Stellar chromospheric activities revealed from the LAMOST-K2 time-domain survey

By using the LAMOST time-domain survey data, we study stellar activities based on the $\rm{H_{\alpha}}$ lines for about 2000 stars in four $K$2 plates. Two indices, $R_{\rm{H\alpha}}^{'}$ and $R_{\rm{H\alpha}}^{+}$, are computed from LAMOST spectra, the former of which is derived by excluding the photospheric contributions to the $\rm{H_{\alpha}}$ lines, while the latter is derived by further subtracting the non-dynamo driven chromospheric emission. Meanwhile, the periodicity and variation amplitudes are computed from \emph{K2} light curves. Both the $R_{\rm{H\alpha}}^{'}$-Ro relation and $R_{\rm{H\alpha}}^{+}$-Ro relation show complicated profiles in the non-saturated decay region. Hot stars show flatter slopes and higher activity level than cool stars, and the behaviour is more notable in the $R_{\rm{H\alpha}}^{+}$-$R_{o}$ relation. This is consistent with recent studies using other activity proxies, including $L_{\rm{x}}/L_{\rm{bol}}$, $R_{\rm{HK}}^{'}$ and amplitudes of optical light curves. % This may suggest different kinds of stars follow different power laws in the decay region. Most of our targets have multiple observations, and some of them exhibit significant variability of ${\rm{H\alpha}}$ emissions, which may cause the large scatters shown in the decay region. We find three targets exhibiting positive correlation in rotational phase, possibly indicating that their optical light curves are dominated by hot faculae rather than cool starspots.