EM [10<sup>52</sup> cm<sup>-3</sup>]</td><td>8.02±0.14</td><td>11.09±0.24</td><td>5.48±0.16</td><td>13.13±0.40</td><td>9.52±0.34</td><td>8.03±0.32</td><td>5.36±0.27</td><td>4.31±0.23</td><td>...</td></tr><tr><td>χ<sup>2</sup>(dof)</td><td>414(220)</td><td>250(168)</td><td>232(177)</td><td>141(126)</td><td>166(125)</td><td>185(129)</td><td>152(127)</td><td>112(118)</td><td>...</td></tr><tr><td>reduced χ<sup>2</sup></td><td>1.88</td><td>1.49</td><td>1.31</td><td>1.12</td><td>1.33</td><td>1.44</td><td>1.19</td><td>0.95</td><td>...</td></tr></tbody></table><table><thead><tr><th>Flare E3's block</th><th>2</th><th>2A</th><th>2B</th><th>2a</th><th>2b</th><th>2c</th><th>2d</th><th>2e</th><th>3</th></tr></thead><tbody><tr><td>T (keV)</td><td>2.67±0.16</td><td>3.22±0.28</td><td>1.92±0.10</td><td>4.50±0.90</td><td>3.13±0.38</td><td>2.41±0.24</td><td>1.44±0.05</td><td>5.30±1.42</td><td>1.00±0.06</td></tr><tr><td>(T [10<sup>7</sup> K])</td><td>3.09±0.18</td><td>3.74±0.33</td><td>2.22±0.11</td><td>5.23±1.04</td><td>3.63±0.44</td><td>2.80±0.27</td><td>1.66±0.06</td><td>6.15±1.64</td><td>1.16±0.07</td></tr><tr><td>EM [10<sup>52</sup> cm<sup>-3</sup>]</td><td>6.09±0.12</td><td>8.11±0.22</td><td>6.92±0.20</td><td>5.66±0.29</td><td>10.35±0.38</td><td>9.90±0.36</td><td>7.23±0.35</td><td>4.66±0.28</td><td>0.70±0.07</td></tr><tr><td>χ<sup>2</sup>(dof)</td><td>388(243)</td><td>246(184)</td><td>278(177)</td><td>125(128)</td><td>151(127)</td><td>145(128)</td><td>177(123)</td><td>138(120)</td><td>279(203)</td></tr><tr><td>reduced χ<sup>2</sup></td><td>1.60</td><td>1.34</td><td>1.57</td><td>0.97</td><td>1.19</td><td>1.13</td><td>1.44</td><td>1.15</td><td>1.37</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 pre-flare value of each flare in Table 5 (0.28 for flare E2 and 0.38 for flare E3).

<table><caption>**Table 7**
Summary of NICER X-Ray Flare Parameters</caption><thead><tr><th>Flare</th><th>EM<sub>peak</sub><br>[10<sup>52</sup> cm<sup>-3</sup>]</th><th>T<sub>EM,peak</sub><br>[10<sup>7</sup> K]</th><th>kT<sub>slope</sub><br>[keV ksec<sup>-1</sup>]</th><th>τ<sub>rise</sub><br>(ks)</th><th>τ<sub>decay</sub><br>(ks)<br>(0.5–3 keV)</th><th>ξ<sub>EM,T</sub></th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th></tr></thead><tbody><tr><td>E2<br>(ext.)</td><td>13.1±0.4</td><td>1.57±0.04</td><td>-0.26±0.91</td><td>(&lt;3.96)</td><td>1.95±0.19</td><td>0.603</td><td>6.3<sup>+0.2</sup><sub>-0.4</sub><br>(26.6<sup>+1.9</sup><sub>-1.7</sub>)</td><td>22.9<sup>+0.5</sup><sub>-1.0</sub><br>(61.9<sup>+1.4</sup><sub>-2.6</sub>)</td></tr><tr><td>E3</td><td>10.4±0.4</td><td>3.63±0.44</td><td>-3.32±1.49</td><td>0.7±0.2</td><td>0.63±0.10</td><td>4.28</td><td>4.9<sup>+0.3</sup><sub>-0.2</sub></td><td>6.9<sup>+0.3</sup><sub>-0.1</sub></td></tr><tr><th>Flare</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(0.1–100 keV)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(0.5–7.9 keV)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(0.2–12 keV)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(1.55–12.4 keV/GOES)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th></tr><tr><td>E2<br>(ext.)</td><td>8.2<sup>+0.4</sup><sub>-0.5</sub><br>(34.5<sup>+1.5</sup><sub>-2.1</sub>)</td><td>29.3<sup>+0.7</sup><sub>-1.2</sub><br>(79.1<sup>+2.0</sup><sub>-3.4</sub>)</td><td>5.9<sup>+0.2</sup><sub>-0.3</sub><br>(24.8<sup>+1.0</sup><sub>-1.2</sub>)</td><td>21.0<sup>+0.5</sup><sub>-0.7</sub><br>(56.6<sup>+1.4</sup><sub>-2.0</sub>)</td><td>7.4<sup>+0.3</sup><sub>-0.5</sub><br>(31.1<sup>+1.4</sup><sub>-2.1</sub>)</td><td>26.1<sup>+0.7</sup><sub>-1.1</sub><br>(70.6<sup>+2.0</sup><sub>-2.9</sub>)</td><td>1.9<sup>+0.2</sup><sub>-0.1</sub><br>(8.0<sup>+0.8</sup><sub>-0.6</sub>)</td><td>5.3<sup>+0.4</sup><sub>-0.3</sub><br>(14.3<sup>+1.1</sup><sub>-0.8</sub>)</td></tr><tr><td>E3</td><td>8.1<sup>+0.7</sup><sub>-0.6</sub></td><td>11.4<sup>+0.6</sup><sub>-0.5</sub></td><td>6.2<sup>+0.5</sup><sub>-0.4</sub></td><td>8.6<sup>+0.4</sup><sub>-0.3</sub></td><td>7.6<sup>+0.7</sup><sub>-0.6</sub></td><td>10.5<sup>+0.5</sup><sub>-0.5</sub></td><td>4.0<sup>+0.6</sup><sub>-0.5</sub></td><td>5.4<sup>+0.4</sup><sub>-0.5</sub></td></tr></tbody></table>

Note. “ext.” means the extrapolated value by the light-curve fits. EM<sub>peak</sub> is the peak emission measure in the observational window. T<sub>EM,peak</sub> is the temperature when the emission measure (EM) is maximum value in the observational window. kT<sub>slope</sub> is the slope of the temperature (kT) evolution. τ<sub>rise</sub> is the rise time of 0.5–3 keV light curve from its onset to peak. τ<sub>decay</sub> is the e-fodling decay time of 0.5–3 keV light curve. ξ<sub>EM,T</sub> is the power-law index of the relation between temperature (T) and emission measure (EM) in decay phase in the formula of T ∝ (EM<sup>0.5</sup>)<sup>ξ<sub>EM,T</sub></sup>. L<sub>X</sub> is the X-ray luminosity and E<sub>X</sub> is the X-ray energy. The energy and flux values are not corrected for light-curve extrapolations in this table.

solar-type star, DS Tuc A (age of 40 Myr, spectral type of G6). Pillitteri et al. (2022) and this study have the same conclusion about the flare heating mechanism on young solar-type stars.

Furthermore, Hα and white light potentially appear to lag slightly behind the time-derivative soft X-rays, or seem to have a longer decay. This suggests that in addition to the heating caused by nonthermal electrons corresponding to hard X-rays, heating due to thermal conduction and/or radiative back-warming also contribute to Hα and WL emissions in decay (Machado et al. 1989; Isobe et al. 2007; Namekata et al. 2017b, 2020b, 2022c). These multiwavelength light-curve variations should be compared with the future numerical calculations.

## 4.2. Flare Radiative Energy Partition

Figure 18(a) shows the relation between Hα and the bolometric soft X-ray flare radiation energy for solar and stellar flares, while Figure 18(b) shows the relation between the

bolometric WL and Hα flare radiation energy. We found that the data of the superflares on EK Dra are almost consistent with a trend from solar flares and stellar flares on M-dwarf and RS CVn stars. This suggests that the multiwavelength emission mechanisms of the flares of EK Dra we detected are equivalent to those occurring in flares on other types of stars.

In Figure 18(b), the Hα energy of flare E1 is plotted (labeled as “E1”) with the upper limit as the total emission energy including the blueshifted spectrum, and the lower limit as the emission energy assuming the presence of a central component. The upper limit (and even possibly the lower limit) is clearly 1–1.5 orders of magnitude larger in Hα emission energy relative to WL emission energy than the other EK Dra flares. This can be attributed to the fact that the emission source of the blueshifted Hα line in flare E1 is different from the other EK Dra flares (not the flare loop or footpoints), suggesting a radiation contribution from stellar prominence eruption, as discussed in Section 5.1.
<table><caption>**Table 6**
Results of NICER X-Ray Spectral Fit for Flares E2 and E3</caption><thead><tr><th>Flare E2's block</th><th>3</th><th>3A</th><th>3B</th><th>3a</th><th>3b</th><th>3c</th><th>3d</th><th>3e</th><th>-</th></tr></thead><tbody><tr><td>T (keV)</td><td>1.14±0.01</td><td>1.27±0.02</td><td>1.01±0.02</td><td>1.35±0.03</td><td>1.19±0.03</td><td>1.20±0.03</td><td>1.05±0.03</td><td>0.96±0.03</td><td>...</td></tr><tr><td>(T [10<sup>7</sup> K])</td><td>1.32±0.01</td><td>1.48±0.02</td><td>1.17±0.02</td><td>1.57±0.04</td><td>1.38±0.03</td><td>1.39±0.03</td><td>1.22±0.04</td><td>1.11±0.03</td><td>...</td></tr><tr><td>EM [10<sup>52</sup> cm<sup>-3</sup>]</td><td>8.02±0.14</td><td>11.09±0.24</td><td>5.48±0.16</td><td>13.13±0.40</td><td>9.52±0.34</td><td>8.03±0.32</td><td>5.36±0.27</td><td>4.31±0.23</td><td>...</td></tr><tr><td>χ<sup>2</sup>(dof)</td><td>414(220)</td><td>250(168)</td><td>232(177)</td><td>141(126)</td><td>166(125)</td><td>185(129)</td><td>152(127)</td><td>112(118)</td><td>...</td></tr><tr><td>reduced χ<sup>2</sup></td><td>1.88</td><td>1.49</td><td>1.31</td><td>1.12</td><td>1.33</td><td>1.44</td><td>1.19</td><td>0.95</td><td>...</td></tr></tbody></table><table><thead><tr><th>Flare E3's block</th><th>2</th><th>2A</th><th>2B</th><th>2a</th><th>2b</th><th>2c</th><th>2d</th><th>2e</th><th>3</th></tr></thead><tbody><tr><td>T (keV)</td><td>2.67±0.16</td><td>3.22±0.28</td><td>1.92±0.10</td><td>4.50±0.90</td><td>3.13±0.38</td><td>2.41±0.24</td><td>1.44±0.05</td><td>5.30±1.42</td><td>1.00±0.06</td></tr><tr><td>(T [10<sup>7</sup> K])</td><td>3.09±0.18</td><td>3.74±0.33</td><td>2.22±0.11</td><td>5.23±1.04</td><td>3.63±0.44</td><td>2.80±0.27</td><td>1.66±0.06</td><td>6.15±1.64</td><td>1.16±0.07</td></tr><tr><td>EM [10<sup>52</sup> cm<sup>-3</sup>]</td><td>6.09±0.12</td><td>8.11±0.22</td><td>6.92±0.20</td><td>5.66±0.29</td><td>10.35±0.38</td><td>9.90±0.36</td><td>7.23±0.35</td><td>4.66±0.28</td><td>0.70±0.07</td></tr><tr><td>χ<sup>2</sup>(dof)</td><td>388(243)</td><td>246(184)</td><td>278(177)</td><td>125(128)</td><td>151(127)</td><td>145(128)</td><td>177(123)</td><td>138(120)</td><td>279(203)</td></tr><tr><td>reduced χ<sup>2</sup></td><td>1.60</td><td>1.34</td><td>1.57</td><td>0.97</td><td>1.19</td><td>1.13</td><td>1.44</td><td>1.15</td><td>1.37</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 pre-flare value of each flare in Table 5 (0.28 for flare E2 and 0.38 for flare E3).

<table><caption>**Table 7**
Summary of NICER X-Ray Flare Parameters</caption><thead><tr><th>Flare</th><th>EM<sub>peak</sub><br>[10<sup>52</sup> cm<sup>-3</sup>]</th><th>T<sub>EM,peak</sub><br>[10<sup>7</sup> K]</th><th>kT<sub>slope</sub><br>[keV ksec<sup>-1</sup>]</th><th>τ<sub>rise</sub><br>(ks)</th><th>τ<sub>decay</sub><br>(ks)<br>(0.5–3 keV)</th><th>ξ<sub>EM,T</sub></th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th></tr></thead><tbody><tr><td>E2<br>(ext.)</td><td>13.1±0.4</td><td>1.57±0.04</td><td>-0.26±0.91</td><td>(&lt;3.96)</td><td>1.95±0.19</td><td>0.603</td><td>6.3<sup>+0.2</sup><sub>-0.4</sub><br>(26.6<sup>+1.9</sup><sub>-1.7</sub>)</td><td>22.9<sup>+0.5</sup><sub>-1.0</sub><br>(61.9<sup>+1.4</sup><sub>-2.6</sub>)</td></tr><tr><td>E3</td><td>10.4±0.4</td><td>3.63±0.44</td><td>-3.32±1.49</td><td>0.7±0.2</td><td>0.63±0.10</td><td>4.28</td><td>4.9<sup>+0.3</sup><sub>-0.2</sub></td><td>6.9<sup>+0.3</sup><sub>-0.1</sub></td></tr><tr><th>Flare</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(0.1–100 keV)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(0.5–7.9 keV)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(0.2–12 keV)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th><th>L<sub>X</sub><br>[10<sup>29</sup> erg s<sup>-1</sup>]<br>(1.55–12.4 keV/GOES)</th><th>E<sub>X</sub><br>[10<sup>32</sup> erg]</th></tr><tr><td>E2<br>(ext.)</td><td>8.2<sup>+0.4</sup><sub>-0.5</sub><br>(34.5<sup>+1.5</sup><sub>-2.1</sub>)</td><td>29.3<sup>+0.7</sup><sub>-1.2</sub><br>(79.1<sup>+2.0</sup><sub>-3.4</sub>)</td><td>5.9<sup>+0.2</sup><sub>-0.3</sub><br>(24.8<sup>+1.0</sup><sub>-1.2</sub>)</td><td>21.0<sup>+0.5</sup><sub>-0.7</sub><br>(56.6<sup>+1.4</sup><sub>-2.0</sub>)</td><td>7.4<sup>+0.3</sup><sub>-0.5</sub><br>(31.1<sup>+1.4</sup><sub>-2.1</sub>)</td><td>26.1<sup>+0.7</sup><sub>-1.1</sub><br>(70.6<sup>+2.0</sup><sub>-2.9</sub>)</td><td>1.9<sup>+0.2</sup><sub>-0.1</sub><br>(8.0<sup>+0.8</sup><sub>-0.6</sub>)</td><td>5.3<sup>+0.4</sup><sub>-0.3</sub><br>(14.3<sup>+1.1</sup><sub>-0.8</sub>)</td></tr><tr><td>E3</td><td>8.1<sup>+0.7</sup><sub>-0.6</sub></td><td>11.4<sup>+0.6</sup><sub>-0.5</sub></td><td>6.2<sup>+0.5</sup><sub>-0.4</sub></td><td>8.6<sup>+0.4</sup><sub>-0.3</sub></td><td>7.6<sup>+0.7</sup><sub>-0.6</sub></td><td>10.5<sup>+0.5</sup><sub>-0.5</sub></td><td>4.0<sup>+0.6</sup><sub>-0.5</sub></td><td>5.4<sup>+0.4</sup><sub>-0.5</sub></td></tr></tbody></table>

Note. “ext.” means the extrapolated value by the light-curve fits. EM<sub>peak</sub> is the peak emission measure in the observational window. T<sub>EM,peak</sub> is the temperature when the emission measure (EM) is maximum value in the observational window. kT<sub>slope</sub> is the slope of the temperature (kT) evolution. τ<sub>rise</sub> is the rise time of 0.5–3 keV light curve from its onset to peak. τ<sub>decay</sub> is the e-fodling decay time of 0.5–3 keV light curve. ξ<sub>EM,T</sub> is the power-law index of the relation between temperature (T) and emission measure (EM) in decay phase in the formula of T ∝ (EM<sup>0.5</sup>)<sup>ξ<sub>EM,T</sub></sup>. L<sub>X</sub> is the X-ray luminosity and E<sub>X</sub> is the X-ray energy. The energy and flux values are not corrected for light-curve extrapolations in this table.

solar-type star, DS Tuc A (age of 40 Myr, spectral type of G6). Pillitteri et al. (2022) and this study have the same conclusion about the flare heating mechanism on young solar-type stars.

Furthermore, Hα and white light potentially appear to lag slightly behind the time-derivative soft X-rays, or seem to have a longer decay. This suggests that in addition to the heating caused by nonthermal electrons corresponding to hard X-rays, heating due to thermal conduction and/or radiative back-warming also contribute to Hα and WL emissions in decay (Machado et al. 1989; Isobe et al. 2007; Namekata et al. 2017b, 2020b, 2022c). These multiwavelength light-curve variations should be compared with the future numerical calculations.

## 4.2. Flare Radiative Energy Partition

Figure 18(a) shows the relation between Hα and the bolometric soft X-ray flare radiation energy for solar and stellar flares, while Figure 18(b) shows the relation between the

bolometric WL and Hα flare radiation energy. We found that the data of the superflares on EK Dra are almost consistent with a trend from solar flares and stellar flares on M-dwarf and RS CVn stars. This suggests that the multiwavelength emission mechanisms of the flares of EK Dra we detected are equivalent to those occurring in flares on other types of stars.

In Figure 18(b), the Hα energy of flare E1 is plotted (labeled as “E1”) with the upper limit as the total emission energy including the blueshifted spectrum, and the lower limit as the emission energy assuming the presence of a central component. The upper limit (and even possibly the lower limit) is clearly 1–1.5 orders of magnitude larger in Hα emission energy relative to WL emission energy than the other EK Dra flares. This can be attributed to the fact that the emission source of the blueshifted Hα line in flare E1 is different from the other EK Dra flares (not the flare loop or footpoints), suggesting a radiation contribution from stellar prominence eruption, as discussed in Section 5.1.
<figure><img src="image_19.png" /><figcaption>**Figure 16.** Fitting results of the X-ray light curves for superflares E2 (a) and E3 (b). The decay phase is fitted with an exponential function (colored solid lines), and the rise phase with a linear function (colored dashed lines), using *curve_fit* (left) For flare E2, two patterns of light-curve extrapolation are presented: assuming the peak time is the same as that of the white light (blue), and assuming the peak time is delayed by 10 minutes compared with the white light. The X-ray peak of flare E2 could possibly be higher by a factor of 4.2 (green) and 5.7 (blue) than the observed peak. The X-ray energy of flare E2 could possibly be higher by a factor of 2.7 (green) and 3.2 (blue) than the observed energy.</figcaption></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 17.** The cross-correlation coefficients for different lag times among light curves for the superflare on 2022 April 17 (E3). The time lags of maximum correlation coefficients, $r_{max}$, is defined as the most likely value. The 90th percentile gives the lag time uncertainty. The time delay of X-ray against $H\alpha$ is 6$^{+3}_{-2}$ minutes, the time delay of X-ray against WL is 7$^{+3}_{-2}$ minutes, the time delay of differential X-ray against $H\alpha$ is -3$^{+1}_{-2}$ minutes, and the time delay of differential X-ray against WL is -3$^{+2}_{-4}$ minutes. See Tristan et al. (2023) for the method.</figcaption></figure>

Incorporating the data from EK Dra (except for flare E1), we derived empirical rules regarding the relationship between $H\alpha$ and X-ray, as well as WL and $H\alpha$. By linking these, we deduced an empirical scaling relation for energy distributions at the bolometric X-ray (0.1–100 keV) and bolometric WL wavelengths, which are releasing a large amount of energy of flares.

$$ \frac{E_{H\alpha}}{10^{33} \text{ erg}} = 10^{-1.15 \pm 0.08} \cdot \left( \frac{E_{X,bol}}{10^{33} \text{ erg}} \right)^{0.90 \pm 0.03}, \quad (1) $$

$$ \frac{E_{\text{WL,bol}}}{10^{33} \text{ erg}} = 10^{1.68 \pm 0.15} \cdot \left( \frac{E_{H\alpha}}{10^{33} \text{ erg}} \right)^{1.04 \pm 0.07}, \quad (2) $$

Equations (1) and (2) are plotted on cyan lines in Figure 18. From Equations (1) and (2), an empirical relation between the X-ray ($E_{X,bol}$) and WL ($E_{WL,bol}$) flare energy can be deduced as

$$ \frac{E_{\text{WL,bol}}}{10^{33} \text{ erg}} = 10^{0.48 \pm 0.19} \cdot \left( \frac{E_{X,bol}}{10^{33} \text{ erg}} \right)^{0.94 \pm 0.07} \quad (3) $$

While this relationship appears to be almost linear, there may be a tendency for X-ray emission energy to slightly dominate as the flare scale increases. This relationship would be useful for statistically investigating the high-energy radiation environment around host stars by connecting to the large statistics of WLFs established by TESS and Kepler (Maehara et al. 2012; Davenport 2016; Feinstein et al. 2019; Notsu et al. 2019; Tu et al. 2020; Okamoto et al. 2021; Tu et al. 2021; Vida et al. 2021).

Furthermore, assuming that the emission energy at different wavelengths can be described by a linear relationship, a corresponding relationship is derived below for reference:

$$ E_{H\alpha} = 10^{-1.06 \pm 0.09} \cdot E_{X,bol}, \quad (4) $$

$$ E_{\text{WL,bol}} = 10^{1.59 \pm 0.06} \cdot E_{H\alpha}, \quad (5) $$

From Equations (4) and (5), another empirical relation can be deduced as

$$ E_{\text{WL,bol}} = 10^{0.54 \pm 0.11} \cdot E_{X,bol} \quad (6) $$

Note that the scaling factor in Equation (6) is so different from that in Equation (3) because Equation (6) is a linear relation, whereas Equation (3) is a nonlinear one. In the above, we collected and compared X-ray data in the 0.1–100 keV energy range.

Many other studies derive emission energy in different energy bands, causing inconsistency in comparison (see Section 3.4). In this paper, to compare with other previous studies, we recalculated the flare energy of EK Dra in all energy bands shown in previous studies. The results are summarized in Table 8. As a result, it was found that the white-light-to-X-ray energy ratios ($E_{WL}/E_X$) were comparable
<figure><img src="image_20.png" /><figcaption>**Figure 16.** Fitting results of the X-ray light curves for superflares E2 (a) and E3 (b). The decay phase is fitted with an exponential function (colored solid lines), and the rise phase with a linear function (colored dashed lines), using *curve_fit* (left). For flare E2, two patterns of light-curve extrapolation are presented: assuming the peak time is the same as that of the white light (blue), and assuming the peak time is delayed by 10 minutes compared with the white light. The X-ray peak of flare E2 could possibly be higher by a factor of 4.2 (green) and 5.7 (blue) than the observed peak. The X-ray energy of flare E2 could possibly be higher by a factor of 2.7 (green) and 3.2 (blue) than the observed energy.</figcaption></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>**Figure 17.** The cross-correlation coefficients for different lag times among light curves for the superflare on 2022 April 17 (E3). The time lags of maximum correlation coefficients, $r_{max}$, is defined as the most likely value. The 90th percentile gives the lag time uncertainty. The time delay of X-ray against $H\alpha$ is 6$^{+3}_{-2}$ minutes, the time delay of X-ray against WL is 7$^{+3}_{-2}$ minutes, the time delay of differential X-ray against $H\alpha$ is -3$^{+1}_{-2}$ minutes, and the time delay of differential X-ray against WL is -3$^{+2}_{-4}$ minutes. See Tristan et al. (2023) for the method.</figcaption></figure>

Incorporating the data from EK Dra (except for flare E1), we derived empirical rules regarding the relationship between $H\alpha$ and X-ray, as well as WL and $H\alpha$. By linking these, we deduced an empirical scaling relation for energy distributions at the bolometric X-ray (0.1–100 keV) and bolometric WL wavelengths, which are releasing a large amount of energy of flares.

$$ \frac{E_{H\alpha}}{10^{33} \text{ erg}} = 10^{-1.15 \pm 0.08} \cdot \left( \frac{E_{X,bol}}{10^{33} \text{ erg}} \right)^{0.90 \pm 0.03}, \quad (1) $$

$$ \frac{E_{\text{WL,bol}}}{10^{33} \text{ erg}} = 10^{1.68 \pm 0.15} \cdot \left( \frac{E_{H\alpha}}{10^{33} \text{ erg}} \right)^{1.04 \pm 0.07}, \quad (2) $$

Equations (1) and (2) are plotted on cyan lines in Figure 18. From Equations (1) and (2), an empirical relation between the X-ray ($E_{X,bol}$) and WL ($E_{WL,bol}$) flare energy can be deduced as

$$ \frac{E_{\text{WL,bol}}}{10^{33} \text{ erg}} = 10^{0.48 \pm 0.19} \cdot \left( \frac{E_{X,bol}}{10^{33} \text{ erg}} \right)^{0.94 \pm 0.07}. \quad (3) $$

While this relationship appears to be almost linear, there may be a tendency for X-ray emission energy to slightly dominate as the flare scale increases. This relationship would be useful for statistically investigating the high-energy radiation environment around host stars by connecting to the large statistics of WLFs established by TESS and Kepler (Maehara et al. 2012; Davenport 2016; Feinstein et al. 2019; Notsu et al. 2019; Tu et al. 2020; Okamoto et al. 2021; Tu et al. 2021; Vida et al. 2021).

Furthermore, assuming that the emission energy at different wavelengths can be described by a linear relationship, a corresponding relationship is derived below for reference:

$$ E_{H\alpha} = 10^{-1.06 \pm 0.09} \cdot E_{X,bol}, \quad (4) $$

$$ E_{\text{WL,bol}} = 10^{1.59 \pm 0.06} \cdot E_{H\alpha}, \quad (5) $$

From Equations (4) and (5), another empirical relation can be deduced as

$$ E_{\text{WL,bol}} = 10^{0.54 \pm 0.11} \cdot E_{X,bol} \quad (6) $$

Note that the scaling factor in Equation (6) is so different from that in Equation (3) because Equation (6) is a linear relation, whereas Equation (3) is a nonlinear one. In the above, we collected and compared X-ray data in the 0.1–100 keV energy range.

Many other studies derive emission energy in different energy bands, causing inconsistency in comparison (see Section 3.4). In this paper, to compare with other previous studies, we recalculated the flare energy of EK Dra in all energy bands shown in previous studies. The results are summarized in Table 8. As a result, it was found that the white-light-to-X-ray energy ratios ($E_{WL}/E_X$) were comparable
<figure><img src="image_22.png" /><figcaption>**Figure 18.** Relations between $H\alpha$, X-ray, and white-light energies for solar and stellar flares. Left: the relation between $H\alpha$ and bolometric X-ray energies (0.1–100 keV = 0.124–124 Å). Data of superflares on the G-dwarf EK Dra detected in this study are represented by red squares. Other solar and stellar data are taken from Kawai et al. (2022). The function fitted to the observational data with a power law is shown by the cyan line. Right: the relation between bolometric white-light and $H\alpha$ energies. Data of superflares on the G-dwarf EK Dra, which are associated with filament/prominence eruptions, are represented by filled red squares, whereas those without eruptions are represented by open red squares (this study, Namekata et al. 2022c; Namekata et al. 2022d). For E1, the total energy, including the blueshift component, is plotted as the upper limit, with the radiative energy of the central component from the two-component fit being plotted as the lower limit. Data of M-dwarf flares are taken from Maehara et al. (2021), Namizaki et al. (2023), and Notsu et al. (2023). Solar flare data are taken from Namekata et al. (2022a). The function fitted to the observational data, excluding flare E1, with a power law is shown by the cyan line.</figcaption></figure>

<table><caption>**Table 8**
Summary of X-Ray and Bolometric White-light Energy of Stellar Flares in This Study and Other Studies</caption><thead><tr><th>X-ray band</th><th>E<sub>WL,bol</sub>/E<sub>X</sub><br>(E2 = 1.2×10<sup>34</sup> erg)</th><th>E<sub>WL,bol</sub>/E<sub>X</sub><br>(E3 = 3.4×10<sup>33</sup> erg)</th><th>E<sub>WL,bol</sub>/E<sub>X</sub><br>(Previous study)</th><th>E<sub>WL,bol</sub> (erg)<br>(Previous study)</th><th>Sp. Type<br>(Previous study)</th><th>References</th></tr></thead><tbody><tr><td>0.5–7.9 keV</td><td>1.8–5.7</td><td>3.9</td><td>0.9–10<sup>a</sup></td><td>0.72–46 × 10<sup>33a</sup></td><td>M-F stars</td><td>(1)</td></tr><tr><td>0.3–3.0 keV</td><td>1.6–5.2</td><td>4.9</td><td>>1–40<sup>b</sup></td><td>0.32–16 × 10<sup>31b</sup></td><td>EV Lac (M-dwarf)</td><td>(2)</td></tr><tr><td>0.2–12 keV</td><td>1.4–4.6</td><td>3.2</td><td>0.1,~1.5,~3–4</td><td>0.62–6.2 × 10<sup>33</sup></td><td>M/K-dwarfs</td><td>(3)</td></tr><tr><td>0.2–12 keV</td><td>1.4–4.6</td><td>3.2</td><td>4.4</td><td>5.6 × 10<sup>33</sup></td><td>AD Leonis (M-dwarf)</td><td>(4)</td></tr><tr><td>1.55–12.4 keV/GOES</td><td>7.0–23</td><td>6.2</td><td>13</td><td>5.6 × 10<sup>33</sup></td><td>AD Leonis (M-dwarf)</td><td>(4)</td></tr><tr><td>1.55–12.4 keV/GOES</td><td>7.0–23</td><td>6.2</td><td>70–100</td><td>10<sup>29–32</sup></td><td>The Sun (G2V)</td><td>(5), (6)</td></tr></tbody></table>

**Notes.** $E_{WL,bol}$ is the bolometric white-light flare energy under the assumption of 10,000 K blackbody radiation. $E_X$ is the X-ray flare energy in the energy band of the first column. “Sp. Type” is the spectral type of the star.

<sup>a</sup> The Kepler-band flare energy is reported.

<sup>b</sup> The TESS-band flare energy is reported. The authors also mentioned that the $E_{WL,bol}/E_X$ values are lower limits because not all of the X-ray flare evolution was covered by NICER. References: (1) Guarcello et al. (2019), (2) Paudel et al. (2021), (3) Kuznetsov & Kolotkov (2021), (4) Stelzer et al. (2022), (5) Emslie et al. (2012), (6) Osten & Wolk (2015).

to those of previous studies in all energy bands. However, in the data compared with solar flares in the GOES band, it was found that solar flares show relatively larger $E_{WL}/E_X$ ratios (~70–100) than superflares on EK Dra (~6.2 and 7.0–22.6) and M-dwarf AD Leonis (~13). This may suggest, as mentioned above, that in large-scale stellar superflares (10$^{33–34}$ erg), X-ray emission energy may become stronger than small-scale solar flares (<10$^{32}$ erg). In particular, the GOES band is at a higher energy compared with other energy

bands in Table 8, and therefore is sensitive to the flare’s temperature increase around 10$^7$ K. Because it is widely known that the flare temperature increases as the energy scale increases (Tsuboi et al. 1998; Shibata & Yokoyama 1999, 2002; Tsuboi et al. 2016; Getman et al. 2021), the energy in the GOES band may tend to increase more than proportionally.

Lastly, Figure 19 shows the relation between the GOES X-ray peak flux of the flare ($F_{GOES}$) and the energy of the white-light flare ($E_{WLF,Bol}$). Conventionally, some studies have used an
<figure><img src="image_23.png" /><figcaption>**Figure 18.** Relations between $H\alpha$, X-ray, and white-light energies for solar and stellar flares. Left: the relation between $H\alpha$ and bolometric X-ray energies (0.1–100 keV = 0.124–124 Å). Data of superflares on the G-dwarf EK Dra detected in this study are represented by red squares. Other solar and stellar data are taken from Kawai et al. (2022). The function fitted to the observational data with a power law is shown by the cyan line. Right: the relation between bolometric white-light and $H\alpha$ energies. Data of superflares on the G-dwarf EK Dra, which are associated with filament/prominence eruptions, are represented by filled red squares, whereas those without eruptions are represented by open red squares (this study, Namekata et al. 2022c; Namekata et al. 2022d). For E1, the total energy, including the blueshift component, is plotted as the upper limit, with the radiative energy of the central component from the two-component fit being plotted as the lower limit. Data of M-dwarf flares are taken from Maehara et al. (2021), Namizaki et al. (2023), and Notsu et al. (2023). Solar flare data are taken from Namekata et al. (2022a). The function fitted to the observational data, excluding flare E1, with a power law is shown by the cyan line.</figcaption></figure>

<table><caption>**Table 8**
Summary of X-Ray and Bolometric White-light Energy of Stellar Flares in This Study and Other Studies</caption><thead><tr><th>X-ray band</th><th>E<sub>WL,bol</sub>/E<sub>X</sub><br>(E2 = 1.2×10<sup>34</sup> erg)</th><th>E<sub>WL,bol</sub>/E<sub>X</sub><br>(E3 = 3.4×10<sup>33</sup> erg)</th><th>E<sub>WL,bol</sub>/E<sub>X</sub><br>(Previous study)</th><th>E<sub>WL,bol</sub> (erg)<br>(Previous study)</th><th>Sp. Type<br>(Previous study)</th><th>References</th></tr></thead><tbody><tr><td>0.5–7.9 keV</td><td>1.8–5.7</td><td>3.9</td><td>0.9–10<sup>a</sup></td><td>0.72–46 × 10<sup>33a</sup></td><td>M-F stars</td><td>(1)</td></tr><tr><td>0.3–3.0 keV</td><td>1.6–5.2</td><td>4.9</td><td>>1–40<sup>b</sup></td><td>0.32–16 × 10<sup>31b</sup></td><td>EV Lac (M-dwarf)</td><td>(2)</td></tr><tr><td>0.2–12 keV</td><td>1.4–4.6</td><td>3.2</td><td>0.1,~1.5,~3–4</td><td>0.62–6.2 × 10<sup>33</sup></td><td>M/K-dwarfs</td><td>(3)</td></tr><tr><td>0.2–12 keV</td><td>1.4–4.6</td><td>3.2</td><td>4.4</td><td>5.6 × 10<sup>33</sup></td><td>AD Leonis (M-dwarf)</td><td>(4)</td></tr><tr><td>1.55–12.4 keV/GOES</td><td>7.0–23</td><td>6.2</td><td>13</td><td>5.6 × 10<sup>33</sup></td><td>AD Leonis (M-dwarf)</td><td>(4)</td></tr><tr><td>1.55–12.4 keV/GOES</td><td>7.0–23</td><td>6.2</td><td>70–100</td><td>10<sup>29–32</sup></td><td>The Sun (G2V)</td><td>(5), (6)</td></tr></tbody></table>

**Notes.** $E_{WL,bol}$ is the bolometric white-light flare energy under the assumption of 10,000 K blackbody radiation. $E_X$ is the X-ray flare energy in the energy band of the first column. “Sp. Type” is the spectral type of the star.

a The Kepler-band flare energy is reported.

b The TESS-band flare energy is reported. The authors also mentioned that the $E_{WL,bol}/E_X$ values are lower limits because not all of the X-ray flare evolution was covered by NICER. References: (1) Guarcello et al. (2019), (2) Paudel et al. (2021), (3) Kuznetsov & Kolotkov (2021), (4) Stelzer et al. (2022), (5) Emslie et al. (2012), (6) Osten & Wolk (2015).

to those of previous studies in all energy bands. However, in the data compared with solar flares in the GOES band, it was found that solar flares show relatively larger $E_{WL}/E_X$ ratios (~70–100) than superflares on EK Dra (~6.2 and 7.0–22.6) and M-dwarf AD Leonis (~13). This may suggest, as mentioned above, that in large-scale stellar superflares (10$^{33–34}$ erg), X-ray emission energy may become stronger than small-scale solar flares (<10$^{32}$ erg). In particular, the GOES band is at a higher energy compared with other energy

bands in Table 8, and therefore is sensitive to the flare's temperature increase around 10$^7$ K. Because it is widely known that the flare temperature increases as the energy scale increases (Tsuboi et al. 1998; Shibata & Yokoyama 1999, 2002; Tsuboi et al. 2016; Getman et al. 2021), the energy in the GOES band may tend to increase more than proportionally.

Lastly, Figure 19 shows the relation between the GOES X-ray peak flux of the flare ($F_{GOES}$) and the energy of the white-light flare ($E_{WLF,Bol}$). Conventionally, some studies have used an
<table><caption>**Table 9**
Length Scale and Area of the Superflares, Prominence/Filament Eruptions, and Starspots on EK Dra in This Study and Past Observations</caption><thead><tr><th rowspan="3">(Methods)<br>(Input)</th><th colspan="3">Flare loop</th><th colspan="2">Prominence</th><th rowspan="2">BV Amp<br>(F<sub>av</sub>)</th><th colspan="2">Spot</th><th rowspan="2">Rot. Phase</th></tr><tr><th colspan="3">(10<sup>10</sup> cm)</th><th rowspan="2">(10<sup>10</sup> cm)</th><th rowspan="2">(10<sup>21</sup> cm<sup>2</sup>)</th><th rowspan="2">(10<sup>10</sup> cm)</th><th rowspan="2">(10<sup>21</sup> cm<sup>2</sup>)</th></tr><tr><th>(S&Y99)<sup>a</sup><br>(X-ray)<sup>a</sup></th><th>(R07)<sup>c</sup><br>(X-ray)</th><th>(N17)<sup>b</sup><br>(WLF)<sup>b</sup></th></tr></thead><tbody><tr><td>2022 Apr 10 (E1)</td><td>...</td><td>...</td><td>0.73</td><td>8.3–300</td><td>18–63</td><td>0.024</td><td>2.1</td><td>0.42</td><td>Decline-Loc.min</td></tr><tr><td>2022 Apr 16 (E2)</td><td>(10.08)</td><td>...</td><td>1.16</td><td>1.4–51</td><td>0.53–1.9</td><td>0.033</td><td>2.4</td><td>0.57</td><td>Rise</td></tr><tr><td>2022 Apr 17 (E3)</td><td>2.06</td><td>0.68</td><td>0.67</td><td>...</td><td>...</td><td>0.032</td><td>2.4</td><td>0.56</td><td>Decline</td></tr><tr><td>2020 Apr 05 (E4)<sup>d</sup></td><td>...</td><td>...</td><td>0.48</td><td>1.4–125</td><td>0.2–16</td><td>0.025</td><td>2.1</td><td>0.43</td><td>Loc.max</td></tr><tr><td>2020 Mar 14 (E5)<sup>e</sup></td><td>...</td><td>...</td><td>1.50</td><td>...</td><td>...</td><td>0.021</td><td>1.9</td><td>0.36</td><td>Decline</td></tr></tbody></table>

**Notes.** “BV Amp” is the brightness variation amplitude relative to average flux in the TESS band due to the stellar rotation. “Rot. Phase” is the timing when the superflares occur relative to stellar rotational phase. “Loc.min” and “Loc.max” are the local minimum and local maximum of the light curve, respectively, and “Rise” and “Decline” are the rising and decline phases of the light curve, respectively. As a reference, stellar radius is 0.94 times solar radius ~6.55×10¹⁰ cm, and stellar disk area is ~13.5×10²¹ cm².

a The loop length is estimated using the method by Shibata & Yokoyama (1999, 2002) under the assumption of coronal electron density $n_e = 10^{11}$ cm⁻³.

b The loop length is estimated using the method by Namekata et al. (2017b) under the assumption of coronal density $n = 10^2 n_\odot \sim 10^{11}$ cm⁻³.

c The estimation from rise timescale of Reale (2007).

d The data are taken from Namekata et al. (2022d).

e The data are taken from Namekata et al. (2022c).

empirical relationship $E_{WLF,Bol} = 10^{35} \cdot F_{GOES}$ (Shibata et al. 2013) to compare the energy scale of solar and stellar flares because most solar flares are evaluated by $F_{GOES}$ while most stellar flares are by $E_{WLF,Bol}$. Later, Namekata et al. (2017b) confirmed observationally that this power-law index becomes linear (~1) for solar flare observations, but its absolute value is slightly different from Shibata et al. (2013)'s law, and the relationship was $E_{WLF,Bol} = 10^{34.3} \cdot F_{GOES}$. Namekata et al. 2017b suggest that this linear relationship can be explained by the well-known Neupert effect, by assuming that WLF is a good proxy of hard X-ray radiation. On the other hand, a nonlinear scaling relation for total solar irradiance (TSI) and GOES X-ray peak flux of solar flares has been reviewed by Cliver et al. (2022), and the relationship $E_{TSI} = 0.32 \times 10^{32} \cdot (F_{GOES}/(10^{-4}Wm^{-2}))^{0.72}$ has been derived. While all of these relationships are scaling laws describing solar flares, they differ slightly, and a consistent view has not yet been established (see Cliver et al. 2022). Then, which scaling law can describe superflares on stars? Figure 19 shows the comparison between the scaling laws and stellar superflares on G/M-dwarfs, including EK Dra's superflares with red color. As a result, we found that all the scaling laws intersect without significant contradiction with the stellar data. In detail, it can be said for now that the two superflares of EK Dra prefer the scaling laws of Namekata et al. (2017b) and Cliver et al. (2022). In the future, it is expected that multiwavelength observations of superflares with $10^{37-39}$ erg in RS CVn-type binary stars, for example, could lead to an understanding of the extension capability of these scaling laws.

### 4.3. Length Scale of Flare Loop

The length scales of the coronal flare loops are estimated by using (1) Shibata & Yokoyama (1999, 2002)'s model (see also Namekata et al. 2017a), (2) Reale (2007)'s model, and (3) Namekata et al. (2017b)'s method. See Table 9 for the result summary.

Shibata & Yokoyama (1999, 2002)'s model is based on the two-dimensional magnetohydrodynamic (MHD) simulations of flares performed in Yokoyama & Shibata (1998). They assumed the balance between heating by magnetic

<figure><img src="image_23.png" /><figcaption>**Figure 19.** Relation between the bolometric white-light flare energy and the peak GOES-band soft X-ray flux (1–8 Å = 1.55–12.4 keV) for solar and stellar flares. Data for the superflares (E2, E3) from the G-dwarf EK Dra derived in this paper are plotted as red squares. Other data for superflares from G/F-dwarfs (orange circles) are taken from Guarcello et al. (2019). Data for superflares for M/K-dwarfs are taken from Guarcello et al. (2019); Kuznetsov & Kolotkov (2021), and Stelzer et al. (2022). Note that data from Guarcello et al. (2019) have been converted to GOES-band flux and bolometric WLF energy. The solar observational scaling laws from Cliver et al. (2022; dashed line) and Namekata et al. (2017b; solid line), as well as the empirical law from Shibata et al. (2013; dashed-dotted line), are also plotted.</figcaption></figure>

reconnection and cooling by thermal conduction in the flare loop and derived the scaling relation to estimate the flare loop length in the following equation

$$L_{\text{loop}} = 10^9 \left( \frac{\text{EM}_{\text{peak}}}{10^{48} \text{cm}^{-3}} \right)^{3/5} \left( \frac{n_e}{10^9 \text{cm}^{-3}} \right)^{-2/5} \left( \frac{T_{\text{EM,peak}}}{10^7 \text{K}} \right)^{-8/5} \text{cm}, \quad (7)$$

where EM\_peak is the peak EM, and T\_EM,peak is the temperature at the EM peak. This reliable method is later validated by solar flare observations (Namekata et al. 2017a). Güdel et al. 1995
<table><caption>**Table 9**
Length Scale and Area of the Superflares, Prominence/Filament Eruptions, and Starspots on EK Dra in This Study and Past Observations</caption><thead><tr><th rowspan="3">(Methods)<br>(Input)</th><th colspan="3">Flare loop</th><th colspan="2">Prominence</th><th rowspan="2">BV Amp<br>(F<sub>av</sub>)</th><th colspan="2">Spot</th><th rowspan="2">Rot. Phase</th></tr><tr><th colspan="3">(10<sup>10</sup> cm)</th><th rowspan="2">(10<sup>10</sup> cm)</th><th rowspan="2">(10<sup>21</sup> cm<sup>2</sup>)</th><th rowspan="2">(10<sup>10</sup> cm)</th><th rowspan="2">(10<sup>21</sup> cm<sup>2</sup>)</th></tr><tr><th>(S&Y99)<sup>a</sup><br>(X-ray)<sup>a</sup></th><th>(R07)<sup>c</sup><br>(X-ray)</th><th>(N17)<sup>b</sup><br>(WLF)<sup>b</sup></th></tr></thead><tbody><tr><td>2022 Apr 10 (E1)</td><td>...</td><td>...</td><td>0.73</td><td>8.3–300</td><td>18–63</td><td>0.024</td><td>2.1</td><td>0.42</td><td>Decline-Loc.min</td></tr><tr><td>2022 Apr 16 (E2)</td><td>(10.08)</td><td>...</td><td>1.16</td><td>1.4–51</td><td>0.53–1.9</td><td>0.033</td><td>2.4</td><td>0.57</td><td>Rise</td></tr><tr><td>2022 Apr 17 (E3)</td><td>2.06</td><td>0.68</td><td>0.67</td><td>...</td><td>...</td><td>0.032</td><td>2.4</td><td>0.56</td><td>Decline</td></tr><tr><td>2020 Apr 05 (E4)<sup>d</sup></td><td>...</td><td>...</td><td>0.48</td><td>1.4–125</td><td>0.2–16</td><td>0.025</td><td>2.1</td><td>0.43</td><td>Loc.max</td></tr><tr><td>2020 Mar 14 (E5)<sup>e</sup></td><td>...</td><td>...</td><td>1.50</td><td>...</td><td>...</td><td>0.021</td><td>1.9</td><td>0.36</td><td>Decline</td></tr></tbody></table>

**Notes.** “BV Amp” is the brightness variation amplitude relative to average flux in the TESS band due to the stellar rotation. “Rot. Phase” is the timing when the superflares occur relative to stellar rotational phase. “Loc.min” and “Loc.max” are the local minimum and local maximum of the light curve, respectively, and “Rise” and “Decline” are the rising and decline phases of the light curve, respectively. As a reference, stellar radius is 0.94 times solar radius ~6.55×10¹⁰ cm, and stellar disk area is ~13.5×10²¹ cm².

a The loop length is estimated using the method by Shibata & Yokoyama (1999, 2002) under the assumption of coronal electron density $n_e = 10^{11}$ cm⁻³.

b The loop length is estimated using the method by Namekata et al. (2017b) under the assumption of coronal density $n = 10^2 n_⊙ \sim 10^{11}$ cm⁻³.

c The estimation from rise timescale of Reale (2007).

d The data are taken from Namekata et al. (2022d).

e The data are taken from Namekata et al. (2022c).

empirical relationship $E_{WLF,Bol} = 10^{35} \cdot F_{GOES}$ (Shibata et al. 2013) to compare the energy scale of solar and stellar flares because most solar flares are evaluated by $F_{GOES}$ while most stellar flares are by $E_{WLF,Bol}$. Later, Namekata et al. (2017b) confirmed observationally that this power-law index becomes linear (~1) for solar flare observations, but its absolute value is slightly different from Shibata et al. (2013)'s law, and the relationship was $E_{WLF,Bol} = 10^{34.3} \cdot F_{GOES}$. Namekata et al. 2017b suggest that this linear relationship can be explained by the well-known Neupert effect, by assuming that WLF is a good proxy of hard X-ray radiation. On the other hand, a nonlinear scaling relation for total solar irradiance (TSI) and GOES X-ray peak flux of solar flares has been reviewed by Cliver et al. (2022), and the relationship $E_{TSI} = 0.32 \times 10^{32} \cdot (F_{GOES}/(10^{-4}Wm^{-2}))^{0.72}$ has been derived. While all of these relationships are scaling laws describing solar flares, they differ slightly, and a consistent view has not yet been established (see Cliver et al. 2022). Then, which scaling law can describe superflares on stars? Figure 19 shows the comparison between the scaling laws and stellar superflares on G/M-dwarfs, including EK Dra's superflares with red color. As a result, we found that all the scaling laws intersect without significant contradiction with the stellar data. In detail, it can be said for now that the two superflares of EK Dra prefer the scaling laws of Namekata et al. (2017b) and Cliver et al. (2022). In the future, it is expected that multiwavelength observations of superflares with $10^{37-39}$ erg in RS CVn-type binary stars, for example, could lead to an understanding of the extension capability of these scaling laws.

### 4.3. Length Scale of Flare Loop

The length scales of the coronal flare loops are estimated by using (1) Shibata & Yokoyama (1999, 2002)'s model (see also Namekata et al. 2017a), (2) Reale (2007)'s model, and (3) Namekata et al. (2017b)'s method. See Table 9 for the result summary.

Shibata & Yokoyama (1999, 2002)'s model is based on the two-dimensional magnetohydrodynamic (MHD) simulations of flares performed in Yokoyama & Shibata (1998). They assumed the balance between heating by magnetic

<figure><img src="image_24.png" /><figcaption>**Figure 19.** Relation between the bolometric white-light flare energy and the peak GOES-band soft X-ray flux (1–8 Å = 1.55–12.4 keV) for solar and stellar flares. Data for the superflares (E2, E3) from the G-dwarf EK Dra derived in this paper are plotted as red squares. Other data for superflares from G/F-dwarfs (orange circles) are taken from Guarcello et al. (2019). Data for superflares for M/K-dwarfs are taken from Guarcello et al. (2019); Kuznetsov & Kolotkov (2021), and Stelzer et al. (2022). Note that data from Guarcello et al. (2019) have been converted to GOES-band flux and bolometric WLF energy. The solar observational scaling laws from Cliver et al. (2022; dashed line) and Namekata et al. (2017b; solid line), as well as the empirical law from Shibata et al. (2013; dashed-dotted line), are also plotted.</figcaption></figure>

reconnection and cooling by thermal conduction in the flare loop and derived the scaling relation to estimate the flare loop length in the following equation

$$L_{loop} = 10^9 \left( \frac{EM_{peak}}{10^{48}cm^{-3}} \right)^{3/5} \left( \frac{n_e}{10^9cm^{-3}} \right)^{-2/5} \left( \frac{T_{EM,peak}}{10^7K} \right)^{-8/5} \text{cm}, (7)$$

where $EM_{peak}$ is the peak EM, and $T_{EM,peak}$ is the temperature at the EM peak. This reliable method is later validated by solar flare observations (Namekata et al. 2017a). Güdel et al. 1995
reported that the coronal density of EK Dra is $>4 \times 10^{10} \text{ cm}^{-3}$, and Ness et al. (2004) also reported the consistent value (e.g., Güdel 2004). Therefore, the assumption of coronal density of $\sim 10^{11} \text{ cm}^{-3}$ would be a reasonable value for EK Dra's coronal active region. Under the assumption of the pre-flare coronal density in active region $n_e=10^{11} \text{ cm}^{-3}$, the loop length of flare E2 and flare E3 are derived to be $1.0 \times 10^{11} \text{ cm}$ and $2.1 \times 10^{10} \text{ cm}$, respectively (see Table 9). The advantage of this approach lies in the fact that information on temporal variation is not required as long as the flare peak is captured. However, as in the case of flare E2, where the flare peak is not captured, it should be noted that accurate values may not be derived (therefore, the value in Table 9 is in brackets).

Reale (2007) applied a one-dimensional hydrodynamic flare model to the rise phase of the flare, suggesting an equation to estimate the flare loop (half-)length:

$$L_{\text{loop}} = 950 \sqrt{T_{\text{peak}}} \tau_{\text{rise}} \psi \text{ cm}, \quad (8)$$

where $T_{\text{peak}}$ is the maximum temperature and $\psi = T_{\text{peak}}/T_{\text{EM,peak}}$. This gives the estimate of the loop length of the flare E3 as $0.68 \times 10^{10} \text{ cm}$. Note that Reale et al. (1997) initially derived the scaling relation to derive the flare loop length from the decay phase of the X-ray flare, but it requires the instrument-calibrated parameters, and no NICER parameters are available for now. But as future development may enable us to estimate the loop length from the decay phase, we derived the required parameters in Table 5.

Namekata et al. (2017b) derived the scaling relation to derive the flare loop length from the WLF's energy and duration. They used the relationship that the WLF's timescale is proportional to the reconnection timescale ($\propto$Alfvén timescale), and flare energy $E_{\text{flare}}$ is determined by the magnetic energy. The derived relation is in the formula of

$$L_{\text{loop}} \sim 1.64 \times 10^9 \left(\frac{\tau_{\text{WL}}}{100\text{s}}\right)^{2/5} \left(\frac{E_{\text{WLF}}}{10^{30}\text{erg}}\right)^{1/5} \left(\frac{n}{n_{\odot}}\right)^{-1/5} \text{ cm}, \quad (9)$$

where the coefficient was calibrated by solar coronal loop observation, $\tau_{\text{WL}}$ is the e-folding decay time of WLFs, $E_{\text{WLF}}$ is the bolometric WLF energy, and $n$ is the pre-flare coronal number density. Note that the dependence on $n$ is not explicitly included in some previous studies (e.g., Namekata et al. 2022c), but we included it because we need to consider it to discuss the results consistently with other methods (see Shibata & Yokoyama 1999, 2002's model, which assumed the pre-flare coronal density). The normalized factor of $n$ is assumed as solar value $n_{\odot}$, which is usually considered as $\sim 10^9 \text{ cm}^{-3}$. Under the assumption of $n \sim 100 n_{\odot} \sim 10^{11} \text{ cm}^{-3}$ (Güdel et al. 1995), the loop length of flares E1, E2, and E3 are derived to be $0.73 \times 10^{10} \text{ cm}$, $1.16 \times 10^{10} \text{ cm}$, and $0.67 \times 10^{10} \text{ cm}$, respectively (see Table 9).

In summary, the flare loop length estimated from X-ray and WL flares are listed in Table 9. The estimated loop length is roughly $\sim 0.5 - 2 \times 10^{10} \text{ cm}$, which corresponds to $\sim 8 - 30\%$ of stellar radius. We found that the loop lengths derived from the X-ray rise time by Reale (2007)'s methods are consistent with those derived from WLF's energy-duration relationship proposed by Namekata et al. (2017b). The method proposed by

Shibata & Yokoyama (1999, 2002) also yields a close value that is approximately twice as large as those from other methods for flare E3 (excluding flare E2, where the flare peak was not captured). Thus, this consistency supports the prediction capability of these different methods, which are widely used but not often simultaneously applied. Particularly, in this campaign, as all flares have been observed by TESS, the estimations from WLFs by Namekata et al. (2017b) appear to be very useful for comparing among flares.

The length of the flare loops derived here will be compared with the length scale of prominences and starspots in Section 6.2. This will enable new discussions on the spatial scale ratios of different aspects of eruptive events. Moreover, the length of the flare loops is important for constraining the initial height of prominence eruptions, and is expected to be useful in future comparisons with numerical calculations in our paper II (see Section 6.4).

# 5. Prominence Eruptions on a Young Solar-type Star

## 5.1. Discovery of Blueshifted "Emission" Spectra as Evidence of Stellar Prominence Eruptions

As revealed in Section 3, among the three $H\alpha$ superflares we detected (labeled E1, E2, E3), two superflares (E1, E2) exhibited a significant blueshifted $H\alpha$ "emission" profile. This is the first discovery of the blueshifted $H\alpha$ emission profile on a solar-type star (G-dwarf), while similar emission profiles have been frequently reported on M-dwarfs. The profile exhibits a more prominent blueshifted component compared to those observed in M-type stars: In flare E1, the entire spectrum is blueshifted in the initial phase, and in flare E2, a bump-like structure is observed at a wavelength different from the $H\alpha$ center. This suggests that something different from the usual phenomena seen at the $H\alpha$ center (i.e., flare ribbons) is occurring and moving in the LOS direction. As mentioned in the introduction, Namekata et al. (2022d) detected a blueshifted "absorption" component moving at a maximum velocity of approximately $-510 \text{ km s}^{-1}$ after a superflare (labeled as flare "E4" in Tables 3 and 4), and comparison with solar observations confirmed that this was due to the filament eruption occurring inside the stellar disk. Our new discovery in this study proposed a picture similar to the Sun, where on the solar-type star EK Dra, the $H\alpha$ line appears as an absorption component when cool plasma are present within the stellar disk (called filament) and as an emission component when they extend beyond the disk (called prominence). Given this context, the blueshifted emission component detected this time could likely be the first evidence of prominence eruption on a solar-type star (i.e., a G-dwarf).

The temporal variation of the velocity strongly supports the idea that the observed blueshifted emission components are stellar prominence eruptions. From the temporal evolution of the shifted velocity, it is possible to derive the initial deceleration rate (discussed in more detail in Section 5.2). For flare E1, the deceleration rate is calculated to be $0.34 \pm 0.15 \text{ km s}^{-2}$ for the one-component fit (or $0.23 \pm 0.14 \text{ km s}^{-2}$ for the two-component fit). This corresponds remarkably well with EK Dra's surface gravity of $0.30 \pm 0.05 \text{ km s}^{-2}$, strengthening the picture that a prominence-like cool plasma is ejected and decelerated by the surface gravity of the star. Interestingly, this value is very similar to those of the filament eruption events E4 of $0.34 \pm 0.04 \text{ km s}^{-2}$.
reported that the coronal density of EK Dra is $>4 \times 10^{10}$ cm$^{-3}$, and Ness et al. (2004) also reported the consistent value (e.g., Güdel 2004). Therefore, the assumption of coronal density of $\sim 10^{11}$ cm$^{-3}$ would be a reasonable value for EK Dra's coronal active region. Under the assumption of the pre-flare coronal density in active region $n_e=10^{11}$ cm$^{-3}$, the loop length of flare E2 and flare E3 are derived to be $1.0 \times 10^{11}$ cm and $2.1 \times 10^{10}$ cm, respectively (see Table 9). The advantage of this approach lies in the fact that information on temporal variation is not required as long as the flare peak is captured. However, as in the case of flare E2, where the flare peak is not captured, it should be noted that accurate values may not be derived (therefore, the value in Table 9 is in brackets).

Reale (2007) applied a one-dimensional hydrodynamic flare model to the rise phase of the flare, suggesting an equation to estimate the flare loop (half-)length:

$$L_{\text{loop}} = 950 \sqrt{T_{\text{peak}}} \tau_{\text{rise}} \psi \text{ cm,} \quad (8)$$

where $T_{\text{peak}}$ is the maximum temperature and $\psi = T_{\text{peak}}/T_{\text{EM,peak}}$. This gives the estimate of the loop length of the flare E3 as $0.68 \times 10^{10}$ cm. Note that Reale et al. (1997) initially derived the scaling relation to derive the flare loop length from the decay phase of the X-ray flare, but it requires the instrument-calibrated parameters, and no NICER parameters are available for now. But as future development may enable us to estimate the loop length from the decay phase, we derived the required parameters in Table 5.

Namekata et al. (2017b) derived the scaling relation to derive the flare loop length from the WLF's energy and duration. They used the relationship that the WLF's timescale is proportional to the reconnection timescale ($\propto$Alfvén timescale), and flare energy $E_{\text{flare}}$ is determined by the magnetic energy. The derived relation is in the formula of

$$L_{\text{loop}} \sim 1.64 \times 10^9 \left(\frac{\tau_{\text{WL}}}{100\text{s}}\right)^{2/5} \left(\frac{E_{\text{WLF}}}{10^{30}\text{erg}}\right)^{1/5} \left(\frac{n}{n_{\odot}}\right)^{-1/5} \text{cm,} \quad (9)$$

where the coefficient was calibrated by solar coronal loop observation, $\tau_{\text{WL}}$ is the e-folding decay time of WLFs, $E_{\text{WLF}}$ is the bolometric WLF energy, and $n$ is the pre-flare coronal number density. Note that the dependence on $n$ is not explicitly included in some previous studies (e.g., Namekata et al. 2022c), but we included it because we need to consider it to discuss the results consistently with other methods (see Shibata & Yokoyama 1999, 2002's model, which assumed the pre-flare coronal density). The normalized factor of $n$ is assumed as solar value $n_{\odot}$, which is usually considered as $\sim 10^9$ cm$^{-3}$. Under the assumption of $n \sim 100n_{\odot} \sim 10^{11}$ cm$^{-3}$ (Güdel et al. 1995), the loop length of flares E1, E2, and E3 are derived to be $0.73 \times 10^{10}$ cm, $1.16 \times 10^{10}$ cm, and $0.67 \times 10^{10}$ cm, respectively (see Table 9).

In summary, the flare loop length estimated from X-ray and WL flares are listed in Table 9. The estimated loop length is roughly $\sim 0.5 - 2 \times 10^{10}$ cm, which corresponds to $\sim 8 - 30\%$ of stellar radius. We found that the loop lengths derived from the X-ray rise time by Reale (2007)'s methods are consistent with those derived from WLF's energy-duration relationship proposed by Namekata et al. (2017b). The method proposed by

Shibata & Yokoyama (1999, 2002) also yields a close value that is approximately twice as large as those from other methods for flare E3 (excluding flare E2, where the flare peak was not captured). Thus, this consistency supports the prediction capability of these different methods, which are widely used but not often simultaneously applied. Particularly, in this campaign, as all flares have been observed by TESS, the estimations from WLFs by Namekata et al. (2017b) appear to be very useful for comparing among flares.

The length of the flare loops derived here will be compared with the length scale of prominences and starspots in Section 6.2. This will enable new discussions on the spatial scale ratios of different aspects of eruptive events. Moreover, the length of the flare loops is important for constraining the initial height of prominence eruptions, and is expected to be useful in future comparisons with numerical calculations in our paper II (see Section 6.4).

# 5. Prominence Eruptions on a Young Solar-type Star

## 5.1. Discovery of Blueshifted "Emission" Spectra as Evidence of Stellar Prominence Eruptions

As revealed in Section 3, among the three $H\alpha$ superflares we detected (labeled E1, E2, E3), two superflares (E1, E2) exhibited a significant blueshifted $H\alpha$ "emission" profile. This is the first discovery of the blueshifted $H\alpha$ emission profile on a solar-type star (G-dwarf), while similar emission profiles have been frequently reported on M-dwarfs. The profile exhibits a more prominent blueshifted component compared to those observed in M-type stars: In flare E1, the entire spectrum is blueshifted in the initial phase, and in flare E2, a bump-like structure is observed at a wavelength different from the $H\alpha$ center. This suggests that something different from the usual phenomena seen at the $H\alpha$ center (i.e., flare ribbons) is occurring and moving in the LOS direction. As mentioned in the introduction, Namekata et al. (2022d) detected a blueshifted "absorption" component moving at a maximum velocity of approximately $-510$ km s$^{-1}$ after a superflare (labeled as flare "E4" in Tables 3 and 4), and comparison with solar observations confirmed that this was due to the filament eruption occurring inside the stellar disk. Our new discovery in this study proposed a picture similar to the Sun, where on the solar-type star EK Dra, the $H\alpha$ line appears as an absorption component when cool plasma are present within the stellar disk (called filament) and as an emission component when they extend beyond the disk (called prominence). Given this context, the blueshifted emission component detected this time could likely be the first evidence of prominence eruption on a solar-type star (i.e., a G-dwarf).

The temporal variation of the velocity strongly supports the idea that the observed blueshifted emission components are stellar prominence eruptions. From the temporal evolution of the shifted velocity, it is possible to derive the initial deceleration rate (discussed in more detail in Section 5.2). For flare E1, the deceleration rate is calculated to be $0.34 \pm 0.15$ km s$^{-2}$ for the one-component fit (or $0.23 \pm 0.14$ km s$^{-2}$ for the two-component fit). This corresponds remarkably well with EK Dra's surface gravity of $0.30 \pm 0.05$ km s$^{-2}$, strengthening the picture that a prominence-like cool plasma is ejected and decelerated by the surface gravity of the star. Interestingly, this value is very similar to those of the filament eruption events E4 of $0.34 \pm 0.04$ km s$^{-2}$