Integrated luminosity distribution of Galactic open clusters

The integrated magnitudes of 221 Galactic open clusters have been used to derive the luminosity function. The completeness of the data has also been discussed. In the luminosity distribution the maximum frequency of clusters occurs nearI (M_v) = −3 _m ^. 5, and some plausible reasons for a sharp cut-off atI (M_v) = −2^m. 0 have been discussed. It is concluded that the paucity of the clusters fainter thanI (M _v) = −2 _m ^.0 is not purely due to selection effects. The surface density of the clusters for different magnitude intervals has. been obtained using the completeness radius estimated from the logN- logd plots. A relation betweenI (M^v) and surface density has been obtained which yields a steeper slope than that obtained by van den Bergh & Lafontaine (1984).     

Dynamics of very rich open clusters

The oldest open clusters in our Galaxy set the lower limit to the age of the Galactic Disk (9–10 Gyr). Although they appear to be very rich now, it is clear that their primordial populations were much larger. Often considered as transitional objects, these populous open clusters show structural differences with respect to globular clusters so their dynamics and characteristic evolutionary time scales can also be different. On the other hand, their large membership lead to different dynamical evolution as compared with average open clusters. In this paper, the differential features of the evolution of rich open clusters are studied using N-body simulations, including several of the largest (10⁴ stars) published direct collisional N-body calculations so far, which were performed on a CRAY YMP. The disruption rate of rich open clusters is analysed in detail and the effect of the initial spatial distribution of the stars in the cluster on its dynamics is studied. The results show that cluster life-time depends on this initial distribution, decreasing when it is more concentrated. The effect of stellar evolution on the dynamical evolution of rich clusters is an important subject that also has been considered here. We demonstrate that the cluster's life-expectancy against evaporation increases because of mass loss by evolving high-mass stars. This revised version was published online in July 2006 with corrections to the Cover Date.     

Examination of the Association between Quasars and Abell Clusters on All Sky

Using the Hewitt-Burbidge QSO Catalogue (1993) and all-sky catalogue of Abell clusters (ACO, 1989) at the region |b| > 40^° we analyze the cross correlation function and find anti-correlation between them at angular separations 3^° < θ < 10^° , which is mainly caused by optical-selected QSOs, rather than radio-selected QSOs. There is no such anti-correlation between QSOs and Abell clusters at smaller separations θ < 3^°. Considering that this phenomenon may be caused by different characters of the objects, we further estimate the correlation function with various subsamples. We find that the correlation is independent of the redshift of QSOs, but depends upon the type of Abell clusters: for the D ≤ 4 clusters there is an obvious tendency of overdensity of quasars at 0^° < θ < 5^°; around the R ≥ 2 Abell clusters there is about an 18.7% deficit of quasars in the region 3^° < θ < 7^°. K-S Test shows the overdensity or deficit of quasars around different types of clusters cannot be explained by the projection effect of background quasars. We get the enhancement factor of quasar overdensity (for D ≤ 4 clusters) q =1.13, and the extinction magnitude factor of QSO deficiency (for R ≥ 2 clusters) Av= 0.14. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cluster-scale magnetic fields

The search for non thermal radio emission from clusters of galaxies is a powerful tool to investigate the existence of magnetic fields on such large scale. Unfortunately, such observations are scarce thus far, mainly because of the very faint large scale radio emission expected in clusters of galaxies. In the present contribution we will first review the status of the radio observations of clusters of galaxies, carried out with the aim of detecting large scale radio emission.We will then focus on the large scale radio emission detected at 327 MHz and 610 MHz in the Coma cluster of galaxies. The features of the detected radio emission suggest that a magnetic field with an intensity of the order of ~ 10^–7 Gauss must be present on a scale of about 2 Mpc (forH _o = 100km s ^–1 Mpc ^–1). The morphology of the radio emission is similar to that of the most recent X-ray images derived with ROSAT, and follows the distribution of the galaxies in the cluster. All these pieces of information will be taken into account in the discussion on the possible origin of this large scale magnetic field.     

The two components in the distribution of sunspot groups with respect to their maximum areas

From an analysis of the distribution of sunspot groups with respect to their maximum areas we find that this distribution consists of two distinct components. One component contributes to spot groups of all possible values of A_* with a distribution density varying as ∼ exp (b₁ á _* ^1/2 ) with b₁ nearly constant from cycleto cycle and having a mean value ∼10^-4 km^-1. The other component is predominantly responsible for spot groups withA* ≲, 30 *10^-6 hemisphere but may provide a few spot groups even above 50 * l0^-6 hemisphere. This component may follow a distribution density ∼ exp (-b₂ A_*). We also determine the widths of the latitude zones over which spot groups in various intervals of A_* appear and study their variation with time. These widths and their variations indicate that the two statistical samples of spot groups may be produced by two families of flux-tube clusters as suggested earlier in a phenomenological model. Very thin flux-tube clusters in the statistical samples seem to be related to the ephemeral active regions and X-ray bright points.     

The system of old clusters in the magellanic clouds

IntegratedUBV colours have been computed for synthetic clusters older than one billion years and for two chemical composition: (a)Y=0.30;Z=10^–4 and (b)Y=0.30;Z=10^–2, taking into account the contribution to the integrated light of Main Sequence, subgiant, red giant and horizontal branch stars. It has been found that integrated colours depend onZ and allow an estimate of the metal content, however not generally. Horizontal branch stars contribute to the integrated colours of clusters not significantly and the contribution of stars in more advanced phases (e.g., asymptotic branch stars) is almost negligible.Old clusters in LMC and SMC have been studied in terms of colour calibrations and this analysis has been supplemented, when possible, by photometric and spectroscopic data of individual stars. It was found that in the LMC clusters withZ=10^–2 andt>5×10⁹ yr are lacking, clusters with relatively blue colours are similar, both in age and chemical composition, to the halo galactic globular clusters. Moreover, there is a group of clusters with 1×10⁹t5×10⁹. In the SMC clusters withZ=10^–2 andt>5×10⁹ yr are lacking and clusters with 1×10⁹t5×10⁹ are rare. Clusters with relatively blue colours are interpreted with the following parameters:t=5×10⁹ yr, 10^–4Z10^–3 andY=0.20.The implication of these results on the chemical history of the two galaxies is discussed.     

Anisotropy in the Hubble relation for the brightest galaxies in clusters

The sky distribution of deviations from the mean Hubble relation for the brightest galaxies in clusters is non-random for the velocity range 4000<V _r<25 000 km s^–1. Deviations in visual magnitude are mainly positive in one large region of the sky and mainly negative in another region; the difference between the regions is 0.37±0.08 ^m and is independent of colour. Various explanations are discussed briefly, and galactic or intergalactic absorption may be excluded.     

A new estimate of the galactic halo mass based on the kinematics of globular clusters

We calculated the energy distribution function for globular clusters in our Galaxy, using the inversion procedure first suggested by Eddington. If the halo mass distribution is of the formM _H=r ^1.21, then the observed data on the velocity dispersion of F-clusters can be explained, resulting an enclosed mass of 4.3×10¹¹ M within a galactocentric radius of 33 kpc.     

On the existence of cosmological evolutionary effects

Parameters of the distant galaxy clusters of 3C295 (z=0.46) and Cl 0024+1654 (z=0.39) are compared with the predictions made using galaxies of the local clusters Coma (z=0.023) and DC 0329–52 (z=0.057) taking theK-effect into account. The distributions of colour and morphological type, and the amplitudesF ⁺/F^– of the ₀ 4000 discontinuity are examined and no evidence for evolution of the galaxies and the clusters can be seen.     

Age distribution of open clusters as a function of their linear diameter and age-dependence of cluster masses

From the well-observed data of star clusters, the age distribution of galactic clusters is obtianed as a function of their linear diameter and it is concluded that the observed age distribution of clusters for different linear diameter intervals within 1500 pc, is not seriously affected by the selection effects. If we assume that the rate of formation of clusters is constant, the lifetimes _1/2 of the clusters for different linear diameter intervals have been obtained and it is found that the clusters with a linear diameter in the range 0–1.9 pc have longer lifetimes than the clusters having linear diameters larger than 2.0 pc.Total masses of 57 clusters have been obtained using the catalogues of Piskunov (1983) and Myakutinet al. (1984). A study of age-dependence of cluster masses, based on the total masses of the clusters obtained in the present study and the cluster masses given by Bruch and Sanders (1983) and Lynga (1983b), shows that there is a decreasing trend in the total mass with the age, however, there is an increasing trend after the age of about 10⁸ yr. It is also concluded that the initial rate of formation of rich clusters was relatively higher than the present rate of formation.     

Dark matter-systematics of its distribution

The dynamical masses of dwarf-spheroidals, spiral and elliptical galaxies, dwarf irregular binaries, groups of galaxies and clusters are shown to lie in a band about the M ∼ ρR³ line. The value of ρ is approximately the same as that estimated for unseen matter in the solar neighbourhood. The clusters themselves lie about theM ∼ R ^-3 line derived for a self-gravitating neutrino gas; their masses are distributed around the maximum Jeans-mass, M_Jmax. corresponding to m_v - 10 eV in an expanding universe. The present day length scales of clusters and the dispersion in the velocities observed within them are understood in terms of a 100-fold expansion subsequent to the initial growth of the fluctuations at M_Jmax. These systematics on theR-M plane imply that the initial condensations in the expanding universe are on the scale of the rich clusters of galaxies, these condensations were triggered dominantly by the gravitation of the neutrinos and the constant density of al systems arises naturally due to the embedding of these systems in the large scale neutrino condensations. If the neutrino density falls off asr ^-2 beyond the cluster edge till the distributions from different clusters overlap, then the mean density of the neutrinos approximately equals the closure density of the universe.     

A calculation of structural parameters of spherical stellar systems by means of characteristic functions method. I. Theory

To calculate structural parameters of stellar systems such as an effective radius and central space (or surface) density, the method of characteristic functions is suggested. The characteristic function of the system is a Fourier image of their normalized space density profile f₃(r). In the case of spherical symmetry the probability distribution of r (Q₃(r) = (3/a³)r²f₃(r)) and its orthogonal projections have the same characteristic functions. This fact is used to calculate the effective radii of a few star cluster models (King law, Plummer model and Gausian profile). It is shown, that the characteristic function for King law clusters tends to a finite generalised function if the concentration parameter c is large. The expression for the effective radius (at c ≫ 1) is given. The formula of the effective radius in the Plummer model as well as the relation between the one-dimensional central velocity dispersion and the root mean square velocity are obtained. It is shown, that in the Gaussian model and for King law clusters the effective radius (half-mass visual radius) can differ from the effective (harmonic) radius a few times. This fact should be taken into account in estimating the mass-to-light ratio from the virial mass of such systems using the King radius.     

The x-ray luminosity function of galaxy clusters

From published data on X-ray sources identified with clusters of galaxies the X-ray luminosity function of the clusters was derived to ϕ_x ˜ L_x^-0.8 in the range 10⁴³ ≦ L_x ≦ (2–3) · 10⁴⁵ ergs/s. For L_x > 3 · 10⁴⁵ ergs/s the function decreases abruptly.     

Abell 851: Are we looking at the beginning of a merging process?

We present an XMM observation of the moderately distant (z=0.41)galaxy cluster CL 0939+4713 (Abell 851), an exceptionally rich cluster. The formation and evolution of clusters depends sensitively on cosmological parameters like the mean matter density in the universe Ο_m. Therefore it is important to determine the dynamical state of clusters at different redshifts, i.e. at different evolutionary states. The X-ray morphology alone is not the best indicator of the dynamical state, but it should be complemented with all other information available, e.g. the temperature map or the galaxy distribution. The combination of all findings gives a detailed picture of the state of a cluster. This analysis, of this relatively distant cluster, can be used as a basis for comparisons at lower and higher redshifts. The capability of XMM to perform spatially resolved spectroscopy can be used also to determine the distribution of the metal abundances. Not only the overall value of metallicity but also its spatial distribution gives important indications on the metal enrichment processes. The X-ray image shows pronounced substructure. There are two main subclusters which have also some internal structure. This is an indication that the cluster is a dynamically young system. This conclusion is supported by the temperature distribution: a hot region is found between the two main subclusters indicating that the cluster is in the process of a major merger, in which the two subclusters will probably collide in a few hundreds of Myr. The intra-cluster gas of CL 0939+4713 shows variations of the metal abundances. The optically richer subcluster has a somewhat higher metallicity. This finding together with the absence of post-starburst galaxies in this region gives interesting hints on the metal enrichment processes favouring recent enrichment processes like ram-pressure stripping or tidal stripping. Throughout this paper we use H ₀ =50 km s^-1Mpc^-1 and q ₀ =0.5; all errors are 90% confidence levels. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structure of clusters with bimodal distribution of radial velocities of galaxies. IV: A1569

We report the results of study of the A1569 cluster (12 ^h 36^m.3, +16°35′) and the neighboring A1589 cluster (12 ^h 41^m.3, +18°34′), making up a pair (a supercluster) with a projected size of about 10Mpc. This study is done within the framework of our program for investigating the galaxy clusters with bimodal velocity distributions (i.e., clusters where the velocities of subsystems differ by more than Δcz ∼ 3000 km/s). In the A1569 cluster we have identified two subsystems: A1569A (cz = 20613 km/s) and A1569B (cz = 23783 km/s). These subsystems have the line-of-sight velocity dispersions of 484 km/s and 493 km/s, and dynamic masses within the R ₂₀₀ radius equal to 1.8 × 10¹⁴ and 2.0 × 10¹⁴ M _⊙, respectively. We directly estimate the distances to these subsystems using three methods applied to earlytype galaxies: the Kormendy relation, photometric plane, and fundamental plane. To this end, we use the results of our observations made with the 1-m telescope of the SAO RAS and the data adopted from the SDSS DR7 catalog. We found that A1569 consists of two independent clusters. The A1569B cluster is located at the Hubble distance corresponding to its radial velocity. The A1569A cluster has a peculiar velocity of −1290 ± 630 km/s, which can be explained by the effect of the more massive A1589 cluster (with a mass of 7.9 × 10¹⁴ M _⊙) and of the supercluster where it resides. In all the four bimodal clusters that we studied within the framework of our program, A1035, A1775, A1831, and A1569, the subsystems are independent clusters lying close to the Hubble relation between redshift and distance.     

Structures in the large-scale distribution of galaxies with different luminosities

The large-scale structures of volume-limites subsample sorted out from the CfA catalog have been analysed by percolation method. The result shows that the features in the distribution of galaxies with different luminosities are significantly different. Especially, the most luminous galaxies are likely to exhibit hierarchical clustering on a scale about 50h ₅₀ ^–1 Mpc, and the least luminous galaxies in our subsamples show string-like or sheet-like character in their distribution. These results suggest that the large-scale distribution of galaxies consists of clusters or cluster cores of most luminous galaxies and the less luminous galaxies spread out from these cores with a string-like or sheet-like structure. This picture of the large-scale distribution consists with previous results from two-point correlation analysis and fractal analysis. The implication of these results has been discussed.     

Cosmic strings and the formation of clusters of galaxies

The relation between the mean separationd of clusters of galaxies and their mean richnessN is found to be well represented byd=3.4N ^2/3. Both this observed result and the Bahcall-Soneira relation(that is, the spatial correlations of clusters of galaxies are increased with their richness) are well explained by the cosmic string picture, lending support to the cosmic-string theory.     

Untersuchungen über den Aufbau offener Sternhaufen

From strip counts in 20 open star clusters the characteristic parameters of their structure are derived. At the boundaries of the clusters the relative potential amounts to 0.32 on the average. The effective mean distance of the stars from the centre of the cluster introduced by SCHWARZSCHILD corresponds nearly to the radius of the cluster. The counts in two clusters allow to continue the cumulative mass functions up to Mv ≈ 8, and their exponential convergence is used for the determination of the cluster masses. The same has been done for the Pleiades and seven clusters according to the counts of VAN DEN BERGH and SHER . The mean velocities and the mean periods of revolution T of the cluster stars are of the order 0.90 km/s and 12 · 10⁶ years respectively. Between the latter and the mean (mass) density the relation T ≈≈ 20 · 10⁶ is valid. During 1 · 10⁹ years the mean cluster loses 50% of its stars by relaxation.     

Distances to 24 Galaxies in the Direction of the Virgo Cluster and a Determination of the Hubble Constant

To study the spatial distribution of galaxies lying between the Virgo cluster and the Local Group, a search was made for probable nearby galaxies. Using the method of brightest stars and of blue and red supergiants made it possible to determine the distances to 24 galaxies, among which six relatively nearby galaxies were identified. The results of the distance determinations showed that the maximum in the number distribution of galaxies lies at 17.0 Mpc, which we take as the distance to the Virgo cluster. Using the difference between the distance moduli of two clusters of galaxies, in Virgo and Coma Berenices, from literature sources and the velocity of the latter cluster, we determined the Hubble constant to be H ₀ = 77 ± 7 km·sec^–1·Mpc^–1.     

Schmidt plate survey in the galactic centre direction. 1. Investigation of open clusters in the Sagittarius-Carina spiral arm

A study of four open clusters on Tautenburg Schmidt plates in the direction to the Galactic Centre (l = 17.0°, b = +0.8°) is presented. In a field of 8.95 square degrees proper motions and B, V magnitudes were determined for about 36 500 stars up to the limiting magnitudes B = 17^m.9, V = 16^m.8. For stars brighter than B = 16^m an accuracy of about 3 mas/year has been estimated for proper motions. The rms errors of stellar magnitudes and (B—V) colours is about 0.1 mag. There are two open clusters already known in this sky area: Trumpler 32 (C 1814-133) and NGC 6611 (C 1816-138). By the inspection of the plates two additional anonymous clusters were identified near the double star ADS 11285 or BD −14°5014 (C 1819-146) and near the star BD −14°5016 (C 1820-146). The cluster membership determination was carried out using information on spatial and proper motion distributions of stars in the field. The colour-magnitude diagrams up to the limiting stellar magnitude were constructed. For each cluster interstellar extinction A_V, diameters of the core and corona, ages and spatial velocity components (V, W) relative to the LSR in the Y, Z-galactic directions were derived. The distances to the clusters were obtained to 1720 pc, 2260 pc, 2130 pc and 2130 pc for Trumpler 32, NGC 6611, C 1819-146 and C 1820-146, respectively. All clusters are situated in the Sagittarius-Carina spiral arm. Their spatial location confirms the assumption that galactic spiral arms are close to logarithmic spirals with a characteristic angle of about 20 degrees.