The form of the galactic globular cluster system and the distance to the Galactic Centre

We develop new quantitative methods for analysing the structure of the galactic globular cluster system. We choose samples limited in galactic latitude which can be assumed complete, and we consider separately the distance independent information contained in the positions of clusters on the sky, and the information contained in the apparent three-dimensional distribution. The cluster system is slightly flattened and there is no significant evidence for any variation in flattening as a function of metallicity. Its density is well described over the range |$0.2 \lt r/R_\odot\lt5$| by a Hubble law, |$\rho\propto r^{-3}$| or by a de Vaucouleurs law with |$r_\text e/R_\odot = 0.50$|⁠. Distance modulus errors of order one magnitude are required to explain the deviation of the apparent distribution of metal-rich clusters from axial symmetry. In addition a systematic difference in distance scale of about 0.5 magnitudes is necessary to reconcile the centroid of this distribution with that of the metal-poor clusters. This shift is in the same sense and of about the size predicted by theoretical pulsation models of RR Lyrae stars. If the standard distance scale is adopted for metal-poor clusters, the estimated distance of the Galactic Centre is |$R_\odot$| = 6.8 ± 0.8 kpc. We consider the effects of these results on our dynamical analysis of the cluster system in an earlier paper and find them to be small. We give a rediscussion of the ‘best’ values for the standard galactic structure and rotation constants in the light of our work.