The frequency by mass of Galactic carbon stars inferred from Gaia measurements of star cluster members

We investigate the frequency of occurrence of Galactic carbon stars as a function of progenitor mass using Gaia data. Small number statistics limit fidelity, but C star frequency agrees with that observed in the Magellanic Clouds (MCs) down to $m\approx 1.67$ M${}_{\odot }$. At $m\approx 1.38$ M${}_{\odot }$, the frequency rises by a factor of three even though the frequency appears to drop to zero for the MCs. In fact this is due to a lack of clusters at the key age range in the MCs. At $m\approx 1.24$ M${}_{\odot }$ and below, no C stars are observed, corresponding to ages older than 4 Gyr. Within uncertainties, C~star frequency in M 31 is consistent with that of the Galaxy and the MCs. We find an ambiguous C-star candidate at $\sim$7 M${}_{\odot }$.