We performed a statistical study of magnetic activities of M-type stars by combining the spectra of LAMOST DR5 with light curves from the Kepler and K2 missions. We mainly want to study the relationship between chromospheric activity and flares, and their relations of magnetic activity and rotation period. We have obtained the maximum catalog of 516,688 M-type stellar spectra of 480,912 M stars from LAMOST DR5 and calculated their equivalent widths of chromospheric activity indicators (Hα, Hβ, Hγ, Hδ, Ca ii H&K, and He i D3). Using the Hα indicator, 40,464 spectra of 38,417 M stars show chromospheric activity, and 1791 of these 5499 M-type stars with repeated observations have Hα variability. We used an automatic detection plus visual inspection method to detect 17,432 flares on 8964 M-type stars from the catalog by cross-matching LAMOST DR5 and the Kepler and K2 databases. We used the Lomb–Scargle method to calculate their rotation periods. We find that the flare frequency is consistent with the ratio of activities of these chromospheric activity indicators as a function of spectral type in M0–M3. We find the equivalent widths of Hα and Ca ii H have a significant statistical correlation with the flare amplitude in M-type stars. We confirm that the stellar flare is affected by both the stellar magnetic activity and the rotation period. Finally, using the Hα equivalent width equal to 0.75 Å and using the rotation period equal to 10 days as the threshold for the M-type stellar flare time frequency are almost equivalent.

We report 15 new VRI light curves of five low-mass eclipsing binaries (NSVS 02502726, NSVS 07453183, NSVS 11868841, NSVS 06550671 and NSVS 10653195) that were observed between 2010 and 2012. We analysed our new data together with three published spectroscopic observations and seven published light curves using a modified version of the Wilson–Devinney program. Orbital solutions of the five low-mass eclipsing binaries were revised and new star-spot parameters were obtained. We found that spot locations on the five low-mass eclipsing binaries changed over several years. However, the star-spots for NSVS 07453183 and NSVS 06550671 were stable for several months. More interestingly, for NSVS 02502726, the spots within a star-spot longitude region of 180°–360° indicated a magnetic activity cycle of 5.9(±0.2) yr. Moreover, we detected the first flare-like event on NSVS 07453183 at phase 0.39. The observations of the chromospheric activity indicators (Hβ and Hγ lines) revealed that NSVS 10653195 and NSVS 06550671 were active. For NSVS 02502726, we found a weak continuous secular decrease at a smaller rate of dp/dt = −2.1(0.8) × 10⁻⁷ d yr⁻¹ than the previous result. For NSVS 07453183, the O−C times appeared to increase at cycle 6000, and this was followed by a decrease at cycle 6500.

Stellar magnetic activity is an interesting phenomenon in late-type stars. We use the medium-resolution spectroscopic observations of 406 069 late-type stars from LAMOST to explore their properties. We perform a statistical analysis on the magnetic activity of the stars and their associated physical parameters. Our samples are cross-matched with other data bases (LAMOST DR5, VSX, and SDSS DR12) to obtain additional observational properties. The equivalent widths (EWs) of Hα lines, an indicator of chromospheric activity, are calculated. According to the EWs of the Hα line, we detect 8816 spectra with apparent Hα emission for a total of 2115 stars among the 2 108 565 spectra analysed. Furthermore, 1521 of these stars show variability in their Hα lines. In addition, we detect 2132 flare events associated with 41 542 stars from the catalogue by cross-matching our LAMOST medium-resolution samples and the Kepler and K2 data bases. We also confirm a weak relationship of the flare amplitude with increasing Rossby number. There is a clear decease in the strength of chromospheric activity (LHα/Lbol) with increasing rotation period. Moreover, the ratio of the flare energy and stellar luminosity is found to decrease with the stellar mass.

We have used the Large Sky Area Multi-Object Fibre Spectroscopic Telescope (LAMOST) low-resolution and medium-resolution spectroscopic surveys to explore the chromospheric statistical properties and variations of M stars. There are 738,477 LAMOST low-resolution spectra of 622,523 M stars. We have calculated equivalent widths of the Ca ii H&K, Hα, Hβ, Hγ, Hδ, He i D3, and Ca ii infrared triplet lines. Based on the Hα EWs, we found that 33,374 objects showed Hα emissions. We revised the relationship between the active fraction and spectral subtype, and confirmed that the active fractions increased from M0 to M3, and possibly declined from M4 to subsequent types. Among 86,005 objects with repeated spectra, 19,422 objects showed Hα variations. The variation fraction of stars with M4 and subsequent types with a fully convective envelope was higher than those of M0–M3 with a partially convective envelope. By combining the distances from Gaia, we have determined the positions of the M dwarfs in the catalog for M stars. The active fraction decreased rapidly in the height range of 0–400 pc above and below the Galactic plane, and maintained a steady trend in 400–1000 pc. We cross-matched the M catalog of the LAMOST low-resolution survey with LAMOST medium-resolution spectra. We obtained 272,181 spectra of 13,355 M objects and calculated the Hα EWs. Among them, 3813 stars show variations, which might be caused by chromospheric activity evolution with orbital phase or time. The Hα emission for 972 objects shows variations over short and long timescales, especially on short timescales of 20 minutes.

Stellar parameters and magnetic activity are important for the understanding of stellar physics and dynamo theory. We have used LAMOST spectroscopic surveys to study stellar parameters and magnetic activity properties of TESS objects. There are 46,684 spectra of 31,385 TESS objects in the LAMOST low-resolution spectral survey. We have calculated equivalent widths of Ca ii H and K, and Hα lines, and discussed the relationship of chromospheric activity with stellar temperature. There are 25,710 spectra of 10,404 stars with repeated low-resolution observations. We found that there are 694 objects with variations of the Hα line and 1406 objects with varying radial velocities. Moreover, there are 14,099 spectra of 5834 TESS objects in the LAMOST medium-resolution survey, of which there are 2666 objects with Hα variations and 1480 objects with variation in radial velocities. By using the light curves of the TESS objects in the LAMOST field, we detected 4269 flare events and determined their flare parameters. We have confirmed that the fraction of the flare stars increases as stellar temperature decreases. There is also an observed relationship between the flare energy and chromospheric activity. We have calculated the power-law index between the flare energy and decay time using TESS data to be 0.27(0.01), which can be explained by the magnetic reconnection theory. We confirmed that R H α ′ is stable for Rossby number R < 0.1 and decreases with the increase of Rossby number R > 0.1. There is a positive correlation between the brightness variation amplitude due to star spots from TESS and the Hα intensity from LAMOST.

Using the short-cadence data (1-min interval) of the Kepler space telescope, we conducted a statistical analysis for the characteristic time of stellar flares on Sun-like stars (SLS). Akin to solar flares, stellar flares show rise and decay light-curve profiles, which reflect the two distinct phases (rise phase and decay phase) of the flare process. We derived characteristic times of the two phases for stellar flares of SLS, resulting in a median rise time of about 5.9 min and a median decay time of 22.6 min. It is found that both the rise time and the decay time of the stellar flares follow a lognormal distribution. The peak positions of the lognormal distributions for flare rise time and decay time are 3.5 min and 14.8 min, respectively. These time values for stellar flares are similar to the time-scale of solar flares, which supports the idea that stellar flares and solar flares have the same physical mechanism. The statistical results obtained in this work for SLS can be a benchmark of flare characteristic times when comparing with other types of stars.