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Appendix A: Classification of Galactic globular clusters

Since the work by Zinn (1985) a few progresses were done with respect to his criteria for the separation of the subpopulations of Galactic GCs. Many classification schemes rest on the appearance of the clusters' CMD and related parameters (namely metallicity, age and HBR index). However, one of the main aims of our project is to explain the HB morphology and its relations with chemical signatures of stellar generations in GC, so we cannot use the distribution of stars along the HB as a separation criterion. In Table A.1 we list the quantities used in Sect. 3.3 to separate disk/bulge clusters from the halo ones according to the combination of their location in the Galaxy and their kinematics.

Table A.1:   Classification and main parameters adopted for GCs.

Table A.2:   Comparison of our classification with the one by Mackey & van den Bergh (2005).

Table A.3:   Globular clusters of LMC, SMC, and Fornax dSph and their properties.

As said in Sect. 3.3, outer halo clusters were simply classified as those currently located at more than 15 kpc from the centre of the Galaxy (see Carollo et al. 2008). Clusters with below 3.5 kpc were considered as bulge GCs, even though some of them might be halo clusters on very elongated orbits presently close to the pericentres. To separate the remaining clusters into inner halo and disk GCs, we computed the differences (dV, Col. 8 in Table A.1) between the observed radial velocity (corrected to the LSR) and the one expected from the Galactic rotation curve (see Clemens 1985). In the dV-Z plane (where Z is the clusters' distance from the Galactic plane, in kpc, see Col. 10 of Table A.1), we defined an ellipse with equation

Clusters with y<1 were classified as disk GCs, while we considered as halo GCs the ones with y>1, see Fig A.1. Of course, a better estimate of GC kinematic is possible when the whole orbit is available. Given the quite good correlation (see Fig. A.2) between dV and the rotational velocity (Col. 9 of Table A.1, where ) given by Dinescu et al. (1999) and Casetti-Dinescu et al. (2007), we replaced our dV values, when available, with the ones provided from those studies. Since we find that , the definition of y was in this case

It should, however, be clear that dV is not at all a synonymous of (-220), and the existing correlation has only a statistical meaning.

Column 11 in Table A.1 shows our classification for the population of the Galactic GCs in disk/bulge (D/B), inner halo (IH), outer halo (OH), and GCs of dSphs. For each cluster we report the integrated magnitude (, Col. 2), the HB morphology parameter (HBR, Col. 6), and the Galactocentric distance ( , Col. 7) as directly retrieved from the Harris catalogue. The metallicity values ([Fe/H], Col. 3) were instead replaced with the determinations by Carretta et al. (2009c). Additionally, we list in Col. 4 the [/Fe] ratios (with corresponding references given in the table notes). Column 5 displays the age parameter; more in detail, we computed an average value between the two different estimates by Marin-Franch et al. (2009) and De Angeli et al. (2005), after applying a correction of 0.08 to the second ones for GCs with [Fe/H] ranging from -1.8 to -1.1 dex, as suggested by a cluster-to-cluster comparison. When neither of these estimates was available, we adopted the ones calculated by Vandenberg (2000), normalised to the Marin-Franch scale by assuming that 13.5 Gyr = 1.00. We then corrected the values so obtained for the difference between the metallicities considered in those papers and those listed in Carretta et al. (2009c), transformed into [M/H] using an average [/Fe] of +0.4 (see Table 2). This correction was made using the sensitivity of age on metallicity given by Marin-Franch et al. (2009).

First, we decided to compare our new classification with the previous ones relying only on metallicity and HB morphology (see Sect. 3.3). As representative of this approach, we chose the work by Mackey & van den Bergh (2005). Briefly, they defined as disk component all the GCs with [Fe/H]>-0.8 dex; the so-called ``old'' halo and ``young'' halo clusters were then divided following Zinn (1993), namely by computing the offset in HB type -at a given metallicity- with respect to the fiducial line of the inner halo clusters. GCs with an offset larger and smaller than -0.3 in HB type were classified as old halo and young halo, respectively. The Table A.2 schematically shows the comparison and emphasises the different natures of the two classifications. As (partially) expected, the matrix is not diagonal; i.e., there is not a one-to-one correlation between old halo (young halo) and inner halo (outer halo) subgroups. More in detail, the metallicity criterion is largely responsible for such a discrepancy: had we adopted the requirement of 0.8 dex, 35 of the 36 clusters that we classified as disk/bulge and Mackey & van den Bergh as old halo should be moved into inner halo+old halo cell, while all the 5 GCs placed in the disk+young halo box should become inner halo+young halo clusters thanks to their low metallicity. However, and most important, even taking these changes into account in the relative population of the matrix cells, the resulting correspondence is not yet one-to-one. As to the inner halo GCs, 80% constitute the old halo and the remaining 20% the young halo clusters; for the outer halo GCs, the promiscuity is even greater, resulting in 40% and 60%, respectively, for old and young haloes. This is direct evidence of the strong difference between kinematics (and/or positional) criteria and the ones based only on metallicity and HB type.

One last word on the classification. While this work was in preparation, a paper by Fraix-Burnet et al. (2009) appeared, where they use a cladistic technique to divide a sample of 54 GCs into three subsamples (called Groups 1, 2, and 3 and later identify with inner halo, outer halo, and disk, respectively) on the basis of [Fe/H], M_V, , and age. We cross-checked the assignments for the clusters in common and found good agreement only for disk clusters, and this in a limited sense. When they classify a cluster as disk, we agree (in 17 cases out of 18), but we have many other disk clusters that they instead classify in the halo subsamples. In particular, for the 19 GCs in our FLAMES sample, the two classifications agree for seven clusters and disagree for seven others (five GCs are not present in their data set). We think that the main factor producing this difference is that they ignored the kinematics, although the information is present for their sample, while our method rests on that.

To conclude, we report in Table A.3 the analogoues of Table A.1, but for the LMC, SMC, and Fornax GC systems; as in the previous case, the number in brackets corresponds to the reference (for [/Fe], [Fe/H], age, and HBR) whose decoding is given in the Notes. The integrated magnitudes M_V for the LMC and Fornax GCs are taken from van den Bergh & Mackey (2000), while for the SMC ones were computed from the apparent magnitudes UBV by van den Bergh (1981), along with the distance moduli as given in those papers providing the clusters' age (Refs. 15-17 see Table A.3). As to age, for LMC and SMC GCs, since absolute values were available (see ref. given in Table A.3), we report them to our relative scale, adopting the previous conversion of 13.5 Gyr = 1.00. For the Fornax clusters, the ages were instead derived starting from the cluster-to-cluster relative differences (Age) obtained by Buonanno et al. (1998, 1999) and assuming that 1.05 = 14.2 Gyr.