Horizontal branch morphology: A new photometric parametrization
  Theory and observations indicate that the distribution of stars along the
horizontal branch of Galactic globular clusters mainly depends on the metal
content. However, the existence of globular clusters with similar metal content
and absolute age but different horizontal branch morphologies, suggests the
presence of another parameter affecting the star distribution along the branch.
To investigate the variation of the horizontal branch morphology in Galactic
globular clusters, we define a new photometric horizontal branch morphology
index, overcoming some of the limitations and degeneracies affecting similar
indices available in the literature. We took advantage of a sample of 64
Galactic globular clusters, with both space-based imaging data and homogeneous
ground-based photometric catalogues in five different bands ($U$,$B$,$V$, $R$,
$I$). The new index, $\tau_{HB}$, is defined as the ratio between the areas
subtended by the cumulative number distribution in magnitude ($I$) and in
colour ($V-I$) of all stars along the horizontal branch. This new index shows a
linear trend over the entire range in metallicity (-2.35 $\leq$ [Fe/H] $\leq$
-0.12) covered by our Galactic globular cluster sample. We found a linear
relation between $\tau_{HB}$ and absolute cluster ages. We also found a
quadratic anti-correlation with [Fe/H], becoming linear when we eliminate the
age effect on $\tau_{HB}$ values. Moreover, we identified a subsample of eight
clusters that are peculiar according to their $\tau_{HB}$ values. These
clusters have bluer horizontal branch morphology when compared to typical ones
of similar metallicity. These findings allow us to define them as the 'second
parameter' clusters in the sample. A comparison with synthetic horizontal
branch models suggests that they cannot be entirely explained with a spread in
helium content.
