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 .