Variability of H$α$ chromospheric activity of solar-like stars revealed by the time-domain data of LAMOST Medium-Resolution Spectroscopic Survey

The variability of H$α$ chromospheric activity of solar-like stars is investigated by using the time-domain data of LAMOST Medium-Resolution Spectroscopic Survey (MRS). We use $R_\mathrm{Hα}$ index (ratio of H$α$ luminosity to bolometric luminosity) to measure the H$α$ activity intensity of a spectrum, and utilize the median of the $R_\mathrm{Hα}$ values of multiple observations ($R_\mathrm{Hα}^\mathrm{median}$) as the representative activity intensity of a stellar source. The H$α$ variability of a stellar source is indicated by the extent of $R_\mathrm{Hα}$ fluctuation ($R_\mathrm{Hα}^\mathrm{EXT}$) of multiple observations. Our sample shows that $R_\mathrm{Hα}^\mathrm{EXT}$ of solar-like stars is about one order of magnitude smaller than $R_\mathrm{Hα}^\mathrm{median}$. The distribution of $\log R_\mathrm{Hα}^\mathrm{EXT}$ versus $\log R_\mathrm{Hα}^\mathrm{median}$ reveals the distinct behaviors between the stellar source categories with lower ($\log R_\mathrm{Hα}^\mathrm{median} < -4.85$) and higher ($\log R_\mathrm{Hα}^\mathrm{median} > -4.85$) activity intensity. For the former stellar source category, the top envelope of the distribution first increases and then decreases with $\log R_\mathrm{Hα}^\mathrm{median}$; while for the latter category, the top envelope of the distribution is largely along a positive correlation line. In addition, for the stellar sources with lower activity intensity, the large-$\log R_\mathrm{Hα}^\mathrm{EXT}$ objects near the top envelope of the $\log R_\mathrm{Hα}^\mathrm{EXT}$ versus $\log R_\mathrm{Hα}^\mathrm{median}$ distribution tend to have long-term and regular variations of H$α$ activity; while for the stellar sources with higher activity intensity, the H$α$ variations are more likely to be random fluctuations.