High Dispersion Spectroscopy of the Superflare Star KIC6934317
Shota Notsu, Satoshi Honda, Yuta Notsu, Takashi Nagao, Takuya Shibayama, Hiroyuki Maehara, Daisaku Nogami, Kazunari Shibata
aa r X i v : . [ a s t r o - ph . S R ] J u l High Dispersion Spectroscopy of the Superflare StarKIC6934317 ∗ Shota
Notsu , Satoshi Honda , Yuta
Notsu , Takashi Nagao , Takuya Shibayama ,Hiroyuki Maehara , Daisaku
Nogami , and Kazunari Shibata Department of Astronomy, Faculty of Science, Kyoto University, Kitashirakawa-Oiwake-cho,Sakyo-ku, Kyoto 606-8502 Kwasan and Hida Observatories, Kyoto University, Yamashina-ku, Kyoto 607-8471 Center for Astronomy, University of Hyogo, 407-2, Nishigaichi, Sayo-cho, Sayo, Hyogo 679-5313 Kiso Observatory, Institute of Astronomy, School of Science, The University of Tokyo, 10762-30,Mitake, Kiso-machi, Kiso-gun, Nagano [email protected] (Received 2013 February 8; accepted 2013 July 18)
Abstract
We conducted the high-resolution spectroscopic observation with Subaru/HDS fora G-type star (KIC6934317). We selected this star from the data of the Keplerspacecraft. This star produces a lot of superflares, and the total energy of the largestsuperflare on this star is ∼ times larger ( ∼ . × erg) than that of the mostenergetic flare on the Sun ( ∼ erg). The core depth and emission flux of Ca IIinfrared triplet lines and H α line show high chromospheric activity in this star, in spiteof its low lithium abundance and the small amplitude of the rotational modulation.Using the empirical relations between emission flux of chromospheric lines and X-rayflux, 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 energyenough to give rise to superflares. We also estimated the stellar parameters, suchas effective temperature, surface gravity, metallicity, projected rotational velocity( v sin i ), and radial velocity. KIC6934317 is then confirmed to be an early G-typemain sequence star. The value of v sin i is estimated to be ∼ .
91 km s − . In contrast,the rotational velocity is calculated to be ∼
20 km s − by using the period of thebrightness variation as the rotation period. This difference can be explained by itssmall inclination angle (nearly pole-on). The small inclination angle is also supportedby the contrast between the large superflare amplitude and the small stellar brightnessvariation amplitude. The lithium abundance and isochrones implies that the age ofthis star is more than about a few Gyr, though a problem why this star with such anage has a strong activity remains unsolved.1 ey words: stars: flare — stars: chromospheres — stars: activity — stars: spots— stars: rotation
1. Introduction
Flares are explosions on the stellar surface, and are thought to occur by intense release ofmagnetic energy stored near starspots (e.g., Shibata & Magara 2011). The typical amount ofenergy released in solar flares is 10 − × erg (e.g., Priest 1981; Shibata & Yokoyama 2002).Schaefer, King, Deliyannis (2000) found 9 candidates of superflares on slowly rotatingstars like the Sun. Superflares are the flares whose total energy is 10 − times larger( ∼ − erg) than that of the most energetic flare on the Sun ( ∼ erg). Recently,Maehara et al. (2012) discovered 365 superflare events on 148 solar-type stars that have effectivetemperature of 5100K ≤ T eff < g ≥ − mag) and continuous time-series data of a lotof stars over a long period (e.g., Walkowicz et al. 2011; Balona 2012).Maehara et al. (2012) and Shibayama et al. (2013) suggested that superflares releasinga total energy in the range ∼ − erg can occur once in 800 − ≤ T eff < g ≥ P ≥
10 days. Many of solar-type stars having superflaresshow quasi-periodic brightness variations with a typical period from one day to a few tensof days. The amplitude of the brightness variations is in the range 0.1 ∼
10% (Maehara et al.2012; Shibayama et al. 2013). Such brightness variations can be explained by the rotationof the star having starspots (e.g., Basri et al. 2011; Debosscher et al. 2011; Harrison et al. 2012).Notsu et al. (2013) found that the brightness variations of superflare-generating starscan be well explained by the rotation of the star with fairly large starspots, taking into accountthe effects of inclination angle and spot latitude. They also confirmed the correlation betweenthe starspot coverage and the maximum energy of superflares. These results indicate that theenergy of superflares can be explained by the magnetic energy stored around the starspots. Inaddition, Shibata et al. (2013) suggested from theoretical estimates that the Sun can generate ∗ Based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatoryof Japan. erg within onesolar cycle period ( ∼
11 years).If such large starspots exist on a star, the activity level of its chromosphere becomeshigh and large plages occur near the starspots (Shine & Linsky 1972). Linsky et al. (1979)and Foing et al. (1989) suggested that the lines of Ca II infrared triplet (Ca II IRT, λ =8498, 8542, 8662˚A) indicate the chromospheric activity of G-type stars. This is becausethese are collision-dominated lines and their cores are formed in the chromosphere, reflectingthe temperature rise in their profiles which go from filled-in to pure emission, dependingon the activity level. The fluxes in these lines are known to correlate well with the Ca IIH+K emission index (log R ′ HK ) and emission flux, which has been used as the indicator ofchromospheric activity more traditionally (e.g., Rutten 1984; Schrijver et al. 1992; Chmielewski2000; Bus`a et al. 2007; Hall 2008; Mart´ınez-Arn´aiz et al. 2011; Takeda et al. 2012). Solarimaging spectroscopy in these lines is also conducted to investigate chromospheric structures,such as plages and fibrils (e.g., Shine & Linsky 1972; Cauzzi et al. 2008; Reardon et al. 2009).In addition, Herbig (1985), Soderblom et al. (1993b), and Frasca et al. (2010) suggestedthat the H α line also indicates the chromospheric activity of the Sun and G-type stars. Thisis because the optical depth in the line core is large, and because the line formation becomesmore and more dominated by collisions in very active stars or in plage regions. Therefore,it is very important to conduct high-resolution spectroscopic observations to investigate thechromospheric activity of stars generating superflares, which is related to their photosphericstarspots.In this research, we analyze the high-resolution spectrum of a G-type superflare star(KIC6934317), and investigate the chromospheric activity and the presence of starspots. Wealso estimate stellar parameters of the star, such as T eff , log g , metallicity represented by theFe abundance relative to the Sun ([Fe/H]) , projected rotational velocity ( v sin i ) and theradial velocity (RV), and discuss some features of this star. This is the first high-resolutionspectroscopic study of G-type superflare-generating stars discovered by Kepler spacecraft.We discuss the selection of the target and our high-resolutions spectroscopic observationin Section 2. We show the method to measure stellar parameters in Section 3. The results of [Fe/H] is presented by the following relation,[Fe/H] = log(N Fe / N H ) star − log(N Fe / N H ) sun , (1)where (N Fe / N H ) star is the ratio of the number of Iron (Fe) atoms to that of Hydrogen (H) atoms in the star, and(N Fe / N H ) sun is the same ratio in the Sun. Asplund et al. (2009) reported that log(N Fe / N H ) sun is − . ± . v sin i , are reported in Section 4.Finally in Section 5, we discuss the stellar activity, the rotational velocity, and the binarity ofthis star.
2. Targets and Observation
We selected the G-type superflare star (KIC6934317) as the target. This star exhibited 48superflares in about 617 days, and hence the superflare occurrence frequency of this star isabout once in 13 days. We selected the star from the data of the Kepler spacecraft (Kochet al. 2010) within the temperature range between 5100K to 6000K. These Kepler data wereretrieved from the Multimission Archive at Space Telescope Science Institute (MAST) . Inaddition, we applied the analysis methods described in Maehara et al. (2012) and Shibayamaet al. (2013) to search for superflares. According to KIC (Kepler Input Catalog, Brown et al.2011), this star is 12.03 mag in the i band and was the brightest superflare star at presentin our data. Table 1 shows the photometric data of KIC6934317 taken from previous studiesin detail. The UBV magnitudes are taken from the photometric survey of the Kepler Field (Everett et al. 2012), and those of J HK s magnitudes are from the data of Two Micron AllSky Servey (2MASS; Skrutskie et al. 2006). The atmospheric parameters reported in the KIC(Brown et al. 2011) are T eff = 5387 ± g = 3 . ± .
4. They also quote a radius of 2.3 R ⊙ .Figure 1(a) shows the light curve of KIC6934317 and reveals a quasi-periodic brightnessvariation. The amplitude of this variation is small ( ∼ . . × erg. Maehara et al. (2012) and Shibayama et al. (2013) described the methodof estimating the total energy of each flare in detail. The largest superflare on KIC6934317was observed around BJD 2455735.3. Its amplitude is about 5.7% of the brightness of thisstar, the duration of this flare is about 0.10 day, and the total radiative energy released duringthis event is about 2 . × erg. Figure 1(c) shows the power spectrum of the time variationof the stellar brightness of KIC6934317 and it shows that the period of the brightness variation( P s ) is about 2.54 days. http://archive.stsci.edu/kepler/ The data of this survey is available at http : // archive . stsci . edu / kepler / kepler fov / search . php / .
4e also selected 59Vir and 61Vir as references of G-type stars. Previous studies (e.g.,Anderson et al. 2010) have shown that 59Vir rotates rather fast and has strong magnetic fields( ∼ We carried out high dispersion spectroscopy of KIC6934317, 59Vir, and 61Vir on August3, 2011 (Hawaii Standard Time) in Subaru service program in semester 11B (S11B-137S).We used High Dispersion Spectrograph (HDS: Noguchi et al. (2002)) at the 8.2-m Subarutelescope. The spectral coverage was about 6100˚A ∼ α (6562.8˚A), the Li I line(6708˚A), and some lines of Fe I and Fe II (for measuring atmospheric parameters, projectedrotational velocity, and radial velocity). The exposure time of KIC6934317 was 1800 × ∼
150 at 8520˚A (around the Ca II IRT lines), andas ∼
210 at 6700˚A (around the line of Li I 6708˚A). The exposure times of 59Vir and 61Virwere 60 × ∼
370 at 8520˚A and ∼
540 at 6700˚Aand that of 61Vir is ∼
410 at 8520˚A and ∼
690 at 6700˚A.The spectral resolution, as evaluated from the full width at half maximum (FWHM) ofthe emission lines of the Th-Ar calibration lamp, was 0.088˚A at 8500˚A, yielding a resolvingpower R= λ /∆ λ ∼ software.Figure 2 shows the lightcurve of KIC6934317 around the period of this observation (aroundBJD 2455778). The spectrum was taken during the minimum of the wave-like modulation.There was a large flare about a day before the observation period. IRAF is distributed by the National Optical Astronomy Observatories, which is operated by the Associationof Universities for Research in Astronomy, Inc., under cooperate agreement with the National ScienceFoundation. . Measurements of Stellar Parameters We measured equivalent widths of 101 Fe I lines and 7 Fe II lines over the range of 6100 − developed by Y. Takeda. Programs contained in SPTOOL are originally based on Kurucz’sATLAS9/WIDTH9 model atmospheric programs (Kurucz 1993).Using these data of equivalent widths of Fe I and Fe II lines, we derived the effectivetemperature ( T eff ), the surface gravity (log g ), microturbulent velocity ( v t ), and [Fe/H] oftarget stars. For deriving these parameters, we used TGVIT program developed by Y.Takeda. The procedures adopted in this program are minutely described in Takeda, Ohkubo,Sadakane (2002) and Takeda et al. (2005b).The resultant parameters of T eff , log g , v t , and [Fe/H] of KIC6934317 are 5694 ± . ± .
08, 0 . ± .
14 km s − , and − . ± .
07, respectively. On the other hand, theatmospheric parameters reported in the KIC (Brown et al. 2011) are T eff = 5387 ± g = 3 . ± .
4, and [Fe/H] = − . ± .
5. There are significant differences between thevalues reported in the KIC and those derived in this observation. However, the atmosphericparameters reported in the KIC are derived from multiband photometry for a first classificationand are not good sources to discuss actual properties of the stars. Furthermore, it is knownthat in some cases the atmospheric parameters taken from the KIC are significantly differentfrom those derived spectroscopically, which are much more accurate than those from the KIC(e.g., Molenda- ˙Zakowicz et al. 2010, Pinsonneault et al. 2012).In addition, the resultant parameters of 59Vir are T eff = 6009 ± g = 4 . ± . v t = 1 . ± .
09 km s − , and [Fe/H]= 0 . ± .
06, and those of 61Vir are T eff = 5558 ± g = 4 . ± . v t = 0 . ± .
08 km s − , and [Fe/H]= − . ± .
06. These values areconsistent with those of previous studies (e.g., Takeda 2007a; Schr¨oder et al. 2009; Andersonet al. 2010). Obviously, the errors of the parameters are internal to the procedure and do not http://optik2.mtk.nao.ac.jp/ ∼ takeda/sptool/ http://optik2.mtk.nao.ac.jp/ ∼ takeda/tgv/ T eff from the ratio of the depth of two differentlines (e.g., Biazzo et al. 2007). We measured the line-depth ratio of three pairs of lines (V I6199˚A/Fe I 6200˚A, V I 6214˚A/Fe I 6213˚A, and V I 6275˚A/Fe I 6270˚A), and roughly estimatedthe average values of T eff by using the method described in Biazzo et al. (2007). The value of T eff of KIC6934317, 59Vir and 61Vir is ∼ ∼ ∼ T eff derived from equivalent widths of Fe I andFe II lines.Pinsonneault et al. (2012) reported a catalog of revised T eff for stars in the KIC (Brownet al. 2011). They estimated T eff by using two different methods and compared their valueswith those in the KIC. In one method, they transformed original griz colors in the KIC into griz colors on the basis of Sloan Digital Sky Survey (SDSS; Aihara et al. 2011) scales andcalculated T eff from the relations between SDSS griz colors and T eff . Hereafter, we refer to thismethod as the SDSS one. In the other method, T eff is derived with the infrared flux method(IRFM; e.g., Casagrande et al. 2010) which uses the relations between T eff and J − K s fromthe data of 2MASS (Skrutskie et al. 2006). We call this the IRFM method. The effects ofinterstellar reddening are also corrected in these two methods of estimating T eff (Casagrandeet al. 2010, Pinsonneault et al. 2012). They argued that these revised values of T eff with twodifferent methods are both about 200K higher than the values of T eff in the KIC, and theserevised values are comparable with the values derived spectroscopically.According to this catalog, the revised T eff of KIC6934317 by using the SDSS method is5710 ± ± T eff , log g , and [Fe/H] of this star are nearly the same as the Sun.Atmospheric parameters of KIC6934317 taken from previous studies and derived in this studyare shown in Table 2, and those of comparison stars (59Vir, 61Vir) are shown in Table 3. This catalog is available at http://vizier.cfa.harvard.edu/viz-bin/VizieR-3 . .2. v sin i We used the method which is basically similar to that described in Takeda, Sato, Murata(2008) in order to derive v sin i of KIC6934317, the Sun, 59Vir, and 61Vir. In this processof calculating v sin i , we took into account the macroturbulence velocity and instrumentalbroadening velocity on the basis of Takeda, Sato, Murata (2008). We used the spectrum ofthe Sun in Kurucz et al. (1984) to calculate v sin i of the Sun.According to Takeda, Sato, Murata (2008), a simple relation holds among the line-broadeningparameters, which can be expressed as: v = v + v + v . (2) v M is e -folding width of the Gaussian macrobroadening function [ f ( v ) ∝ exp( − ( v/v M ) )]including instrumental broadening ( v ip ), rotation ( v rt ), and macroturbulence ( v mt ). Wederived v M by applying automatic spectrum-fitting technique, given the model atmospherecorresponding to the atmospheric parameters (e.g, Takeda 1995; Takeda 2007a; Takeda et al.2008). In this process, we used the MPFIT program contained in SPTOOL software package.Although Takeda, Sato, Murata (2008) applied this fitting technique to the 6080-6089˚A region,we applied this technique to the 6212-6220˚A region, which contains four Fe I lines. This isbecause the 6080-6089˚A region is out of the spectral coverage of our observation. In deriving v M of KIC6934317, 59Vir, and 61Vir, we used the atmospheric parameters derived in Section3.1 (See also Table 2 and 3). In order to calculate v M of the Sun, we used the values ofatmospheric parameters in Kurucz (1993) (log g = 4 . T eff = 5777K). We also determined v t of the Sun is 1 km s − . v ip is e-folding width of the Gaussian instrumental broadening function. v ip was calcu-lated by using the following relation (Takeda, Sato, Murata 2008), v ip = 3 × R √ ln , (3)where R is a resolving power of the observation. v mt is e -folding width of the Gaussian macro-turbulence broadening function. v mt was estimated by using the relation, v mt ∼ . ζ RT (Takeda,Sato, Murata (2008)). ζ RT is the radial tangential macroturbulence and we calculated ζ RT bythe relation (Valenti & Fischer 2005), ζ RT = (cid:18) . − T eff − K K (cid:19) , (4)where T eff is the effective temperature of stars.Using these equations, we derived v rt , which is e -folding width of the Gaussian rotationalbroadening function, and finally we could derive v sin i by using the relation v rt ∼ . v sin i v rt and v sin i (Gray 2005). Hirano et al. (2012) estimated the systematic uncertaintyfor v sin i by chaging ζ RT by ±
15% from Equation (4) for cool stars ( T eff ≤ ζ RT (See also Figure 3 in Valenti & Fischer 2005). They explainedthat the statistical errors in fitting each spectrum are generally smaller than the systematicerrors arising from different values of ζ RT . α In order to investigate the chromospheric activity of the target stars, we used r (8498), r (8542), and r (8662), which are the residual flux normalized by the continuum at the linecores of Ca II Infrared Triplet (Ca II IRT, λ =8498, 8542, 8662˚A). As the chromosphericactivity is enhanced and plages appear, r (8498), r (8542), and r (8662) become large,since a greater amount of emission from the chromosphere fills in the core of the lines (e.g.,Linsky et al. 1979; Foing et al. 1989; Takeda et al. 2010). These indicators are knownto correlate well with the Ca II H+K emission index (log R ′ HK ), which has been used asthe indicator of chromospheric activity more traditionally (e.g., Rutten 1984; Schrijver etal. 1992; Chmielewski 2000; Bus`a et al. 2007; Hall 2008; Takeda et al. 2012). We alsoused r (H α ) as an indicator of chromospheric activity. Herbig (1985), Soderblom et al.(1993b), and Frasca et al. (2010) described that H α is also a useful indicator of chromo-spheric activity, and r (H α ) is correlated well with Ca II H+K emission index (log R ′ HK ).On the other hand, Ca II IRT lines are more easily used as diagnostics of chromosphericactivity compared to Ca II H&K lines, because they lie in a wavelength region where thecontinuum is well defined and the spectrograph detectors are more efficient (Frasca et al. 2010).We also used emission flux of Ca II IRT and H α lines. The residual flux at the coresof Ca II IRT and H α lines, as defined in the previous paragraph, is an indicator of chrom-spheric activity which is widely used (e.g., Linsky et al. 1979; Foing et al. 1989), but it alsodepends on the value of v sin i of the star (e.g., Takeda et al. 2010). A large value of v sin i canindeed rise the residual flux, mimicking the effect of filling the line core with chromosphericemission. In order to remove this influence of v sin i , we used the spectral subtraction technique(e.g., Frasca & Catalano 1994; Frasca et al. 2011; Mart´ınez-Arn´aiz et al. 2011; Fr¨ohlich et al.2012). Mart´ınez-Arn´aiz et al. (2011) pointed out that this subtraction process also permitsthe subtraction of the underlying photospheric contribution from the spectrum of the star,and in this way we could investigate the spectral emission originated from the chromospherein detail. We used the spectrum of 61Vir obtained in this observation as an inactive templateto be subtracted from the spectrum of KIC6934317. 61Vir is a slowly rotating and non-activeearly G-type main sequence star (e.g., Anderson et al. 2010), whose atmospheric parameters9re very similar to those of KIC6934317 (See Tables 2 and 3).We measured the excess equivalent width ( W em λ ) of the Ca II IRT and H α lines in theresidual spectrum resulting from this subtraction process. We subsequently derived emissionfluxes ( F em λ ) of Ca II IRT and H α lines from W em λ of these lines by the following relation, F em λ = W em λ F cont λ (Mart´ınez-Arn´aiz et al. (2011)). F cont λ is the continuum flux around thewavelength of each line. We calculated F cont λ by using the the following empirical relationshipsbetween F cont λ and color index ( B − V ) derived by Hall (1996),log F contH α = [7 . − . B − V )] ± . , +0 . ≤ B − V ≤ +1 . , (5)log F contIRT = [7 . − . B − V )] ± . , − . ≤ B − V ≤ +0 . , (6)log F contIRT = [7 . − . B − V )] ± . , +0 . ≤ B − V ≤ +1 . . (7)Mart´ınez-Arn´aiz et al. (2011) also used the same method to calculate F cont λ .In Section 3.1, we show that KIC6934317 is T eff = 5694 ±
25K and [Fe/H]= − . ± .
07. Alonsoet al. (1996) showed the empirical relations of low mass main sequence stars (F0V − K5V)among [Fe/H], T eff , and color index. We estimated the unreddened color ( B − V ) of this staras ∼ . ± .
023 mag in the B-band and 12 . ± .
017 mag in the V-band (SeeTable 1), and thus B − V simply derived from these photometric data is 0 . ± . B − V )=0 . ± . B − V estimated from atmospheric parameters derived spectroscopically(( B − V ) ) agrees with the corrected value of B − V on the basis of the photometric datawithin the error range, and is considered to be more accurate than the corrected value onthe basis of photometric data. We consequently use the value estimated from atmosphericparameters derived spectroscopically (( B − V ) ) and the resulting color excess E( B − V ) ∼ . ± .
04 mag in the following discussions.Mart´ınez-Arn´aiz et al. (2011) described that emission fluxes ( F em λ ) of Ca II IRT andH α lines are correlated well with one another, and are also correlated well with F em λ of Ca II H& K lines, which have been used as the indicator of chromospheric activity more traditionally(e.g., Rutten 1984; Schrijver et al. 1992; Chmielewski 2000; Bus`a et al. 2007; Hall 2008;Takeda et al. 2012). Furthermore, F em λ of Ca II IRT, Ca II H & K, and H α lines are correlatedwell with X-ray surface flux ( F X ), which indicates coronal activity (e.g., Schrijver et al. 1992;Mart´ınez-Arn´aiz et al. 2011). 10 . Results Figure 3 shows that the photospheric lines of 59Vir are shallow and broad, indicating 59Vir isa fast rotator. On the other hand, the line of KIC6934317 is narrow and deep like those of61Vir and the Sun, which rotate slowly. Using the methods explained in Section 3.2, the valuesof v sin i of KIC6934317, 59Vir, 61Vir and the Sun are about 1.91, 6.27, 1.38, and 1.82 km s − ,respectively. We show these results in Table 2 and 3. The results of 59Vir and 61Vir of thisobservation are roughly consistent with those of previous researches which are described inTable 3 (e.g., Anderson et al. 2010, Schr¨oder et al. 2009). In Section 5.2, we discuss the resultsof v sin i in detail. We measured the radial velocity (RV) of the target stars by using about 65 Fe I lines. Aswe showed in Table 2 and 3, the RV values of KIC6934317, 59Vir, and 61Vir measured onour spectra are -12.238 ± ± ± − , respectively. Thesevalues are derived from the spectra obtained by integrating all frames of spectra of individualstars. The errors of RV values are the standard errors of the mean RV values which arecalculated by using the values derived from individual lines. The results for 59Vir and 61Viragree with those of previous studies (e.g., Takeda et al. 2005a), which are described in Table3. In Section 5.3, we discuss the results of RV in detail. In Section 3.1, we derived T eff , log g , and [Fe/H] of target stars from our observed spectra.On the basis of these parameters, we can estimate the stellar age, the stellar mass ( M s ), theabsolute V magnitude ( M V ), and the stellar bolometric luminosity ( L s ) for the target stars byapplying the isochrones of Girardi et al. (2000). In addition, using the values of L s and T eff ,we can also estimate the stellar radius ( R s ).The values of the stellar age, M s , M V , L s , and R s of KIC6934317 are ∼ . − . ∼ . M ⊙ , ∼ . − . ∼ . L ⊙ , and ∼ . R ⊙ , respectively. Though the range of stellarage is wide, this value is roughly similar to the age of the Sun.11n addition, Table 1 shows that the apparent V magnitude of this star is 12 . ± . B − V ) estimated in Section 3.3, the value of interstellar extinctionin the V band (A(V)) is A(V)= 3 . × E( B − V ) ∼ . ± .
12 mag (Cardelli et al. 1989). Usingthese values and M V , we estimate that the distance of this star ( d ) is ∼
300 pc. α In the top of Figure 4(a) and 4(b), normalized spectra of KIC6934317, 59Vir and 61Vir aroundthe cores of λ λ r (8498) and r (8542) of KIC6934317 are largerthan those of 61Vir, which rotates slowly and has very weak magnetic field, while they arecomparable to those of 59Vir, which rotates fast ( ∼ − ) and has strong magneticfields. We show r (8498), r (8542), r (8662), and r (H α ) of KIC6934317, 59Vir, 61Vir, andthe Sun in Table 4. The spectrum of the Sun is obtained by Kurucz et al. (1984). Theoriginal resolving power (R= λ /∆ λ ) of this solar spectrum is ∼ ∼ ∼ r (8498) betweenKIC6934317 and the Sun is 0.14 and the difference of r (8542) between KIC6934317 andthe Sun is 0.15. This table shows that the tendencies of r (8662) and r (H α ) are similarto those of r (8498) and r (8542). Chmielewski (2000) reported a value of r (8542) = 0.24for 61Vir. Comparing this data with the results described in Table 4, we find that theerror range of r (8542) is ∼ r (8498), r (8542), r (8662), and r (H α )become large as the star shows high chromospheric activity and large plages appear on the star.Altogether, these results suggest that KIC6934317 shows high chromospheric activity like 59Vir.Table 5 shows the excess equivalent width ( W em λ ) of the Ca II IRT and H α lines, andemission flux ( F em λ ) of these lines. The values of F em λ are derived by using the methodexplained in Section 3.3. In Table 5, we report these values not only of KIC6934317, but alsoof the stars investigated in Fr¨ohlich et al. (2012) (KIC7985370 and KIC7765135), with the aimof comparing chromospheric activity. Fr¨ohlich et al. (2012) reported that KIC7985370 andKIC7765135 are early G-type main sequence stars. They also reported that these stars areyoung (Age; 100 −
200 Myr) and show high chromospheric activity. On the basis of the values12n Table 5, F emH α of KIC6934317 is roughly as large as of those of KIC7985370 and KIC7765135.In contrast, F em λ of Ca II IRT lines of KIC6934317 are about a few times smaller than thoseof KIC7985370 and KIC7765135. Consequently, the chromospheric activity of KIC6934317is fairly high, and this star displays an excess of H α flux with respect to Ca II IRT flux,compared to KIC7985370 and KIC7765135.In Section 5.1, we further discuss the stellar activity of KIC6934317. Figure 5 shows normalized spectra of KIC6934317, 59Vir, 61Vir, and the Sun around the Li Iline (6708˚A). This figure shows that 59Vir has a deep line of Li, and that the Li line of 61Viris absent while that of the Sun and KIC6934317 are very weak and just visible against the noise.We measured the lithium abundance (A(Li) ) of KIC6934317, 59Vir, 61Vir, and theSun on the basis of the automatic profile fitting method described in details in Takeda &Kawanomoto (2005). In this process of calculating A(Li), we used the MPFIT program con-tained in SPTOOL software package, and assumed LTE (Local Thermodynamical Equilibrium)for the formation of all lines including the Li I line. We also assumed Li / Li = 0 throughoutthis study. The line lists we used are the same of Takeda & Kawanomoto (2005).The result of KIC6934317 is A(Li)= 1 .
25. In addition, the result of 59Vir is A(Li)= 2 .
81 andthat of the Sun is A(Li)= 0 .
88. We could not derive A(Li) of 61Vir, because the Li line of61Vir is absent.Takeda & Kawanomoto (2005) shows that in the case of calculating A(Li) by LTE, theresults of 59Vir are W Li9 = 83 . .
91, those of the Sun are W Li = 2 . .
85, and those of 61Vir are W Li < < .
86. In the case of calculatingA(Li) by NLTE (Non Local Thermodynamical Equilibrium), A(Li) of 59Vir and the Sunare 2.91 and 0.92, respectively. Asplund et al. (2009) also shows that A(Li) of the solarphotosphere calculated by NLTE is 1 . ± .
10. In table 2 and 3, we show the values of previousstudies and this study. The values of 59Vir, 61Vir, and the Sun of this observation are roughlyconsistent with those of previous studies. These results show that the lithium abundance A(Li) is defined by the following relation,A(Li) = log(N Li / N H ) + 12 . , (8)where (N Li / N H ) star is the ratio of the number of Lithium (Li) atoms to that of Hydrogen (H) atoms in the star. W Li is the equivalent width of the line of Li I 6708˚A.
13f KIC6934317 is quite lower than that of 59Vir, and a bit higher than that of 61Vir and the Sun.It has been known that the lithium abundances could provide a fairly rough constrainton the age of early G-type stars (e.g., Soderblom et al. 1993a; Sestito & Randich 2005),though there are a lot of unknown problems about the behavior of lithium abundances in earlyG-type stars (e.g., Ryan et al. 2001; Israelian et al. 2004; Sestito & Randich 2005; Takeda etal. (2007b); Takeda et al. 2010; Takeda et al. 2012). On the basis of the fairly rough relationbetween A(Li) and the stellar age discussed in Sestito & Randich (2005), Takeda et al. (2007b),and Takeda et al. (2010), the age of KIC6934317 is more than about a few Gyr. This value isroughly consistent with the age derived by using the isochrones of Girardi et al. (2000) (seeSection 4.3), though the ranges of these two values are wide.
5. Discussion
In Figure 6, we plot r (8542) as a function of effective temperature ( T eff ) of the stars. Inmaking this figure, we use both the results described in Table 4 and the data from Chmielewski(2000). There appears to be a clear dividing gap between active and quiescent stars whichshow some slope with effective temperature (Foing et al. 1989, Chmielewski 2000). r (8542)become large as the activity of chromosphere is enhanced and plages appear (e.g., Linskyet al. 1979; Foing et al. 1989; Chmielewski 2000; Takeda et al. 2010). Nearly all giant andsub-giant stars (log g ≤ − Preston gap in Ca II H&K (Vaughan & Preston 1980). Mart´ınez-Arn´aiz et al. (2011) reported that the Vaughan − Preston gap is also dividing in two separateclasses stars with large emission flux and those with small emission flux in other chromosphericlines like H α . It is widely accepted that the differences of stellar age and dynamo regimes aredeeply related to exisitence of this gap between active and quiescent stars (e.g., Durney et al.1981; Noyes et al. 1984; B¨ohm-Vitense 2007; Pace et al. 2009; Mart´ınez-Arn´aiz et al. 2011). Itis also believed that nanoflare heating, which is supposed to be one of the main heating mecha-nism of the stellar outer atmospheres, contributes to form the gap (Mart´ınez-Arn´aiz et al. 2011).14s apparent from Figure 6, KIC6934317 turns out to be a relatively active star, inspite of its low lithium abundance (see Section 4.5). This figures also indicates that 59Viris an active star, and 61Vir and the Sun are not active stars. These results of 59Vir, 61Vir,and the Sun are consistent with the findings of previous researches (e.g. Anderson et al. 2010,Takeda et al. 2012).Mart´ınez-Arn´aiz et al. (2011) plotted the emission flux in H α versus B − V , and dis-played the existence of the Vaughan − Preston gap. On the basis of that relation, G-type starsabove the gap (active stars) have log F emH α ∼ −
7. With a log F emH α = 6 . B − V ) ∼ . α flux as compared to Ca II IRT fluxes.) and the results in Mart´ınez-Arn´aiz et al.(2011) (A star above the Vaughan − Preston gap has an excess of H α flux with respect to CaII IRT fluxes.) also shows that this star belongs to the active star group above the gap.X-ray flux is widely used as a measure of coronal activity and a direct measure of stel-lar magnetic activity, because it is unlikely to include contribution from other sources suchas basal atmosphere (e.g., Schrijver et al. 1992; Pevtsov et al. 2003; Pizzolato et al. 2003).Mart´ınez-Arn´aiz et al. (2011) presented the emprical relationship between H α flux and X-rayflux ( F X ), and this empirical relationship is given by the following equation,log F X = ( − . ± .
39) + (1 . ± .
07) log F emH α . (9)Using this equation, we estimate that F X of KIC6934317 is F X ∼ × erg cm − s − , theX-ray luminosity ( L X ) of this star is L X ∼ πR F X ∼ × erg s − , and log L X / L s is ∼ − . R s ∼ . R ⊙ and L s ∼ L ⊙ , as calculated inSection 3.3. L X estimated for KIC6934317 is as large as that of KIC7985370 (an active early G-typemain sequence star), which is L X = (3 − × erg s − (Fr¨ohlich et al. 2012), and muchlarger than that of the Sun, which varies from about 5 × erg s − to about 2 × erg s − from the minimum to the maximum of the activity cycle (e.g., Schmitt et al. 1995). HenceKIC6934317 is considered to have high coronal activity.Nevertheless, we do not find the X-ray counterpart of this star in the ROSAT All-SkySurvey (RASS) Faint Source Catalog (Voges et al. 2000). Indeed, the detection limit of theX-ray flux for the RASS survey is ∼ × − erg cm − s − (Schmitt et al. 1995), which15orresponds to the X-ray luminosity of ∼ × erg s − assuming the distance of ∼
300 pc.This explains why KIC6934317 was not detected by the RASS.On the basis of the discussions and considerations described in this Section and the re-sults of observations that we mentioned in Section 4.3, KIC6934317 shows high chromosphericand coronal activity and it very likely has large plages. In addition, a star with such a highchromospheric activity is also believed to have large starspots (e.g., Schrijver et al. 1992; Bus`aet al. 2007; Hall 2008). Therefore, given its high activity level, we believe that KIC6934317has large starspots which can store a large amount of magnetic energy that cause superflares(Shibata et al. 2013).
The value of v sin i of KIC6934317 estimated by this spectroscopic observation is ∼ − , R s estimated in Section 3.3 is ∼ R ⊙ , and P s is about 2.54 days. Assuming that the brightnessvariation of this star is caused by the rotation of the star with starspots, we estimate rotationalvelocity ( v ) as ∼
20 km s − by using following relation: v = 2 πR s P s (10)We think that the difference between the values of v and v sin i can be explained by the inclina-tion effect. Once v is estimated, we estimate that i (the stellar inclination angle) is ∼ i = arcsin " ( v sin i ) spec v (11)This result suggest that KIC6934317 has a small value of i and is a nearly pole-on star.We can confirm this inclination effect from another point of view. Figure 7 shows thescatter plot of the superflare amplitude as a function of the amplitude of the brightnessvariation. The data are taken from Notsu et al. (2013). The solid line corresponds to theanalytic relation between the stellar brightness variation amplitude and superflare amplitudefor B =1000G (Notsu et al. 2013). The amplitude of the brightness variation of the superflarestar is considered to be a good indicator of the starspot coverage. In addition, the energy ofthe superflare can be estimated with the superflare amplitude and duration time. The dashedline corresponds to the same relation in case of nearly pole-on ( i =2.0 deg) for B =1000G,assuming that the brightness variation of a star become small as the inclination angle of thestar become small. These lines are considered to give an upper limit for the flare amplitude ineach inclination angle. These results suggest that i of KIC6934317 is small (nearly pole-on)16nd that this star has large starspots generating superflares, though the stellar brightnessvariation amplitude of this star is small ( ∼ . On the basis of the stellar parameters derived in this study, this star proves to be anearly G-type main sequence star. Noyes et al. (1984) argued that the rotational periodis correlated with the chromospheric activity, which is known to be an indicator of themagnetic activity of the star. Pallavicini et al. (1981) and Pizzolato et al. (2003) showed thatrapidly rotating stars have high coronal and magnetic activity than slowly rotating stars. Onthe basis of these studies, it is not strange that KIC6934317 show high chromospheric andmagnetic activity. This is because KIC6934317 has the high rotational velocity ( v ∼
20 km s − ).Ayres (1997) discussed the dependence of stellar rotational velocity on age for solar-type starsand presented the following relation, v v sun = (cid:20) tt sun (cid:21) − . ± . , (12)where v is the rotational velocity of a star, v sun is the rotational velocity of the Sun ( ∼ − ), t is age of a star, and t sun is the solar age ( ∼ v ∼
20 km s − ), we can estimate that the age of KIC6934317 is ∼
100 Myr. This value is incompatible with the value estimated in this observation by usingthe lithium abundance of this star, and the isochrones (See Section 4.3 and 4.5), though thereare a lot of unknown problems about the behavior of lithium abundances in early G-type starsas we mention in Section 4.5, and the ranges of values estimated by using these two methodsare wide. Thus, one hypothesis that explains the large rotational velocity and high level ofactivity would be that this star is a binary which has maintained a high rotation rate thanksto the tidal interaction that has coupled spin and orbit (Walter & Bowyer 1981).First, we checked the slit viewer images of Subaru/HDS for this star taken simultane-ously with the spectra, and we cannot find companions for this star as far as we looked thisimages.Second, if a star is a binary star and has a companion, RV of the primary star is ex-pected to change between the observations. We estimate the value of the RV change by usingthe following relation, f ( M ) = ( M sin i ) ( M + M ) = P o K πG , (13)17here G is the gravitational constant (= 6 . × − m s − kg − ), M is the mass of theprimary star, M is that of the companion, and f ( M ) is the mass function. K is the amplitudeof radial velocity variation of the primary star, and P o is the period of orbital motion of thebinary system. Thanks to the parameters and v sin i derived from our obtained spectrum, wecan reasonably assume i = 5.5 deg and M ∼ . M ⊙ . In addition, if we suppose that this is aclose binary system and these stars are expected to be tidally locked with each other, we canassume that P o is ∼ K is larger than the v sin i ( ∼ − ). Adopting the minimumvalue of K , we can derive a minimum mass for the unseen secondary component, M ∼ . M ⊙ .In this observation, we get 6 frames of spectra of KIC6934317, and the exposure timeper frame is 1800 seconds (see Section 2.2). Since a frame was obtained ∼ ± ± ± ± ± ± − (As we explained in Section 4.2, RV of the star derived from the spectra obtained byintegrating all frames of spectra of this star is -12.238 ± − ). The difference betweenthe values of RV of the first frame and the last frame is 0.124 ± − , and thus RVof this star is supposed to change between the first and the last frames. Considering theminimum value of K described in the former paragraph and the time interval between thetwo frames, however, we cannot claim that this star is definitely a binary. This is because theperiod of observation is small and because the values of RV change are very small. Especially,the values of RV of last four frames are almost the same values within the ranges of errors.In the future we will observe KIC6934317 again and estimate the change of RV between theobservations in detail to investigate whether this star is a binary or not.
6. Summary
In this paper, we present the results of the analysis of a high-resolution spectrum ofKIC6934317, a star which displays many strong white-light flares (superflares) in the high-precision Kepler light curve. We measured the core depth and emission flux of Ca II infraredtriplet lines and H α line in order to investigate the chromospheric activity and the presence ofstarspots. Our analysis shows that KIC6934317 has high chromospheric activity, in spite ofthe low lithium abundance and the small amplitude of the rotational modulation. Using theempirical relations between flux of chrompspheric lines and X-ray flux, it should also have amuch higher coronal activity than that of the Sun. We believe that the low amplitude of therotational modulation evident in the Kepler light curve is due only to foreshortening effects18nd that this star has actually large starspots which can store a large amount of magneticenergy that can generate superflares. We also estimated some stellar parameters, such as T eff ,log g , [Fe/H], v sin i , and RV. We confirmed that this star is an early G-type main sequencestar, on the basis of these parameters. The value of v sin i of KIC6934317 is ∼ − ,though v is estimated to be ∼
20 km s − by using the period of the brightness variation asthe rotation period, and R s of this star. This difference between the values of v sin i and v can be explained by small inclination angle (nearly pole-on). The amplitude of the brightnessvariation of superflare stars is considered to correspond to the spot coverage, and it is knownto correlate with the superflare amplitude, which corresponds to the energy of superflare.The relation between the superflare amplitude and the brightness variation amplitude in thisstar is also found to be explained by the effect of small inclination angle. On the basis ofthe lithium abundance and isochrones, it is implied that the age of this star is more thanabout a few Gyr, though the problem of the strong activity at such a high age remains unsolved.This study is based on observational data collected at Subaru Telescope, which is operatedby the National Astronomical Observatory of Japan. We are grateful to Dr.Akito Tajitsuand other staffs of the Subaru Telescope for making large contributions in carrying out ourobservation. We further thank Dr.Kazuhiro Sekiguchi (NAOJ) and Dr.Yoichi Takeda (NAOJ)for useful advices. Kepler was selected as the tenth Discovery mission. Funding for thismission is provided by the NASA Science Mission Directorate. The Kepler data presented inthis paper were obtained from the Multimission Archive at STScI. This work was supportedby the Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technologyof Japan (No. 25287039). References
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020 [mag] B † . ± .
023 [mag] V † . ± .
017 [mag] J ‡ . ± .
019 [mag] H ‡ . ± .
017 [mag] K s ‡ . ± .
012 [mag]
Notes ∗ Brown et al. (2011) † Everett et al. (2012) ‡ Skrutskie et al. (2006)
Table 2.
Atmospheric parameters, projected rotational velocity, radial velocity, and lithiumabundance of KIC6934317
Parameter Value Reference T eff [K] 5694 ±
25 present work5387 ±
200 15710 ±
81 25604 ±
103 3[Fe/H] − . ± .
07 present work − . ± . g . ± .
08 present work3 . ± . v sin i [km s − ] 1.91 present workRV [km s − ] − . ± .
018 present workA(Li) 1.25 present work
References (1)Brown et al. (2011)(2)Pinsonneault et al. (2012) (the SDSS method)(3)Pinsonneault et al. (2012) (the IRFM method) able 3. Atmospheric parameters, projected rotational velocity, radial velocity, and lithiumabundance of comparison stars
Name T eff [Fe/H] log g v sin i RV W Li A(Li) Reference[K] [km s − ] [km s − ] [m˚A]59Vir 6009 ±
28 0 . ± .
06 4 . ± .
06 6.27 − . ± .
026 2.81 present work6234 4.60 6.67 16120 0.21 4.25 83.1 2.91 25986 4.25 4.5 3 − . ± − . ± .
06 4 . ± .
04 1.38 − . ± .
027 present work5571 4.47 0.46 15720 0.11 4.67 ( ≤
2) ( ≤ .
86) 25509 4.51 0.4 3 − . References (1)Anderson et al. (2010); (2)Takeda & Kawanomoto (2005); (3)Schr¨oder et al. (2009); (4)Takeda et al. (2005a)
Table 4. r of Ca II IRT and H α Name r (8498) ∗ r (8542) ∗ r (8662) ∗ r (H α ) ∗ KIC6934317 0.43 0.33 0.37 0.4259Vir 0.47 0.36 0.37 0.2761Vir 0.28 0.18 0.19 0.19Sun 0.30 † † † † Notes ∗ r is the residual flux normalized by the continuum at the line core. † The spectrum of the Sun is obtained by Kurucz et al. (1984). The originalresolving power (R= λ /∆ λ ) of this solar spectrum is ∼ ∼ able 5. The excess equivalent width and the emission flux
Line W em λ F em λ W em λ F em λ W em λ F em λ [˚A] [erg cm − s − ] [˚A] [erg cm − s − ] [˚A] [erg cm − s − ]KIC6934317 KIC7985370 ∗ KIC7765135 ∗ (The target star)Ca II λ . × . × . × Ca II λ . × . × . × Ca II λ . × . × . × H α . × . − .
26 (1 . − . × . × Notes ∗ We use the values of KIC7985370 and KIC7765135 presented in Fr¨ohlich et al. (2012). These stars are early G-typemain sequence stars. They are also young, and show high chromospheric activity. D F / F a v Barycentric Julian Date (BJD) − 2400000 [day] (a) 0 0.02 55257.8 55258 (b) 0.0e+00 5.0e−09 1.0e−08 1.5e−08 0.1 1 1 10 P o w e r frequency [day −1 ]Period [day] (c) Fig. 1. (a): Lightcurve of KIC6934317 obtained by the Kepler spacecraft. The vertical axisis the brightness variation to the average brightness. We can see quasi-periodic modulationwith an about 0.1% amplitude of the total luminosity of the star. (b): The enlargedlightcurve of a superflare observed around BJD 2455257.9. The amplitude of this superflareis about 2.1% of the brightness of the star. The duration of the flare is about 0.12 day, andthe total radiative energy released during this event is estimated to be about 5 . × erg. (c): Power spectra of the light curves of KIC6934317. This figure indicates that theperiod of the modulation of KIC6934317 ( P s ) is 2.54 days.28 D F / F a v Barycentric Julian Date (BJD) − 2400000 [day]Subaru Observation Period
Fig. 2.
Lightcurve of KIC6934317 around the period we observed this star with Subarutelescope (August 3, 2012 (HST)). The observation period is in the dark phase of brightnessvariations. There is a flare about a day before the observation period. N o r m a li z ed I n t en s i t y l [Å] Fe I 6533.9
KIC693431759Vir61VirSun
Fig. 3.
Normalized spectra of KIC6934317 (solid line), 59Vir (dashed line), 61Vir (dottedline), and the Sun (dash-dotted line)around Fe I 6533.9. The spectrum of the Sun isobtained by Kurucz et al. (1984). The original resolving power (R= λ /∆ λ ) of this solarspectrum is ∼ ∼ v sin i . 29 N o r m a li z ed I n t en s i t y l [Å] (a) Ca II 8498
KIC693431759Vir61VirResidual N o r m a li z ed I n t en s i t y l [Å] (b) Ca II 8542
KIC693431759Vir61VirResidual
Fig. 4.
Top of each panel : Normalized spectra of KIC6934317 (thick solid line), 59Vir(dashed line), and 61Vir (dotted line) around the core-regions of Ca II 8498 and 8542.59Vir and 61Vir are the comparison stars which have strong and weak magnetic fields,respectively (e.g., Anderson et al. 2010). These spectra show that r (8498) and r (8542)of KIC6934317 are larger than those of 61Vir, and are similar to those of 59Vir. Previousstudies (e.g., Linsky et al. 1979; Herbig (1985); Chmielewski 2000) indicate that r (8498)and r (8542) become large as the star shows high chromospheric activity. Therefore theseresults suggest that KIC6934317 shows high chromospheric activity like 59Vir. We showthe values of r (8498) and r (8542) of these stars in Table 4. Bottom of each panel :The spectrum after subtracting the spectrum of 61Vir (the inactive template star) fromKIC6934317 (thin solid line). The residual Ca II 8542 profile is plotted shifted downwardsby 0.1 for the sake of clarity. There are clear excess emission around the core-regions of CaII 8498 and 8542, and we integrated the excess emission regions to get excess equivalentwidth and emission flux (See Table 5). 30 N o r m a li z ed I n t en s i t y l [Å] Li I 6708
KIC693431759Vir61VirSun
Fig. 5.
Normalized spectra of KIC6934317 (solid line), 59Vir (dashed line), 61Vir (dottedline), and the Sun (dash-dotted line) around Li I 6708. The spectrum of the Sun is thesame one which we used in Figure 3. According to these spectra, 59Vir has a deep lineof Li, and the Li line of 61Vir is absent while that of the Sun and KIC6934317 are veryweak and just visible against the noise. In Table 2 and 3, we show the values of lithiumabundance (A(Li)) of KIC6934317, 59Vir, and 61Vir measured in this study on the basisof the method described in Takeda & Kawanomoto (2005).31 r ( ) T eff Sun 59Vir 61Vir KIC6934317 log g ‡ ‡ < Fig. 6. r (8542) (Residual flux normalized by the continuum at the line core of Ca II 8542.)as a function of effective temperature ( T eff ) of the stars. In this figure, we plot the resultsof this observation (large symbols), and the data in Chmielewski (2000)(small symbols).Small filled squares represent active dwarf stars (log g ≥ g ≥ g< −4 −3 −2 −1 −4 −3 −2 −1 F l a r e A m p li t ude Brightness Variation Amplitude
B=1000Gi=90 ˚ B=1000Gi=2 ˚ KIC6934317
Fig. 7.