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, $N_{\mathrm{R}}$(= rotational period $P$ / convective turnover time ${\tau }_{\mathrm{c}}$), 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 ${\tau }_{\mathrm{c}}$ for them. Yamashita et al. (2020) investigated the relationship between $N_{\mathrm{R}}$ and strengths of the Ca I\hspace{-.1em}I infrared triplet ($\lambda 8498,8542,8662$ $\text{angstrom}$) 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 $N_{\mathrm{R}}<{10}^{-1.0}$ 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 $N_{\mathrm{R}}$, it was not possible to estimate the appropriate ${\tau }_{\mathrm{c}}$ model for the PMS stars. We noticed that Mg I emission lines at $8807.8\text{angstrom}$ is an optically thin chromospheric line, appropriate for determination of the adequate ${\tau }_{\mathrm{c}}$ 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 $R_{\mathrm{M}\mathrm{g}\mathrm{I}}^{\prime }$ 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. ${10}^{-1.6}<N_{\mathrm{R}}<{10}^{-0.8}$. Therefore, the adequate ${\tau }_{\mathrm{c}}$ for PMS stars can be determined by measuring of their $R_{\mathrm{M}\mathrm{g}\mathrm{I}}^{\prime }$ values.