On the Fundamental Line of Galactic and Extragalactic Globular Clusters
  In a previous paper we found that the Globular Clusters of our Galaxy lie
around a line in the log(Re), SBe, log(sigma) parameter space, with a moderate
degree of scatter and remarkable axi-symmetry. This implies the existence of a
purely photometric scaling law obtained by projecting such a line onto the
log(Re), SBe plane. Such photometric quantities are readily available for large
samples of clusters, as opposed to stellar velocity dispersion data. We study a
sample of 129 Galactic and extragalactic clusters on such photometric plane in
the V-band. We look for a linear relation between SBe and log(Re) and study how
the scatter around it is influenced by age and dynamical environment. We
interpret our results as a test on the evolutionary versus primordial origin of
the Fundamental Line. 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. We find a linear relation between
SBe and log(Re), in the form SBe = (5.25 +- 0.44) log(Re) + (15.58 +- 0.28),
where SBe is measured in mag/arcsec^2 and Re in parsec. Both young and old
clusters lie on the scaling law, with a scatter of approximately 1 mag in SBe.
However, young clusters display more scatter and a clear trend of such scatter
with age, which old clusters do not. Such 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 SBe, log(Re), and cluster
age. We argue that the log(Re)-SBe relation and hence the Fundamental Line
scaling law is not primordially set at cluster formation, but rather is the
result of combined stellar evolution and collisional dynamical evolution.
