The mass-loss rates of red supergiant stars (RSGs) are poorly constrained by direct measurements, and yet the subsequent evolution of these stars depends critically on how much mass is lost during the RSG phase. In 2012 the Geneva evolutionary group updated their mass-loss prescription for RSGs with the result that a 20 solar mass star now loses 10x more mass during the RSG phase than in the older models. Thus, higher mass RSGs evolve back through a second yellow supergiant phase rather than exploding as Type II-P supernovae, in accord with recent observations (the so-called RSG Problem). Still, even much larger mass-loss rates during the RSG phase cannot be ruled out by direct measurements of their current dust-production rates, as such mass-loss is episodic. Here we test the models by deriving a luminosity function for RSGs in the nearby spiral galaxy M31 which is sensitive to the total mass loss during the RSG phase. We carefully separate RSGs from asymptotic giant branch stars in the color-magnitude diagram following the recent method exploited by Yang and collaborators in their Small Magellanic Cloud studies. Comparing our resulting luminosity function to that predicted by the evolutionary models shows that the new prescription for RSG mass-loss does an excellent job of matching the observations, and we can readily rule out significantly larger values.
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