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T.Borkova, V.Marsakov, Population of Galactic globular clusters

Globular Cluster Subsystems in the Galaxy.

T. V. Borkova and V. A. Marsakov

Astronomy Reports, Vol. 44, No. 10, 2000, pp. 665?684.

PostScript-format, Russian-win1251, ]

Abstract

     Data from the literature are used to construct a homogeneous catalog of fundamental astrophysical parameters for 145 globular clusters of the Milky Way Galaxy. The catalog is used to analyze the relationships between chemical composition, horizontal-branch morphology, spatial location, orbital elements, age, and other physical parameters of the clusters. The overall globular-cluster population is divided by a gap in the metallicity function at [Fe/H]=?1.0 into two discrete groups with well-defined maxima at [Fe/H]=-1.60±0.03 and ?0.60±0.04. The mean spatial?kinematic parameters and their dispersions change abruptly when the metallicity crosses this boundary. Metal-poor clusters occupy a more or less spherical region and are concentrated toward the Galactic center. Metal-rich clusters (the thick disk subsystem), which are far fewer in number, are concentrated toward both the Galactic center and the Galactic plane. This subsystem rotates with an average velocity of Vrot=165±28 km/s and has a very steep negative vertical metallicity gradient and a negligible radial gradient. It is, on average, the youngest group, and consists exclusively of clusters with extremely red horizontal branches. The population of spherical-subsystem clusters is also inhomogeneous and, in turn, breaks up into at least two groups according to horizontal-branch morphology. Clusters with extremely blue horizontal branches occupy a spherical volume of radius &sime9 kpc, have high rotational velocities (Vrot=77±33 km/s), have substantial and equal negative radial and vertical metallicity gradients, and are, on average, the oldest group (the old halo subsystem). The vast majority of clusters with intermediate-type horizontal branches occupy a more or less spherical volume &rovn18 kpc in radius, which is slightly flattened perpendicular to the Z direction and makes an angle of &rovn30° to the X-axis. On average, this population is somewhat younger than the old-halo clus-ters (the young halo subsystem), and exhibits approximately the same metallicity gradients as the old halo. As a result, since their Galactocentric distance and distance from the Galactic plane are the same, the young halo clusters have metallicities that are, on average, &delta[Fe/H]&rovn0.3 higher than those for old halo clusters. The young halo subsystem, which apparently consists of objects captured by the Galaxy at various times, contains many clusters with retrograde orbits, so that its rotational velocity is low and has large errors, Vrot=-23±54 km/s. Typical parameters are derived for all the subsystems, and the mean characteristics of their member globular clusters are determined. The thick disk has a different nature than both the old and young halos. A scenario for Galactic evolution is proposed based on the assumption that only the thick disk and old-halo subsystems are genetically associated with the Galaxy. The age distributions of these two subsystems do not overlap. It is argued that heavy-element enrichment and the collapse of the proto-Galactic medium occurred mainly in the period between the formation of the old-halo and thick-disk subsystems.

1. INTRODUCTION

     Quite recently, globular clusters (GCs) were considered to form a homogeneous group and to be typical representatives of the spherical component of the Milky Way. However, a large amount of recently published observational material has demonstrated a substantial scatter in the physical and chemical parameters of clusters, and shown that the distributions of these parameters are discrete. This suggests the existence of several populations of GCs belonging to different subsystems of the Galaxy. Even the earliest metallicity functions revealed a gap near [Fe/H]&rovn-1.0, which divides the GC population into two discrete groups: a metal-poor, spherically symmetric, slowly rotating halo subsystem and a metal-rich, rather rapidly rotating, thick-disk subsystem Marsakov & Suchkov (1977), Zinn (1985). Halo GCs were further shown to separate into two groups with different horizontal-branch (HB) morphologies. These subgroups, whose distributions are both spherical, differ in their kinematics and the spatial volume they occupy Zinn (1993). Halo clusters, which have redder HBs for a given metallicity, are mostly located outside the solar circle and have a large velocity dispersion, lower rotational velocities, and smaller ages than clusters with blue HBs, which are concentrated inside the solar circle Da Costa & Armandroff (1995). This difference can be explained if the old-halo subsystem formed simulta-neously with the entire Galaxy, whereas the young-halo clusters were captured from intergalactic space during later evolutionary stages Zinn (1993).

     The aim of this paper is to analyze relationships between the physical, chemical, and spatial?kinematic parameters of GCs both for the Galaxy as a whole and within each subsystem, and to determine the characteristic parameters of the subsystems. This requires, first and foremost, a homogeneous catalog of fundamental GC parameters.

2. THE CATALOG OF GLOBULAR бLUSTERS

     Our catalog is based on the computer-readable version of the compiled catalog of Harris (1996), which gives measured quantities for 147 Galactic GCs. These data are complete through May 15, 1997. We adopted most parameters directly from Harris (1996) and computed some using data from this same catalog. We further added some fundamental parameters that are missing from Harris (1996), taking them from other sources.

     We adopted the positions of the clusters in the Galaxy from Harris (1996), who used the horizontal-branch magnitude averaged over several sources as his main distance indicator. We transformed the Galactocentric coordinates given in Harris (1996) into Galactic coordinates X, Y, and Z (for a Galactocentric distance of the Sun RG=8 kpc), and computed cos &psi, where &psi is the angle between the GC line of sight and the vector of rotation about the Z-axis, using the formula

&forml1;

Here, Rsun; - is the heliocentric distance of the GC.

     The radial velocities (Vr) in Harris (1996) were derived by averaging the data for a large number of sources using weights inversely proportional to the errors, which were ≃ 1 km/s for most of the sources. We also computed VS, the GC line-of-sight velocities relative to an observer at rest at the position of the Sun, using the formula

&forml2;

where V0 is the radial velocity corrected for the solar motion relative to the local centroid from Harris (1996), V=225 km/s is the velocity of circular motion of the local centroid of the Sun, and A is the angle between the apex of the circular motion of the local centroid of the Sun and the direction to the GC (cos A =Y/R). See Thomas (1989) for a detailed description of the angle and velocity computations.

     One of the most important parameters of a cluster is its metallicity. In his catalog, Harris (1996) compiled all published GC metallicities reduced to the [Fe/H] scale of Zinn & West (1984) and averaged them with equal weights. The mean [Fe/H] values in the compiled catalog have relatively high internal accuracies, due to the large number of sources considered (>40) and the exclusive use of spectroscopic metallicity determinations and well calibrated color-magnitude diagrams. The metallicity scale Zinn & West (1984)[7] is somewhat nonlinear, resulting in overestimated metallicities for the most metal-rich clusters Carreta & Gratton (1997); however, only the relative [Fe/H] values are important to us here.

     The horizontal branch can be used not only to determine the cluster distance, but also to obtain information about the conditions under which GCs form and evolve. In particular, Mironov & Samus (1974) subdivided all clusters into two groups based on their HB morphologies and found them to differ distinctly in their metallicities and spatial?kinematic characteristics. On the otherhand, according to Oosterhoff, GCs divide into two distinct groups separated by a gap in the period distribution for their typical horizontal-branch representatives ? RR Lyr variables. The periods of RR Lyrae in clusters are closely related to the HB morphology, allowing clusters to be conveniently characterized by the parameter (B?R)/(B+V+R), where B, V, and R are the numbers of stars in the blue end of the HB, the Hertzsprung gap, and the red end, respectively. Harris (1996) computed this parameter by simply averaging the data for several sources.

     Age t is one of the most uncertain parameters, and Harris (1996) does not give it in his compiled catalog. The recently published Hipparcos catalog contains high-precision stellar parallaxes based on satellite measurements, and even a first-level analysis of these data requires substantial revision of GC distances. As a result, the ages of even the most metal-poor (i.e., oldest) clusters do not exceed ≃10 Gyr (see, e.g., Reid(1997)). However, we adopted the old scale here, because the refinement of the age-scale zero point based on the new data is probably now only in its initial stage, and we are primarily interested in relative parameters.

     Accurate relative GC ages have recently been published in a number of studies. To be able to use age data for as many clusters as possible, we reduced all these age lists to a unified scale and computed weighted average age estimates by assigning weights both to each source and to each individual age determination. We used the two-tiered iteration procedure suggested by Hauck & Mermilliod (1998), assigning lower weights to age determinations that differ strongly from the initially computed mean. We used homogeneous relative ages for 36 GCs from Buonanno et.al. (1989) as our basic scale, where the mean age of metal-poor clusters was assumed to be 15 Gyr. We then used a least squares method to reduce the age scales of the nine most extensive lists (containing Gratton (1985)-26 иб, Buonanno et.al. (1989)-12 иб, Sarajedini et.al. (1989)-31 иб, Chabouer et.al. (1992)-32 иб, Sarajedini et.al. (1995)-14 иб, Chabouer et.al. (1995)-40 иб, Chabouer et.al. (1996)-43 иб, Richer et.al. (1996)-36 иб, Salaris & Weiss (1997)-25 GCs) to the reference age scale. We included age determinations for single clusters from other studies only if their theoretical isochrones coincided with those adopted in one of the papers listed above. We used a total of 47 sources (not given in the references) and 336 individual age determinations, and derived weighted average estimates for a total of 63 GCs. The resulting ages had an internal accuracy of st &sigmat&rovn 0.89±0.03 Gyr.

     The central concentrations б=lg(rt/rc) where rt and rc are the tidal radius and the measured core radius, respectively, were taken from Harris (1996). We transformed the cluster radii in angular units, which Harris (1996) derived by averaging published angular measurements, into linear radii in pc (rh) using the heliocentric cluster distances given in the same catalog. We adopted the central cluster densities lg &ro;o from Buonanno et.al. (1997) and, for clusters absent from this source, from Fusi Pecci et.al. (1993). Both papers were written by the same team of authors, but they report different densities and cluster lists. We used the more recent paper as our basic source.

     We took the orbital elements for 25 GCs from [26]. The cluster radial velocities and distances used in Dauphole et.al. (1996) differ somewhat from those adopted here, but only slightly. The high accuracy of the distances and proper motions in Dauphole et.al. (1996) is demonstrated, in particular, by the fact that the mean rotational velocities of the GC subsystems derived from the radial velocities alone agree well with those derived from the full velocity vectors, as pointed out by Douphole et al. Dauphole et.al. (1996). We subjected these orbital elements to a statistical test. More than half of the GCs analyzed in [26] are located near computed apogalactic orbital radii, in full consistency with the theoretical phase distribution of GC orbital locations. We also found the minimum orbital radii from Dauphole et.al. (1996) to agree satisfactorily with the perigalactic distances estimated in van den Bergh (1985) from the tidal criterion (r=0.55±0.17). These orbital elements are thus suitable for analysis of the properties of GC populations.

     We derived the cluster masses from the integrated absolute magnitudes from Harris (1996) assuming M/LV=3 Chernoff et.al. 1989, where the mass M and luminosity LV are in solar units. Table 1 lists some of the above parameters for 145 GCs with known distances.

TРСЫШжР 1—Master catalog of fundamental GC parameters

3. GLOBULAR CLUSTERS OF THE DISK AND HALO

Metallicity Function

     Figure 1 shows the distribution of heavy-element abundance (i.e., the metallicity function) for all the GCs from Table 1. The solid curve shows an approximation of the histogram using a superposition of two Gaussian curves with parameters estimated using a maximum - likelihood method. The probability that we would be wrong to discard the null hypothesis that the distribution can be described by a single Gaussian in favor of a fit using the superposition of two Gaussians is <<1%. Thus, the entire GC population can be divided into two metallicity groups, with maxima at [Fe/H]=-0.60±0.04 and -1.60±0.03 and equal dispersions &sigma&rovn;0.30±0.03 separated by a well-defined gap at [Fe/H]=-1.0. When fitting the distribution, we ignored an outlier cluster with [Fe/H]=+0.22. Our gap position is shifted by &delt[Fe/H]&rovn;-0.2 toward lower metallicities compared to Zinn's Zinn (1985) result, which has usually been used to determine whether a particular cluster belongs to the halo or thick-disk population (see, e.g., Armandroff (1989)). (Note that the same metallicity scale is used in both cases.) The breakdown of the GC population into two subsystems separated by [Fe/H]=-1.0 is further supported by the fact that diagrams depicting the spatial locations and kinematics of the clusters show each characteristic parameter to have a discontinuity precisely at this (or somewhat lower) metallicity (see Fig. 3 below).

Fig. 1.—Globular cluster metallicity function. The curve shows an approximation by a superposition of two Gaussians.

Fig. 2.— The distribution of globular clusters projected onto the XY [(a) and (c)] and YZ [(b) and (d)] planes for metal-rich clusters of the thick disk with [Fe/H]&bolrovn;-1.0 [(a) and (b)] and metal-poor clusters of the halo [(c) and (d)]. The closed curves are upper envelopes drawn by eye. Clusters lying far from the central concentrations in the diagrams are outlined and their numbers indicated.

Spatial Distribution

     Figure 2 shows the distributions of metal-rich and metal-poor GC groups projected onto the XY and YZ planes. (The figures do not show six clusters with Galactocentric distances exceeding 60 kpc.) The two subsystems can easily be seen to differ strongly in both the volume and shape of the domain they occupy. The metal-rich group, which is much smaller in size, is concentrated toward both the center and the Galactic plane, and its shape can be very roughly described as an ellipsoid of revolution flattened along the Z coordinate. The envelope of its XY projection forms a circle ≃7 kpc in radius, and the envelope of the YZ projection forms an ellipse with a Z semimajor axis of &rovn;3 kpc. A comparison of these parameters with those of high-velocity field stars suggests that this GC group belongs to the thick disk. (The differences in the sizes in the X and Y directions are probably due to the poor statistics for this group.)

     The squares in Figs. 2a and 2b denote clusters that are far from the upper envelopes. The name of the cluster is given near each square. A more detailed discussion of these clusters is given below. We did not use these outlier clusters when determining the parameters of the thick disk. Similarly, the circles in Figs. 2c and 2d indicate halo clusters lying outside the circular envelope. However, we did not exclude these clusters when determining the characteristic parameters of the halo and Galaxy as a whole. To characterize the subsystem sizes, we used scale lengths and scale heights in (X0, Y0, Z0), equal to the Galactocentric distances along the corresponding coordinates over which the cluster density decreases by a factor of e. The corresponding quantities are listed in Table 2.

Fig. 3.—Relations between the metallicity and other GC parameters. The open triangles are thick-disk clusters; open circles, old halo clusters; filled circles, young-halo clusters; filled triangles, corona clusters; and crosses, metal-poor clusters with unknown (B?R)/(B+V+R). Only clusters with R<60 kpc are shown in (c). A sharp jump near [Fe/H]=-1.0 is seen in all plots.

Properties of GC Groups with Different Metallicities

     Figure 3 presents diagrams illustrating the relations between some GC parameters and heavy-element abundance. Abrupt changes in the velocity and distance dispersions, maximum distances of the cluster orbits from the Galactic center and plane (characterizing the total cluster energy), and orbital eccentricities are immediately apparent near the [Fe/H] value separating the halo and disk. This sharp transition suggests a real separation of the GC population into two discrete groups. These groups differ in other parameters as well. For example, all the disk clusters have extremely red HBs, with virtually no normal stars on the HB on the high-temperature side of the gap occupied by variable stars (Fig. 3a). By contrast, the halo clusters can have any HB type (from an extremely red to extremely blue). Age and metallicity are well correlated (r=-0.5±0.1): on average, age decreases with increasing metallicity. Parameters characterizing the internal states of disk and halo clusters do not differ within the errors (Table 2), albeit there are certain systematic effects. We will discuss these in more detail in the next section.

TABLE. 2.— Characteristic parameters of GC subsystems Parameter Galaxy Disk Halo.

Rotation of Subsystems

     The two GC metallicity groups have different angular momenta. If a system is assumed to rotate differentially with constant linear velocity Vrot, this velocity can be derived via least-squares fitting, given only the cluster distances, sky positions, and radial velocities reduced to those for an observer at rest coincident with the Sun (see Zinn (1985) for details). Figure 4 shows cosy cosψ- VS kinematic diagrams for all Galactic GCs and for the disk and halo subgroups. The straight lines are least-squares regression fits whose slopes yield the rotational velocities of the corresponding subsystems.

Fig. 4.— Kinematic diagrams for (a) all Galactic GCs, (b) thick-disk clusters, and (c) halo clusters. The dot sizes are proportional to the weights assigned. The straight lines are rms regression fits and their slopes yield the rotational velocity of the corresponding subsystem, Vrot

     The large scatter of data points in the diagrams, which is due to the intrinsic velocity dispersion and large distance errors, and the small number of objects make the rotational velocities inferred for the GC subsystems quite uncertain. The most difficult case is that of the thick disk, since most of the disk clusters are located near the Galactic center and are thus subject to strong extinction, which distorts the apparent distance moduli. Even a relatively small distance error for a cluster located near the Galactic center translates into a very large error in cosψ. Therefore, Vrot cannot be determined correctly without allowing for the errors in cosψ. The errors in the measured radial velocities and HB magnitudes of the clusters also contribute to the uncertainty in Vrot ; however, here we allow only for errors in the color excesses E(B-V) since their contribution is dominant in our case. To estimate the errors in the distance moduli, we used the following empirical relation proposed by Harris:

δ(m-M)=0.1+0.3E(B-V).

We then transformed the resulting &delta(m-M)i into distance errors &deltaRi and computed the variation of cosψ for each cluster by adding and subtracting the error δRi to and from the cataloged distance. We used the inverses of the mean errors dcosy as weights. (Unit weights were assigned if &deltacos&psi&menrov0.05.) We used these weights when analyzing all the kinematic diagrams in this paper. It follows from Fig. 4 and Table 2 that the resulting difference in the disk and halo rotational velocities exceeds 2&sigma (the metal-rich subsystem rotates significantly faster). It is also evident from Table 2 that the residual velocity dispersion about the direct regression line, &sigmaV, for the disk clusters is significantly (i.e., by an amount exceeding the rms error) lower than &sigmaV for the halo clusters. Dauphole et.al. (1996) determined the orbital elements for 25 Galactic GCs, of which 23 belong to the spherical subsystem and only two to the disk. The rotational parameters for the halo subsystem derived in Dauphole et.al. (1996) are in good agreement with the corresponding quantities in Table 2 (the rotational velocity <&teta>=24±29km/s and &sigma&teta=137±20 km/s). Both disk clusters from Dauphole et.al. (1996) have almost the same rota-tional velocity <&teta>=187±3 km/s, which also coin-cides with the corresponding velocity in Table 2 within the errors. Thus, the rotational parameters of GC subsystems with different metallicities differ markedly, and this can naturally explain the shape of each of these subsystems.

Fig. 5.— Relation between metallicity and (a) cluster Galactocentric distance and (b) distance from the Galactic plane. The straight lines are the rms regression fits for the thick-disk, entire Galaxy, and halo from top to bottom, respectively. The slopes of the lines yield the corresponding metallicity gradients.

Metallicity Gradients

     Figure 5 shows R-[Fe/H] and |Z|-[Fe/H] diagrams for the entire Galactic GC population. From top to bottom, the straight lines are orthogonal regression fits for the GC systems of the disk, entire Galaxy, and halo within R<60 kpc, respectively. The slopes of the regression lines are equal to the corresponding radial and vertical metallicity gradients in Table 2. We can see that the sample of Galactic GCs as a whole demonstrates negative metallicity gradients that are consistent with numerous estimates from other studies. The two correlation coefficients are roughly the same, and are equal to r&rovn-0.40±0.07. As noted above, both diagrams exhibit an abrupt change in the spatial characteristics near [Fe/H]&rovn-1.0, indicating that most of the gradients are due to the presence of two GC subsystems with different chemical compositions and spatial distributions. The diagrams for the two GC groups selected according to metallicity, indeed, yield radial gradients that are equal to zero within the errors (Table 2). This result also supports the well known fact that the radial metallicity gradient is zero beyond the solar circle (where only halo clusters are found). However, the vertical gradients for both groups differ from zero, though the value for the halo group is very small, and much smaller than the gradient for the entire sample. However, the disk subsystem has a very large gradient. Note that the large [Fe/H] gradient for the thick-disk subsystem is not surprising in view of the fact that an even higher value has been derived for the young thin-disk subsystem (see, e.g., Shevelev & Marsakov (1995))

     It thus follows from our catalog that the metallicity selected GC subsystems have substantially different ages, spatial distributions, rotational velocities, velocity dispersions, and HB morphologies. Let us now consider the complex structure of the halo

4. GLOBULAR-CLUSTER POPULATIONS IN THE HALO

[Fe/H]-(B-R)/(B+V+R) Diagram

     One striking feature of Fig. 3a is the very strong concentration of the color indices of the HBs of halo GCs toward extremely blue values. The distribution of this index shows that the number of GCs increases abruptly at (B-R)/(B+V+R)&rovn;0.85, which roughly divides the halo population into two subgroups. In his pioneering work, Zinn (1993) included clusters located within the solar circle in the old halo population. His sample contains most extremely blue clusters and some GCs located within a narrow band along the upper envelope (in the color parameter) of the [Fe/H]-(B-R)/(B+V+R) diagram. The remaining clusters were assigned to the young halo. In addition, Zinn (1993) left a number of very metal-poor clusters with intermediate colors lying well beyond the solar circle in the old-halo group (see Figs. 6c and 6d below). This approach overestimated the size of the old-halo population. Therefore, we consider it more natural to leave only extremely blue clusters in the old-halo population, thereby excluding doubtful members of this subsystem.

Fig. 6.—The distributions of halo clusters projected onto the XY [(a) and (c)] and YZ [(b) and (d)] planes for old-halo clusters with (B-R)/(B+V+R)&bolrov;0.85 [(a) and (b)] and young-halo clusters [(c) and (d)]. The open and filled circles in (c) and (d) show clusters with (B-R)/(B+V+R)&menrov;0.32 and (B-R)/(B+V+R)>0.32, respectively. Other notation is the same as in Fig. 2.

Spatial Distribution

     Figure 6 shows the spatial distributions of the two groups selected according to HB color. We can see that the old-halo clusters are appreciably concentrated toward the Galactic center, and their distribution is enclosed by a circle of radius &rovn;9 kpc in the YZ plane. In the projection onto the Galactic plane, a circle of the same radius describes only the half of the space nearest to the Sun, whereas the more distant half-space is free of clusters. This asymmetry can hardly be due to exces-sive extinction near the Galactic center, since disk and young-halo clusters, as well as more distant clusters of the old-halo subsystem, are observed in these locations. On the whole, this problem requires more detailed anal-ysis, and we will not consider it further here.

     The squares in Figs. 6a and 6b indicate clusters that lie well beyond the central concentration for this group, but are within the radius of the young-halo population, as shown in Figs. 6c and 6d. The circles in Figs. 6c and 6d indicate clusters located at Galactocentric distances &bolrov;20 kpc. The distribution of young-halo clusters in the YZ plane fits well inside a circle of radius r&rovn;19 kpc. The clusters occupy a much smaller area in the XY plane, and their distribution can be described by an elongated figure with semi-axes equal to 18 and 10 kpc (which to some extent can be considered a Galactocen-tric ellipse). The semi-minor axis is perpendicular to the Z axis and makes an angle of about 30o to the X axis. Interestingly, the clusters of the Galactic corona have a somewhat similar distribution. This is partially (within 40 kpc) visible in Figs. 2c, 2d, 6c, and 6d. It also fol-lows from Table 2 that the size of the young-halo sub-system in the Z direction substantially exceeds its sizes in the X and Y directions, which are approximately equal to each other.

Fig. 7.—Distributions of height above the Galactic plane for (a) thick-disk, (b) old-halo, and (c) young-halo clusters. The curves are exponential least-squares approximations of the corresponding distributions.

Scale Heights of the GC Subsystems

     Figure 7 shows |Z| distributions for thick-disk, old-halo, and young-halo clusters. The curves are exponen-tial least-squares fits:

n(Z)=Ce-Z/ZO

where Z0 is the scale height. We similarly computed the scale lengths X0 and Y0. The corresponding values for all the GC subsystems are listed in Table 2..

GC Horizontal Branch Colors

     Let us return once more to the boundary separating the GC population into the old and young halo sub-systems. For comparison, different symbols in Figs. 6c and 6d show young-halo clusters, which we further subdivided into two color groups separated by (B?R)/(B+V+R)=0.32. This is not an arbitrarily boundary: tests showed that it precisely corresponds to an Oosterhoff-type dichotomy in the clusters (red and blue clusters correspond to types I and II, respectively). It is clear from these figures that these intermediate-color sub-groups have similar spatial distributions, and apparently both belong to the young halo. To test this conclu-sion and refine the position of the boundary separating the old and young halos, we analyzed the dependence of the HB color on other cluster parameters. The corresponding diagrams are shown in Fig. 8. (Here, the five distant GCs shown by squares in Figs. 6a and 6b are included in the young-halo population.)

Fig. 8.—Relations between GC parameters and the horizontal-branch color index. The open circles correspond to the old halo, filled circles to the young halo (large filled circles correspond to clusters with (B?R)/(B+V+R)>0.32), and filled triangles to the corona.

     Comparison of the positions of the points in the first diagram demonstrates that the degree of concentration toward the Galactic center does change abruptly at the value (B?R)/(B+V+R)=0.85 separating the young and old halo populations. Moreover, some clusters with (B?R)/(B+V+R)>0.32 in Fig. 8b have apogalactic orbital radii appreciably exceeding those for redder clusters (and even exceeding the size of the young-halo subsystem). It is evident from Fig. 8d that the velocity dispersion for this group is also higher than for the old halo. [Note that, logically, clusters with Ra>20 kpc should be assigned to the corona (see below); however, we have not done this because of the high probability of substantial errors in the orbital elements.] In addition, the clusters of this subgroup, whose average age is 15.3 Gyr (virtually the same as that of the old halo in Table 2), have a very low age dispersion of only σt=0.5±0.2 Gyr (Fig. 8c). The fact that these clusters also have approx-imately the same metallicities ([Fe/H]=-1.93Б0.10, see Fig. 3a) and eccentricities (e=0.62±0.05) suggests that most are members of a homogeneous group, and must have been captured simultaneously by the Galaxy. The figures also show that the greatest distances (exceeding the size of the old halo), smallest ages (younger than that of the young halo), and highest velocities (higher than those for the old halo) are found for clusters located near the boundary (B?R)/(B+V+R)=0.85. As a result, we assigned all clusters with intermediate-type HBs and distant clusters (R>10 kpc) with extreme HB colors to the young-halo subsystem.

     For now, we consider the most distant clusters (R&bolrov;20. kpc) to be a separate group, which we tentatively call the Galactic "corona". We can see from Table 2 that the corona clusters differ significantly from the clusters of all the other subsystems in both the spatial volume they occupy and their physical parameters. We will attempt to interpret these differences below.

Fig. 9.—Kinematic diagrams for (a) old-halo, (b) young-halo, and (c) corona clusters. Notation is the same as in Fig. 4.

Rotation of the Halo Subsystems

     The kinematic diagrams in Fig. 9 show that all the halo subsystems differ dramatically in their rotational velocities. The parameters V rot and sV are given in Table 2. The old halo exhibits a fairly well-defined (at the 1.7s level) prograde rotation whose parameters agree reasonably well with those derived by other authors (see, e.g., [3], where Vrot=74±39 km/s and σV=129±19 km/s). Such a low rotational velocity for this subsystem (almost half that for the disk) is consistent with its spherical shape.

     The diagram in Fig. 9b indicates retrograde rotation of the young halo and a rather high velocity dispersion (Table 2). The substantial deviation of the regression line from the coordinate origin suggests inhomogeneity of this system. It appears that the rotation of the system about the Z axis must be not entirely axially symmetric. The flattening of the young halo along an axis that does not coincide with the Z axis could only come about as the result of a chance coincidence of the orbital inclinations of clusters whose origin is not related to that of the protogalaxy. The most plausible hypothesis seems to be that these clusters have an extragalactic origin, and were captured one after another as the Galaxy (with some definite orientation) crossed regions of cluster concentration. The enormous prograde rotational velocity of the corona, together with its relatively low σV and the large deviation of the line in Fig. 8c from the origin, also testify to an extragalactic origin for the corona clusters. The prograde rotation of this group is beyond question, since it follows from Table 2 that Vrot differs from zero by more than σ.

Fig. 10.—Dependence of cluster metallicity on (a) Galactocentric distance and (b) distance from the Galactic plane. The filled and open circles correspond to the young and old halos, respectively, and the straight lines are the corresponding rms regressions. The small square shows the old-halo cluster excluded from computations based on a 3σ criterion.

Metallicity Gradients

     The different symbols in Fig. 10 indicate clusters of the old and young halos. The solid and dashed straight lines are rms regression fits based on the data for GCs of the young and old halo, respectively. The corresponding metallicity gradients are given in Table 2. For the old halo, we computed both gradients excluding NGC 288 (indicated by a square in all diagrams), which is both the most metal-rich and the most distant cluster in the group. It follows from Fig. 10 and Table 2 that the old-halo subsystems all have the same values of corresponding gradients. Moreover, the gradients in the two directions coincide within the errors in all the subsystems. Our result for the young halo is at variance with Zinn's (1993) conclusion that this GC group exhibits no radial metallicity gradient. The discrepancy is due to our different cluster subsystem selection criteria: Zinn (1993) included neither the group of distant (R>10 kpc), metal-poor clusters with HB color parameters 0.32&menrovn;(B?R)/(B+V+R)&menrovn;1 nor the group of the most metal-rich halo clusters with ?1.0<(B?R)/(B+V+R)<0.32, which (being the extreme points in the diagrams) deter-mine to a considerable degree the gradients for this sub-system. Our results thus show that, at all Galactocentric distances, the young-halo clusters are, on average, ~0.3 dex richer in metals than old-halo clusters. The most extended group ? the corona ? exhibits no gradients in either direction.

Fig. 11.—Galactocentric distance dependences of the physical parameters of globular clusters. Notation is the same as in Fig. 3. The straight line in (a) is the rms regression. The large circles in (b) show mean masses within narrow R intervals, and the solid lines show the rms regression fits for thick-disk and old-halo (left) and young-halo and corona (right) clusters. The dashed lines in (c) and (d) are upper and lower envelopes drawn by eye.

Physical Parameters

     It is immediately apparent from an analysis of Table 2 that all the mean physical parameters of the corona clusters differ radically from those for the other groups. This group is the most distant, and therefore we should check whether the parameters exhibit any Galactocentric trends. If they do, this large difference in parameters could simply reflect changes of the internal structure of clusters with Galactocentric distance. Figure 11 shows relationships between some physical parameters and Galactocentric distance. Van den Bergh (1991) showed that, on average, the cluster sizes increase with Galactocentric distance, and obey the relation &forml3; within 40 kpc. The new distance scale and refined angular sizes of GCs confirm that this relation remains valid even for the most distant clusters. The direct rms regression line in (logR, logrh ) in Fig. 11 has a slope of 0.44±0.04, in satisfactory agreement with the relation given by van den Bergh (1991). The approximately constant scatter along the entire regression line indicates that the cluster sizes reduced to the solar Galactocentric distance with van den Bergh's (1991) formula &forml4; are roughly the same for all subsystems. In other words, the large observed radii of the corona clusters are in no way indicative of a different origin.

     It follows from Table 2 that, on average, the corona clusters have the smallest masses. We can see from Fig. 11b that the GC masses indeed decrease as the distance increases from 10?120 kpc. However, the opposite relation is found for nearby clusters: the cluster masses slightly increase with Galactocentric distance. The large circles in the diagrams show the mean masses for narrow R intervals, making this pattern immediately apparent. The relationship becomes even more conspicuous if we recall that R=10 kpc is near the boundary of the old halo, and analyze the massdistance relations separately for the disk and old-halo groups (open symbols in the diagram), on the one hand, and for the young-halo and corona groups (filled symbols), on the other hand.

     The fact that the mean mass of the more distant old-halo clusters in Table 2 exceeds that of clusters belonging to the more compact thick-disk subsystem is enough for us to conclude that the selected groups show different trends. The first two groups, whose clusters are genetically associated with the Galaxy, exhibit a small, positive, radial mass gradient, whereas the GCs in the two other groups, which purportedly have an extragalactic origin, exhibit a very strong, negative, radial mass gradient (see the direct rms regression lines in the diagram).

     Table 2 indicates that the corona GCs have the lowest densities. These reflect the overall trend in the R-log&ro; diagram, with a negative gradient for the internal cluster density. In this sense, the corona clusters are linked to the other clusters through a common relation (the dashed lines in Fig. 11c are upper and lower envelopes drawn by eye). According to Table 2 and Fig. 11d, the central concentration also monotonically decreases with Galactocentric distance. Thus, of the four physical parameters considered, only the cluster mass is independent of distance and exhibits somewhat different Galactocentric trends in the subsystems lying inside and outside the solar radius.

Fig. 12—Age dependences of the physical parameters of globular clusters. Notation is the same as in Fig. 11. The dashed lines are envelopes drawn by eye.

Cluster Ages

     It follows from Figs. 3b and 8c that the cluster ages are strongly correlated with two main parameters-metallicity and HB-morphology index. It is therefore of interest to analyze how other parameters depend on age. The corresponding diagrams are shown in Fig. 12. Three diagrams have nonzero correlation coefficients. In this figure, we reduced the cluster radii to the solar Galactocentric radius in accordance with the relation of van den Bergh (1991), thereby removing the Galactocentric distance trend in cluster size. Figure 12a shows that the reduced cluster radii exhibit no age dependence. The radii of clusters of all ages are confined to the interval 1<r*h<6 pc. Only a few clusters of the young halo and corona populations have larger sizes. In the t-logM/M&sun;) diagram, the cluster masses clearly grow with age, with a correlation coefficient of r=0.4±0.1. This may suggest that old clusters live longer; however, this is inconsistent with the complete lack of young, massive clusters.

     Likewise, it is evident from Figs. 12c, 12d that old clusters have, on average, higher densities and more prominent central cores (the correlation coefficients are 0.5±0.1 and 0.2±0.1, respectively). No young clusters with similar parameters are known. At the same time, no objects with low mass, density, and central concentration can be found among the oldest clusters. The same pattern is demonstrated by corresponding parameters in all the GC subsystems. The parameters of individual clusters of a given age exhibit a rather large scatter, whatever subsystem they belong to.

     It appears that, of all the parameters considered, mass is the only one that remains constant from the time of cluster formation and is independent of the position of the cluster in the Galaxy. If we suppose that some clusters are genetically unrelated to the Galaxy and have been captured, we must conclude that, throughout the entire Local Group of galaxies, the most massive GCs formed first, and younger clusters formed later from gas and dust clouds of ever decreasing mass.

Cluster Classification

     Let us briefly summarize the criteria used to assign GCs to particular subsystems. The thick-disk sub-system is made up of metal-rich clusters with [Fe/H]&bolrovn;-1.0, marked "1" in Table 1. The four metal-rich GCs lying outside the volume occupied by disk clusters probably belong to the young halo (they are marked "3(1)" in Table 1) (The number of the subsystem to which the cluster would have been assigned according to the basic criterion (in our case, metal-licity) is given in parentheses.) Extremely blue, metal-rich clusters with (B?R)/(B+V+R)&bolrovn;0.85 form the old halo ("2"). Extremely blue GCs located outside the spherical volume occupied by the old-halo subsystem are assumed to belong to the young halo ("3(2)"). All metal-poor clusters with red and intermediate-color HBs make up the young halo ("3"). GCs of unknown metallicity (or HB color) are either unclassified or tentatively assigned to some subsystem according to the parameter in parentheses.

     The GC classification into subsystems proposed here must be considered only tentative. We tried to identify primarily pure examples of members of the thick-disk and old-halo populations in order to reliably determine the characteristic parameters of these subsystems (and vice versa). Burkert and Smith (1997) showed that thick-disk GCs do not form a homogeneous group, and can be divided into three discrete subgroups according to their mass and kinematics. Each of the subsystems identified here (especially, the young halo) appears to have a fairly complex structure and requires further study.

Fig. 13.—The (a) metallicity and (b) age distributions of the globular clusters of Galactic origin. Different shadings are used to show the thick-disk and old-halo clusters. The curves are Gaussian fits to the corresponding histograms.

Fig. 14.—Age dependences of (a) metallicity, (b) Galactocentric distance, and (c) distance from the Galactic plane for the globular clusters of Galactic origin. Notation is the same as in Fig. 3. The dashed lines are rms regression fits for both subsystems taken together, and the solid lines are the individual regression fits for each subsystem. The squares indicate clusters excluded from the regression solutions according to a 3σ criterion.

5. CONCLUSIONS. A SCENARIO FOR GALACTIC EVOLUTION

     Thus, analysis of astrophysical data from recent accurate observations confirms earlier conclusions that the Galactic globular-cluster population is inhomogeneous. The thick-disk and old-halo subsystems identified here based on their heavy-element abundances and HB colors also differ markedly in the size and shape of the spatial volume they occupy, their kinematics, and their orbital elements. The combined metallicity function of the two subsystems is a superposition of two more or less equal normal distributions separated by a gap &delt;[Fe/H]&rovn;0.2 (Fig. 13a). The age distribution of the same clusters also forms two virtually non-overlapping Gaussians (Fig. 13b).

     It follows from Fig. 13b that the age dispersion for the halo clusters is nearly equal to the error in the ages themselves, (σt )halo=0.8±0.2 Gyr. The disk-cluster ages exhibit a much larger scatter, (σt )disk=1.4±0.3 Gyr. In other words, the halo clusters formed almost simultaneously, whereas the corresponding processes in the disk required at least several billion years. The age gap between subsystems, if any, might be swamped by the errors in the estimated ages.

     Figure 14 shows the age dependences of the metallicity, Galactocentric distance, and distance from the Galactic plane for the two subsystems considered. The straight lines in these plots are individual rms regression fits for each of the subsystems and for the Galactic GC sample as a whole. The correlation coefficients indicate that at least the first two dependences for the entire sample are real (r=0.8±0.1, 0.6±0.1, and 0.3�.2, respectively). Separately, the thick-disk subsystem exhibits no age?metallicity correlation (r=0.3±0.3), whereas the old-halo population, in spite of its narrow age spread, shows a weak dependence (r=0.4±0.2) with a slope that is close to that for the entire sample. Galactocentric distances are completely uncorrelated with age in the old halo (r=0.1±0.3). However, the corresponding dependence in the disk proved to be rather significant (r=0.7±0.2) and in agreement with that for the Galaxy as a whole (Fig. 14b). An interesting pattern can be seen in Fig. 14c, which shows an abrupt jump in |Z| between the subsystems rather than an age dependence for cluster height above the Galactic plane, with virtually no correlation within each subsystem.

     Analysis of these patterns suggests the following scenario for the early evolution of our Galaxy. The first globular clusters formed when the protogalactic cloud had already collapsed to the size of the modern Milky Way, RGC&rovn;12 kpc. (It remains unclear, however, whether the slightly reddened, metal-poorest old GCs at distances R=15?25 kpc belong to the old halo.) The old-halo subsystem formed over a short time interval, making it impossible to confidently identify age trends in either cluster size or metallicity. The radial and vertical metallicity gradients in this oldest known Galactic subsystem provide evidence that the first heavy-element enrichment of the gasdust medium took place before the clusters of this subsystem formed, and that this enrichment was more active near the Galactic center. (Note that the clusters maintain the orbits of their parent protoclouds. Evidence for the absence of relaxation is provided, in particular, by the existence of a large number of fairly old and simultaneously very distant clusters in the young halo.)

     Both the spatial and chemical characteristics change abruptly as we move to the thick-disk subsystem. The formation of stars in these two subsystems was apparently separated by a substantial time lag, which shows up only as a gap in the age distributions. This time lag enabled the gas and dust clouds to become appreciably enriched in heavy elements (which had time to mix) and to collapse to much smaller sizes before the new generation of globular clusters began to form. As a result, a rather flat, metal-rich, thick-disk subsystem formed. This subsystem acquired a much higher rotational velocity and much lower velocity dispersion compared to the old halo. Neither the mean metallicity nor the thickness of the thick disk changed with time. Star formation in the protoclouds of the clusters of this subsystem began at the largest Galactocentric distances, then began to propagate toward the center. The appreciable collapse of the protodisk cloud after the formation of the halo subsystem resulted in an increase of the rotational velocity and a rapid flattening of the future subsystem. Apparently, the interstellar medium did not undergo deep mixing in the process, since we observe a strong, negative vertical metallicity gradient with virtually no radial gradient in this subsystem.

     In other words, our analysis suggests that there was a rapid collapse of the gas?dust medium toward the Galactic plane with simultaneous heavy-element enrichment and partial homogenization, which took place mainly during the period between the formation of the old-halo and thick-disk subsystems. This scenario requires further refinement, since the quality of current observational data is insufficient to enable a deeper understanding of the processes within each subsystem of Galactic globular clusters during its formation.

     The young-halo and corona subgroups are made up of clusters (or proloclusters) captured by the Galaxy from the intergalactic medium in various stages of its evolution. They differ from subsystems genetically associated with the Galaxy primarily in the volume they occupy. For example, the sizes of the young halo and the corona are factors of two and ten larger than that of the old halo. Note also the very large uncertainty in our rotational velocities of the subsystems and the great radial velocity dispersions. The separation of these clusters into two subgroups is somewhat arbitrary, and we have done this only to demonstrate the extreme inhomogeneity of the spatial?kinematic structure of the member clusters. It would be more correct to represent the two subgroups as a single subsystem consisting of clusters randomly captured by the Galaxy, which could be called the "outer halo."

ACKNOWLEDGMENTS

     This study was supported by the Russian Foundation for Basic Research (project no. 00-02-17689).

REFERENCES

E-Mail:marsakov@ip.rsu.ru