The C/M Ratio of AGB Stars in the Local Group Galaxies

The number ratio of carbon-rich to oxygen-rich asymptotic giant branch (AGB) stars (the so-called C/M ratio) is closely related to the evolution environment of the host galaxy. This work studies the C/M ratio in 14 galaxies within the Local Group with the most complete and clean sample of member stars identified in our previous works. The borderlines between carbon-rich AGB and oxygen-rich AGB stars as well as red supergiants are defined by Gaussian mixture model fitting to the number density in the $(J - K)/K$ diagram for the member stars of the LMC and M33, and then applied to the other galaxies by shifting the difference in the position of tip red giant branch (TRGB). The C/M ratios are obtained after precise and consistent categorization. Although for galaxies with larger distance modulo there is greater uncertainty, the C/M ratio is clearly found to decrease with the color index $(J - K)_0$ of TRGB as the indicator of metallicity, which agrees with previous studies and can be explained by the fact that carbon stars are more easily formed in a metal-poor environment. Furthermore, the C/M ratio within M33 is found to increase with galactocentric distance, which coincides with this scenario and the galactic chemical evolution model. On the other hand, the C/M ratio within M31 is found to decrease with galactocentric radius, which deserves further study.