Statistical studies of visual double and multiple stars. I - Incompleteness of the IDS, intrinsic fraction of visual doubles and multiples, and number of optical systems
In an attempt to obtain a relatively uniform and homogeneous group of double stars for statistical studies, the Index Catalogue of Visual Double Stars has been subjected to a "filtering" procedure, so as to eliminate optical systems. Spurious systems were also left out. The filtered IDS (FIDS) contains 51,201 entries out of 69,819 in IDS II. To describe the process of discovering and registering a double or multiple star, a simple stochastic model is postulated and applied to the FIDS. The main results of this study are the following: (i) The fraction of field stars searched for visual duplicity as a function of magnitude has been determined; it turns out that virtually all stars brighter than tenth magnitude (in the "magnitude system" of the IDS) have been so searched. (ii) About 80% of the visual binaries with primaries brighter then tenth magnitude and with components differing by less than 1 mag are contained in the FIDS; these comprise 3% of the intrinsic visual binaries. (iii) The expected number of optical systems remaining in the FIDS is about 1000. (iv) To arrive at the FIDS, a total of about 650,000 stars had to be searched for visual duplicity. (v) The intrinsic fraction of visual binaries and multiples to field stars has been determined. It is found that on the average almost every star should have at least one "visual" stellar companion, and nearly one out of three field stars is a multiple. Most companions are undetected.