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Solar flares are often accompanied by filament/prominence eruptions (~10⁴ K and ~10¹⁰⁻¹¹ cm⁻³), sometimes leading to coronal mass ejections that directly affect the Earth’s environment. ‘Superflares’ are found on some active solar-type (G-type main-sequence) stars, but the filament eruption–coronal mass ejection association has not been established. Here we show that our optical spectroscopic observation of the young solar-type star EK Draconis reveals evidence for a stellar filament eruption associated with a superflare. This superflare emitted a radiated energy of 2.0 × 10³³ erg, and a blueshifted hydrogen absorption component with a high velocity of −510 km s⁻¹ was observed shortly afterwards. The temporal changes in the spectra strongly resemble those of solar filament eruptions. Comparing this eruption with solar filament eruptions in terms of the length scale and velocity strongly suggests that a stellar coronal mass ejection occurred. The erupted filament mass of 1.1 × 10¹⁸ g is ten times larger than those of the largest solar coronal mass ejections. The massive filament eruption and an associated coronal mass ejection provide the opportunity to evaluate how they affect the environment of young exoplanets/the young Earth6 and stellar mass/angular momentum evolution., 太陽型星のスーパーフレアから噴出する巨大フィラメントを初検出 --昔の、そして今の惑星環境や文明に与える脅威--. 京都大学プレスリリース. 2021-12-10.

Star spot evolution is visible evidence of the emergence/decay of the magnetic field on stellar surface, and it is therefore important for the understanding of the underlying stellar dynamo and consequential stellar flares. In this paper, we report the temporal evolution of individual star spot area on the hot-Jupiter-hosting active solar-type star Kepler 17 whose transits occur every 1.5 days. The spot longitude and area evolution are estimated (1) from the stellar rotational modulations of Kepler data and (2) from the brightness enhancements during the exoplanet transits caused by existence of large star spots. As a result of the comparison, number of spots, spot locations, and the temporal evolution derived from the rotational modulations is largely different from those of in-transit spots. We confirm that although only two light curve minima appear per rotation, there are clearly many spots present on the star. We find that the observed differential intensity changes are sometimes consistent with the spot pattern detected by transits, but they sometimes do not match with each other. Although the temporal evolution derived from the rotational modulation differs from those of in-transit spots to a certain degree, the emergence/decay rates of in-transit spots are within an order of magnitude of those derived for sunspots as well as our previous research based only on rotational modulations. This supports a hypothesis that the emergence/decay of sunspots and extremely-large star spots on solar-type stars occur through the same underlying processes., Comment: 37 pages, 12 figures, 1 table. Accepted for publication in The Astrophysical Journal

Recently, many superflares on solar-type stars were discovered as white-light flares (WLFs). A correlation between the energies (E) and durations (t) of superflares is derived as $t\propto E^{0.39}$, and this can be theoretically explained by magnetic reconnection ($t\propto E^{1/3}$). In this study, we carried out a statistical research on 50 solar WLFs with SDO/HMI to examine the t-E relation. As a result, the t-E relation on solar WLFs ($t\propto E^{0.38}$) is quite similar stellar superflares, but the durations of stellar superflares are much shorter than those extrapolated from solar WLFs. We present the following two interpretations; (1) in solar flares, the cooling timescale of WL emission may be longer than the reconnection one, and the decay time can be determined by the cooling timescale; (2) the distribution can be understood by applying a scaling law $t\propto E^{1/3}B^{-5/3}$ derived from the magnetic reconnection theory., 4 pages, 1 figures, paper of the Proceedings of the IAUS340, accepted

We report the latest statistical analyses of superflares on solar-type (G-type main-sequence; effective temperature is 5100 - 6000 K) stars using all of the $Kepler$ primary mission data, and $Gaia$-DR2 (Data Release 2) catalog. We updated the flare detection method from our previous studies by using high-pass filter to remove rotational variations caused by starspots. We also examined the sample biases on the frequency of superflares, taking into account gyrochronology and flare detection completeness. The sample size of solar-type stars and Sun-like stars (effective temperature is 5600 - 6000 K and rotation period is over 20 days in solar-type stars) are $\sim$4 and $\sim$12 times, respectively, compared with Notsu et al. (2019, ApJ, 876, 58). As a result, we found 2341 superflares on 265 solar-type stars, and 26 superflares on 15 Sun-like stars: the former increased from 527 to 2341 and the latter from 3 to 26 events compared with our previous study. This enabled us to have a more well-established view on the statistical properties of superflares. The observed upper limit of the flare energy decreases as the rotation period increases in solar-type stars. The frequency of superflares decreases as the stellar rotation period increases. The maximum energy we found on Sun-like stars is $4 \times 10^{34}$ erg. Our analysis of Sun-like stars suggest that the Sun can cause superflares with energies of $\sim 7 \times 10^{33}$ erg ($\sim$X700-class flares) and $\sim 1 \times 10^{34}$ erg ($\sim$X1000-class flares) once every $\sim$3,000 years and $\sim$6,000 years, respectively., 49 pages, 22 figures, 6 tables, supplementary table, Accepted for publication in The Astrophysical Journal (03-Nov-2020)

Active solar-type stars show large quasi-periodic brightness variations caused by stellar rotations with star spots, and the amplitude changes as the spots emerge and decay. The Kepler data are suitable for investigations on the emergence and decay processes of star spots, which are important to understand underlying stellar dynamo and stellar flares. In this study, we measured temporal evolutions of star spot area with Kepler data by tracing local minima of the light curves. In this analysis, we extracted temporal evolutions of star spots showing clear emergence and decay without being disturbed by stellar differential rotations. We applied this method to 5356 active solar-type stars observed by Kepler and obtained temporal evolutions of 56 individual star spots. We calculated lifetimes, emergence and decay rates of the star spots from the obtained temporal evolutions of spot area. As a result, we found that lifetimes ($T$) of star spots are ranging from 10 to 350 days when spot areas ($A$) are 0.1-2.3 percent of the solar hemisphere. We also compared them with sunspot lifetimes, and found that the lifetimes of star spots are much shorter than those extrapolated from an empirical relation of sunspots ($T\propto A$), while being consistent with other researches on star spot lifetimes. The emerging and decay rates of star spots are typically $5 \times 10^{20}$ $\rm Mx\cdot h^{-1}$ ($8$ $\rm MSH\cdot h^{-1}$) with the area of 0.1-2.3 percent of the solar hemisphere and are mostly consistent with those expected from sunspots, which may indicate the same underlying processes., Comment: 19 pages, 11 figures, accepted for publication in ApJ

We analyze the correlation between starspots and superflares on solar-type stars using observations from the Kepler mission. The analysis shows that the observed fraction of stars with superflares decreases as the rotation period increases and as the amplitude of photometric variability associated with rotation decreases. We found that the fraction of stars with superflares among the stars showing large-amplitude rotational variations, which are thought to be the signature of the large starspots, also decreases as the rotation period increases. The small fraction of superflare stars among the stars with large starspots in the longer-period regime suggests that some of the stars with large starspots show a much lower flare activity than the superflare stars with the same spot area. Assuming simple relations between spot area and lifetime and between spot temperature and photospheric temperature, we compared the size distribution of large starspot groups on slowly-rotating solar-type stars with that of sunspot groups. The size distribution of starspots shows the power-law distribution and the size distribution of larger sunspots lies on this power-law line. We also found that frequency-energy distributions for flares originating from spots with different sizes are the same for solar-type stars with superflares and the Sun. These results suggest that the magnetic activity we observe on solar-type stars with superflares and that on the Sun is caused by the same physical processes., Accepted for publication in PASJ

We searched for superflares on solar-type stars using the Kepler short-cadence (1-min sampling) data in order to detect superflares with short duration. We found 187 superflares on 23 solar-type stars whose bolometric energy ranges from the order of $10^{32}$ erg to $10^{36}$ erg. Using these new data combined with the results from the data with 30-min sampling, we found the occurrence frequency ($dN/dE$) of superflares as a function of flare energy ($E$) shows the power-law distribution ($dN/dE \propto E ^{-\alpha}$) with $\alpha=1.5$ for $10^{33}, Comment: 6 pages, 4 figures, submitted to the proceedings of the IAU Symposium 320 "Solar and Stellar Flares and Their Effects on Planets" (eds. A. G. Kosovichev, S. L. Hawley, P. Heinzel)

Recent studies of solar-type superflare stars have suggested that even old slowly rotating stars similar to the Sun can have large starspots and superflares. We conducted high dispersion spectroscopy of 49 nearby solar-analog stars (G-type main sequence stars with $T_{\rm{eff}}\approx5,600\sim6,000$ K) identified as ROSAT soft X-ray sources, which are not binary stars from the previous studies. We expected that these stars can be used as a proxy of bright solar-analog superflare stars, since superflare stars are expected to show strong X-ray luminosity. More than half (37) of the 49 target stars show no evidence of binarity, and their atmospheric parameters ($T_{\rm{eff}}$, $\log g$, and [Fe/H]) are within the range of ordinary solar-analog stars. We measured Ca II 8542 and H$\alpha$ lines, which are good indicators of the chromospheric activity. The intensity of these lines indicates that all the target stars have large starspots. We also measured $v\sin i$ (projected rotational velocity) and Lithium abundance for the target stars. Li abundance is a key to understanding the evolution of the stellar convection zone, which reflects the stellar age, mass and rotational history. We confirmed that many of the target stars rapidly rotate and have high Li abundance, compared with the Sun, as suggested by many previous studies. There are, however, also some target stars that rotate slowly ($v\sin i$=2$\sim$3 km s$^{-1}$) and have low Li abundance like the Sun. These results support that old and slowly rotating stars similar to the Sun could have high activity level and large starspots. This is consistent with the results of our previous studies of solar-type superflare stars. In the future, it is important to conduct long-term monitoring observations of these active solar-analog stars in order to investigate detailed properties of large starspots from the viewpoint of stellar dynamo theory., Comment: 52 pages, 18 figures, 6 tables, accepted for publication in PASJ. arXiv admin note: text overlap with arXiv:1412.8243

Observations of superflares on solar-type stars indicate that they are associated with much larger starspots than appear on the Sun, occur more frequently on rapidly rotating stars and, contrary to a previous proposal, are not frequently associated with hot Jupiters. Solar flares are the most energetic explosions in the solar atmosphere, and similar flares occur on many stars. 'Superflares' many thousands of times more energetic than the average solar flare have been observed from a variety of stars, but the relatively small number observed on solar-type stars has hitherto precluded a detailed study of them. Now, on the basis of an analysis of data from the Kepler satellite, Maehara et al. report observations of 365 superflares, including 101 from slowly rotating solar-type stars, from a sample of around 83,000 stars observed over 120 days. The data suggest that superflares occur more frequently on rapidly rotating stars and on stars with 'starspots' much larger than the sunspots with which we are familiar. There is no historical record of superflares on the Sun in the past 2,000 years, and it is probable that none has occurred in the past one billion years. Bradley Schaefer discusses these findings in an accompanying News and Views, and concludes that it is extremely unlikely that the Sun will host a superflare. Solar flares are caused by the sudden release of magnetic energy stored near sunspots. They release 1029 to 1032 ergs of energy on a timescale of hours1. Similar flares have been observed on many stars, with larger ‘superflares’ seen on a variety of stars2,3, some of which are rapidly rotating4,5 and some of which are of ordinary solar type3,6. The small number of superflares observed on solar-type stars has hitherto precluded a detailed study of them. Here we report observations of 365 superflares, including some from slowly rotating solar-type stars, from about 83,000 stars observed over 120 days. Quasi-periodic brightness modulations observed in the solar-type stars suggest that they have much larger starspots than does the Sun. The maximum energy of the flare is not correlated with the stellar rotation period, but the data suggest that superflares occur more frequently on rapidly rotating stars. It has been proposed that hot Jupiters may be important in the generation of superflares on solar-type stars7, but none have been discovered around the stars that we have studied, indicating that hot Jupiters associated with superflares are rare.

Recently, many superflares on solar-type stars have been discovered as white-light flares (WLFs). The statistical study found a correlation between their energies ($E$) and durations ($\tau$): $\tau \propto E^{0.39}$ (Maehara et al. 2017 $EP\& S$, 67, 59), similar to those of solar hard/soft X-ray flares: $\tau \propto E^{0.2-0.33}$. This indicates a universal mechanism of energy release on solar and stellar flares, i.e., magnetic reconnection. We here carried out a statistical research on 50 solar WLFs observed with \textit{SDO}/HMI and examined the correlation between the energies and durations. As a result, the $E$--$\tau$ relation on solar WLFs ($\tau \propto E^{0.38}$) is quite similar to that on stellar superflares ($\tau \propto E^{0.39}$). However, the durations of stellar superflares are one order of magnitude shorter than those expected from solar WLFs. We present the following two interpretations for the discrepancy. (1) In solar flares, the cooling timescale of WLFs may be longer than the reconnection one, and the decay time of solar WLFs can be elongated by the cooling effect. (2) The distribution can be understood by applying a scaling law ($\tau \propto E^{1/3}B^{-5/3}$) derived from the magnetic reconnection theory. In this case, the observed superflares are expected to have 2-4 times stronger magnetic field strength than solar flares., Comment: 43 pages, 15 figures, accepted for publication in ApJ

We performed the high dispersion spectroscopy of solar-type superflare stars by Subaru/HDS, and estimate the stellar parameters and lithium abundance of the stars to compare with the Sun. Our spectroscopic analysis of superflare stars show more than half of targets have no evidence of binary system and the stellar parameters are in the range of solar-type stars (Notsu et al. 2015a&b). We also investigate the correlations of Lithium abundance with stellar atmospheric parameters, rotational velocity, and superflare activities to understand the nature of superflare stars and the possibility of the nucleosynthesis of lithium by superflares. The derived lithium abundance in superflare stars do not show the correlation with stellar parameters. As compared with the lithium abundance in Hyades cluster which is younger than the sun, it is suggested that half of observed stars are young. However, there are some objects which show the low lithium and slowly rotate from the estimated v sin(i) and period of brightness variation. These results indicate that the superflare stars are not only young stars but also old stars like our sun. In our observations, we could not find the any evidence of lithium productions by superflare.

We carried out spectroscopic observations with Subaru/HDS of 50 solar-type superflare stars found from Kepler data. More than half (34 stars) of the target stars show no evidence of the binary system, and we confirmed atmospheric parameters of these stars are roughly in the range of solar-type stars. We then conducted the detailed analyses for these 34 stars. First, the value of the "$v\sin i$" (projected rotational velocity) measured from spectroscopic results is consistent with the rotational velocity estimated from the brightness variation. Second, there is a correlation between the amplitude of the brightness variation and the intensity of Ca II IR triplet line. All the targets expected to have large starspots because of their large amplitude of the brightness variation show high chromospheric activities compared with the Sun. These results support that the brightness variation of superflare stars is explained by the rotation of a star with large starspots., Comment: 6 pages, 3 figures, to appear in the Proceedings of IAU Symposium No. 320 "Solar and Stellar Flares and Their Effects on Planets". The main results of this manuscript are based on Notsu et al. (2015a, PASJ, 67, 32) and (2015b, PASJ, 67, 33)

We report on the abundance analysis of Li in solar-type (G-type main sequence) superflare stars which were found by the analysis of Kepler photometric data. Li is a key element to understand the evolution of the stellar convection zone which reflects the age of solar-type stars. We performed the high dispersion spectroscopy of solar-type superflare stars with Subaru/HDS, and confirmed that 34 stars show no evidence of binarity in our previous study. In this study, we derived the Li abundances of these 34 objects. We investigate correlations of Li abundance with stellar atmospheric parameters, rotational velocity, and superflare activities to understand the nature of superflare stars and the possibility of the nucleosynthesis of Li by superflares. We confirm the large dispersion in the Li abundance, and the correlation with stellar parameters is not seen. As compared with the Li abundance in Hyades cluster which is younger than the Sun, it is suggested that half of the observed stars are younger than Hyades cluster. The measured value of $v \sin i$ (projected rotational velocity) supports those objects are younger than the Sun. However, there are some objects which show the low Li abundance and slowly rotate on the basis of the estimated $v \sin i$ and $P$ (period of brightness variation). This result indicates that the superflare stars are not only young stars but also old stars like our Sun. In our observations, we could not find any evidence of Li productions by superflares. Further research on Li isotope abundances of superflare stars would clarify the Li production by stellar flares., Comment: 19 pages, 6 figures, 2 tables, accepted for publication in PASJ

We conducted high dispersion spectroscopic observations of 50 superflare stars with Subaru/HDS, and measured the stellar parameters of them. These 50 targets were selected from the solar-type (G-type main sequence) superflare stars that we had discovered from the Kepler photometric data. As a result of these spectroscopic observations, we found that more than half (34 stars) of our 50 targets have no evidence of binary system. We then estimated effective temperature ($T_{\rm{eff}}$), surface gravity ($\log g$), metallicity ([Fe/H]), and projected rotational velocity ($v\sin i$) of these 34 superflare stars on the basis of our spectroscopic data. The accuracy of our estimations is higher than that of Kepler Input Catalog (KIC) values, and the differences between our values and KIC values ($(\Delta T_{\rm{eff}})_{\rm{rms}} \sim 219$K, $(\Delta \log g)_{\rm{rms}} \sim 0.37$ dex, and $(\Delta\rm{[Fe/H]})_{\rm{rms}} \sim 0.46$ dex) are comparable to the large uncertainties and systematic differences of KIC values reported by the previous researches. We confirmed that the estimated $T_{\rm{eff}}$ and $\log g$ values of the 34 superflare stars are roughly in the range of solar-type stars. In particular, these parameters and the brightness variation period ($P_{0}$) of 9 stars are in the range of "Sun-like" stars ($5600\leq T_{\rm{eff}}\leq 6000$K, $\log g\geq$4.0, and $P_{0}>$10 days). Five of the 34 target stars are fast rotators ($v \sin i \geq 10$km s$^{-1}$), while 22 stars have relatively low $v \sin i$ values ($v \sin i, Comment: 45 pages, 15 figures, 5 tables, PASJ in press (Already published online on February 22, 2015. doi:10.1093/pasj/psv001 )

We present the results of an extensive survey of superflares on late-type stars (G, K, and M-type main sequence stars) using the Kepler satellite data. Wefound about 6,800 superflares on late-type stars from the data of about 120,000 stars observed over 500 days. The total bolometric energy of superflares in oursample ranges from 1032 erg to 1036 erg. Our data suggest that the occurrencefrequency of superflares depends on the surface temperature and the rotationperiod of stars. Superflares on M-type stars occur about 10-100 times morefrequently than those on G-type stars. Our results suggest that the average frequency ofsuperflares releasing 1034–1035 erg of energy (100-1,000 times larger than the largestsolar flares) on M-type stars and Sun-like stars is once in 10 years and once in a few thousand years respectively.

We report on the results of high dispersion spectroscopy of two `superflare stars', KIC 9766237, and KIC 9944137 with Subaru/HDS. Superflare stars are G-type main sequence stars, but show gigantic flares compared to the Sun, which have been recently discovered in the data obtained with the Kepler spacecraft. Though most of these stars are thought to have a rotation period shorter than 10 days on the basis of photometric variabilities, the two targets of the present paper are estimated to have a rotation period of 21.8 d, and 25.3 d. Our spectroscopic results clarified that these stars have stellar parameters similar to those of the Sun in terms of the effective temperature, surface gravity, and metallicity. The projected rotational velocities derived by us are consistent with the photometric rotation period, indicating a fairy high inclination angle. The average strength of the magnetic field on the surface of these stars are estimated to be 1-20 G, by using the absorption line of Ca II 8542. We could not detect any hint of binarity in our spectra, although more data are needed to firmly rule out the presence of an unseen low-mass companion. These results claim that the spectroscopic properties of these superflare stars are very close to those of the Sun, and support the hypothesis that the Sun might cause a superflare., Comment: 11 pages, 6 figures, accepted for publication in PASJ

By extending our previous study by Maehara et al. (2012), we searched for superflares on G-type dwarfs (solar type stars) using Kepler data for a longer period (500 days) than that (120 days) in our previous study. As a result, we found 1547 superflares on 279 G-type dwarfs, which are much more than previous 365 superflares on 148 stars. Using these new data, we studied the statistical properties of occurrence frequency of superflares, and basically confirmed the previous results, i.e., the occurrence frequency (dN/dE) of superflares vs flare energy (E) shows power-law distribution with dN/dE \propto E^{-\alpha}, where \alpha ~ 2. It is interesting that this distribution is roughly on the same line as that for solar flares. In the case of the Sun-like stars (with surface temperature 5600-6000K and slowly rotating with a period longer than 10 days), the occurrence frequency of superflares with energy of 10^34 -10^35 erg is once in 800-5000 years. We also studied long term (500 days) stellar brightness variation of these superflare stars, and found that in some G-type dwarfs the occurrence frequency of superflares was extremely high, ~ 57 superflares in 500 days (i.e., once in 10 days). In the case of Sun-like stars, the most active stars show the frequency of one superflares (with 10^34 erg) in 100 days. There is evidence that these superflares have extremely large starspots with a size about 10 times larger than that of the largest sunspot. We argue that the physical origin of extremely high occurrence frequency of superflares in these stars may be attributed to the existence of extremely large starspots., Comment: Accepted to the ApJ Supplement in August 2013

We conducted the high-resolution spectroscopic observation with Subaru/HDS for a G-type star (KIC6934317). We selected this star from the data of the Kepler spacecraft. This star produces a lot of superflares, and the total energy of the largest superflare on this star is ~10^3 times larger (~2.2*10^35 erg) than that of the most energetic flare on the Sun (~10^32 erg). The core depth and emission flux of Ca II infrared triplet lines and Ha line show high chromospheric activity in this star, in spite of its low lithium abundance and the small amplitude of the rotational modulation. Using the empirical relations between emission flux of chromospheric lines and X-ray flux, this star is considered to show much higher coronal activity than that of the Sun. It probably has large starspots which can store a large amount of magnetic energy enough to give rise to superflares. We also estimated the stellar parameters, such as effective temperature, surface gravity, metallicity, projected rotational velocity (v sin_i), and radial velocity. KIC6934317 is then confirmed to be an early G-type main sequence star. The value of v sin_i is estimated to be ~1.91 km s^-1. In contrast, the rotational velocity is calculated to be ~20 km s^-1 by using the period of the brightness variation as the rotation period. This difference can be explained by its small inclination angle (nearly pole-on). The small inclination angle is also supported by the contrast between the large superflare amplitude and the small stellar brightness variation amplitude. The lithium abundance and isochrones implies that the age of this star is more than about a few Gyr, though a problem why this star with such an age has a strong activity remains unsolved., Comment: 33 pages, 7 figures, accepted by Publications of the Astronomical Society of Japan (PASJ) on July 18, 2013 (to be published on PASJ vol. 65, No. 5 (October 25, 2013))

Recent observations of solar type stars with the Kepler satellite by Maehara et al. have revealed the existence of superflares (with energy of 10^33 - 10^35 erg) on Sun-like stars, which are similar to our Sun in their surface temperature (5600 K - 6000 K) and slow rotation (rotational period > 10 days). From the statistical analysis of these superflares, it was found that superflares with energy 10^34 erg occur once in 800 years and superflares with 10^35 erg occur once in 5000 years on Sun-like stars. In this paper, we examine whether superflares with energy of 10^33 - 10^35 erg could occur on the present Sun through the use of simple order-of-magnitude estimates based on current ideas relating to the mechanisms of the solar dynamo., Accepted by Publ. Astron. Soc. Japan on Dec. 6, 2012 (to be published on PASJ vol. 65, No. 3, (2013) June 25)

We conducted high dispersion spectroscopic observations of 50 superflare stars with Subaru/HDS. These 50 stars were selected from the solar-type superflare stars that we had discovered from the Kepler data. More than half (34 stars) of these 50 target superflare stars show no evidence of binarity, and we estimated stellar parameters of these 34 stars in our previous study (Notsu et al. 2015, hereafter called Paper I). According to our previous studies using Kepler data, superflare stars show quasi-periodic brightness variations whose amplitude (0.1-10\%) is much larger than that of the solar brightness variations (0.01-0.1\%) caused by the existence of sunspots on the rotating solar surface. In this study, we investigated whether these quasi-periodic brightness variations of superflare stars are explained by the rotation of a star with fairly large starspots, by using stellar parameters derived in Paper I. First, we confirmed that the value of the projected rotational velocity $v \sin i$ is consistent with the rotational velocity estimated from the period of the brightness variation. Next, we measured the intensity of Ca II infrared triplet lines and H$\alpha$ line, good indicators of the stellar chromospheric activity, and compared them with other stellar properties. The intensity of Ca II infrared triplet lines indicates that the mean magnetic field strength ($\langle fB\rangle$) of the target superflare stars can be higher than that of the Sun. A correlation between the amplitude of the brightness variation and the intensity of Ca II triplet line was found. All the targets expected to have large starspots because of their large amplitude of the brightness variation show high chromospheric activities compared to the Sun. These results support that the brightness variation of superflare stars is due to the rotation with large starspots., Comment: 25 pages, 9 figures, 1 tables, accepted for publication in PASJ

We performed simple spot-model calculations for quasi-periodic brightness variations of solar-type stars showing superflares, by using Kepler photometric data. Most of superflare stars show quasi-periodic brightness modulations with the typical period of one to a few tens of days. Our results indicate that these brightness variations of superflare stars can be explained by the rotation of the star with fairly large starspots. Using the result of the period analysis, we investigated the relation between the energy and frequency of superflares and the rotation period. Stars with relatively slower rotation rates can still produce flares that are as energetic as those of more rapidly rotating stars, although the average flare frequency is lower for more slowly rotating stars. We found that the energy of superflares are related to the total coverage of starspots. The correlation between the spot coverage and the flare energy in superflares is similar to that in solar flares. These results suggest that the energy of superflares can be explained by the magnetic energy stored around starspots., Comment: 34 pages, 10 figures, Published. (2013, ApJ, 771, 127)