Statistics of binaries in the Pleiades cluster

We present a statistical analysis of binaries in galactic clusters, based on photometric properties. Synthetic clusters are used to solve the deconvolution problem. If the colourmagnitude relation for single stars is given and if triple stars are treated as binaries, the distribution of systems in a colourmagnitude diagram (CMD) can be used to determine cluster properties. They include the maximum number of single stars N1max which is compatible with the distribution of systems, a standard deviation σ (describing the scatter of stars on the main sequence), a critical mass ratio qc, and the mass ratio distribution in the case of N1 = N1max. In the general case (N1 ≤ N1max) the mass ratio distribution can be determined for q > qc, and in favourable cases (if N1 is sufficiently large) for all mass ratios. A first application concerns the Pleiades cluster in the colour range 0.2 ≤ B− V < 0.98. The concentration of systems near the main sequence in the CMD is used to derive an approximation for the colour-magnitude relation. A small positive number c is involved as a parameter. The mass ratio distribution depends sensitively on c and increases towards small mass ratios, at least up to q ' 0.5 and probably up to q ' 0.3. The distribution is bimodal, with a peak at q = 1. Photometric arguments show that c <∼ 0.02. A binary frequency of 60–70% as expected from cluster simulations (Kroupa 1995) requires c <∼ 0.03. An adjustment of two parameters (c = 0.02 and a 70% binary frequency) is sufficient to reproduce the mass ratio distribution for binaries in the galactic field. This suggests that the mass ratio distribution in the Pleiades is similar to the distribution in the field, in accordance with a conjecture of Bouvier et al. (1997, BRN).