Do Kepler Superflare Stars Really Include Slowly Rotating Sun-like Stars?—Results Using APO 3.5 m Telescope Spectroscopic Observations and Gaia-DR2 Data

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Abstract
We report the latest view of Kepler solar-type (G-type main-sequence) superflare stars, including recent updates with Apache Point Observatory (APO) 3.5 m telescope spectroscopic observations and Gaia-DR2 data. First, we newly conducted APO 3.5 m spectroscopic observations of 18 superflare stars found from Kepler 1-minute 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 APO 3.5 m and our previous Subaru/HDS observations. The measurements of v sin i (projected rotational velocity) and chromospheric lines (Ca ii H and K and Ca ii λ8542) support that 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 rot increases. Superflares with energies ≲5 × 1034 erg occur on old, slowly rotating Sun-like stars (P rot ∼ 25 days) approximately once every 2000–3000 yr, while young, rapidly rotating stars with P rot ∼ a few days have superflares up to 1036 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 rot ≳ 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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