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

= 0.3 km s-1

c = 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

WOCS ClustersWOCS Clusters[F

e/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 188

1840 pc

E(B-V) = 0.04

7 Gyr

[Fe/H] = -0.12

≈ 1000 Mo

( = +85o)

Sarajedini et al. 1999;WOCS II

Photometry

Precision ≈ 0.012 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

Positions0.2 mas

7812 objectsV=21

0.75 deg2

Radial Velocities

0.4 km s-1

500 VR/nightV < 16.5 0.75 deg2

(WIYN 3.5m)

VR

Mathieu et al. 2004;WOCS XVIII

93 spectroscopic binaries55 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

SpectroscopicBinaries

Mathieu, Latham & Griffin 1990Mathieu et al. 2004

Binary Frequency

For P < 1000d

M67 19% ± 4 Field 16% ± 3

S1063P=18.4 d

e = 0.21

= 34.3 km/s

pm = 97%

S1113P=2.8 d

e = 0

= 33.4 km/s

pm = 98%

Mathieu et al. 2003

Tidal Circularization Rates

NGC 188 7 Gyr Pcutoff = 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 ClustersWOCS Clusters[F

e/H

]

Log Age (Gyrs)

First Generation

Second Generation

• 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 < < +20o

• observable from both hemispheres

• Out of Plane | b | > 10o

• minimize field-star contamination, especially at Rt

Optimal Cluster Properties (with an observational bias)