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 \pm 0.1 M _ { \odot } /L _ { \odot } and an inclination i = 50 ^ { \circ } \pm 4 ^ { \circ } , which corresponds to an average intrinsic axial ratio of 0.78 \pm 0.03 .
The best-fit dynamical distance D = 4.8 \pm 0.3 kpc ( distance modulus 13.75 \pm 0.13 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 \pm 0.2 kpc obtained by photometric methods .
The total mass of the cluster is ( 2.5 \pm 0.3 ) \times 10 ^ { 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 .