  Mass-loss in red supergiants (RSGs) is generally recognized to be episodic,
but mass-loss prescriptions fail to reflect this. Evolutionary models show that
the total amount of mass lost during this phase determines if these stars
evolve to warmer temperatures before undergoing core collapse. The current
Geneva evolutionary models mimic episodic mass loss by enhancing the quiescent
prescription rates whenever the star's outer layers exceed the Eddington
luminosity by a large factor. This results in a 20 solar-mass model undergoing
significantly more mass loss during the RSG phase than it would have otherwise,
but has little effect on models of lower masses. We can test the validity of
this approach observationally by measuring the proportion of high-luminosity
RSGs to that predicted by the models. To do this, we use our recent
luminosity-limited census of RSGs in M31 and M33, making modest improvements to
membership, and adopting extinctions based on the recent panchromatic M31 and
M33 Hubble surveys. We then compare the proportions of the highest luminosity
RSGs found to that predicted by published Geneva models, as well as to a
special set of models computed without the enhanced rates. We find good
agreement with the models which include the supra-Eddington enhanced mass loss.
The models with lower mass-loss rates predict a larger fraction of
high-luminosity RSGs than observed, and thus can be ruled out. We also use
these improved data to confirm that the upper luminosity limit of RSGs is log
L/Lo~5.4, regardless of metallicity, using our improved data on M31 and M33
plus previous results on the Magellanic Clouds.
