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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.

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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.