Superflares, chromospheric activities and photometric variabilities of solar-type stars from the second-year observation of TESS and spectra of LAMOST

In this work, 1272 superflares on 311 stars are collected from 22,539 solar-type stars from the second-year observation of Transiting Exoplanet Survey Satellite (TESS), which almost covered the northern hemisphere of the sky. Three superflare stars contain hot Jupiter candidates or ultrashort-period planet candidates. We obtain $\gamma = -1.76\pm 0.11$ of the correlation between flare frequency and flare energy ($dN/dE\propto E^{-\gamma}$) for all superflares and get $\beta=0.42\pm0.01$ of the correlation between superflare duration and energy ($T_{\text {duration }} \propto E^{\beta}$), which supports that a similar mechanism is shared by stellar superflares and solar flares. Stellar photometric variability ($R_{\rm var}$) is estimated for all solar-type stars, and the relation of $E\propto {R_{\rm var}}^{3/2}$ is included. An indicator of chromospheric activity ($S$-index) is obtained by using data from the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) for 7454 solar-type stars. Distributions of these two properties indicate that the Sun is generally less active than superflare stars. We find that saturation-like feature of $R_{\rm var}\sim 0.1$ may be the reason for superflare energy saturating around $10^{36}$ erg. Object TIC 93277807 was captured by the TESS first-year mission and generated the most energetic superflare. This superflare is valuable and unique that can be treated as an extreme event, which may be generated by different mechanisms rather than other superflares.