Globular clusters as indicators of Galactic evolution

We have studied the system of globular clusters (GCs) that formed in other galaxies and eventually accreted onto the Milky Way. Thus, the samples of GCs belonging to different tidal streams, obtained on the basis of the latest data from the Gaia observatory, were taken from the literature. We measured the anisotropy of the distribution of these GCs using the gyration tensor and found that the distribution of GCs in the streams is isotropic. Nevertheless, it can be seen that some of the accreted GCs included into existing samples actually belong to the disk of the Galaxy. To clarify the origin of GCs, we investigated the ``age--metallicity'' relation. This dependence demonstrates bimodality and its two different branches clearly show the difference between the clusters formed in the streams and in the disk of the Galaxy. Furthermore, we have studied the influence of the large--scale environment of the Galaxy (i.e., the Local Supercluster) on the distribution of satellite galaxies and Galactic GCs. The satellite galaxies of the Milky Way are known to form an anisotropic planar structure, so we included them in our analysis too. An inspection has shown that the plane of the satellite galaxies is perpendicular both to the disk of the Galaxy and the supergalactic plane. For GCs more distant than 100~Kpc, a similar picture is observed.

galaxies, and then were accreted [5,6]. In the results of studies by different authors, the percentage of GCs formed ex-situ differs. For example, Forbes [7] claims that 54% of GCs (87 out of 160 clusters) were formed ex-situ and then accreted, while Kruijssenn et al. [8] claim that the percentage of accreted clusters is 43. According to Massari et al. [9], this value reaches 60%.
Thus, a significant part of the GCs of the Galaxy was accreted from the outside. Information about the origin of GCs can be preserved both in the properties of the stellar population of GCs and in the spatial distribution and dynamics of GCs themselves. In particular, it is well known that both satellite galaxies and GCs exhibit a disk-like structure perpendicular to the disk of the Galaxy [see, e.g. [10][11][12]. This structure may be a result of the accretion of several galaxies that arrived in our Galaxy mainly from polar directions. According to Zeldovich theory [13], formation of the large-scale structure of the Universe occurs through independent contraction or expansion of the matter in the three mutually perpendicular directions. A good example of a structure contractingin one direction and expanding in two other directions is the Local Supercluster of Galaxies, which looks likea typical Zeldovich "pancake". This structure sets the preferred direction in the vicinity of the Galaxy, and therefore can affect the preferrential direction of accretion and distribution of accreted material in our Galaxy.
Tidal streams of the Galaxy are actively dis-cussed in the literature [e.g. . Recent measurement of the GCs proper motions using GAIA data made it possible to identify GCs belonging to specific tidal streams. The problem regarding the difference in the physical properties of GCs formed in-situ and ex-situ was studied in detail in [36]. It was shown there that accreted GCs differ by the abundance of alpha-elements, as well as by the range of masses. The purpose of our study is to check the spatial orientation of the GCs system belonging to the streams, i.e., admittedly accreted onto the Galaxy from outside. For this, the orientation of the systems identified by different authors was compared with the disk of the Galaxy, as well as with the plane of the Local Supercluster. In addition, the "age-metallicity" relation (AMR) for GCs belonging to the streams was analyzed and the relation between GCs colors and their origin was discussed.
The paper is organized as follows. In Section 2, the studied GC samples are described and the anisotropy of their distribution is investigated. In Section 3 the AMR for GCs is discussed. In Section 4, the influence of the Local Supercluster is measured. Conclusions are presented in Section 5.
papers regarding new clusters in the Milky Way appear (e.g., F SR 1716 [47], F SR 1758 [40,48], Although even before obtaining high-precision GAIA data, there were attempts to identify GCs belonging to the tidal streams [33,[37][38][39], but after the appearance of GAIA data, these attempts significantly advanced [4,7,9,[40][41][42][43][44]. In this paper, we draw our attention to three studies: [9] (hereinafter, Massari), [40] (hereinafter, Myeong), and [7] where S -gyration tensor, N -the number of objects, x k i -the distance of k th object to the Galactic center along coordinate axis i. In [12] [p. 7, Fig. 7], for the entire sample of GCs at the distance from 2 to 10 kpc, statistically significant anisotropy is observed, which the authors associated with GCs belonging to the disk of the Galaxy, that is, formed in-situ.
In this paper, we studied spatial distributions of GCs, which, according to a number of authors, belong to the tidal streams, that is, were formed ex-situ. As seen in Fig. 1, for all samples, the spatial distribution of GCs belonging to the tidal streams is isotropic. This is consistent with the conclusion of Arakelyan et al. [12] that the statistically significant anisotropy for the entire GCs sample is due to the clusters that were most likely formed in the Galaxy or have been interacting with the Galaxy disk for a very long time. It is also important that the clusters that belong to the tidal streams do not exhibit significant structure, which we might expect, first, because clustering occurs mainly along the distinguished directions associated with the walls and filaments of a large-scale structure, and, second, because anisotropic distribution is observed for satellite galaxies.
Nevertheless, it is seen in Fig. 1 that for all three samples (Forbes, Massari, Myeong) for GCs that belong to the streams, the major axis of the gyration tensor is in the disk, at the distances from about 3 to 10-20 kpc. It seems unlikely that such a situation can arise for a random isotropic GCs distribution. The distribution of the directions of the axes of the tensor as in Fig. 1, one can expect if a part of the GCs in each of the samples belongs to the disk. We demonstrate this below using random catalogs.
To check the probability of entering of the GCs from the disk into the GCs sample from the tidal streams, we generate random catalogs containing the same number of GCs as the real samples. Moreover, we take the galactocentric GC distances from the real samples. Angular coordinates are assigned randomly. To simulate a situation in which some of the clusters belong to the disk, for n clusters the height above the disk is set to zero (Cartesian coordinate z).
Using such models, we calculated the conditional probability of obtaining a distribution similar to the right-hand column in Fig. 1, i.e., when the major axes of the gyration tensor in the For this probability to exceed, for example, 10%, the disk must contain n = 6, 16, and 8 GCs for the Forbes, Massari, and Myeong samples, respectively. From this, we can conclude that a part of the GCs, formed to the opinion of these authors outside our Galaxy, actually belongs to its disk. It should be noted that in [36], based on the analysis of the abundance of alphaelements, it was shown that the group of Low energy clusters from the Massari work was most likely formed in-situ, which also indicates the inaccuracy of the in-situ/ex-situ separation in the Massari sample. In order to verify further the origin of the GCs, we use the "age-metallicity" diagram. To understand the difference between in-situ clusters and ex-situ clusters, we plotted respective samples from Massari, Forbes, and Myeong in the "age-metallicity" diagram. The results are shown in Fig. 2.
The "age-metallicity" dependence clearly shows that GCs have two branches. The lowmetals branch contains mainly clusters that belong to different tidal streams formed by the partial destruction of satellite galaxies. The clusters in this sequence show a wide variation in age and metallicity, but there are no clusters less than 6 Gyr old. The clusters of a more metals-rich branch, formed in-situ, also have a scatter in metallicity, but all clusters are more than 11 Gyr old.
It is worth noting that the in-situ clusters were formed not in the Galaxy as we know it, but in its progenitor. In the hierarchical model of the formation of galaxies, the mass of a galaxy is accumulated gradually due to mergers, and galaxies as a whole do not have a clearly defined moment of formation. Therefore, for the objects formed long ago, it is difficult to distinguish between the concepts of in-situ and ex-situ. However, specifically for our Galaxy, it is believed that it did not experience mergers with the objects of comparable mass since z = 2 or less than 10.5 Gyr ago [88]. By that time, it had gained only 1/5 of its current total mass (including the dark halo). Six Gyr ago (the age of the youngest GCs), its mass was about 60% ofthe current one [89]. We have tested the influence of the Local Supercluster on the spatial distribution of GCs, as well as dwarf satellite galaxies of the Milky Way. The satellite galaxies were a priori ac-creted onto our Galaxy from the outside. At the same time, they form a clear-cut flat structure [10][11][12]. Therefore, we did not limit ourselves to analyzing the GCs distribution, but also considered satellite galaxies. For this, the angle distributions between the axes of the gyration tensor   It is believed that the accretion onto the Galaxy was anisotropic, which is manifested, for example, as a disk-like structure of satellite galaxies. We measured the anisotropy of the distribution of GCs that belonged to the streams using the gyration tensor. The measurement result showed that no statistically significant anisotropy is observed for accreted GCs.
Having obtained this result, we can state that the anisotropic structure that is observed for the complete sample of GCs (see [12], p. 7, Fig. 7) is due to the presence of many GCs in the Galactic disk, and is associated with the clusters formed in-situ.
However, in Fig. 1 for the three samples of the accreted GCs, the major axis of the gyration tensor at a distance from 3 to 20 kpc is in the disk. This may be due to the fact that the samples contain a significant number of GCs that have formed in the disk of the Galaxy. To estimate their number, the distribution of GCs with random angular coordinates was modeled and it was shown that the probability of a random realization of such a distribution, in which there are no GCs belonging to the disk, is 4.5, 0.6, and 1.1% for the Forbes, Massari, and Myeong samples, respectively. This conclusion is consistent with the conclusion of Marsakov et al. [36], who had shown that some of the clusters from the Massari catalog claimed to be ex-situ are in fact genetically related to our Galaxy.
We also checked how the clusters formed insitu and ex-situ behave respective to the AMR (Fig. 2). Two branches can be easily distinguished; the low-metals branch contains mainly clusters belonging to different streams, and they have a large spread in the age and metallicity. At the same time, the clusters in the more metallic branch, which most likely formed in the Galaxy, have a scatter in metallicity, but their age is over 11 Gyr.
To check the likely influence of the Local Supercluster on the distribution of satellite galaxies and GCs of the Milky Way, we presented the Figures, which show the angle between the LSC plane and the axes of distribution of GCs sys-tems or satellite galaxies, as a function of the galactocentric distance. Fig. 3 (top row, left) shows that the plane of the satellite galaxies is both perpendicular to the disk of the Galaxy and to the supergalactic plane. For GCs at the distances of up to 20 kpc, only the influence of the Galactic disk is traced; at the distances of about 30 kpc, the orientation of the GCs system may coincide with the supergalactic plane, and at larger distances (more than 100 kpc), the orientation resembles that for satellite galaxies.