Determination of the mass-ratio distribution, II: double-lined spectroscopic binary stars

Abstract

The application of the Richardson-Lucy iterative technique for the rectification of measurement errors, to the mass-ratio distribution of the double-lined spectroscopic binary stars (sbii) intheSixth Catalogue of the Orbital Elements of Spectroscopic Binary Stars, is evaluated for the sbii systems in the Eighth version of the Catalogue. The estimates of the real distribution, produced by the Richardson-Lucy method after successive iterations, do not converge in a trivial way. The stop criterion, suggested in the original paper on the method, is used in the application of the method to both real and simulated distributions. It is shown that, in the application to the mass-ratio distribution of the sbii systems, the iterations should stop considerably earlier than was previously assumed. The enhanced peak at mass-ratios near unity, that was found to exist in the real mass-ratio distribution, based on the earlier application of the iterative technique to the sbii systems, is likely to be due to an overshoot effect that occurs when the iterations are carried too far. When the stop criterion is used in the application of the method to the sbii systems in the Eighth version of the Catalogue, the resulting estimate of the real mass-ratio distribution does not show evidence for an enhanced number of binary stars with mass ratios near unity.