M 型主序星通常是有著接近或完全對流的外層，由於他們對流的外層產生 強烈的磁場，常常可以在光譜上有見到色球層的 Hα 譜線的 M 型主序星也會有 閃焰的發生。另外，跟 G 型主序星（類似太陽的恆星）相比，M 型主序星的適 居帶非常靠近他們主星，對於在 M 型主序星適居帶上的系外行星的適居性可能 會受到閃焰的影響，因此研究 M 型主序星的閃焰一個有趣的研究題目。 本篇論文是用了 Kepler 太空望遠鏡的資料以及 LAMOST 望遠鏡的光譜資 料來做研究，主要的 M 型主序星都是屬於 M0 到 M3 的分類，從 Kepler 的觀測 資料中計算出來的自轉週期跟閃焰的大小、閃焰頻率分布的指數、以及 Hα 譜 線的等值寬度有密切的關聯，可以看到有明顯的趨勢在快速自轉（自轉週期低 於 15 天）的 M 型主序星上。;The M dwarfs are usually known with their convective envelopes. Due to the strong magnetic activities associated with their convective envelopes, M dwarfs showing strong chromospheric emission in Hα line have large flare activities in general. Moreover, comparing with G dwarfs, the habitable zone is much closer to M dwarfs. The habitability of the exoplanet might be affected by flares of M dwarfs and, therefore, it is interesting to investigate the flare phenomena of M dwarfs. This thesis provides a sample of the LAMOST spectra of the early M dwarfs (i.e., M0 – M3) to compare with the Kepler observations. The rotational periods derived from the Kepler measurements are highly correlated with flare intensity, the power-law index of distribution and the equivalent widths of the Hα line emission. We found that fast rotating (i.e., rotational periods < 15 day) M dwarfs have more magnetic activities.
