Anchoring the Chromospheric Activity$-$Rotation Relation: A Study of the Pleiades and Group X

We present a study of the rotation and the chromospheric H$\alpha$ activity of low-mass stars in the $\approx$120 Myr-old Pleiades and the $\approx$400 Myr-old Group X open clusters. We combine published and new rotation periods ($P_{\mathrm{r}\mathrm{o}\mathrm{t}}$) from TESS and ZTF, and use LAMOST, SDSS, and MDM spectra to measure H$\alpha$ equivalent widths (EWs). While overall the Group X distributions of $P_{\mathrm{r}\mathrm{o}\mathrm{t}}$ and EWs are as expected, detailed comparisons to the Pleiades and to the 700-Myr-old benchmark Praesepe produce some surprises. For F through mid K stars, the Group X color$-$period sequence lies between those of the Pleiades and of Praesepe, as expected. But the $P_{\mathrm{r}\mathrm{o}\mathrm{t}}$ for its late K and early M dwarfs and the Praesepe slow-rotator sequence overlap, indicating that the 700 Myr-old stars have not spun down significantly despite being nearly twice as old as their Group X counterparts. In the Rossby number$-L_{\mathrm{H}\alpha }\mathrm{/}{L}_{\mathrm{b}\mathrm{o}\mathrm{l}}$ plane, rapid rotators in Group X are saturated, as is seen in older clusters, whereas the rapid rotators in the Pleiades show a weak but measurable dependence of $L_{\mathrm{H}\alpha }\mathrm{/}{L}_{\mathrm{b}\mathrm{o}\mathrm{l}}$ on rotation. This implies that the chromospheric activity$-$rotation relation attains its mature form between 120 and 400 Myr. Dividing the sample by color reveals that K, M0, and M1 dwarfs are no longer saturated by $\approx$120 Myr, M2 and M3 dwarfs become unsaturated between $\approx$400 and $\approx$700 Myr, and later M dwarfs remain largely saturated through field ages even as their saturated $L_{\mathrm{H}\alpha }\mathrm{/}{L}_{\mathrm{b}\mathrm{o}\mathrm{l}}$ levels decline, indicating that chromospheric evolution is not determined by rotation period alone.