Modelling the components of binaries in Hyades: The dependence of the mixing-length parameter on stellar mass

Abstract

We present our findings based on a detailed analysis for the binaries of the Hyades, in which the masses of the components are well known. We fit the models of components of a binary system to the observations so as to give the observed total V and B-V of that system and the observed slope of the main-sequence in the corresponding parts. According to our findings, there is a very definite relationship between the mixing-length parameter and the stellar mass. The fitting formula for this relationship can be given as $alpha = 9.19 (M/M_sun-0.74)^{0.053}-6.65$, which is valid for stellar masses greater than 0.77 M_sun. While no strict information is gathered for the chemical composition of the cluster, as a result of degeneracy in the colour-magnitude diagram, by adopting Z=0.033 and using models for the components of 70 Tau and theta^2 Tau we find the hydrogen abundance to be X=0.676 and the age to be 670 Myr. If we assume that Z=0.024, then X=0.718 and the age is 720 Myr. Our findings concerning the mixing length parameter are valid for both sets of the solution. For both components of the active binary system V818 Tau, the differences between radii of the models with Z=0.024 and the observed radii are only about 4 percent. More generally, the effective temperatures of the models of low mass stars in the binary systems studied are in good agreement with those determined by spectroscopic methods.