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

We present our findings based on a detailed analysis of the binaries of the Hyades, in which the masses of the components are well known. We fit the models of the components of a binary system to 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-circle dot-0.74)(0.053)-6.65, which is valid for stellar masses greater than 0.77 M-circle dot. 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 per cent. 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.