## 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 colour-magnitude relation for single stars is given and if triple stars are treated as binaries, the distribution of systems in a colour-magnitude diagram (CMD) can be used to determine cluster properties. They include the maximum number of single stars which is compatible with the distribution of systems, a standard deviation (describing the scatter of stars on the main sequence), a critical mass ratio , and the mass ratio distribution in the case of . In the general case () the mass ratio distribution can be determined for , and in favourable cases (if is sufficiently large) for all mass ratios. A first application concerns the Pleiades cluster in the colour
range . 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 The mass ratio distribution depends sensitively on
## Contents- 1. Introduction
- 2. Outline of the method
- 3. Photometric properties of an ideal cluster
- 4. Complications in real clusters
- 5. Statistics of binaries and triple stars
- 5.1. Basic data
- 5.2. Assumptions and approximations
- 5.3. Distribution functions
- 5.4. Smoothing operators
- 5.5. The mathematical problem
- 6. Synthetic stellar clusters
- 7. The Pleiades cluster
- 8. Summarising comments
- Acknowledgements
- Appendix A: smoothing operators for mass ratio distributions
- References
© European Southern Observatory (ESO) 1999 Online publication: May 6, 1999 |