Red supergiants in M31: the Humphreys-Davidson limit at high metallicity

The empirical upper limit to red supergiant (RSG) luminosity, known as the Humphreys-Davidson (HD) limit, has been commonly explained as being caused by the stripping of stellar envelopes by metallicity-dependent line-driven winds. As such, the theoretical expectation is that the HD limit should be higher at lower metallicity, where weaker mass-loss rates mean that higher initial masses are required for an envelope to be stripped. In this paper, we test this prediction by measuring the luminosity function of RSGs in M31 and comparing it to those in the LMC and SMC. We find that log (L-max/L-circle dot) = 5.53 +/- 0.03 in M31 (Z greater than or similar to Z(circle dot)), consistent with the limit found for both the LMC (Z similar to 0.5 Z(circle dot)) and SMC (Z similar to 0.25 Z(circle dot)), while the RSG luminosity distributions in these three galaxies are consistent to within 1 sigma. We therefore find no evidence for a metallicity dependence on both the HD limit and the RSG luminosity function, and conclude that line-driven winds on the main sequence are not the cause of the HD limit.