A PROPER-MOTION STUDY OF THE OPEN CLUSTER NGC-3680

Relative proper motions and cluster membership probabilities have been determined for 2711 stars in a region containing the old open cluster NGC 3680. The Yale-Columbia 26 in. refractor plates used in this study contain significant magnitude equation as well as color equation. A procedure is developed for transforming the measures from each of the plates into a common magnitude/color equation system, thus yielding differential positions from plate to plate, (i.e., proper motions) which are free of these systematic errors. For well measured stars the mean standard error of the proper motions is ±0.35 mas/yr. Three different membership calculation techniques are described in detail. The best fit to the proper-motion distributions yields 74 cluster members. Almost all known red giants are cluster members according to the proper motion membership criterion. The luminosity function of NGC 3680 shows a characteristic turnover at Mv≈+3 mag and an essentially flat faint end. Monte-Carlo simulations are used in order to explore the mutual dependence of the luminosity function and membership probabilities. The bimodality of the upper main sequence found in earlier photometric studies probably still exists even after eliminating proper-motion nonmembers.