Modelling rich clusters of galaxies

We develop a self-consistent dynamical model for spherically-symmetric clusters of galaxies. The total mass profile and velocity dispersion profiles of galaxies are derived by taking both, galaxies and intracluster gas, in hydrostatic equilibrium, and by assuming the latter to follow a polytropic distributionT^–1. We use the strongest and better established correlations among observed properties of clusters to fix the values of the resulting free parameters, and so, to reduce the general freedom of the model.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Orientation of first-ranked galaxies in rich clusters

We present new evidence that first ranked galaxies are aligned with their parent cluster and with the direction of the nearest neighbour cluster (scale 15h ^–1 Mpc). The effect is stronger for cD and gE galaxies than for first-ranked galaxies of later type. The relevance of this result for different galaxy formation scenarios is discussed. In hierarchical clustering scenarios like the cold dark matter theory, galactic halos and clusters of galaxies are expected to have moderate asphericity. We present some numerical results of an on-going study of the dissipationless collapse of moderately aspherical systems. Our results indicate that the central part of the collapsed and virialized system does show the large scale elongation imposed by the initial conditions. It is pointed out that this may have important implications also for the properties of disk galaxies in dark halos.     

Photometric evolution of galaxies in rich clusters: Numerical simulations

This paper briefly presents a numerical code which simulates the evolution of galaxies belonging to rich clusters. The evolutionary model considers both, cluster dynamics and galaxy photometry, taking into account the galaxy-cluster interactions (collisional stripping, merging and ram-pressure stripping by the ICM) and the intrinsic galaxy evolution. We use different initial mass distributions for galaxies and we briefly discuss the influence of the initial segregation in mass on the evolution of the photometrical properties.Paper presented at the 11th European Regional Astronomical Meetings of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in the light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes, which provide a good fit to large numerical simulations; (3) more accurate mass–temperature relations from larger catalogues of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multiparameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on σ ₈, the normalization of the matter power spectrum on scales of 8  h ⁻¹ Mpc, as a function of the matter density and cosmological constant in a universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the normalization, approximately independent of power spectrum shape, can be expressed as constraints on σ at an appropriate cluster normalization scale R _Cl. We provide fitting formulas for R _Cl and σ ( R _Cl) for general cosmologies, as well as for σ ₈ as a function of cosmology and shape parameter Γ. For flat models we find approximately σ ₈≃(0.495_−0.037^+0.034)Ω_M^−0.60 for Γ=0.23, where the error bar is dominated by uncertainty in the mass–temperature relation.     

The power spectrum of rich clusters of galaxies on large spatial scales

We present an analysis of the redshift-space power spectrum, P ( k ), of rich clusters of galaxies based on an automated cluster catalogue selected from the APM Galaxy Survey. We find that P ( k ) can be approximated by a power law, P ( k )∝ kⁿ , with n ≈−1.6 over the wavenumber range 0.04< k <0.1 h Mpc⁻¹. Over this range of wavenumbers, the APM cluster power spectrum has the same shape as the power spectra measured for optical and IRAS galaxies. This is consistent with a simple linear bias model in which different tracers have the same power spectrum as that of the mass distribution, but shifted in amplitude by a constant biasing factor. On larger scales, the power spectrum of APM clusters flattens and appears to turn over on a scale k ∼0.03 h Mpc⁻¹. We compare the power spectra estimated from simulated APM cluster catalogues with those estimated directly from cubical N -body simulation volumes, and find that the APM cluster survey should give reliable estimates of the true power spectrum at wavenumbers k ≳0.02 h Mpc⁻¹. These results suggest that the observed turnover in the power spectrum may be a real feature of the cluster distribution, and that we have detected the transition to a near-scale-invariant power spectrum implied by observations of anisotropies in the cosmic microwave background radiation. The scale of the turnover in the cluster power spectrum is in good agreement with the scale of the turnover observed in the power spectrum of APM galaxies.     

Measurement of dwarf galaxies in the rich clusters Abell 665 and 963 at z=0.2

We show that the luminosity functions of the distant rich clusters Abell 665 ( z =0.182) and Abell 963 ( z =0.206) are flat or gradually rising down to M_R =−14, with α≈−1.2±0.4 [here α is the logarithmic slope of the luminosity function: φ( L )∝ L ^α at the faint end]. We do not confirm the steep luminosity functions (α≤−1.8) that have been recently proposed for these two clusters.
Several technical points are discussed in detail. In particular, we compute the corrections to the background contamination caused by gravitational lensing from the cluster dark matter, and show that the corrections are small unless we wish to determine variations in the luminosity function on small scales.
Recent observations have also shown that the field galaxy luminosity function at z ≈0.2 is also shallow between M_B =−19 and M_B =−13. Abell 665 and 963 are two of the richest clusters known at that redshift. We therefore propose that the galaxy luminosity function might be universal in this magnitude range at z =0.2.
The dwarf galaxies that we see in Abell 665 have a colour distribution that is strongly peaked at B − R =1.9. We compute K -corrections based on the spectral energy distributions of local galaxies, and show that these are probably dwarf spheroidal galaxies. This might suggest that the dwarf spheroidal population observed in Virgo already existed at z =0.2.     

Double galaxies in galactic clusters

We have identified 127 galactic pairs in six of Abell's rich galactic clusters. We have established positive correlations between certain parameters of the components of the pairs. We conclude that, despite the gravitational influence of other members of the cluster, a subsystem of double galaxies exists in rich clusters as a structural element of these structures.Translated fromAstrofizika, Vol. 37, No. 3, 1994.The author is grateful to L. V. Mirzoyan and A. R. Petrosyan for helpful remarks.     

Cooling flows in clusters of galaxies

Summary X-ray images and spectra of clusters of galaxies show strong evidence for cooling flows. In many clusters, the hot gas in the core is cooling at rates of 100Myr^–1 and greater. Few traces of the cooled gas have been observed, but it probably forms into low-mass stars (perhaps brown dwarf or even Jupiter-mass objects). X-ray surface-brightness profiles show that the cooling gas is highly inhomogeneous. Overdense gas cools rapidly to form cooled clumps distributed throughout the flow, with little of the gas ever reaching the cluster centre. Cooled and cooling clumps are disrupted because of their motion relative to the remainder of the gas, tending to produce small cooled fragments and, ultimately, low-mass stars. Large molecular clouds, which are the sites of massive star formation in our galaxy, do not occur in the outer parts of cooling flows. There is evidence of larger gas clumps and the formation of more massive stars in the central few kpc of some cooling flows. It is argued that cooling flows efficiently form dark matter. This has wider implications for the formation of dark matter in massive galaxies.     

Probing galactic dark matter in dense environments: on the strong lensing efficiency of galaxies in rich clusters

The recent detection by Limousin et al. of five new strong lensing events dominated by galaxy cluster members in Abell 1689, and outside the critical regime of the cluster itself, offers a way to obtain constraints on the cluster mass distribution in a region inaccessible to standard lensing analysis. In addition, modelling such systems will provide another window on the dark matter haloes of galaxies in very dense environments. Here, it is shown that the boost in image separation due to the external shear and convergence from a smooth cluster component means that more numerous, less massive galaxies have the potential to create multiple images with detectable separations, relative to isolated field galaxies. This comes in addition to a potential increase in their lensing (source plane) cross-section. To gain insight into the factors involved and as a precursor to a numerical study using N -body simulations, a simple analytic model of a cluster at   z = 0.3  lensing background galaxies at   z = 2  is considered here. The fiducial model has cluster members with isothermal density profiles and luminosities L , distributed in a Schechter function (faint-end slope  ν=−1.25  ), related to their velocity dispersions σ via the Faber–Jackson scaling L ∝σ⁴. Just outside the critical regime of the cluster, the scale of galaxy-dominated image separations is significantly increased. Folding in the fact that less massive galaxies present a lower lensing cross-section, and that the cross-section can itself be enhanced in an external field leads to a factor of a few times more detected events relative to field galaxies. These values will be higher closer to the critical curve. Given that the events in Abell 1689 were detected over a very small region of the cluster where ACS data were available, this motivates the search for such events in other clusters.     

Supersonic motions of galaxies in clusters

We study motions of galaxies in galaxy clusters formed in the concordance Λ cold dark matter cosmology. We use high-resolution cosmological simulations that follow the dynamics of dark matter and gas and include various physical processes critical for galaxy formation: gas cooling, heating and star formation. Analysing the motions of galaxies and the properties of intracluster gas in a sample of eight simulated clusters at z = 0, we study the velocity dispersion profiles of the dark matter, gas and galaxies. We measure the mean velocity of galaxy motions and gas sound speed as a function of radius and calculate the average Mach number of galaxy motions. The simulations show that galaxies, on average, move supersonically with the average Mach number of ≈1.4, approximately independent of the cluster-centric radius. The supersonic motions of galaxies may potentially provide an important source of heating for the intracluster gas by driving weak shocks and via dynamical friction, although these heating processes appear to be inefficient in our simulations. We also find that galaxies move slightly faster than the dark matter particles. The magnitude of the velocity bias,   b _v ≈ 1.1  , is, however, smaller than the bias estimated for subhaloes in dissipationless simulations. Interestingly, we find velocity bias in the tangential component of the velocity dispersion, but not in the radial component. Finally, we find significant random bulk motions of gas. The typical gas velocities are of order ≈20–30 per cent of the gas sound speed. These random motions provide about 10 per cent of the total pressure support in our simulated clusters. The non-thermal pressure support, if neglected, will bias measurements of the total mass in the hydrostatic analyses of the X-ray cluster observations.