On the Fundamental Plane of the Galactic globular cluster system

Context. The globular clusters of our Galaxy have been found to lie close to a plane in the $\log{R_{\rm e}}$, $\log{\sigma}$, ${\mathit{SB}}_{\rm e}$ space, on the continuation of the Fundamental Plane that is known to characterize the global properties of early-type galaxies. There is no apparent reason why such physically different self-gravitating systems should follow the same scaling law. Aims. We reexamine the issue by focusing on a sample of 48 globular clusters selected with homogeneity criteria for the photometric data available from the literature. Methods. We perform a model-independent analysis of surface brightness profiles and distance moduli, estimating error bars and studying selection effects with robust non-parametric statistical tests. Results. We determine the values of the coefficients that define the Fundamental Plane and their error bars and show that the scatter from the Fundamental Plane relation is likely to be intrinsic, i.e. not due to measurement errors only. Curiously, we find that in the standard Fundamental Plane coordinates the set of points for our sample occupies a rather slim, axisymmetric, cylindrical region of parameter space, which suggests that the relevant scaling relation might be around a line, rather than a plane, confirming results noted earlier. This is likely to be the origin of the difficulties in the fit by a plane, often mentioned in previous investigations. In addition, such a Fundamental Line relation would imply a pure photometric scaling law relating luminosity to the effective radius which might be tested on wider samples and on extra-galactic globular cluster systems. As to the residuals from the Fundamental Plane relation, we find a correlation of the deviations from the plane with the central slope of the surface brightness profile. No other statistically significant correlations are identified. Finally, given the constraint imposed by the virial theorem, we study the distribution of the values of the quantity $K_V/(M/L)$ (virial coefficient divided by the relevant mass-to-light ratio); the distribution of the logarithms, reconstructed through kernel density estimation methods, shows evidence for bimodality, which suggests that the galactic globular cluster system may be composed of at least two dynamically different populations. Yet, these populations do not appear to reflect the standard dichotomy between disk and halo clusters