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.

中文翻译：

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本星系群中AGB星的C/M比

富碳与富氧渐近巨星分支（AGB）星的数量比（即所谓的C/M比）与宿主星系的演化环境密切相关。这项工作研究了本星系群内 14 个星系的 C/M 比，其中包含我们之前工作中确定的最完整和最干净的成员恒星样本。富碳的 AGB 和富氧的 AGB 恒星以及红超巨星之间的边界是由拟合中数密度的高斯混合模型定义的。$(Ĵ-ķ)/ķ$LMC和M33的成员星图，然后通过移动尖端红巨星分支（TRGB）位置的差异应用于其他星系。C / M比率是在精确和一致的分类后获得的。尽管对于距离模较大的星系存在较大的不确定性，但明显发现 C/M 比随着颜色指数而降低${(Ĵ-ķ)}_0$TRGB 作为金属丰度的指标，这与之前的研究一致，可以用碳星更容易在贫金属环境中形成的事实来解释。此外，发现 M33 内的 C/M 比随着星系中心距离的增加而增加，这与这种情况和星系化学演化模型一致。另一方面，发现M31内的C/M比随半心半径而减小，值得进一步研究。