On the initial cluster mass distribution inferred from synthesis models

In this contribution we examine the problem of inferring ages and initial cluster masses from synthesis models at the limit of low-mass clusters (M≤ a few ×10⁴ M_⊙). We show that it is not possible to apply directly synthesis models using standard methods to such clusters, since the basic hypothesis implicit in the models (a fixed proportionality between the number of stars in different evolutionary phases) is not fulfilled due to an insufficient number of stars for a reliable sampling of the stellar initial mass function. The consequence of this incomplete sampling is a non-Gaussian distribution of the mass–luminosity relation for clusters that share the same evolutionary conditions (age, metallicity and stellar initial mass distribution function). We review some tests, that can be performed before the start of the analysis, to estimate if the observed cluster can be analyzed with synthesis models following traditional procedures (like χ ² minimization) or if it is necessary make use of synthesis models in a probabilistic framework. Finally, we show the implications of these results for estimating the low-mass tail in the initial cluster mass distribution function.     

The Substellar Population in the Young σ Orionis Cluster, Spatial Distribution

We review different surveys, in the optical and infrared, conducted in the very young (age 1–8 Myr), nearby (d ～ 350 pc) σ Orionis cluster aimed to characterize the substellar population. We describe spectral characteristics of very low mass stars, brown dwarfs and planetary mass objects in the cluster with spectral types from K7 to T6. We study the spatial distribution of the substellar population detected in a IZJ survey covering an area of 1.12 deg.² We find that the radial distribution of substellar objects can be well fitted by an exponential law (ρ = ρ_o e ^?r/ro ), with a central density (ρ _o ) of 0.26 ± 0.03 objects/arcmin² and a characteristic radius (r _o) of 8.8 arcmin ± 0.6 (equivalent to 0.90 ± 0.06 pc at the distance of the cluster). We discuss the presence of possible inhomogeneities in this distribution due to the existence of subclustering. We also compare the spatial distribution of the substellar population with previously known stars in the cluster. We report the initial mass spectrum in the substellar domain.     

Surveying the Local Supercluster Plane

We investigate the distribution and velocity field of galaxies situated in a band of 100 by 20 degrees centered on M87 and oriented along the Local supercluster plane. Our sample amounts 2158 galaxies with radial velocities less than 2000 km s^?1. Of them, 1119 galaxies (52%) have distance and peculiar velocity estimates. About 3/4 of early-type galaxies are concentrated within the Virgo cluster core, most of the late-type galaxies in the band locate outside the virial radius. Distribution of gas-rich dwarfs with M_HI >M_* looks to be insensitive to the Virgo cluster presence. Among 50 galaxy groups in the equatorial supercluster band 6 groups have peculiar velocities about 500–1000 km s^?1 comparable with virial motions in rich clusters. The most cryptic case is a flock of nearly 30 galaxies around NGC4278 (Coma I cloud), moving to us with the mean peculiar velocity of ?840 km s^?1. This cloud (or filament?) resides at a distance of 16.1 Mpc from us and approximately 5 Mpc away from the Virgo center. Galaxies around Virgo cluster exhibit Virgocentric infall with an amplitude of about 500 km s^?1. Assuming the spherically symmetric radial infall, we estimate the radius of the zero-velocity surface to be R₀ = (7.0±0.3) Mpc that yields the total mass of Virgo cluster to be (7.4 ± 0.9)× 10¹⁴M_⊙ in tight agreement with its virial mass estimates. We conclude that the Virgo outskirts does not contain significant amounts of dark mater beyond its virial core.     

The mass distribution in the galaxy cluster Abell 2744

The mass distribution for the galaxy cluster Abell 2744 (z = 0.308) is investigated on the base of the archival X-ray data of the Chandra observatory. The temperature of the hot gas in the cluster (kT = 9.82_−0.41^+0.43 keV) and the cluster total mass (M ₂₀₀ = 2.22_−0.12^+0.13 × 10¹⁵ M _⊙) for the radius R ₂₀₀ = 2.38_−0.31^+0.36 Mpc are estimated. The density and mass profiles for the intergalactic gas and dark matter are obtained. The fractions of the intergalactic gas and dark matter in the total mass of the cluster are 15.4_−1.3^+1.3% and 84.6_−1.3^+1.4%, respectively.     

Westerlund 1: bound or unbound?

The Galactic open cluster Westerlund 1 (Wd 1) represents the ideal local template for extragalactic young massive star clusters, because it is currently the only nearby young cluster with a mass of ～10⁵?M_⊙. Its proximity makes spatially resolved studies of its stellar population feasible, and additionally permits direct comparison of its properties with measurements of velocity dispersion and dynamical mass for spatially unresolved extragalactic clusters. Recently, we published the dynamical mass estimate based on spectra of four red supergiants. We have now identified six additional stars which allow a determination of radial velocity from the wavelength covered in our VLT/ISAAC near-infrared spectra (CO bandhead region near 2.29 μm), significantly improving statistics. Using a combination of stepping and scanning the slit across the cluster center, we covered an area which included the following suitable spectral types: four red supergiants, five yellow hypergiants, and one B-type emission-line star. Our measured velocity dispersion is 9.2 km?s^?1. Together with the cluster size of 0.86 pc, derived from archival near-infrared SOFI-NTT images, this yields a dynamical mass of 1.5×10⁵ M_⊙. Comparing this to the mass derived via photometry, there is no indication that the cluster is currently undergoing dissolution.     

On the lifetimes of galactic clusters

From the observed age distribution of galactic clusters within 1 kpc we deduce that the typical total lifetime of a galactic cluster is about 2×10⁸ yr. The individual lifetimes vary between 10⁸ and 10¹⁰ yr. The observed lifetimes are compared with the evaporation times which are found from numerical experiments with star cluster models. These models contain up to 250 stars with a realistic mass spectrum. The effect of the galactic tidal field is taken into account and enhances the rate of escape significantly. Escapers are identified by using the Jacobian integral. We give the evaporation time in years as a function of the median radius for different values of the total mass of a cluster. The agreement between the resulting theoretical lifetimes and the observed values is sufficiently good. We estimate that the tidal field of passing interstellar clouds should be in most cases less efficient in dissolving a galactic cluster than the internal evaporation process combined with the effect of the general galactic field.     

Intermediate-mass black holes in globular clusters

The mass of central bodies in a number of Milky-Way globular clusters is estimated based on the stellar radial-velocity dispersion data. It is assumed that stars located close to the center of the cluster (i.e., to the black hole) rotate about it, have masses on the order of the solar mass, and that the mass of the gravitating center is greater by a factor of 1000. The radial velocities of stars in the vicinity of cluster centers are analyzed for two hypothetical extreme cases: (1) ordered orbital motion of stars about the gravitating center and (2) chaotic orbital motions. The masses inferred for most of the clusters (10²–10⁴ M _⊙) correspond to intermediate-mass black holes. Another important result of this study consists in the determination of the quantity l, the characteristic scale length of the additional spatial dimension. Given the age and mass of the globular cluster NGC 6397 we estimate l to be between 0.02 and 0.14 mm.     

Astrometry of the Open Cluster M25

The young open star cluster M25 (IC 4725) is located in the direction of the galactic center, near much irregular absorption features on Sagittarius arm. This system is found to be at a distance of 600 pc, with a median age of 9.45 × 10⁷ years and a distance from the galactic plane of –52.82 pc The mass data available in the literature has been gathered and many statistical methods have been applied for this cluster. Depending only on these methods, the stellar density, the distribution of dark matter, the luminosity and the mass functions have been estimated. The center of the cluster has been defined, it is shifted by 45 arc sec in the northeast direction. The radius of the cluster is found to be 4 pc. More than 220 stars with mean reddening of 0.50 mag and absorption of 1.62mag are found inside this aria. The total mass of the cluster has been estimated with the mass of the interstellar matter (gas and dust). It is found to be 1937 M _⊙, whereas about 24% of the material mass of the cluster has remained as interstellar matter after the processes of formation. This revised version was published online in July 2006 with corrections to the Cover Date.     

How do binaries affect the derived dynamical mass of a star cluster?

The dynamical mass of a star cluster can be derived from the virial theorem, using the measured half-mass radius and line-of-sight velocity dispersion of the cluster. However, this dynamical mass may be a significant overestimation of the cluster mass if the contribution of the binary orbital motion is not taken into account. Here, we describe the mass overestimation as a function of cluster properties and binary population properties, and briefly touch on the issue of selection effects. We find that for clusters with a measured velocity dispersion of σ _los?10 km?s^?1 the presence of binaries does not affect the dynamical mass significantly. For clusters with σ _los?1 km?s^?1 (i.e., low-density clusters), the contribution of binaries to σ _los is significant, and may result in a major dynamical mass overestimation. The presence of binaries may introduce a downward shift of Δlog?(L _V /M _dyn)=0.05–0.4 (in solar units) in the log?(L _V /M _dyn) versus age diagram.     

Physical properties of X-ray gas in galaxy cluster CL0024+17

We analyzed the X-ray data obtained by the Chandra telescope for the galaxy cluster CL0024+17 (z = 0.39). The mean temperature of the cluster is estimated (kT = 4.35 _?0.44 ^+0.51 keV) and the surface brightness profile is derived. We generated the mass and density profiles for dark matter and gas using numerical simulations and the Navarro-Frenk-White dark matter density profile (Navarro et al., 1995) for a spherically symmetric cluster in which gas is in hydrostatic equilibrium with the cluster field. The total mass of the cluster is estimated to be M ₂₀₀ = 3.51 _?0.47 ^+0.38 × 10 _Sun ¹⁴ within a radius of R ₂₀₀ = 1.24 _?0.17 ^+0.12 Mpc of the cluster center. The contribution of dark matter to the total mass of the cluster is estimated as ${{M_{200_{DM} } } \mathord{\left/ {\vphantom {{M_{200_{DM} } } {M_{tot} }}} \right. \kern-0em} {M_{tot} }} = 0.89$ .     

Analysis of the properties of clusters of galaxies in the region of the Ursa Major supercluster

We analyze the properties of the clusters of galaxies in the region of the Ursa Major (UMa) supercluster using observational data from SDSS and 2MASS catalogs. The region studied includes a supercluster (with a galaxy and cluster overdensity of 3 and 15, respectively) and field clusters inside the 150-Mpc diameter surrounding region. The total dynamical mass of 10 clusters of galaxies in UMa is equal to 2.25 × 10¹⁵ M _⊙, and the mass of 11 clusters of galaxies in the UMa neighborhood is equal to 1.70 × 10¹⁵ M _⊙. The fraction of early-type galaxies brighter than M _K ^* + 1 in the virialized regions of clusters is, on the average, equal to 70%, and it is virtually independent on the mass of the cluster. The fraction of these galaxies and their average photometric parameters are almost the same both for UMa clusters and for the clusters located in its surroundings. Parameters of the clusters of galaxies, such as infrared luminosities up to a fixed magnitude, the mass-to-luminosity ratio, and the number of galaxies have almost the same correlations with the cluster mass as in other samples of galaxies clusters. However, the scatter of these parameters for UMa member clusters is twice smaller than the corresponding scatter for field clusters, possibly, due to the common origin of UMa clusters and synchronized dynamical evolution of clusters in the supercluster.     

Structure of clusters with bimodal distribution of galaxy line-of-sight velocities III: A1831

We study the A1831 cluster within the framework of our program of the investigation of galaxy clusters with bimodal velocity distributions (i.e., clusters where the velocities of subsystems differ by more than Δ _cz ∼ 3000 km/s).We identify two subsystems in this cluster: A1831A (cz = 18970 km/s) and A1831B (cz = 22629 km/s) and directly estimate the distances to these subsystems using three methods applied to early-type galaxies: the Kormendy relation, the photometric plane, and the fundamental plane. To this end, we use the results of our observations made with the 1-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences and the data adopted from the SDSS DR6 catalog. We confirmed at a 99% confidence level that (1) the two subsystems are located at different distances, which are close to their Hubble distances, and (2) the two subsystems are located behind one another along the line of sight and are not gravitationally bound to each other. Both clusters have a complex internal structure, which makes it difficult to determine their dynamical parameters. Our estimates for the velocity dispersions and masses of the two clusters: 480 km/s and 1.9 × 10¹⁴ M _⊙ for A1831A, 952 km/s and 1.4 × 10¹⁵ M _⊙ for A1831B should be views as upper limits. At least three spatially and kinematically distinct groups of galaxies can be identified in the foreground cluster A1831A, and this fact is indicative of its incomplete dynamical relaxation. Neither can we rule out the possibility of a random projection. The estimate of the mass of the main cluster A1831B based on the dispersion of the line-of-sight velocities of galaxies is two-to-three times greater than the independent mass estimates based on the total K-band luminosity, temperature, and luminosity of the X-ray gas of the cluster. This fact, combined with the peculiarities of its kinematical structure, leads us to conclude that the cluster is in a dynamically active state: galaxies and groups of galaxies with large line-of-sight velocities relative to the center of the cluster accrete onto the virialized nucleus of the cluster (possibly, along the filament directed close to the line of sight).     

Proper motion Pleiades candidate L‐type brown dwarfs

We present results of an optical and near‐infrared (IR) 1.8 deg² survey in the Pleiades open cluster to search for substellar objects. From optical I ‐band images from the CFHT and J ‐band images from the 3.5m CAHA Telescope, we identify 18 faint and very red L brown dwarf candidates, with I > 20.9 and I – J > 3.2. The follow‐up observations of nine objects in the H ‐ and K _s‐bands confirm that eight belong to the IR sequence of the cluster and the proper motion measurements of seven candidates confirm that they are Pleiades members. A preliminary estimation of the substellar mass spectrum dN/ dM in the form of a power law M c^–α provides α = +0.57 ± 0.14. We extrapolate this function to estimate the number of planetary mass objects that could be present in the cluster down to 1 M_Jup. Sensitive searches combining far red and near‐IR observations may unveal these objects in a near future. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Possible dark matter in spiral galaxies of the coma cluster

The relationship between the rotation curves for the galaxies and the distribution of mass and angular momentum within the galaxies is examined. The theory of angular momentum transfer is applied to the observed properties of the galaxies. The coupling between the dynamical mass of a spiral galaxy and its luminosity is studied. Most of the spiral galaxies in subclusters surrounding NGC 4889, NGC 4874, and NGC 4839 in the Coma cluster are galaxies that have lower luminosities, with M_B fainter than −21^m.5. These galaxies are characterized by a higher mass-to-luminosity ratio than that of the galaxies with higher luminosities M_B brighter than −21^m.5, which suggests the presence of a large fraction of dark matter in the spiral galaxies of the subclusters. Translated from Astrofizika, Vol. 52, No. 1, pp. 75–84 (February 2009).     

Clues to Substellar Formation: Rotation and the Low-Mass End of the Initial Mass Function

We have monitored S Ori 45, a young, low-mass (20 M _j up) brown dwarf of the σ Orionis cluster (～3 Myr, 352 pc), using optical and near-infrared filters. S Ori 45 (spectral type M8.5) is found to be multi-periodic with a dominant modulation at 2.5–3.5 h, and a short modulation at about 46 min. We ascribe the longer of these modulations to a rotation period. After comparing these results with observations of more massive cluster brown dwarfs and field brown dwarfs, we conclude that substellar objects present rotational and angular momentum evolution. We have also obtained intermediate-resolution near-infrared spectroscopy of S Ori 70, which is a T-class, free-floating planetary candidate member in the σ Orionis cluster. Its observed spectrum has been compared to data of field brown dwarfs of similar types and to theoretical spectra computed for different surface temperatures and gravities. We conclude that S Ori 70 has a significantly cool, low-gravity atmosphere. This supports the young age of this object and its membership in the cluster. From state-of-the-art evolutionary models, the mass of S Ori 70 is estimated at 3 times the Jovian mass (⁺⁵ _?2 M _j up), challenging current stellar/substellar formation models. S Ori 70 remains the lowest mass object so far identified in any open cluster.     

Parameters of oscillation generation regions in open star cluster models

We determine the masses and radii of central regions of open star cluster (OCL) models with small or zero entropy production and estimate the masses of oscillation generation regions in clustermodels based on the data of the phase-space coordinates of stars. The radii of such regions are close to the core radii of the OCL models. We develop a new method for estimating the total OCL masses based on the cluster core mass, the cluster and cluster core radii, and radial distribution of stars. This method yields estimates of dynamical masses of Pleiades, Praesepe, and M67, which agree well with the estimates of the total masses of the corresponding clusters based on proper motions and spectroscopic data for cluster stars.We construct the spectra and dispersion curves of the oscillations of the field of azimuthal velocities v _φ in OCL models. Weak, low-amplitude unstable oscillations of v _φ develop in cluster models near the cluster core boundary, and weak damped oscillations of v _φ often develop at frequencies close to the frequencies of more powerful oscillations, which may reduce the non-stationarity degree in OCL models. We determine the number and parameters of such oscillations near the cores boundaries of cluster models. Such oscillations points to the possible role that gradient instability near the core of cluster models plays in the decrease of the mass of the oscillation generation regions and production of entropy in the cores of OCL models with massive extended cores.     

Mass of Galaxies in Pairs

We have compared the frequency distribution of the dynamical observedquantity log (V _z ² r _p), for a sample of 46 pairs of elliptical galaxies, to the distribution of this quantity obtained from numerical simulations of pairs of galaxies. From such an analysis, where we have considered the structure of the galaxies and its influence in the orbital evolution of the system, we have obtained the characteristic mass and the mass-luminosity ratio for the sample. Our results show that the hypothesis of point-mass in elliptical orbits is, for this sample, an approximation as good as the model that takes into account the structure of the galaxies. The statistical method used here gives an estimate of a more reliable mass, it minimizes the contamination of spurious pairs and it considers adequately the contribution of the physical pairs. We have obtained a characteristic mass to the 46 elliptical pairs of 1.68 × 10¹² ± 7.01 ×10¹¹ M_⊙ with M/L = 17.6 ± 7.3 (H ₀ = 60 km s^-1Mpc^-1). This revised version was published online in July 2006 with corrections to the Cover Date.     

The empirical upper limit for mass loss of cool main sequence stars

The knowledge of mass loss rates due to thermal winds in cool dwarfs is of crucial importance for modeling the evolution of physical parameters of main sequence single and binary stars. Very few, sometimes contradictory, measurements of such mass loss rates exist up to now. We present a new, independent method of measuring an amount of mass lost by a star during its past life. It is based on the comparison of the present mass distribution of solar type stars in an open cluster with the calculated distribution under an assumption that stars with masses lower than M_lim have lost an amount of mass equal to ΔM. The actual value of ΔM or its upper limit is found from the best fit. Analysis of four clusters: Pleiades, NGC 6996, Hyades and Praesepe gave upper limits for ΔM in three of them and the inconclusive result for Pleiades. The most restrictive limit was obtained for Praesepe indicating that the average mass loss rate of cool dwarfs in this cluster was lower than 6 × 10^–11 M_⊙/yr. With more accurate mass determinations of the solar type members of selected open clusters, including those of spectral type K, the method will provide more stringent limits for mass loss of cool dwarfs. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the detectability of turbulence and bulk flows in X-ray clusters

Coolingflows, cluster mergers, and the motions of galaxies through cluster gas with supersonic and sonic velocities must lead to large scale motions of the intracluster medium (ICM). A high-resolution numerical simulation of X-ray cluster formation by Norman and Bryan (1999) predicts cluster-wide turbulence with ν_turb ≈300–600 km s^?1 and eddy scales l_outer ≈100–500 kpc, the larger numbers being characteristic of turbulence near the virial radius, while the smaller numbers pertain to the core. The simulation also predicts the existence of ordered bulk flows in the core with v≈400 km s^?1 on scales of several hundred kpc. In this paper, we consider the observability of such fluid motions via the distortions they induce in the CMB via the kinematic SZ effect, as well as via Doppler broadening and shifting of metal lines in the X-ray spectrum. We estimate |ΔT/T|_kinematic?6—at or below current limits of detectability. However, we find that an energy resolution of a few eV is sufficient to detect several Doppler shifted components in the 6.7 keV Fe line in the cluster core.     

Black hole at the center of the globular cluster M15: Estimation of the mass and specific angular momentum

Using the technique of determining the sum of the masses of double stars, we have estimated the mass of the central object in the globular cluster M15. The radial velocities of stars at distances up to 1″ from the cluster center have been used. The parameters of circular orbits and the space velocities of 11 selected field stars relative to the cluster center have been determined from the calculated velocity dispersions with respect to the mean radial velocity. Based on the mean space velocity V, 14 km s^?1, and using the energy integral, we have estimated the mass of the central object to be within the range (1?9) × 10³ M _⊙. We have estimated the kinetic power of the outflow of matter from the region surrounding the black hole in M15 and the specific angular momentum of the black hole.