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Observational Windows on the Dynamics of Open Clusters Robert D. Mathieu University of Wisconsin - Madison “Typical” Open Cluster M = 300 Mo Rc = 1 pc Rt = 20 pc s = 0.3 km s-1 rc = 10 Mo pc-3 WIYN Open Cluster Study • Comprehensive and definitive photometric, astrometric, and spectroscopic databases for new fundamental open clusters. • A body of investigations which address critical astrophysical problems through study of open clusters. WOCS Senior Scientists • C. Deliyannis Indiana photometry, spectroscopy, abundances • P. Demarque Yale theoretical stellar evolution • T. Girard Yale astrometry, proper motions • K. Honeycutt Indiana photometric monitoring, compact binaries • R. Mathieu Wisconsin radial velocities, binary populations • I. Platais JHU astrometry, proper motions, photometry • A. Sarajedini Florida photometry, stellar evolution • W. van Altena Yale astrometry, proper motions • T. von Hippel Texas photometry, luminosity functions [Fe/H] WOCS Clusters Log Age (Gyrs) First Generation Second Generation WOCS Strategy • Imaging/Photometry – Deep UBVRI images of cluster cores – UBVRI wide-field surveys to tidal radii – Photometric monitoring for variability • Astrometry – Precise stellar positions – Deep, wide-field proper motions • Spectroscopy – Abundance determinations • Metallicity, CNO, and lithium – Precise radial velocities – Projected rotation velocities – Stellar activity NGC 188 1840 pc E(B-V) = 0.04 7 Gyr [Fe/H] = -0.12 ≈ 1000 Mo (d = +85o) Photometry Precision ≈ 0.012 mag (BVRI) ≈ 0.03 mag (U) Accuracy ≈ 0.02 mag (BVRI) Sarajedini et al. 1999; WOCS II Photometry Von Hippel et al. 1999; WOCS I Proper Motions 0.15 mas yr-1 Positions 0.2 mas 7812 objects V=21 0.75 deg2 Platais et al. 2004; WOCS XVII Radial Velocities 0.4 km s-1 500 VR/night V < 16.5 0.75 deg2 (WIYN 3.5m) VR Mathieu et al. 2004; WOCS XVIII 93 spectroscopic binaries 55 orbital solutions P < 3000d Outcomes for Stellar Dynamics • Superb 3-dimensional membership determination for entire evolved cluster population to beyond tidal radius • Reliable 2-dimensional membership determination to 0.5 Mo and beyond tidal radius • Photometric mass function to 0.1 Mo in cluster core • Complete census of short-period, solar-type binary population, with orbital elements The Interface of Two Classical Fields: Stellar Astrophysics and Stellar Dynamics M67 4.5 Gyr [Fe/H] = -0.04 ≈ 1000 Mo 1.3 Mo Binary Frequency Spectroscopic Binaries For P < 1000d M67 19% ± 4 Field 16% ± 3 Mathieu, Latham & Griffin 1990 Mathieu et al. 2004 Mathieu et al. 2003 S1113 P=2.8 d e=0 g = 33.4 km/s pm = 98% S1063 P=18.4 d e = 0.21 g = 34.3 km/s pm = 97% Tidal Circularization Rates NGC 188 Mathieu et al. 2004 7 Gyr Pcutoff = 14.9 days Zahn & Bouchet 1989 Witte & Savonije 2002 Claret & Cunha 1997 (Zahn 1977) Meibom & Mathieu 2004 Opening Thoughts on Choice of Open Cluster(s) [Fe/H] WOCS Clusters Log Age (Gyrs) First Generation Second Generation Optimal Cluster Properties (with an observational bias) • Rich several thousand members to 0.1 Mo • evolution without complete evaporation • meaningful statistics • “Old” age greater than 1 Gyr • multiple relaxation times • solar-mass evolution • “Nearby” d < 2 kpc • accessible main-sequence binary population • Accessible -20o < d < +20o • observable from both hemispheres • Out of Plane | b | > 10o • minimize field-star contamination, especially at Rt