235 Acta Polytechnica CTU Proceedings 1(1): 235–239, 2014 235 doi: 10.14311/APP.2014.01.0235 Data Analysis of Globular Cluster Harris Catalogue in View of the King Models and Their Dynamical Evolution. II. Observational Evidences Marco Merafina1, Daniele Vitantoni1 1Department of Physics, University of Rome La Sapienza, Piazzale Aldo Moro 2, I-00185 Rome, Italy Corresponding author: marco.merafina@roma1.infn.it Abstract We summarize some observational comparison concerning the features of globular clusters (GCs) population in connection to the evolution of King models. We also make a comparison with some extragalactic GCs systems, in order to underline the effects of the main body on the dynamical evolution. Keywords: globular clusters - gravothermal catastrophe - King models - thermodynamical stability. 1 Introduction Globular clusters (GCs), for their proprieties of sym- metry and their high relaxation times, are important to test theories about thermodynamical stability of spherical self gravitating systems. The actual sample of is a mixture of various and not homogeneus GCs types. Therefore, it is difficult to analyze properties of Milky Way (MW) GCs population in connection to core-collapse and gravotermal instability. The last version (2010) of Harris GCs Catalogue (see also Harris, 1996) includes 157 objects. It was pointed out by van Der Bergh (2011) that Harris catalogue could includes three not typical GCS, probably rem- nant cores of DSph galaxies: Omega Centauri, Terzan 5 and NGC 6715 (M54). The Harris catalogue also in- cludes PCC GCs, namely GCs with collapsed cores that cannot be described by classical single mass King mod- els profiles. Zinn (1985) identifies two classes of GCs, respectively known as disk population (metal rich) and halo population (metal poor), distinct by the threshold value [Fe/H] ' −0.8 (or, according to some authors, −0.75). Recently Bica et al. (2006) showed that the ac- tual GCs population seems to have been contaminated by capture of smaller galaxies (and their possible GCs populations) during the Milky Way formation. Possible evidences of extragalactic origin of some GCs are ret- rograde motion (compared to galactic disk motion) and unusual young absolute age. It seems that the original GCs population suffered deep and incisive processes of disruption (see Aguilar et al., 1988; Hut & Djorgovski, 1992; Gnedin & Ostriker, 1997; Mackey & Gilmore, 2004), until almost 50% of original GCs are destroyed in the last Hubble time. 2 Discussion We start to consider the problem introduced by Katz in the paper about thermodynamic stability in 1980. The study of the distribution of galactic GCs in terms of W0 (central gravitational potential) shows a peak value of 6.9. We should expect that the peak value coincides with the known stability critical value W0 = 7.4, due to the old age of MW GCs and the onset of the instabil- ity in the high W0 region. This problem had remained unsolved (Fig.1). Figure 1: Distribution of galactic GCs at different K (Katz, 1980). The quantity K is related to W0 (see Merafina & Vitantoni, Part I). With the introduction of the effective potential (see Merafina & Vitantoni, Part I) and including the addi- tional term in the expression of the total energy, we can revise the Katz study. The result is a very satisfactory coincidence of the observative peak value with the sta- bility limit. We can also repeat the analysis on a more detailed and updated sample (using data of the Harris GCs Catalogue). The peak value, in the non-symmetric 235 http://dx.doi.org/10.14311/APP.2014.01.0235 Marco Merafina, Daniele Vitantoni Gaussian hypothesis, is exactly at W0 = 6.9 (Fig.2). 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 Figure 2: W0 distribution of pre-core-collapse MW GCs. For a better understanding of the evolution of a GCs population, we briefly analyze the role of environmental features. The effect of the distance from the Galactic center (Fig.3) is not clear at all. Generally speaking, the more a GC lives near the galactic center, the more quickly it evolves towards the gravothermal catastro- phe, being more affected by tidal forces of the Galaxy. 2 4 6 8 10 12 14 1 10 100 r g c Figure 3: Galactocentric distance rgc in function of W0. The dashed lines represent the values at 3Kpc and 30Kpc. If we look at the GCs distribution in the [Fe/H]-W0 plane (Fig.4), we find no correlations between these two quantities. This means that the difference between halo and disk population, first introduced by Zinn (1985) does not influence the dynamical features and the evo- lution. Nevertheless, if we analyze the disk population (Fig.5), this seems to be more dynamically evolved than the halo one. The W0 peak value is slightly larger for the disk population, mainly due to a lower rgc (in av- erage) for this class of objects. On the other hand, it is well known that the tidal shocks played a more incisive role in the evolution of the disk GCs. 2 4 6 8 10 12 14 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 Figure 4: Total metallicity [Fe/H] in function of W0. 2 4 6 8 10 12 14 0 2 4 6 8 10 12 N W0 External Halo Internal Halo Figure 5: W0 distribution of astronomical popula- tions. The contamination of the Halo GCs with the ex- tragalactic origin ones is suggested by the bimodality in the absolute age distribution, by the rotation in the plane of Galactic Disk, and by the Age-Metallicity de- pendence. The situation is shown in Figs.6, 7 and 8. Regarding the Age-Metallicity dependence, we can say that few objects are located out of the main well defined sequence of clusters (and probably have a different ori- gin with respect to all the others). 236 Data Analysis of Globular Cluster Harris Catalogue... part II Figure 6: Absolute age distribution for MW GCs. Older GCs, presumably all native in the Milky Way, are evidenced in dark grey. Figure 7: Motion over the Galactic plane for MW GCs (from Dinescu et al., 1999). Figure 8: Age-Metallicity behavior, using the abso- lute age values extimated by Dotter et al. (2010). PCC clusters are indicated by grey squares, suspected PCC ones by white triangles. If we analyze the behavior of the central relaxation time trc in function of W0 (Fig.9), we can note a lin- ear decreasing, that indicates an increasing of evolu- tional speed towards the collapse. Below the treshold value log trc = 8.0 there is a region of coexistence of Pre-Core Collapse GCs with Post-Core Collapse (PCC) ones. The behavior of core collapse time tcc (that is the remaining time before the collapse of the model), changes over the stability limit W0 = 6.9 (Fig.10). 2 4 6 8 10 12 14 4 5 6 7 8 9 10 11 r gc < 3 Kpc 3 Kpc < r gc < 30 Kpc r gc > 30 Kpc lo g (t r c/ 1y r) W0 NGC6717 Figure 9: Behavior of trc in function of W0; three classes of cluster distances are represented. Vertical dashed line represent the stability limit, whereas the horizontal one represent the trc critical value (Cohn & Hut, 1984) distinguishing pre-core-collapsed and post- core-collapsed objects. Suspected PCC clusters are in- dicated by filled symbols. In the Harris Catalogue NGC6723 has been erroneously included among the sus- pected PCC clusters in place of NGC6717. 2 4 6 8 10 12 14 7 8 9 10 11 12 lo g (t c c/ 1y r) Figure 10: Core-collapse time in function to W0. The tcc values are estimated as in Quinlan (1996). We also consider a comparison among four GCs pop- ulations, shown in Fig.11: the LMC is the less evolved, as well as the SMC and Fornax systems (Mackey & Gilmore, 2003b, 2003c); it presents a peak value close to W0 = 4.3. For this kind of GCs population, the presence of a low massive main body allowed to preserve 237 Marco Merafina, Daniele Vitantoni more informations about primeval distribution features. On the contrary, NGC5128, whose main body is a giant elliptical galaxy, seems to be an evolved population with a maximum value up to the threshold value W0 = 6.9. Finally, the M31 system is the most similar to our GCs population, with a main peak value around the stabil- ity limit and an extended tail in low-W0 region, that is produced by the presence of low evolutionary speed objects or extragalactic origin clusters. Also the effects of disk and bulge shocking, realistically, concurred to the formation of the tail. 3 Conclusions In order to analyze the dynamical evolution of King single mass GCs, we have analyzed the MW GCs pop- ulation. The MW clusters W0 distribution presents a peak very close to the new stability limit W0 = 6.9 and a pronounced tail in the low-W0 region. 3 6 9 12 0 5 10 0 5 10 0 3 6 3 6 9 12 0 3 6 W0 MW N M31 LMC Figure 11: Comparison among W0 distributions of different GCs systems. In addition to MW system, M31, NGC5128 and LMC systems are reported. M31 data come (or are deduced) from Barmby et al. (2007), NGC5128 ones from Gòmez et al. (2005), LMC data from Mackey & Gilmore (2003a). MW histogram differ- ences from Fig.2 are given by a different binning choice. We can instead exclude a direct relation between as- tronomical GCs populations and dynamical evolution, except for a very weak increasing of W0 peak value for disk clusters. From the time-scales we can deduce that clusters with high W0 value have an higher collapsing speed. The gravothermal catastrophe produce an alteration of the natural evolutionary sequence for clusters with W0 ≥ 6.9. From the comparison with extragalactic GCs sys- tems we have deduced that, in the case of LMC, SMC and Fornax system, these clusters have a Gaussian like distribution around a peak value W0 ∼ 5. MW and M31 system are very similar in their features and W0 distribution, with low-W0 tail and a peak value in cor- rispondence of the stability limit. We can assume this as the main product of disk shocking, as well as extra- galactic capture and low speed evolution objects men- tioned above. For NGC5128 there is no low W0 region tail, but only a narrow peaked distribution around the stability limit. 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