arXiv subjects

Shota Notsu

Publications and source records attributed to Shota Notsu.

At least 37 records · Page 2Linked to original sources

arXiv2022

The Molecular Composition of Shadowed Protosolar Disk Midplanes beyond the Water Snowline

The disk midplane temperature is potentially affected by the dust traps/rings. The dust depletion beyond the water snowline will cast a shadow. In this study, we adopt a detailed gas-grain chemical reaction network, and investigate the radial gas and ice abundance distributions of dominant carbon-, oxygen-, and nitrogen-bearing molecules in disks with shadow structures beyond the water snowline around a protosolar-like star. In shadowed disks, the dust grains at around $3-8$ au are predicted to have more than around $5-10$ times amounts of ices of organic molecules such as H$_{2}$CO, CH$_{3}$OH, and NH$_{2}$CHO, saturated hydrocarbon ices such as CH$_{4}$ and C$_{2}$H$_{6}$, in addition to H$_{2}$O, CO, CO$_{2}$, NH$_{3}$, N$_{2}$, and HCN ices, compared with those in non-shadowed disks. In the shadowed regions, we find that hydrogenation (especially of CO ice) is the dominant formation mechanism of complex organic molecules. The gas-phase N/O ratios show much larger spatial variations than the gas-phase C/O ratios, thus the N/O ratio is predicted to be a useful tracer of the shadowed region. N$_{2}$H$^{+}$ line emission is a potential tracer of the shadowed region. We conclude that a shadowed region allows the recondensation of key volatiles onto dust grains, provides a region of chemical enrichment of ices that is much closer to the star than within a non-shadowed disk, and may explain to some degree the trapping of O$_{2}$ ice in dust grains that formed comet 67P/Churyumov-Gerasimenko. We discuss that, if formed in a shadowed disk, Jupiter does not need to have migrated vast distances.

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arXiv2021

X-ray induced chemistry of water and related molecules in low-mass protostellar envelopes

Recent water line observations toward several low-mass protostars suggest low water gas fractional abundances in the inner warm envelopes. Water destruction by X-rays has been proposed to influence the water abundances in these regions, but the detailed chemistry, including the nature of alternative oxygen carriers, is not yet understood. In this study, we aim to understand the impact of X-rays on the composition of low-mass protostellar envelopes, focusing specifically on water and related oxygen bearing species. We compute the chemical composition of two low-mass protostellar envelopes using a 1D gas-grain chemical reaction network, under various X-ray field strengths. According to our calculations, outside the water snowline, the water gas abundance increases with $L_{\mathrm{X}}$. Inside the water snowline, water maintains a high abundance of $\sim 10^{-4}$ for small $L_{\mathrm{X}}$, with water and CO being the dominant oxygen carriers. For large $L_{\mathrm{X}}$, the water gas abundances significantly decrease just inside the water snowline (down to $\sim10^{-8}-10^{-7}$) and in the innermost regions ($\sim10^{-6}$). For these cases, the O$_{2}$ and O gas abundances reach $\sim 10^{-4}$ within the water snowline, and they become the dominant oxygen carriers. The HCO$^{+}$ and CH$_{3}$OH abundances, which have been used as tracers of the water snowline, significantly increase/decrease within the water snowline, respectively, as the X-ray fluxes become larger. The abundances of some other dominant molecules, such as CO$_{2}$, OH, CH$_{4}$, HCN, and NH$_{3}$, are also affected by strong X-ray fields, especially within their own snowlines. These X-ray effects are larger in lower density envelope models. Future observations of water and related molecules (using e.g., ALMA and ngVLA) will access the regions around protostars where such X-ray induced chemistry is effective.

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arXiv2020

The composition of hot Jupiter atmospheres assembled within chemically evolved protoplanetary discs

The radial-dependent positions of snowlines of abundant oxygen- and carbon-bearing molecules in protoplanetary discs will result in systematic radial variations in the C/O ratios in the gas and ice. This variation is proposed as a tracer of the formation location of gas-giant planets. However, disc chemistry can affect the C/O ratios in the gas and ice, thus potentially erasing the chemical fingerprint of snowlines in gas-giant atmospheres. We calculate the molecular composition of hot Jupiter atmospheres using elemental abundances extracted from a chemical kinetics model of a disc midplane where we have varied the initial abundances and ionization rates. The models predict a wider diversity of possible atmospheres than those predicted using elemental ratios from snowlines only. As found in previous work, as the C/O ratio exceeds the solar value, the mixing ratio of CH$_{4}$ increases in the lower atmosphere, and those of C$_{2}$H$_{2}$ and HCN increase mainly in the upper atmosphere. The mixing ratio of H$_{2}$O correspondingly decreases. We find that hot Jupiters with C/O$>1$ can only form between the CO$_{2}$ and CH$_{4}$ snowlines. Moreover, they can only form in a disc which has fully inherited interstellar abundances, and where negligible chemistry has occurred. Hence, carbon-rich planets are likely rare, unless efficient transport of hydrocarbon-rich ices via pebble drift to within the CH$_{4}$ snowline is a common phenomenon. We predict combinations of C/O ratios and elemental abundances that can constrain gas-giant planet formation locations relative to snowline positions, and that can provide insight into the disc chemical history.

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arXiv2020

Starspot mapping with adaptive parallel tempering I: Implementation of computational code

Starspots are thought to be regions of locally strong magnetic fields, similar to sunspots, and they can generate photometric brightness modulations. To deduce stellar and spot properties, such as spot emergence and decay rates, we implement computational code for starspot modeling. It is implemented with an adaptive parallel tempering algorithm and an importance sampling algorithm for parameter estimation and model selection in the Bayesian framework. For evaluating the performance of the code, we apply it to synthetic light curves produced with 3 spots. The light curves are specified in the spot parameters, such as the radii, intensities, latitudes, longitudes, and emergence/decay durations. The spots are circular with specified radii and intensities relative to the photosphere, and the stellar differential rotation coefficient is also included in the light curves. As a result, stellar and spot parameters are uniquely deduced. The number of spots is correctly determined: the 3-spot model is preferable because the model evidence is much greater than that of 2-spot models by orders of magnitude and more than that of 4-spot model by a more modest factor, whereas the light curves are produced to have 2 or 1 local minimum during one equatorial rotation period by adjusting the values of longitude. The spot emergence and decay rates can be estimated with error less than an order of magnitude, considering the difference of the number of spots.

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arXiv2020

Temporal Evolution of Spatially-Resolved Individual Star Spots on a Planet-Hosting Solar-type Star: Kepler 17

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.

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arXiv2019

The First Detection of 13C17O in a Protoplanetary Disk: a Robust Tracer of Disk Gas Mass

Measurements of the gas mass are necessary to determine the planet formation potential of protoplanetary disks. Observations of rare CO isotopologues are typically used to determine disk gas masses; however, if the line emission is optically thick this will result in an underestimated disk mass. With ALMA we have detected the rarest stable CO isotopologue, 13C17O, in a protoplanetary disk for the first time. We compare our observations with the existing detections of 12CO, 13CO, C18O and C17O in the HD163296 disk. Radiative transfer modelling using a previously benchmarked model, and assuming interstellar isotopic abundances, significantly underestimates the integrated intensity of the 13C17O J=3-2 line. Reconciliation between the observations and the model requires a global increase in CO gas mass by a factor of 3.5. This is a factor of 2-6 larger than previous gas mass estimates using C18O. We find that C18O emission is optically thick within the CO snow line, while the 13C17O emission is optically thin and is thus a robust tracer of the bulk disk CO gas mass.

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arXiv2019

Impact of Stellar Superflares on Planetary Habitability

High-energy radiation caused by exoplanetary space weather events from planet-hosting stars can play a crucial role in conditions promoting or destroying habitability in addition to the conventional factors. In this paper, we present the first quantitative impact evaluation system of stellar flares on the habitability factors with an emphasis on the impact of Stellar Proton Events. We derive the maximum flare energy from stellar starspot sizes and examine the impacts of flare associated ionizing radiation on CO$_2$, H$_2$, N$_2$+O$_2$ --rich atmospheres of a number of well-characterized terrestrial type exoplanets. Our simulations based on the Particle and Heavy Ion Transport code System [PHITS] suggest that the estimated ground level dose for each planet in the case of terrestrial-level atmospheric pressure (1 bar) for each exoplanet does not exceed the critical dose for complex (multi-cellular) life to persist, even for the planetary surface of Proxima Centauri b, Ross-128 b and TRAPPIST-1 e. However, when we take into account the effects of the possible maximum flares from those host stars, the estimated dose reaches fatal levels at the terrestrial lowest atmospheric depth on TRAPPIST-1 e and Ross-128 b. Large fluxes of coronal XUV radiation from active stars induces high atmospheric escape rates from close-in exoplanets suggesting that the atmospheric depth can be substantially smaller than that on the Earth. In a scenario with the atmospheric thickness of 1/10 of Earth's, the radiation dose from close-in planets including Proxima Centauri b and TRAPPIST-1 e reach near fatal dose levels with annual frequency of flare occurrence from their hoststars.

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arXiv2019

Do Kepler superflare stars really include slowly-rotating Sun-like stars ? - Results using APO 3.5m telescope spectroscopic observations and Gaia-DR2 data -

We report the latest view of Kepler solar-type (G-type main-sequence) superflare stars, including recent updates with Apache Point Observatory (APO) 3.5m telescope spectroscopic observations and Gaia-DR2 data. First, we newly conducted APO3.5m spectroscopic observations of 18 superflare stars found from Kepler 1-min time cadence data. More than half (43 stars) are confirmed to be "single" stars, among 64 superflare stars in total that have been spectroscopically investigated so far in this APO3.5m and our previous Subaru/HDS observations. The measurements of $v\sin i$ (projected rotational velocity) and chromospheric lines (Ca II H\&K and Ca II 8542Å) support the brightness variation of superflare stars is caused by the rotation of a star with large starspots. We then investigated the statistical properties of Kepler solar-type superflare stars by incorporating Gaia-DR2 stellar radius estimates. As a result, the maximum superflare energy continuously decreases as the rotation period $P_{\mathrm{rot}}$ increases. Superflares with energies $\lesssim 5\times10^{34}$ erg occur on old, slowly-rotating Sun-like stars ($P_{\mathrm{rot}}\sim$25 days) approximately once every 2000--3000 years, while young rapidly-rotating stars with $P_{\mathrm{rot}}\sim$ a few days have superflares up to $10^{36}$ erg. The maximum starspot area does not depend on the rotation period when the star is young, but as the rotation slows down, it starts to steeply decrease at $P_{\mathrm{rot}}\gtrsim$12 days for Sun-like stars. These two decreasing trends are consistent since the magnetic energy stored around starspots explains the flare energy, but other factors like spot magnetic structure should also be considered.

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arXiv2019

Dust continuum emission and the upper limit fluxes of sub-millimeter water lines of the protoplanetary disk around HD 163296 observed by ALMA

In this paper, we analyse the upper limit fluxes of sub-millimeter ortho-H$_{2}$$^{16}$O 321 GHz, para-H$_{2}$$^{18}$O 322 GHz, and HDO 335 GHz lines from the protoplanetary disk around the Herbig Ae star HD 163296, using the Atacama Large Millimeter/Submillimeter Array (ALMA). These water lines are considered to be the best candidate sub-millimeter lines to locate the position of the H$_{2}$O snowline, on the basis of our previous model calculations. We compare the upper limit fluxes with the values calculated by our models with dust emission included, and we constrain the line emitting region and the dust opacity from the observations. We conclude that, if the outer edge of the region with high water vapor abundance and if the position of the water snowline are beyond 8 au also, the mm dust opacity will have a value larger than 2.0 cm$^{2}$ g$^{-1}$. In addition, the position of the water snowline will be inside 20 au, if the mm dust opacity is 2.0 cm$^{2}$ g$^{-1}$. Future observations of the dust continuum emission at higher angular resolution and sub-millimeter water lines with longer observation time are required to clarify the detailed structures and the position of the H$_{2}$O snowline in the disk midplane.

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arXiv2018

Lifetimes and Emergence/Decay Rates of Star Spots on Solar-type Stars Estimated by Kepler Data in Comparison with Those of Sunspots

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.

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arXiv2018

Candidate Water Vapor Lines to Locate the $\mathrm{H_2O}$ Snowline through High-dispersion Spectroscopic Observations. III. Submillimeter $\mathrm{H_2}$$^{16}\mathrm{O}$ and $\mathrm{H_2}$$^{18}\mathrm{O}$ Lines

In this paper, we extend the results presented in our former papers (Notsu et al. 2016, 2017) on using ortho-$\mathrm{H_2}$$^{16}\mathrm{O}$ line profiles to constrain the location of the $\mathrm{H_2O}$ snowline in T Tauri and Herbig Ae disks, to include sub-millimeter para-$\mathrm{H_2}$$^{16}\mathrm{O}$ and ortho- and para-$\mathrm{H_2}$$^{18}\mathrm{O}$ lines. Since the number densities of the ortho- and para-H$_{2}$$^{18}$O molecules are about 560 times smaller than their $^{16}$O analogues, they trace deeper into the disk than the ortho-H$_{2}$$^{16}$O lines (down to $z=0$, i.e., the midplane). Thus these H$_{2}$$^{18}$O lines are potentially better probes of the position of the H$_{2}$O snowline at the disk midplane, depending on the dust optical depth. The values of the Einstein $A$ coefficients of sub-millimeter candidate water lines tend to be lower (typically $<$$10^{-4}$ s$^{-1}$) than infrared candidate water lines (Notsu et al. 2017). Thus in the sub-millimeter candidate water line cases, the local intensity from the outer optically thin region in the disk is around $10^{4}$ times smaller than that in the infrared candidate water line cases. Therefore, in the sub-millimeter lines, especially H$_{2}$$^{18}$O and para-H$_{2}$$^{16}$O lines with relatively lower upper state energies ($\sim$ a few 100K) can also locate the position of the $\mathrm{H_2O}$ snowline. We also investigate the possibility of future observations with ALMA to identify the position of the water snowline. There are several candidate water lines that trace the hot water vapor inside the $\mathrm{H_2O}$ snowline in ALMA Bands $5-10$.

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arXiv2018

Time resolved spectroscopic observations of an M-dwarf flare star EV Lacertae during a flare

We have performed 5 night spectroscopic observation of the Halpha line of EV Lac with a medium wavelength resolution (R~ 10,000) using the 2m Nayuta telescope at the Nishi-Harima Astronomical Observatory. EV Lac always possesses the Halpha emission line; however, its intensity was stronger on August 15, 2015 than during other four-night periods. On this night, we observed a rapid rise (~ 20min) and a subsequent slow decrease (~ 1.5h) of the emission-line intensity of Halpha, which was probably caused by a flare. We also found an asymmetrical change in the Halpha line on the same night. The enhancement has been observed in the blue wing of the Ha line during each phase of this flare (from the flare start to the flare end), and absorption components were present in its red wing during the early and later phases of the flare. Such blue enhancement (blue asymmetry) of the Halpha line is sometimes seen during solar flares, but only during the early phases. Even for solar flares, little is known about the origin of the blue asymmetry. Compared with solar-flare models, the presented results can lead to the understanding of the dynamics of stellar flares.

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arXiv2018

Statistical Study of Solar White-light Flares and Comparison with Superflares on Solar-type Stars

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.

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arXiv2017

Statistical Studies of Solar White-Light Flares and Comparisons with Superflares on Solar-type Stars

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 ($τ$): $τ\propto E^{0.39}$ (Maehara et al. 2017 $EP\& S$, 67, 59), similar to those of solar hard/soft X-ray flares: $τ\propto E^{0.2-0.33}$. 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 $E$--$τ$ relation on solar WLFs ($τ\propto E^{0.38}$) is quite similar to that on stellar superflares ($τ\propto E^{0.39}$). 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 ($τ\propto E^{1/3}B^{-5/3}$) 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.

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arXiv2017

Starspot activity and superflares on solar-type stars

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.

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arXiv2017

Candidate Water Vapor Lines to Locate the H$_{2}$O Snowline through High-Dispersion Spectroscopic Observations II. The Case of a Herbig Ae Star

Observationally measuring the location of the H$_{2}$O snowline is crucial for understanding the planetesimal and planet formation processes, and the origin of water on Earth. In disks around Herbig Ae stars ($T_{\mathrm{*}}\sim$ 10,000K, $M_{\mathrm{*}}\gtrsim$ 2.5$M_{\bigodot}$), the position of the H$_{2}$O snowline is further from the central star compared with that around cooler, and less massive T Tauri stars. Thus, the H$_{2}$O emission line fluxes from the region within the H$_{2}$O snowline are expected to be stronger. In this paper, we calculate the chemical composition of a Herbig Ae disk using chemical kinetics. Next, we calculate the H$_{2}$O emission line profiles, and investigate the properties of candidate water lines across a wide range of wavelengths (from mid-infrared to sub-millimeter) that can locate the position of the H$_{2}$O snowline. Those line identified have small Einstein $A$ coefficients ($\sim 10^{-6} -10^{-3}$ s$^{-1}$) and relatively high upper state energies ($\sim$ 1000K). The total fluxes tend to increase with decreasing wavelengths. We investigate the possibility of future observations (e.g., ALMA, SPICA/SMI-HRS) to locate the position of the H$_{2}$O snowline. Since the fluxes of those identified lines from Herbig Ae disks are stronger than those from T Tauri disks, the possibility of a successful detection is expected to increase for a Herbig Ae disk.

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arXiv2016

Spectroscopic observations of active solar-analog stars having high X-ray luminosity, as a proxy of superflare stars

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$α$ 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.

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arXiv2016

Statistical properties of superflares on solar-type stars with Kepler data

Superflares are flares that release total energy 10$\sim$10$^{4}$ times greater than that of the biggest solar flares with energy of $\sim$10$^{32}$ erg. We searched superflares on solar-type stars (G-type main sequence stars) using the Kepler 30-min (long) and 1-min (short) cadence data. We found more than 1500 superflares on 279 stars from 30-min cadence data (Q0-6) and 187 superflares on 23 stars from 1-min cadence data (Q0-17). The bolometric energy of detected superflares ranges from the order of 10$^{32}$ erg to 10$^{36}$ erg. Using these data, we found that the occurrence frequency ($dN/dE$) of superflares is expressed as a power-law function of flare energy ($E$) with the index of -1.5 for $10^{33}<E<10^{36}$erg. Most of the superflare stars show quasi-periodic light variations with the amplitude of a few percent, which can be explained by the rotation of the star with large starspots. The bolometric energy released by flares is consistent with the magnetic energy stored around such large starspots. Furthermore, our analyses indicate that the occurrence frequency of superflares depends on the rotation period, and that the flare frequency increases as the rotation period decreases. However, the energy of the largest flares observed in a given period bin does not show any clear correlation with the rotation period. We also found that the duration of superflares increases with the flare energy as $E^{0.39+/-0.03}$. This can be explained if we assume the time-scale of flares is determined by the Alfv$\acute{\rm{e}}$n time.

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