Observational Windows on the Dynamics of Open Clusters Robert D. Mathieu University of Wisconsin - Madison

“Typical” Open Cluster M = 300 M o R c = 1 pc R t = 20 pc  = 0.3 km s -1  c = 10 M o 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. DeliyannisIndianaphotometry, spectroscopy, abundances P. DemarqueYaletheoretical stellar evolution T. GirardYaleastrometry, proper motions K. Honeycutt Indiana photometric monitoring, compact binaries R. MathieuWisconsinradial velocities, binary populations I. PlataisJHUastrometry, proper motions, photometry A. Sarajedini Floridaphotometry, stellar evolution W. van Altena Yaleastrometry, proper motions T. von HippelTexasphotometry, luminosity functions

WOCS Clusters [Fe/H] 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 pc E(B-V) = Gyr [Fe/H] = ≈ 1000 M o (  = +85 o )

Sarajedini et al. 1999; WOCS II Photometry Precision ≈ mag (BVRI) ≈ 0.03 mag (U) Accuracy ≈ 0.02 mag (BVRI)

Von Hippel et al. 1999; WOCS I Photometry

Platais et al. 2004; WOCS XVII Proper Motions 0.15 mas yr -1 Positions 0.2 mas 7812 objects V= deg 2

Radial Velocities 0.4 km s V R /night V < deg 2 (WIYN 3.5m)

VRVR

Mathieu et al. 2004; WOCS XVIII 93 spectroscopic binaries 55 orbital solutions P < 3000 d

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 M o and beyond tidal radius Photometric mass function to 0.1 M o 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

M Gyr [Fe/H] = ≈ 1000 M o 1.3 M o

Spectroscopic Binaries Mathieu, Latham & Griffin 1990 Mathieu et al Binary Frequency For P < 1000 d M6719% ± 4 Field 16% ± 3

S1063 P=18.4 d e = 0.21  = 34.3 km/s pm = 97% S1113 P=2.8 d e = 0  = 33.4 km/s pm = 98% Mathieu et al. 2003

Tidal Circularization Rates

NGC Gyr P cutoff = 14.9 days Mathieu et al. 2004

Meibom & Mathieu 2004 Zahn & Bouchet 1989 Claret & Cunha 1997 (Zahn 1977) Witte & Savonije 2002

Opening Thoughts on Choice of Open Cluster(s)

WOCS Clusters [Fe/H] Log Age (Gyrs) First Generation Second Generation

Rich several thousand members to 0.1 M o 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 -20 o <  < +20 o observable from both hemispheres Out of Plane | b | > 10 o minimize field-star contamination, especially at R t Optimal Cluster Properties (with an observational bias)