Calibrating the Color-Magnitude Relation of M Giants by Using Open Clusters

M giants, with their distinctive properties such as high luminosity, serve as excellent indicators for mapping the structure of the Milky Way. The distance to distant M giants can be determined by using the color-magnitude relation (CMR), which is derived from color-magnitude diagrams of specific systems in previous studies. In this work, we aimed to achieve more accurate distance determination for M giants by focusing on open clusters (OCs) with a large number of member stars and thus improve the CMR. For the first time, we compiled a census of OCs harboring M giants using Gaia Data Release 3 (DR3) and Large Sky Area Multi-Object Fiber Spectroscopic Telescope Data Release 9. We identified 58 M giants associated with 43 OCs and obtained their astrometric and photometric parameters from Gaia DR3. Using the distances of these OCs, we derived the CMR for M giants as a linear correlation, expressed as $M_{Ks}=3.85-8.26(J-K_s$). This linear relation proved superior to the empirical distance relation in characterizing the CMR of M giants. The photometric distances of M giants derived from the CMR are consistent with the parallax distances from Gaia and known spectroscopic distances, with median deviations of 1.5% and 2.3%, respectively. Using the distances of M giants derived from the CMR, we computed their radial velocity ($V_R$), azimuthal velocity ($V{\phi}$), and vertical velocity ($V_Z$), respectively. The distributions of these velocities revealed key features of the Galactic disk, including oscillation, north-south rotational asymmetry, and warp. These findings are consistent with previous studies and further validate the reliability of the derived CMR.