F. Mardirossian

Optical Mass Estimates of Galaxy Clusters

We evaluate in a homogeneous way the optical masses of 170 nearby clusters (z ≤ 0.15). The sample includes both data from the literature and the new ESO Nearby Abell Clusters Survey (ENACS) data. On the assumption that mass follows the galaxy distribution, we compute the mass of each cluster by applying the virial theorem to the member galaxies. We constrain the masses of very substructured clusters (about 10% of our clusters) between two limiting values. After appropriate rescaling to the X-ray radii, we compare our optical mass estimates to those derived from X-ray analyses, which we compiled from the literature (for 66 clusters). We find a good overall agreement. This agreement is expected in the framework of two common assumptions: that mass follows the galaxy distribution and that clusters are not far from a situation of dynamical equilibrium, with both gas and galaxies reflecting the same underlying mass distribution. We stress that our study strongly supports the reliability of present cluster mass estimates derived from X-ray analyses and/or (appropriate) optical analyses.

The Observational Distribution of Internal Velocity Dispersions in Nearby Galaxy Clusters

We analyze the internal velocity dispersion σ of a sample of 172 nearby galaxy clusters (z ≤ 0.15), each of which has at least 30 available galaxy redshifts and spans a large richness range. Cluster membership selection is based on nonparametric methods. In the estimate of galaxy velocity dispersion, we consider the effects of possible velocity anisotropies in galaxy orbits, the infall of late-type galaxies, and velocity gradients. The dynamical uncertainties due to the presence of substructures are also taken into account. Previous σ-distributions, based on smaller cluster samples, are complete for the Abell richness class R ≥ 1. In order to improve σ completeness, we enlarge our sample by also including poorer clusters. By resampling 153 Abell—Abell-Corwin-Olowin clusters, according to the richness class frequencies of the Edinburgh-Durham Cluster Catalog, we obtain a cluster sample which can be taken as representative of the nearby universe. Our cumulative σ-distribution agrees with previous distributions within their σ completeness limit (σ 800 km s–1). We estimate that our distribution is complete for at least σ ≥ 650 km s–1. In this completeness range, a fit of the form dN ∝ σα dσ gives α = -(7.4–0.8+0.7 in fair agreement with results coming from the X-ray temperature distributions of nearby clusters. We briefly discuss our results with respect to p-distributions for galaxy groups and to theories of large-scale structure formation.

Velocity Dispersions and X-Ray Temperatures of Galaxy Clusters

Using a large and well-controlled sample of clusters of galaxies, we investigate the relation between cluster velocity dispersions and X-ray temperatures of intra-cluster gas. In order to obtain a reliable estimate of the total velocity dispersion of a cluster, independent of the level of anisotropies in galaxy orbits, we analyze the integrated velocity dispersion profiles over increasing distances from the cluster centers. Distortions in the velocity fields, the effect of close clusters, the presence of substructures, and the presence of a population of (spiral) galaxies not in virial equilibrium with the cluster potential are taken into account. Using our final sample of 37 clusters, for which a reliable estimate of the velocity dispersion could be obtained, we derive a relation between the velocity dispersions and the X-ray temperatures, with a scatter reduced by more than 30 % with respect to previous works. A chi square fit to the temperature-velocity dispersion relation does not exclude the hypothesis that the ratio between galaxy and gas energy density (the so-called spectral beta) is a constant for all clusters. In particular, the value of beta=1, corresponding to energy equipartition, is acceptable.

Velocity dispersions in galaxy clusters

We analyze the velocity dispersions of 79 galaxy clusters having at least 30 galaxies with available redshifts. We show that different estimates of velocity dispersion give similar results on cluster samples of at least ∼20 galaxies each. However, only robust estimates of velocity dispersion seem to be efficient on cluster samples with ∼10 galaxies each. A significant correlation is found to exist between the velocity dispersion and the cluster richness. We provide the distribution function of cluster velocity dispersions, normalized to the complete sample by Abell, Corwin, & Olowin (1989). Available theoretical models are compared with this distribution function

The Observational Mass Function of Nearby Galaxy Clusters

We present a new determination of the mass function of galaxy clusters, based on optical virial mass estimates for a large sample of 152 nearby (z ? 0.15) Abell-ACO clusters, as provided by Girardi et al. This sample includes both data from the literature and the new ENACS data. The resulting mass function is reliably estimated for masses larger than Mlim 4 ? 1014 h-1 M?, while it is affected by sample incompleteness at smaller masses. We find N(>Mlim) = (6.3 ? 1.2) ? 10-6 (h-1 Mpc)-3 for cluster masses estimated within a 1.5 h-1 Mpc radius. Our mass function is intermediate between the two previous estimates of Bahcall & Cen and Biviano et al. Based on the Press-Schechter (PS) approach, we use this mass function to constrain the amplitude of the fluctuation power spectrum at the cluster scale. After suitably convolving the PS predictions with observational errors on cluster masses and COBE-normalizing the fluctuation power spectrum, we find ? -->8=(0.60?0.04)?--> 0?0.46 + 0.09?0 for flat low-density models and ? -->8=(0.60?0.04)?--> 0?0.48 + 0.17?0 for open models (at the 90% confidence level).

Optical Substructures in 48 Galaxy Clusters: New Insights from a Multiscale Analysis

We analyze the presence of substructures in a set of 48 galaxy clusters by using galaxy positions and redshifts. The data are taken from literature sources, with the addition of some new data provided by recent observations of galaxy clusters. We use a multiscale analysis that couples kinematical estimators with the wavelet transform. With respect to previous works, we introduce three new kinematical estimators. These estimators parameterize the departures of the local means and/or local dispersions of the measured radial velocities with respect to their global values for the environment. We classify the analyzed clusters as unimodal, bimodal, and complex systems. We find that about 14% of our clusters are strongly substructured (i.e., they are bimodal or complex) and that about 24% of the remaining unimodal clusters contain substructures at small scales. Thus, in substantial agreement with previous studies, about one-third of clusters show substructures. We find that the presence of substructures in unimodal clusters does not affect the estimates of both velocity dispersions and virial masses. Moreover, the galaxy velocity dispersion is generally in good agreement with the X-ray temperature, according to the expectations of the standard isothermal model for galaxy clusters. These facts suggest that unimodal clusters, which are the most frequent cases in the nearby universe, are not too far from a status of dynamical equilibrium. In contrast, the estimates of velocity dispersions and masses for some bimodal or complex clusters strongly depend on whether they are treated as single systems or as sums of different clumps. In these cases the X-ray temperature and the velocity dispersion may be very different.

Optical Luminosities and Mass-to-Light Ratios of Nearby Galaxy Clusters

We analyze a sample of 105 clusters having virial mass homogeneously estimated and for which galaxy magnitudes are available with a well-defined high degree of completeness. In particular, we consider a subsample of 89 clusters with Bj-band galaxy magnitudes taken from the COSMOS/UKST Southern Sky Object Catalog. After suitable magnitude corrections and uniform conversions to Bj band, we compute cluster luminosities L within several clustercentric distances, 0.5, 1.0, 1.5 h-1 Mpc and within the virialization radius Rvir. In particular, we use the luminosity function and background counts estimated by Lumsden et al. on the Edinburgh/Durham Southern Galaxy Catalog, which is the well-calibrated part of the COSMOS catalog. We analyze the effect of several uncertainties connected to photometric data, fore/background removal, and extrapolation below the completeness limit of the photometry, in order to assess the robustness of our cluster luminosity estimates. We draw our results on the relations between luminosity and dynamical quantities from the COSMOS sample by considering mass and luminosities determined within the virialization radius. We find a very good correlation between cluster luminosity, L, and galaxy velocity dispersion, σv, with L ∝ σ. Our estimate of the typical value for the mass-to-light ratio is M/L ~ 250 h M☉/L☉. We do not find any correlation of M/L with cluster morphologies, i.e., Rood-Sastry and Bautz-Morgan types, and only a weak significant correlation with cluster richness. We find that mass has a slight, but significant, tendency to increase faster than the luminosity does, M ∝ L. We verify the robustness of this relation against a number of possible systematics. We verify that this increasing trend of M/L with cluster mass cannot be entirely due to a higher spiral fraction in poorer clusters, thus suggesting that a similar result would also be found by using R-band galaxy magnitudes.

Velocity segregation in galaxy clusters

We have investigated the velocity field of galaxies in clusters. Our sample consists of the 68 clusters with at least 30 galaxies for which redshifts are available in the literature; for 61 of these clusters we were also able to collect most of the galaxy magnitudes. We have unambiguously found that galaxies brighter than the magnitude of third-ranked object, m 3 , have velocities lower than average. These galaxies are preferentially located in the central regions. The effect is not induced by morphological segregation, it is not restricted to cD clusters, and it does not depend on the presence of substructures

New Optical Insights into the Mass Discrepancy of Galaxy Clusters: The Cases of A1689 and A2218

We analyze the internal structures of clusters A1689 and A2218 by applying a recent development of the method of wavelet analysis, which uses the complete information obtained from optical data, i.e. galaxy positions and redshifts. We find that both clusters show the presence of structures superimposed along the line of sight with different mean redshifts and smaller velocity dispersions than that of the system as a whole, suggesting that the clusters could be cases of the on-going merging of clumps. In the case of A2218 we find an acceptable agreement between our estimate of optical virial mass and X-ray and gravitational lensing masses. On the contrary, in the case of A1689 we find that our mass estimates are smaller than X-ray and gravitational lensing ones at both small and large radii. In any case, at variance with earlier claims, there is no evidence that X-ray mass estimates are underestimated.

STRUCTURES IN GALAXY CLUSTERS

The analysis of the presence of substructures in 16 well-sampled clusters of galaxies suggests a stimulating hypothesis: Clusters could be classified as unimodal or bimodal, on the basis of to the sub-clump distribution in the {\em 3-D} space of positions and velocities. The dynamic study of these clusters shows that their fundamental characteristics, in particular the virial masses, are not severely biased by the presence of subclustering if the system considered is bound.The analysis of the presence of substructures in 16 well-sampled clusters of galaxies suggests a stimulating hypothesis: Clusters could be classified as unimodal or bimodal, on the basis of to the sub-clump distribution in the {\em 3-D} space of positions and velocities. The dynamic study of these clusters shows that their fundamental characteristics, in particular the virial masses, are not severely biased by the presence of subclustering if the system considered is bound.