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

Abstract 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>3.85</mml:mn> <mml:mo>−</mml:mo> <mml:mn>8.26</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mi>J</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> . 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 ϕ ), 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.