Magnetic activity of M dwarf stars from the LAMOST DR10 medium-resolution survey

Aims. M dwarf stars (red dwarfs) are the most common stars in the Milky Way (70$%$ of all stars). Their temperatures and masses are low, but their magnetic activity is strong and includes flares, starspots, and coronal mass ejections. The internal structure and evolutionary processes of stars can be understood by studying their magnetic activity, as can their effect on the environments of surrounding planets. We used medium-resolution spectrum data of M dwarf stars from Data Release 10 (DR10) of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) to conduct a comprehensive and in-depth investigation of the stellar magnetic activity, flare, and starspot variations. Methods. By cross-matching the low-resolution spectrum M dwarf star catalog from LAMOST DR10 medium-resolution spectrum data, we successfully identified 20,279 M dwarfs and obtained a total of 708,969 datasets of medium-resolution spectrum. These data provide a rich foundation for studying stellar magnetic fields and activity characteristics. Additionally, we cross-matched the data with light curves from the Transiting Exoplanet Survey Satellite (TESS), from which we acquired light-curve data for 2,868 stars. We identified 891 flare stars in this sample, which provide an important sample for the statistical characteristics and physical mechanisms of flare events. By combining them with Gaia data, we clarified the characterisspatial distribution characteristics of M dwarfs in the Milky Way. Results. Statistical studies of the magnetic activity of M dwarf stars based on LAMOST medium-resolution spectrum, showed that as the effective temperature of M dwarf stars increases, their stellar activity diminishes, although this trend becomes less evident for T_ eff >3600 K, and the amplitude of Hα line variations increases strongly for later spectral types. In a sample of 11,868 M dwarfs with a signal-to-noise ratio higher than 10, we found that 1,676 of the stars exhibited Hα emission features, that is, were active stars. In the 891 flare stars identified from TESS light-curve data, we also detected 7,496 flare events. Twenty-five of the 119 stars had EW_Hα flare-like variations in TESS light-curve data. Research also clarified that the activity of M dwarf stars in the Milky Way decreases with increasing vertical distance from the Galactic disk. Furthermore, by combining LAMOST spectrum surveys with TESS light-curve data, a positive correlation between chromospheric activity as indicated by Hα lines and the starspot area was established. Additionally, studies showed a positive correlation between the flare energy and their duration in M dwarf stars, and the slope of this correlation decreases for later spectral types. Finally, through analyzing the asymmetry of Hα lines, two candidate coronal mass ejections were identified.