Rotation-Activity Relation of Ca II and Mg I Infrared Emission Lines of Young Stars

To reveal the detail of the internal structure, the relationship between chromospheric activity and the Rossby number, $N_{\rm R}$(= rotational period $P$ / convective turnover time $\tau_{\rm c}$), has been extensively examined for main-sequence stars. The goal of our work is to apply the same methods to pre-main-sequence (PMS) stars and identify the appropriate model of $\tau_{\rm c}$ for them. Yamashita et al. (2020) investigated the relationship between $N_{\rm R}$ and strengths of the Ca I\hspace{-.1em}I infrared triplet ($\lambda 8498, 8542, 8662 $ $\, \mathrm{\angstrom}$) emission lines of 60 PMS stars. Their equivalent widths are converted into the emission line to the stellar bolometric luminosity ratio ($R^{\prime}$). The 54 PMS stars have $N_{\rm R} < 10^{-1.0}$ and show $R^{\prime} \sim 10^{-4.2}$ as large as the maximum $R^{\prime}$ of the zero-age main-sequence (ZAMS) stars. However, because all $R^{\prime}$ was saturated against $N_{\rm R}$, it was not possible to estimate the appropriate $\tau_{\rm c}$ model for the PMS stars. We noticed that Mg I emission lines at $8807.8 \, \mathrm{\angstrom}$ is an optically thin chromospheric line, appropriate for determination of the adequate $\tau_{\rm c}$ for PMS stars. Using the archive data of the AAT/the University College London Echelle Spectrograph, we investigated the Mg I line of 52 ZAMS stars. After subtracting photospheric absorption component, the Mg I line is detected as an emission line in 45 ZAMS stars, whose $R^{\prime}_{\rm Mg I}$ is between $10^{-5.9}$ and $10^{-4.1}$. The Mg I line is not saturated yet in "the saturated regime for the Ca I\hspace{-.1em}I emission lines", i.e. $10^{-1.6} < N_{\rm R} < 10^{-0.8}$. Therefore, the adequate $\tau_{\rm c}$ for PMS stars can be determined by measuring of their $R^{\prime}_{\rm Mg I}$ values.