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 α= 9.19(M/M[SUB]solar[/SUB]- 0.74)[SUP]0.053[/SUP]- 6.65, which is valid for stellar masses greater than 0.77M[SUB]solar[/SUB]. 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 θ[SUP]2[/SUP] 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.