Solar flares are caused by the sudden release of magnetic energy stored near sunspots. They release 10(29) to 10(32) ergs of energy on a timescale of hours. Similar flares have been observed on many stars, with larger 'superflares' seen on a variety of stars, some of which are rapidly rotating and some of which are of ordinary solar type. The small number of superflares observed on solar-type stars has hitherto precluded a detailed study of them. Here we report observations of 365 superflares, including some from slowly rotating solar-type stars, from about 83,000 stars observed over 120 days. Quasi-periodic brightness modulations observed in the solar-type stars suggest that they have much larger starspots than does the Sun. The maximum energy of the flare is not correlated with the stellar rotation period, but the data suggest that superflares occur more frequently on rapidly rotating stars. It has been proposed that hot Jupiters may be important in the generation of superflares on solar-type stars, but none have been discovered around the stars that we have studied, indicating that hot Jupiters associated with superflares are rare.

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

Recent observations of solar type stars with the Kepler satellite by Maehara et al. have revealed the existence of superflares (with energy of 10 33 ~ 10 35 erg) on Sun-like stars, which are similar to our Sun in their surface temperature (5600 K ~ 6000 K) and slow rotation (rotational period > 10 days). From the statistical analysis of these superflares, it was found that superflares with energy 10 34 erg occur once in 800 years and superflares with 10 35 erg occur once in 5000 years on Sun-like stars. In this paper, we examine whether superflares with energy of 10 33 ~ 10 35 erg could occur on the present Sun through the use of simple order-of-magnitude estimates based on current ideas relating to the mechanisms of the solar dynamo. If the magnetic flux is generated by the differential rotation at the base of convection zone as assumed in typical dynamo models, it is possible that the present Sun would generate a large sunspot with total magnetic flux ~2 x 10 23 Mx within one solar cycle period, and lead to superflares with energy of 10 34 erg. On the other hand, it would take ~40 years to store total magnetic flux ~ 10 24 Mx for generating 10 35 erg superflares. Many questions remain relating to how to store 10 24 Mx below the base of convection zone and how to erupt a magnetic flux tube in a short time to create a sunspot with 10 24 Mx, which presents a challenge to dynamo theorists. Hot Jupiters, however, which have been often argued to be a necessary ingredient for generation of superflares, do not play any essential role on generation of magnetic flux in the star itself, if we consider only magnetic interaction between the star and the hot Jupiter. This seems to be consistent with Maehara et al.'s finding of 148 superflare-generating solar type stars which do not have a hot Jupiter companion. Altogether, our simple calculations, combined with Maehara et al.'s analysis of superflares on Sun-like stars, show that there is a possibility that superflares of 10 34 erg would occur once in 800 years on our present Sun, while it is premature to conclude whether it is possible for 10 35 erg superflares to occur on our present Sun on the basis of application of current dynamo theory.

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

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