An empirical calibration of the mixing-length parameter alpha

Abstract

We present an empirical calibration of the Mixing-Length free parameter $α$ based on a homogeneous Infrared database of 28 Galactic globular clusters spanning a wide metallicity range (-2.15$<$[Fe/H]$<$-0.2). Empirical estimates of the red giant effective temperatures have been obtained from infrared colors. Suitable relations linking these temperatures to the cluster metallicity have been obtained and compared to theoretical predictions. An appropriate set of models for the Sun and Population II giants have been computed by using both the standard solar metallicity $[Z/X]_{\odot}=0.0275$ and the most recently proposed value $[Z/X]_{\odot}=$0.0177. We find that when the standard solar metallicity is adopted, a unique value of $α$=2.17 can be used to reproduce both the solar radius and the population II red giant temperature. Conversely, when the new solar metallicity is adopted, two different values of $α$ are required: $α=1.86$ to fit the solar radius and $α\approx2.0$ to fit the red giant temperatures. However, it must be noted that, regardless the adopted solar reference, the $α$ parameter does not show any significant dependence on metallicity.