Statistical analysis of Galactic globular cluster type properties

Seen as a single system, the Galactic Globular Clusters (GCs) were classically used to establish the non-preferential position of the Sun with respect to our Galaxy (Shapley, 1918). Being the oldest astronomical objects for wich reliable ages could be estimated, they were also used to put strong constraints to cosmological theories (see e.g. Marín-Franch et al. 2009; Charbonnel 2016 and references therein). In the Milky Way (MW) they populate a spheroid that extends out to various tens of kiloparsecs from the center of our Galaxy. A multitude of studies were oriented to them in order to find hints on MW formation processes (Zinn 1985; 2001segc.book..223H).

For the first time, Zinn (1985) provided evidence that pointed to the existence of distinct sub-populations of GCs inside the MW. In his work, a halo population was detected in the Galaxy along with a disk population. GCs associated to the halo population are characterized by lower metallicity and a small net rotation around the Galactic center. On the other hand, the disk population is more metal rich and has been found to have a velocity close to that of the local standard of rest. At that time, this was used to promote the vision that, at least part of MW GCs have extragalactic origins and were later incorporated into MW via merging processes.

Since then, an increasing number of refinements in the number and components of distinct GC populations in the MW was proposed. Ibata et al. (1995) discovered the Sagittarius dwarf galaxy. Its chemical and kinematical patterns were detected in a large area of the sky supporting the idea that this satellite of the MW is being subject to tidal stripping. The authors, also suggested that some MW GCs originally were part of this galaxy. The existence of others nearby, stripped dwarf galaxies was proposed, along with a list of GCs likely associated with them (see for example Marín-Franch et al. 2009 — hereafter MF09 and references therein).

More recently, in the first decade of this century, the advent of deep, high resolution photometry of Galactic GCs, led to the detection of distinct and detached sequences at different stellar evolutionary stages in the Color-Magnitude Diagrams (CMD) of these objects. This result, coupled with the growing number of spectroscopical evidence, was interpreted in terms of multiple stellar populations (MPs, Gratton et al. 2012; Bastian & Lardo 2018). It is worth mentioning that distinct sequences of stars, that appear detached in the CMD, put strong constraints to modelling the processes of star formation in GCs. This evidence, in fact, rules out a continous star formation process and suggests that bursts of star formation occurred in these systems (Piotto et al. 2015 — hereafter Paper I, but see also Bastian et al. 2013 and Hopkins 2014).

At first, the MPs phenomenon was detected in the CMD of single GCs. But with the completion of a large photometric survey, namely the Hubble Space Telescope (HST) UV Legacy Survey of Galactic Globular Clusters (PI: Piotto, Paper I), it has been confirmed that this phenomenon is a common characteristic of virtually all Galactic GCs (Paper I; Milone et al. 2017 — hereafter Paper IX).

Even more interesting is that, with the introduction of the chromosome maps (Paper IX), MW GC population has been once again subdivided. These two-color diagrams, in fact, fully exploit the potential of the UV observations taken in the context of the HST UV Legacy Survey of Galactic GCs. Specifically, they maximize the color difference between the various stellar populations inside each GC, optimizing their detection and characterization (Paper I; Paper IX). Indeed, in Paper IX it was shown that the chromosome maps of the majority of the observed GCs show the presence of two major distinct groups of stars (1G population and 2G population). Samples of stars taken from these two groups display chemical abundance differences in light elements; for example the well known Na-O anticorrelation. These clusters were named type I clusters.

The remaining GCs show more complex chromosome maps: other groups of stars can be detected, in addition to the two main groups present in type I clusters, all with their own Na-O anticorrelation. These additional groups of stars also have different Ba and Fe abundances, and more in general a different abundance of elements produced via slow neutron capture reactions (Paper IX). In this respect, it is worth mentioning that the presence of small intrinsic iron spread, at least for some GCs, is still debated, as they can be artificially introduced by the method used to derive atmospheric parameters of stars (Mucciarelli et al. 2015, Lardo et al. 2016; but see also Lee 2016). GCs that have chromosome maps of this kind are defined as type II clusters. In Paper IX, 10 type II clusters have been detected: NGC 362, NGC 1261, NGC 1851, NGC 5139, NGC 5286, NGC 6388, NGC 6656, NGC 6715, NGC 6934 and NGC 7089. Subsequently, by means of a detailed characterization of the CM of M15, Nardiello et al. (2018) have re-classified this cluster as type II. We thus added NGC 7078 to the list of type II GCs.

In this work we performed a principal component analysis (PCA) in order to investigate the correlation of cluster type with other GC parameters. Noteworthy previous applications of this technique to GCs is by Djorgovski, & Meylan (1994), who identified a correlation between cluster luminosities and concentration, and by Recio-Blanco et al. (2006), who examined the effect of various parameters on the morphology of the horizontal branch revealing the influence of cluster mass, thus providing hints of self-enrichment in Galactic globular clusters. Another example is Carretta et al. (2010) who studied the effect of detailed chemical composition of the distinct stellar populations in GCs.

The structure of this paper is as follows: in Section 2 we present the details of the PCA and briefly discuss the results. In Section 3 possible relations among various cluster parameters are presented in more details. In particular, we reviewed the age-metallicity and age-Galactocentric distance relations (Section 3.1); the metallicity vs. Galactocentric distance relation (Section 3.2); the relation between orbital parameters and cluster type (Section 3.3); the mass distribution (Section 3.4); and finally the spatial distribution of GCs (Section 3.5).

We investigated a large sample of variables through principal component analysis. In particular, we focus on $11$ quantities, reported in Table 1: cluster type, Oosterhoff type, metallicity, relative age, orbit total energy, orbit total angular momentum, orbit eccentricity, orbit inclination with respect to the Glactic plane, cluster masses, core radii and tidal radii. This sample of GC properties was chosen in order to have a complete view of the relations affecting the cluster type. In particular, these quantities were collected from several catalogues that provide information for different GC samples. Our final sample consist on 25 GCs, 7 of them of type II and the rest of type I. The 7 type II clusters are NGC 362, NGC 1851, NGC 5139, NGC 6656, NGC 6934, NGC 7078, NGC 7089. The full list of parameters of our sample is given in Table 2.

The resulting principal component values, along with the fraction of total variance explained by each component are listed in Table 3. The first four components explain respectively $26\%$, $19\%$, $16\%$ and $13\%$ of the total variance of the sample, for a total of $74\%$. Table 4 lists the correlation coefficients between principal components and the 11 quantities considered in the analysis.

Figure 1 shows the eigenvector projections of the 11 quantities considered in the planes defined by the first and the second components (upper-left panel), the first and the third components (lower panel) and the third and the second components (upper-right panel).

The first component correlates mainly with orbital parameters like total energy, total angular momentum and inclination (5, 6 and 8 respectively); it also correlates with tidal radius (11), which points to a connection between this parameter and orbital ones. To a lesser extent it also correlates with Oosterhoff type (2) and metallicity (3), confirming the well known relation between metallicity and Oosterhoff type.

The second component shows correlations with relative age (4), Oosterhoff type (2), orbit total energy (5) and eccentricity (7). It can be also observed a mild correlation between this component and cluster type (4). In particular, the alignment of the eigenvectors associated to cluster type and relative age in the upper-left panel of Figure 1, call for further investigation on its origin. We will discuss this result in the following section.

The third component mainly correlates with GC mass (9) and cluster type (4) pointing to a correlation between both parameters.

The fourth component mainly correlates with the orbit eccentricity and with the metallicity. This relation was discussed in Dinescu et al. (1999). This component mildly also correlates with Oosterhoff type and core radius (2 and 10 respectively) both in the same sense as eccentricity.

Since the first component mainly correlates only with orbital parameters and tidal radius, the conclusion that can be reached is that it describes general properties of the whole GC sample. But our interest is to investigate how the new classification in type I and type II clusters affects the sample, so we concentrated on the second and third components, which have the strongest correlation with cluster type. The relations between it and other parameters are shown in the upper-right panel of Figure 1. A possible relation between cluster type (1) and relative age (4) can be observed. In fact, the two associated vectors points in opposite directions and are almost parallels.

The PCA analysis performed in the previous section highlighted some possible correlations between various GC properties. In particular, we are interested in studying those that involve cluster type. For this reason, we reviewed in more details some of them, this time without the use of PCA, but quantifying the statistical significance of each one. Our choice is also motivated by the fact that the sample of clusters we could use in PCA is more limited than the entire sample used in this paper because of the lack of some of the parameters used in the PCA.

For clarity, we report in Table 5 the Spearman rank coefficients (${\rm r_{S}}$) of the various correlations we investigated. In the first column we report the coefficients for type I clusters. The coefficients for type II ones are in the second column and, in the last column, we provide ${\rm r_{S}}$ for the sample of type II clusters excluding NGC 6388. This cluster is among the type II clusters that are not present in the sample used for the PCA in Section 2 beacuse we could not find some of the parameters used in the analysis. Its metallicity and position in the Galaxy make it rather peculiar among this group of GCs (see also Paper IX).

Chromosome maps (Milone et al. 2015, Paper IX) showed that virtually all Galactic GCs host multiple stellar populations. Chromosome maps also allowed us to identify a family of Galactic GCs that shows an above-the-mean complexity in their stellar population. These clusters were classified as type II clusters, the remaining ones being labelled as type I clusters (Paper IX).

In this paper we study if and how cluster type correlates with GC properties. We performed principal component analysis based on 11 quantities: cluster type, Oosterhoff type, metallicity, relative age, orbit total energy, orbit total angular momentum, orbit eccentricity, orbit inclination with respect to the Glactic plane, cluster masses, core radii and tidal radii. The main sources of variance in the considered sample results to be contained in orbital parameters and, at a lesser extent, in the relation between cluster type and relative age. Below we summarize the main results.

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  In the plane age-metallicity, type II clusters define a clear trend, with more metal-rich clusters being younger. NGC 6388 is an exception, but it also is the only type II cluster located in the bulge.

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  There are hints of a possible relation between age and Galactocentric distance for type II GCs, with younger clusters being located outwards.

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  In the [Fe/H]-${\rm r_{GC}}$ plane, halo type II clusters show a trend, with more metal-rich clusters being located outwards. This trend is consistent with the radial distribution of their Oosterhoff type and apparently inconsistent with the trend found for type I GCs.

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  The orbits of type II clusters are more eccentric than the average of type I clusters. A large dispersion of the orbital inclinations with respect to the Galactic plane is also observed and is similar for both groups.

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  Type II clusters are, on average, more massive than type I ones. There are, in any case, type I clusters with mass comparable to those of type II.

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  Nowadays, type II GCs are preferentially located below the plane of the Galaxy. Specifically, no type II GC has been observed above Z$\sim 2$ kpc.

This suggest two further investigations: (i) it will be of primary interest to search for additional type II clusters, especially at Z$>0$ kpc; (ii) it would be quite informative to perform detailed simulation of the kinematics of type II GCs.

For the first point, we are suggesting to trace the path to a photometric survey aimed at enlarging the sample of Galactic GCs for which chromosome maps could be used to discern their type. Extending the survey to the full sample of the MW will improve the statistical significance of the present results.

For the second point we find of particular interest to establish, in the light of this new classification, if some remnants of a common dynamical pattern could be detected among the known type II clusters. In fact, the high incidence of negative values of Z for type II GCs could indicate a common extragalactic origin for these systems.

We thank the anonymous referee for the careful revision that improved the quality of the present manuscript. M.S., A.A. and G.P. acknowledge support from the Spanish Ministry of Economy and Competitiveness (MINECO) under grants AYA2013-42781 and AYA2017-89841-P. M.S. and A.A. acknowledge support from the Instituto de Astrofísica de Canarias (IAC) under grant 309403. G.P. acknowledges partial support by the Università degli Studi di Padova Progetto di Ateneo CPDA141214 and by INAF under the program PRIN-INAF2014.