We analyze resolved stellar near-infrared photometry of 21 HST fields in M31 to constrain the impact of metallicity on the formation of carbon stars. Observations of nearby galaxies show that the carbon stars are increasingly rare at higher metallicity. Models indicate that carbon star formation efficiency drops due to the decrease in dredge-up efficiency in metal-rich thermally-pulsing Asymptotic Giant Branch (TP-AGB) stars, coupled to a higher initial abundance of oxygen. However, while models predict a metallicity ceiling above which carbon stars cannot form, previous observations have not yet pinpointed this limit. Our new observations reliably separate carbon stars from M-type TP-AGB stars across 2.6-13.7 kpc of M31s metal-rich disk using HST WFC3/IR medium-band filters. We find that the ratio of C to M stars (C/M) decreases more rapidly than extrapolations of observations in more metal-poor galaxies, resulting in a C/M that is too low by more than a factor of 10 in the innermost fields and indicating a dramatic decline in C star formation efficiency at metallicities higher than [M/H] $approx$ -0.1 dex. The metallicity ceiling remains undetected, but must occur at metallicities higher than what is measured in M31s inner disk ([M/H] $gtrsim$ +0.06 dex).
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