  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.
