High Dispersion Spectroscopy of Solar-type Superflare Stars. III. Lithium Abundances
Satoshi Honda, Yuta Notsu, Hiroyuki Maehara, Shota Notsu, Takuya Shibayama, Daisaku Nogami, Kazunari Shibata
aa r X i v : . [ a s t r o - ph . S R ] M a y High Dispersion Spectroscopy of Solar-type SuperflareStars. III. Lithium Abundances ∗ Satoshi Honda , Yuta Notsu , Hiroyuki Maehara , Shota Notsu , Takuya Shibayama ,Daisaku Nogami , and Kazunari Shibata Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo, 407-2,Nishigaichi, Sayo-cho, Sayo, Hyogo 679-5313, [email protected] Department of Astronomy, Kyoto University, Kitashirakawa-Oiwake-cho,Sakyo-ku, Kyoto 606-8502 Okayama Astrophysical Observatory, National Astronomical Observatory of Japan, 3037-5Honjo,Kamogata, Asakuchi, Okayama 719-0232, Japan Solar-Terrestrial Environment Laboratory, Nagoya University, Furo-cho, Chikusa-ku, Nagoya,Aichi, 464-8601, Japan Kwasan Observatory, Kyoto University, Yamashina-ku, Kyoto 607-8471, Japan (Received ; accepted )
Abstract
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 akey element to understand the evolution of the stellar convection zone which reflectsthe 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 evidenceof binarity in our previous study. In this study, we derived the Li abundances of these34 objects. We investigate correlations of Li abundance with stellar atmosphericparameters, rotational velocity, and superflare activities to understand the nature ofsuperflare stars and the possibility of the nucleosynthesis of Li by superflares. Weconfirm the large dispersion in the Li abundance, and the correlation with stellarparameters is not seen. As compared with the Li abundance in Hyades cluster whichis younger than the Sun, it is suggested that half of the observed stars are youngerthan Hyades cluster. The measured value of v sin i (projected rotational velocity)supports those objects are younger than the Sun. However, there are some objectswhich 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 superflarestars 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 onLi isotope abundances of superflare stars would clarify the Li production by stellar1ares. Key words: stars: flare — stars: solar-type —stars: rotation — stars: activity— stars:abundances
1. Introduction
Lithium (Li) is easily destroyed in the hotter region (p, α reactions ; Li : T ≥ × K, Li : T ≥ × K) of stellar atmosphere. We can obtain the information about theevolution of convection layer from the behavior of Li abundance. The accurate spectroscopicdetermination of the Li abundance in young solar-type stars provide independent and reliableage diagnostics (e.g., Herbig 1965, Duncan 1981). In addition, accurate measurements of theLi abundance and, in particular, the Li/ Li isotopic ratio in stellar atmospheres are of crucialimportance for addressing questions about the Big Bang nucleosynthesis (e.g., Spite & Spite1982, Boesgaard & Steigman 1985), the chemical evolution of the Galaxy (e.g., Ryan et al.2001), mixing processes in stellar interiors, and the evolution of extra-solar planetary systems(e.g., Bouvier 2008, Israelian 2009, Gonzalez 2015).Solar flares are the most energetic explosions on the surface of the Sun, and are thoughtto occur by release of magnetic energy (Shibata & Magara 2011). Flares are also known tooccur on various types of stars including solar-type stars. Among them, young stars, closebinary stars, and dMe stars sometimes produce “superflares”, flares whose total energy is 10-10 times larger (10 − erg) than the largest flares on the Sun ( ∼ erg) (Schaefer et al.2000). It has been recognized that the superflares will not occur on the slowly-rotating singlesolar-type stars. However, Maehara et al. (2012) analyzed the photometric data by the Keplerspacecraft, and discovered 365 superflare events on 148 solar-type stars that have the effectivetemperature of 5,100K ≤ T eff ≤ g ≥ ≤ T eff ≤ g ≥ P ) >
10 days). Maehara et al. (2015) also found 187 * Based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatoryof Japan. dN/dE ) of superflares versus flare energy ( E ) shows a power-law distributionwith dN/dE ∝ E − α where α ∼ α lines of KIC 6934317. Theseresults support the idea of existence of large starspots. They also found the low Li abundancein that star. Nogami et al. (2014) obtained spectroscopic data of the slowly-rotating superflarestars KIC 9766237 and KIC 9944137, and found that these superflare stars have very Sun-likeatmospheric parameters including the Li abundance of the Sun. Wichmann et al. (2014) carriedout high dispersion spectroscopy for superflare stars from the list of Maehara et al. (2012). Theyfound that several of those stars are very young and active, but some other stars do not showthe cause of occurrence of superflares.Notsu et al. (2015a,b; hereafter Paper I, II) observed a large sample of “solar-type”superflare stars. They picked up single stars and confirmed the atmospheric parameters of“solar-type” superflare stars are similar to the solar ones by high dispersion spectroscopy. Inparticular, they found that 9 stars are in the range of “Sun-like” stars. This result supportsthe hypothesis that the Sun might cause a superflare. In paper II, they showed the correlationbetween the intensity of Ca II infrared triplet lines, which are good indicators of the stellarchromospheric activities, and amplitude of brightness variation among their observed superflarestars. These results clearly show that all the targets have large starspots and high chromo-spheric activity compared with the Sun. From those observational results, we can say that thebrightness variation of superflare stars is due to the rotation with large spots. The problemwhich we have to consider next is whether the present Sun causes the superflare or not.Several studies have been done on the behavior of Li abundances in solar-type stars so far.Takeda et al. (2007, 2010) observed the large sample of “solar-analog” stars (selected with thephotometric criteria of 0 . < ∼ B − V < ∼ .
67 and 4 . < ∼ M v < ∼ .
1) and investigated the correlationsof stellar parameters with Li abundance. They found clear correlations among Li abundance,stellar activity and rotation. Mishenina et al. (2012) also investigated the correlations amongLi abundance, stellar parameters and activity in the F,G,K dwarfs. They show the Li-activitycorrelation is evident only in a restricted temperature range (5,200 < T eff < Li observed in the interstellarmedium are caused by stellar flares. de la Reza et al. (1981) determined the Li abundancein flare stars. They did not find a general relation between Li abundance and chromosphericactivity. On the other hand, Tatischeff & Thibaud (2007) show that the Li could be producedby the reaction He( He, p ) Li in situ by solar-like flares. Montes & Ramsey (1998) reportedthe Li line enhancement during a long-duration flare in active binary. They suggest this Lienhancement is caused by spallation reactions during the flare. However, there is no clearevidence of productions of Li by stellar flares. In addition, Giampapa (1984) demonstratedthat the spots and plages could alter the observed Li line on the basis of solar observations.Although many attempts have been made to study the possibilities of Li production in stellarflares, it is still controversial.Here we show the lithium abundance in superflare stars and discuss it’s relation withstellar activity, rotation velocity, and age of stars. In paper I and II, we determined theatmospheric parameters of superflare stars with high dispersion spectroscopy and discuss thespots and activity for understanding the nature of superflare stars. This is the third paper ofour spectroscopic studies of superflare stars. In Sect. 2 and 3, we describe the observationsand analysis of Li abundance in superflare stars, and in Sect. 4 we show the behaviors of Liabundance as a function of stellar parameters, discuss the reasons of Li distribution and thepossibility of Li production by superflares. In Sect. 5 we summarize the paper.
2. Observations
High dispersion spectroscopy was carried out for 50 solar-type superflare stars (Notsuet al. 2013a, 2015a), which were found by Maehara et al. (2012) and Shibayama et al. (2013),on 2011 Aug. 3 (S11B-137S), 2012 Aug. 6-8, Sep. 22-25 (S12B-111N) and 2013 June 23-24(S13A-045N) using Subaru High Dispersion Spectrograph (HDS : Noguchi et al. 2002). Weapplied the image slicer ( ♯
2) in the observations of S13A (Tajitsu et al. 2012). In addition, wehave observed 10 bright solar-type stars and the Moon for comparison. Among them, 8 starsare reported as “solar-twin” stars by the previous studies (King et al. 2005, Takeda & Tajitsu2009, Datson et al. 2012). The details of observations and target stars are shown in Paper I.The spectrum covers 6100-8820 ˚A with a resolving power ( R = λ/ ∆ λ ) of 97,000 forS11B, 51,000 for S12B and 80,000 for S13A by 2 × α (6563 ˚A), and Ca II triplet (8498, 8542, 8662 ˚A). Thereduction was carried out in a standard manner using the IRAF echelle package . We haveexcluded the binary stars in the following analysis. The 16 of 50 targets were recognized to be IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Associationof Universities for Research in Astronomy, Inc. under cooperative agreement with the National ScienceFoundation.
3. Analysis
We derived the Li abundances and v sin i (projected rotational velocity) from thosespectra using the atmospheric parameters determined by Paper I. The method of estimationsof v sin i is described in Notsu et al. (2013a) and Paper I. The objects are distributed in therange of T eff from 5,000K to 6,300K and log g from 3.5 to 4.9. We note that there are largedifferences between atmospheric parameters taken from Kepler Input Catalog (KIC : Brown etal. 2011) and our obtained values (Paper I). The estimated values of atmospheric parametersby spectroscopy are more reliable than that from photometric data such as KIC values (cf.,Paper I). The adopted values in this analysis are shown in Table 1.For the abundance analysis, we used the analysis program SPTOOL which was devel-oped by Y. Takeda (private communication), based on Kurucz’s ATLAS9/WIDTH9 (Kurucz1993). We assumed local thermodynamic equilibrium (LTE) and derived abundances usingthe synthesis spectrum with interpolated model atmospheres taken from Kurucz (1993). Theline data around Li I 6708 ˚A region are taken from the list of Takeda & Kawanomoto (2005),which are based on the list of Smith et al. (1998) and Lambert et al. (1993). We assumed thecontributions of Li are negligible. Figure 1 shows the spectra of all sample stars in the portionof the Li I 6708 line region. We used the value of solar abundances obtained by Asplund et al.(2009). The upper limit of Li abundance is estimated by the method of Takeda & Kawanomoto(2005). They used the averaged FWHM (full width at half maximum) of weak Fe lines andsignal to noise ratios (S/N) for deriving the upper limit value. Adopted atmospheric parametersand derived Li abundances are shown in Table 1.We assume that there are two main sources of error. One is a systematic error byatmospheric parameters, and another is a random error depending on S/N. Systematic errorsare caused by the choice of the model atmosphere. The typical estimated errors for T eff , log g , v turb , and [Fe/H] are 50 K, 0.2 dex, 0.2 km s − , and 0.1 dex on the basis of Paper I. Changesin the abundance of Li caused by errors of the above parameters are 0.05, 0.01, 0.06, and 0.00dex for the typical atmospheric parameter. The total systematic error is 0.08 dex, which isestimated from the root sum square of the above 4 systematic error values.The uncertainties arising from profile fitting error depend on the S/N and equivalentwidth of Li I line. We estimate the errors of measurement of equivalent width by using theformula derived by Cayrel (1988), which is taking in the S/N, resolution, and FWHM of line.Then, we estimate the severity of the value of A (Li) from that estimation. In most cases, thechanges of A (Li) are smaller than 0.05 dex. However, a few objects show larger than 0.1 dex. http://optik2.mtk.nao.ac.jp/ ∼ takeda/sptool/ A (Li)stars have larger error than that of high A (Li) stars.In the case of typical atmospheric parameter and Li abundance ( T eff = 5,500K, log g =4.4, A (Li) = 2.1) in our sample, the effect of non-LTE is about 0.06 dex by using the grid ofcorrections (Carlsson et al. 1994). However, it must be noted that the correction of –0.3 dex isthe most effective case for KIC 11610797, which has the highest T eff and Li abundance in oursample.We then assume the typical error of Li abundance is about 0.15 dex in those objectsfrom what has been discussed above.
4. Results and Discussion T eff ) Figure 2 shows the behavior of the Li abundances as a function of T eff of our target starswith F,G,K type stars (Takeda & Kawanomoto 2005). The Li depletion is remarkably seenin the stars whose temperature is lower than the Sun ( T eff < ∼ T eff stars. The depletion of Li in the stellarsurface by convective mixing increases with a lapse of time. Hence, we can consider that highLi stars are young stars.However, a large diversity (by more than 2 dex) of the Li abundance is seen in stars withthe solar temperature, despite the similarity of stellar parameters (cf., Takeda & Kawanomoto2005). Especially, the solar Li abundance is quite low. The standard stellar model cannotexplain this diversity. The behavior of the Li abundance in solar-analog stars is still unclear.The Li abundances of superflare stars do not show clear relations with T eff . The temper-ature distribution of our target stars is slightly lower than that of the Sun. We have selected thetarget of superflare stars having the parameters similar to the Sun based on the temperature ofKIC. The estimated temperature by KIC is systematically about 200K lower than other studies(e.g., Pinsonneault et al. 2012, Paper I).We can find the trend of low Li for rotation period ( P ) ≥
10 days and high Li for
P <
10 days. This trend is the same for the superflare stars having the parameters similar to theSun (Figure 2b). The stellar rotation also might affect the Li depletion in superflare stars.We can consider that three stars (KIC 11610797, KIC 9652680, and KIC 8429280) whichshow an especially high value of Li are very young stars. It is also supported that these starsare young, because they show large projected rotational velocity ( v sin i ) and small rotationperiod ( P ). In addition to these three stars, about half of the objects show high Li comparedwith the stars in the Hyades cluster (Figure 3). The estimated age of Hyades cluster is 6.25 × yr (e.g., Perryman et al. 1998), which is one of the old open clusters but younger than thesolar age. It is acceptable to suppose that the young stars show high activities and superflares.However, more than ten stars with superflares do not show high values of Li (includingupper limits) compared with the Hyades cluster. In particular, some objects show quite lowvalues of Li like the Sun. Among them, stellar parameters of KIC 9766237 and KIC 9944137are also very similar to the Sun (Nogami et al. 2014). Maehara et al. (2012) found the frequency of superflares increases with increasing thestellar rotation velocity. In general, the stellar rotation has a correlation with the age and activ-ity of the star. The young stars have rapid rotation, high activity and high Li abundance, butthey have the decrease in the rotation, the activity and Li abundance with the age (Skumanich1972). Takeda et al. (2010) proposed that the stellar rotation ( v sin i ) may be the most importantparameter in determining the surface Li content in the solar-analog stars. Figure 4 showsthe correlation of Li abundance with v sin i of superflare stars and ordinary solar-analog stars(Takeda et al. 2010). The v sin i of solar-analog stars distributed mainly between from 2 to 5km s − , and which show a clear correlation with Li abundance.Superflare stars show a wider range of v sin i than the solar-analog stars. We must notethat this is not the typical distribution of superflare stars due to the selection bias (Paper I).However, we can find the trend of low Li and large v sin i in superflare stars compared withsolar-analog stars. Some of them have a lower temperature ( T eff ≤ g<
4) than those of the Sun. Those stars tend to show lower Li abundances since they have theconvection layer deeper than the typical solar-analog stars (5,500 K < T eff < g ≥ v sin i > P <
10 days).Exception is KIC 11764567, which shows large v sin i and low Li, but it has Sun-likeatmospheric parameters. The rotational velocity of this star estimated from P is inconsistentwith v sin i (cf., Paper II). This star might belong to a binary system. In the case of a binarysystem, observed superflares do not always reflect the primary solar-type star’s phenomenon.The Li abundances of KIC 4831454 and KIC 7354508 are remarkably deviated from thesolar-analog stars. KIC 4831454 has a small inclination angle (Paper II), which should be rapidrotation by the estimation from P . On the other hand, KIC 7354508 shows lower Li abundancethan the solar one in spite of slightly larger v sin i than the solar one. We also found that thestar shows a large value of radial velocity ( –112.8 km s − ; Paper I ). It is quite likely that thisstar is also belongs to a binary system.We can find that there are some superflare stars with low Li abundance ( A (Li) < v sin i ( < ∼ − ) like the Sun. Among them, KIC 1197517, KIC 8359398,7IC 11303472, and KIC 6504503 are not Sun-like stars. KIC 1197517, KIC 8359398, and KIC11303472 have low temperature ( T eff < g =3.6). However, there are some Sun-like superflare stars which show slow-rotation and low Liabundance like the Sun.In Paper I, we tried to estimate the age of superflare stars from isochrone. It is difficultto distinguish whether slightly low log g stars are post-MS or pre-MS only from the isochrone.Li abundance gives important clues about the age of the star. The Li abundances in manysuperflare stars have higher values than that of the Sun. Especially, those stars with a very highLi abundance are suggested to have a rapid rotation velocity from large v sin i and brightnessvariations having a short period. The stellar rotation is also an index of the age. It seemsreasonable to assume that the age of those stars are young. However, some superflare starsshow small v sin i (slow rotation) and low Li abundance. This result may indicate that thosestars are not young. Superflare stars are not necessarily young on the basis of our spectroscopicobservations. r (8542)) indexes and Li abundances. The r (8542) index is residual core flux normalized by the continuum level at the linecore of the Ca II (8542 ˚A). The r (8542) index reflects the activity of stellar chromosphere (e.g.,Linsky et al. 1979) and well correlates with the intensity of the stellar mean magnetic field (cf.,Paper II). Takeda et al. (2010) shows the positive correlation among Li abundances, r (8542)and v sin i for solar-analog stars. They conclude the depletion of surface Li in solar-type starsoperates more efficiently as stellar rotation decelerates.In Paper II, the measured r (8542) index shows that the superflare stars have higherchromospheric activity compared with the Sun. In addition to this, we found the correlationbetween the amplitude of the brightness variation and the r (8542). This correlation can beexplained by the difference of the spot size of superflare stars.Figure 5 shows the Li abundances as a function of r (8542) index for solar-analog stars(Takeda et al. 2010). We could not find the positive correlation between Li abundance and r (8542) of superflare stars compared with solar-analog stars. Duncan (1981) investigated theLi abundances and core flux of Ca II K line in solar-type stars. They found there are a numberof high Li abundances and very little chromospheric emission flux, and the converse is rare.However, there are some low Li and high r (8542) stars, which are not rare in superflare stars.These results indicate that some superflare stars have large active region but low Liabundance. Our results are not consistent with the Skumanich’s law (Skumanich 1972). TheSkumanich’s law cannot apply to these superflare stars. We cloud not determine whether thosestars are young or old from Ca II flux.The large spots are constituted to make enhancement of Li abundance than the normalregion. Pallavicini et al. (1987) suggested that the strong Li line could be due to large cool8pots in RS CVn stars. Superflare stars should have large spots on the stellar surface estimatedfrom the amplitude of brightness variations. However, we can not find the strong Li line insuch superflare stars with large spots. That effect may not be seen on about region of 10%(e.g., Notsu et al. 2013b) in the stellar surface. Tatischeff & Thibaud (2007) showed the possibilities of Li ( Li) production by stellarflares. However, there is no conclusive evidence that Li is produced in situ by stellar flares.Superflare stars are good objects to investigate whether flares can make Li or not. If Li produc-tion occurs during superflares, we could see an increase in the Li abundance of the superflarestars with frequent large flares. Contrary to such hypothesis, the results indicated that the Liabundance decreases as the number of superflares increases. Figure 6 shows the Li abundanceas a function of the number of superflares and frequency of superflares in our target stars. Wemust note that the numbers of superflares should be a lower limit. It is because the detectionof relatively small superflares is somewhat affected by stellar brightness variations (Shibayamaet al. 2013). The frequency of superflares is obtained by dividing the number of superflares bythe total observation time. KIC 8547383, KIC 7420545, KIC 6934317, and KIC 11764567 hadsuperflares many times ( >
30) in spite of their not high value of Li abundances ( A (Li) < . × erg : Paper I), but Li abundance is not high ( A (Li) < . Li. Further research onLi isotope abundances of superflare stars would clarify the Li production by stellar flares. Inorder to know the reason for the high Li abundance of young stars, it is important to investigatethe ratio of Li to Li in the solar-analog superflare stars.
5. Summary
We have estimated the Li abundance of superflare stars and investigate the correlations ofLi abundance with stellar parameters, and the possibility of Li productions in stellar flares. Ourspectroscopic observations show the slightly young solar-type stars tend to produce superflares,but old superflare stars exist. There is a possibility that superflares would be generated onour Sun. We could not find any evidence of nucleosynthesis of Li in stellar flares from ourobservations.We would like to thank Dr. Yoichi Takeda for useful comments and providing theanalysis tools. This study is based on observational data collected with Subaru Telescope,which is operated by the National Astronomical Observatory of Japan. We are grateful to9r. Akito Tajitsu and other staffs of the Subaru Telescope for making large contributionsin carrying out our observation. We also thank an anonymous referee for helpful comments.Funding for this mission is provided by the NASA Science Mission Directorate. The Keplerdata presented in this paper were obtained from the Multimission Archive at STScI. This workwas supported by the Grant-in-Aids from the Ministry of Education, Culture, Sports, Scienceand Technology of Japan (No. 25287039, 26400231, and 26800096).
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KIC3626094KIC4742436KIC4831454KIC6503434KIC6504503KIC6865484KIC6934317KIC7093547KIC7354508KIC7420545KIC8359398KIC8429280
Li 6708FeI 6703.6 FeI 6705.1 N o r m a li z ed I n t en s i t y ( + C on s t an t ) Wavelength [Å]
KIC8547383KIC8802340KIC9412514KIC9459362KIC9583493KIC9652680KIC9766237KIC9944137KIC10252382KIC10387363KIC10471412
Li 6708FeI 6703.6 FeI 6705.1 N o r m a li z ed I n t en s i t y ( + C on s t an t ) Wavelength [Å]
KIC10528093KIC11140181KIC11197517KIC11303472KIC11390058KIC11455711KIC11494048KIC11610797KIC11764567KIC11818740KIC12266582
Li 6708FeI 6703.6 FeI 6705.1 N o r m a li z ed I n t en s i t y ( + C on s t an t ) Wavelength [Å]
Li 6708FeI 6703.6 FeI 6705.1
Fig. 1.
Spectra around Li I 6708 line of the 34 superflare stars that show no evidence of binarity, 10comparison stars, and the Moon. The wavelength scale is adjusted to the laboratory frame. Co-addedspectra are used here in case that the star was observed multiple times. (cid:19)(cid:19)(cid:19)(cid:25)(cid:19)(cid:19)(cid:19)(cid:19)(cid:20)(cid:21)(cid:22) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:55) (cid:72)(cid:73)(cid:73) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:51)(cid:3)(cid:31)(cid:3)(cid:20)(cid:19)(cid:71)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:51)(cid:3)(cid:33)(cid:3)(cid:20)(cid:19)(cid:71)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:54)(cid:88)(cid:81)(cid:3)(cid:38)(cid:82)(cid:80)(cid:83)(cid:68)(cid:85)(cid:76)(cid:86)(cid:82)(cid:81)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:9)(cid:3)(cid:46)(cid:68)(cid:90)(cid:68)(cid:81)(cid:82)(cid:80)(cid:82)(cid:87)(cid:82)(cid:3)(cid:11)(cid:21)(cid:19)(cid:19)(cid:24)(cid:12) (cid:831) (cid:68) (cid:24)(cid:19)(cid:19)(cid:19)(cid:25)(cid:19)(cid:19)(cid:19)(cid:19)(cid:20)(cid:21)(cid:22) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:55) (cid:72)(cid:73)(cid:73) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:51)(cid:3)(cid:31)(cid:3)(cid:20)(cid:19)(cid:71)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:51)(cid:3)(cid:33)(cid:3)(cid:20)(cid:19)(cid:71)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:54)(cid:88)(cid:81)(cid:3)(cid:38)(cid:82)(cid:80)(cid:83)(cid:68)(cid:85)(cid:76)(cid:86)(cid:82)(cid:81)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:9)(cid:3)(cid:46)(cid:68)(cid:90)(cid:68)(cid:81)(cid:82)(cid:80)(cid:82)(cid:87)(cid:82)(cid:3)(cid:11)(cid:21)(cid:19)(cid:19)(cid:24)(cid:12) (cid:831) (cid:69) Fig. 2.
Lithium abundances ( A (Li)) vs. effective temperatures ( T eff ). a : Filled circles and squaresindicate the Li abundance of superflare stars with P <
10 and P ≥
10 days respectively, and triangles alsoindicate the upper limit of Li abundance of superflare stars. Open small circles indicate the ordinary F,G, K-type main sequence stars (Takeda & Kawanomoto 2005), and open large circles indicate comparisonstars in this observation. b :All symbols are the same as a , but the data points of superflare stars arelimited to solar-analog (5,500K < T eff < g ≥
4) superflare stars. (cid:19)(cid:19)(cid:19)(cid:25)(cid:19)(cid:19)(cid:19)(cid:19)(cid:20)(cid:21)(cid:22) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:55) (cid:72)(cid:73)(cid:73) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:51)(cid:3)(cid:31)(cid:3)(cid:20)(cid:19)(cid:71)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:51)(cid:3)(cid:33)(cid:3)(cid:20)(cid:19)(cid:71)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:54)(cid:88)(cid:81)(cid:3)(cid:38)(cid:82)(cid:80)(cid:83)(cid:68)(cid:85)(cid:76)(cid:86)(cid:82)(cid:81)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:43)(cid:92)(cid:68)(cid:71)(cid:72)(cid:86)(cid:3)(cid:11)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:72)(cid:87)(cid:3)(cid:68)(cid:79)(cid:17)(cid:3)(cid:21)(cid:19)(cid:20)(cid:22)(cid:12) (cid:831) Fig. 3. A (Li) vs. T eff with stars in the Hyades cluster. Upper panel : The symbols of filled circles andsquares are the same as in Figure 1, but crosses indicate the stars of the Hyades cluster (Takeda et al.2013). The age of Hyades is 6.25 × yr (e.g., Perryman et al. 1998). (cid:19) (cid:19) (cid:20)(cid:19) (cid:20) (cid:19)(cid:20)(cid:21)(cid:22) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:89)(cid:3)(cid:86)(cid:76)(cid:81)(cid:3)(cid:76) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:76)(cid:3)(cid:31)(cid:3)(cid:21)(cid:19)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:76)(cid:3)(cid:31)(cid:3)(cid:21)(cid:19)(cid:3)(cid:54)(cid:88)(cid:81)(cid:3)(cid:38)(cid:82)(cid:80)(cid:83)(cid:68)(cid:85)(cid:76)(cid:86)(cid:82)(cid:81)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:72)(cid:87)(cid:3)(cid:68)(cid:79)(cid:17)(cid:3)(cid:21)(cid:19)(cid:20)(cid:19) (cid:11)(cid:78)(cid:80)(cid:18)(cid:86)(cid:12) (cid:68)(cid:20)(cid:19) (cid:19) (cid:20)(cid:19) (cid:20) (cid:19)(cid:20)(cid:21)(cid:22) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:89)(cid:3)(cid:86)(cid:76)(cid:81)(cid:3)(cid:76) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:76)(cid:3)(cid:31)(cid:3)(cid:21)(cid:19)(cid:3)(cid:54)(cid:88)(cid:81)(cid:3)(cid:38)(cid:82)(cid:80)(cid:83)(cid:68)(cid:85)(cid:76)(cid:86)(cid:82)(cid:81)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:72)(cid:87)(cid:3)(cid:68)(cid:79)(cid:17)(cid:3)(cid:21)(cid:19)(cid:20)(cid:19) (cid:11)(cid:78)(cid:80)(cid:18)(cid:86)(cid:12) (cid:69) Fig. 4. A (Li) vs. v sin i . a : The symbols of filled circles, triangles, squares, and diamond indicate themeasurements of this work. The plot of small open circles are taken from Takeda et al. (2010), whichare the solar-analog stars. The small inclination angle stars ( i <
20 ; Paper II) are shown as squaresand diamond. b : All symbols are the same as a , but the data points of superflare stars are limited tosolar-analog (5,500K < T eff < g ≥
4) superflare stars. (cid:17)(cid:21) (cid:19)(cid:17)(cid:23) (cid:19)(cid:17)(cid:25) (cid:19)(cid:17)(cid:27)(cid:19)(cid:20)(cid:21)(cid:22) (cid:85)(cid:3)(cid:3)(cid:11)(cid:27)(cid:24)(cid:23)(cid:21)(cid:12) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:86)(cid:82)(cid:79)(cid:68)(cid:85)(cid:16)(cid:68)(cid:81)(cid:68)(cid:79)(cid:82)(cid:74)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:72)(cid:87)(cid:3)(cid:68)(cid:79)(cid:17)(cid:3)(cid:21)(cid:19)(cid:20)(cid:19)(cid:3)(cid:3)(cid:54)(cid:88)(cid:81) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:19) (cid:68)(cid:19)(cid:17)(cid:21) (cid:19)(cid:17)(cid:23) (cid:19)(cid:17)(cid:25) (cid:19)(cid:17)(cid:27)(cid:19)(cid:20)(cid:21)(cid:22) (cid:85)(cid:3)(cid:3)(cid:11)(cid:27)(cid:24)(cid:23)(cid:21)(cid:12) (cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:86)(cid:82)(cid:79)(cid:68)(cid:85)(cid:16)(cid:68)(cid:81)(cid:68)(cid:79)(cid:82)(cid:74)(cid:12)(cid:3)(cid:54)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:3)(cid:86)(cid:87)(cid:68)(cid:85)(cid:86)(cid:3)(cid:11)(cid:88)(cid:83)(cid:83)(cid:72)(cid:85)(cid:3)(cid:79)(cid:76)(cid:80)(cid:76)(cid:87)(cid:12)(cid:3)(cid:55)(cid:68)(cid:78)(cid:72)(cid:71)(cid:68)(cid:3)(cid:72)(cid:87)(cid:3)(cid:68)(cid:79)(cid:17)(cid:3)(cid:21)(cid:19)(cid:20)(cid:19)(cid:3)(cid:3)(cid:54)(cid:88)(cid:81) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:19) (cid:69) Fig. 5. A (Li) vs. r (8542). a : The symbols of filled circles, squares, and triangles indicate the measure-ments of this work. The plot of small open circles are taken from Takeda et al. (2010), which are thesolar-analog stars. b : All symbols are the same as a , but the data points of superflare stars are limitedto solar-analog (5,500K < T eff < g ≥
4) superflare stars. (cid:20)(cid:19) (cid:21)(cid:19) (cid:22)(cid:19) (cid:23)(cid:19) (cid:24)(cid:19)(cid:19)(cid:20)(cid:21)(cid:22) (cid:49)(cid:88)(cid:80)(cid:69)(cid:72)(cid:85)(cid:3)(cid:82)(cid:73)(cid:3)(cid:86)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:86) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:68) (cid:19) (cid:19)(cid:17)(cid:19)(cid:21) (cid:19)(cid:17)(cid:19)(cid:23) (cid:19)(cid:17)(cid:19)(cid:25) (cid:19)(cid:17)(cid:19)(cid:27) (cid:19)(cid:17)(cid:20)(cid:19)(cid:20)(cid:21)(cid:22) (cid:36) (cid:11) (cid:47) (cid:76) (cid:12) (cid:41)(cid:85)(cid:72)(cid:84)(cid:88)(cid:72)(cid:81)(cid:70)(cid:92)(cid:3)(cid:82)(cid:73)(cid:3)(cid:86)(cid:88)(cid:83)(cid:72)(cid:85)(cid:73)(cid:79)(cid:68)(cid:85)(cid:72)(cid:86)(cid:3)(cid:62)(cid:18)(cid:71)(cid:68)(cid:92)(cid:64) (cid:69) Fig. 6. a : A (Li) vs. the number of superflares (Shibayama et al. 2013). The symbols of filled circles andtriangles indicate the measurements of this work. The triangles indicate the upper limit of Li abundanceof superflare stars. b : A (Li) vs. the frequency of superflares (the number of superflares divided by totalobservation time). able 1. Stellar parameters, estimated rotation period, v sin i , Li abundance, r index, number of superflares, and total obser-vation time. KIC ID T eff1 log g v t1 [Fe/H] A (Li) v sin i P r (8542) N f T obs Remarks[K] [cm s − ] [km s − ] [km s − ] [days] [days]3626094 6026 4.15 1.17 –0.03 2.56 2.9 0.7 0.24 6 483 i < i < i < < i < –0.03
48 483 i < –0.02 < i < –0.16 < –0.10 < < < < < < The atmospheric parameters and brightness variation periods ( P ) which are estimated in Notsu et al. (2015a : Paper I). Normalized intensity of the line center of Ca II 8542 line taken from Notsu et al. (2015b : Paper II). N f is the number of superflares (Shibayama et al. 2013). T obs is the observation time of each superflare stars by Kepler (Q0 - Q6). Notsu et al. (2015b :Paper II). Notsu et al. (2013b). Frasca et al. (2013). Nogami et al. (2014). able 2. Stellar parameters, estimated rotation period, v sin i , and Li abundance. ID T eff1 log g v t1 [Fe/H] v sin i A (Li)[K] [cm s − ] [km s − ] [km s − ]59 Vir 6127 4.32 1.38 0.19 6.2 2.9261 Vir 5581 4.52 0.89 0.01 1.2 < < .