Evolutionary models of red supergiants: Evidence for a
  metallicity-dependent mixing length and implications for Type IIP supernova
  progenitors
  Recent studies on the temperatures of red supergiants (RSGs) in the local
universe provide us with an excellent observational constraint on RSG models.
We calibrate the mixing length parameter by comparing model predictions with
the empirical RSG temperatures in Small and Large Magellanic Clouds, Milky Way,
and M31, which are inferred from the TiO band and the spectral energy
distribution (SED). Although our RSG models are computed with the MESA code,
our result may be applied to other stellar evolution codes, including the BEC
and TWIN codes. We find evidence that the mixing length increases with
increasing metallicity for both cases where the TiO and SED temperatures of
RSGs are used for the calibration. Together with the recent finding of a
similar correlation in low-mass red giants by Tayar et al, this implies that
the metallicity dependence of the mixing length is a universal feature in
post-main sequence stars of both low and high masses. Our result implies that
typical Type IIP supernova (SN IIP) progenitors with initial masses of $\sim 10
- 16~M_\odot$ have a radius range of $400 R_\odot \lesssim R \lesssim 800
R_\odot$ regardless of metallicity. As an auxiliary result of this study, we
find that the hydrogen-rich envelope mass of SN IIP progenitors for a given
initial mass is predicted to be largely independent of metallicity if the
Ledoux criterion with slow semiconvection is adopted, while the Schwarzschild
models predict systematically more massive hydrogen-rich envelopes for lower
metallicity.
