On the fundamental line of galactic and extragalactic globular clusters

Context. In a previous paper, we found that globular clusters in our Galaxy lie close to a line in the (log R_e, SB_e, log σ) parameter space, with a moderate degree of scatter and remarkable axi-symmetry. This implies that a purely photometric scaling law exists, that can be obtained by projecting this line onto the (log R_e, SB_e) plane. These photometric quantities are readily available for large samples of clusters, as opposed to stellar velocity dispersion data. Aims. We study a sample of 129 Galactic and extragalactic clusters on this photometric plane in the V-band. We search for a linear relation between SB_e and log R_e and study how the scatter around the best-fit relation is influenced by both age and dynamical environment. We interpret our results in terms of testing the evolutionary versus primordial origin of the fundamental line. Methods. We perform a detailed analysis of surface brightness profiles, which allows us to present a catalogue of structural properties without relying on a given dynamical model. Results. We find a linear relation between SB _e and log R_e, in the form SB_e = (5.25 ± 0.44) log R_e + (15.58 ± 0.28), where SB_e is measured in mag/arcsec² and R_e in parsec. Both young and old clusters follow the scaling law, which has a scatter of approximately 1 mag in SB_e. However, young clusters display more of a scatter and a clear trend in this with age, which old clusters do not. This trend becomes tighter if cluster age is measured in units of the cluster half-light relaxation time. Two-body relaxation therefore plays a major role, together with passive stellar population evolution, in shaping the relation between SB_e, log R _e, and cluster age. We argue that the log R_e-SB _e relation and hence the fundamental line scaling law does not have a primordial origin at cluster formation, but is rather the result of a combination of stellar evolution and collisional dynamical evolution.