EDP Sciences
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Volume 445, Number 2, January II 2006
Page(s) 513 - 543
Section Galactic structure, stellar clusters and populations
DOI http://dx.doi.org/10.1051/0004-6361:20053061

A&A 445, 513-543 (2006)
DOI: 10.1051/0004-6361:20053061

The dynamical distance and intrinsic structure of the globular cluster $\omega$ Centauri

G. van de Ven, R. C. E. van den Bosch, E. K. Verolme and P. T. de Zeeuw

Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The Netherlands
    e-mail: glenn@strw.leidenuniv.nl

(Received 14 March 2005 / Accepted 9 August 2005 )

We determine the dynamical distance D, inclination i, mass-to-light ratio M/L and the intrinsic orbital structure of the globular cluster $\omega$ Cen, by fitting axisymmetric dynamical models to the ground-based proper motions of van Leeuwen et al. and line-of-sight velocities from four independent data-sets. We bring the kinematic measurements onto a common coordinate system, and select on cluster membership and on measurement error. This provides a homogeneous data-set of 2295 stars with proper motions accurate to 0.20 mas yr-1 and 2163 stars with line-of-sight velocities accurate to 2 km s-1, covering a radial range out to about half the tidal radius.

We correct the observed velocities for perspective rotation caused by the space motion of the cluster, and show that the residual solid-body rotation component in the proper motions (caused by relative rotation of the photographic plates from which they were derived) can be taken out without any modelling other than assuming axisymmetry. This also provides a tight constraint on $D\tan i$. The corrected mean velocity fields are consistent with regular rotation, and the velocity dispersion fields display significant deviations from isotropy.

We model $\omega$ Cen with an axisymmetric implementation of Schwarzschild's orbit superposition method, which accurately fits the surface brightness distribution, makes no assumptions about the degree of velocity anisotropy in the cluster, and allows for radial variations in M/L. We bin the individual measurements on the plane of the sky to search efficiently through the parameter space of the models. Tests on an analytic model demonstrate that this approach is capable of measuring the cluster distance to an accuracy of about 6 per cent. Application to $\omega$ Cen reveals no dynamical evidence for a significant radial dependence of M/L, in harmony with the relatively long relaxation time of the cluster. The best-fit dynamical model has a stellar V-band mass-to-light ratio $M/L_V=2.5\pm0.1$ $M_\odot$/$L_\odot$ and an inclination $i=50^\circ\pm4^\circ$, which corresponds to an average intrinsic axial ratio of $0.78\pm0.03$. The best-fit dynamical distance $D=4.8\pm0.3$ kpc (distance modulus $13.75\pm0.13$ mag) is significantly larger than obtained by means of simple spherical or constant-anisotropy axisymmetric dynamical models, and is consistent with the canonical value $5.0\pm0.2$ kpc obtained by photometric methods. The total mass of the cluster is $(2.5\pm0.3)\times10^6$ $M_\odot$.

The best-fit model is close to isotropic inside a radius of about 10 arcmin and becomes increasingly tangentially anisotropic in the outer region, which displays significant mean rotation. This phase-space structure may well be caused by the effects of the tidal field of the Milky Way. The cluster contains a separate disk-like component in the radial range between 1 and 3 arcmin, contributing about 4% to the total mass.

Key words: Galaxy: globular clusters: individual: NGC 5139 -- Galaxy: kinematics and dynamics

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