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.     

Peculiar velocities of galaxies and clusters

We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both non-linear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with exponential wings. The model is easily extended to study how the statistic depends on the type of particle used to trace the velocity field (dark matter particles, dark matter haloes, galaxies), and on the density of the environment in which the test particles are located. Comparisons with simulations suggest that our model is accurate. We also show that the evolution of the peculiar velocities depends on the local, rather than the global, density. Since clusters populate denser regions on average, using cluster velocities with the linear theory scaling may lead to an overestimate of the global value of Ω₀. Conversely, using linear theory with the global value of Ω₀ to scale cluster velocities from the initial to the present time results in an underestimate of their true velocities. In general, however, the directions of motions of haloes are rather well described by linear theory. Our results help to simplify models of redshift-space distortions considerably.     

The formation and evolution of clusters of galaxies in different cosmogonies

The formation of galaxy clusters in hierarchically clustering universes is investigated by means of high-resolution N -body simulations. The simulations are performed using a newly developed multimass scheme which combines a PM code with a high-resolution N -body code. Numerical effects resulting from time-stepping and gravitational softening are investigated, as well as the influence of the simulation box size and of the assumed boundary conditions. Special emphasis is laid on the formation process and the influence of various cosmological parameters. Cosmogonies with massive neutrinos are also considered. Differences between clusters in the same cosmological model seem to dominate over differences caused by differing background cosmogony. The cosmological model can alter the time evolution of cluster collapse, but the merging pattern remains fairly similar, e.g. the number of mergers and the mass ratio of mergers. The gross properties of a halo, such as its size and total angular momentum, also evolve in a similar manner for all cosmogonies, and can be described using analytical models. It is shown that the density distribution of a halo shows a characteristic radial dependence which follows a power law with a slope of =1 at small radii and =3 at large radii, independent of the background cosmogony or the considered redshift. The shape of the density profiles follows the generic form proposed by Navarro et al. for all hierarchically clustering scenarios, and retains very little information about the formation process or the cosmological model. Only the central matter concentration of a halo is correlated with the formation time and therefore the corresponding cosmogony. We emphasize the role of non-radial motions of the halo particles in the evolution of the density profile.     

Velocity dispersion estimates of APM galaxy clusters

We present 83 new galaxy radial velocities in the field of 18 APM clusters with redshifts between 0.06 and 0.13. The clusters have Abell identifications and the galaxies were selected within 0.75  h ⁻¹ Mpc in projection from their centres. We derive new cluster velocity dispersions for 13 clusters using our data and published radial velocities.
We analyse correlations between cluster velocity dispersions and cluster richness counts as defined in Abell and APM catalogues. The correlations show a statistically significant trend although with a large scatter, suggesting that richness is a poor estimator of cluster mass irrespectively of cluster selection criteria and richness definition. We find systematically lower velocity dispersions in the sample of Abell clusters that do not fulfil APM cluster selection criteria, suggesting artificially higher Abell richness counts owing to contamination by projection effects in this subsample.     

Ram pressure stripping the hot gaseous haloes of galaxies in groups and clusters

We use a large suite of carefully controlled full hydrodynamic simulations to study the ram pressure stripping of the hot gaseous haloes of galaxies as they fall into massive groups and clusters. The sensitivity of the results to the orbit, total galaxy mass, and galaxy structural properties is explored. For typical structural and orbital parameters, we find that ∼30 per cent of the initial hot galactic halo gas can remain in place after 10 Gyr. We propose a physically simple analytic model that describes the stripping seen in the simulations remarkably well. The model is analogous to the original formulation of Gunn & Gott, except that it is appropriate for the case of a spherical (hot) gas distribution (as opposed to a face-on cold disc) and takes into account that stripping is not instantaneous but occurs on a characteristic time-scale. The model reproduces the results of the simulations to within ≈10 per cent at almost all times for all the orbits, mass ratios, and galaxy structural properties we have explored. The one exception involves unlikely systems where the orbit of the galaxy is highly non-radial and its mass exceeds about 10 per cent of the group or cluster into which it is falling (in which case the model underpredicts the stripping following pericentric passage). The proposed model has several interesting applications, including modelling the ram pressure stripping of both observed and cosmologically simulated galaxies and as a way to improve present semi-analytic models of galaxy formation. One immediate consequence is that the colours and morphologies of satellite galaxies in groups and clusters will differ significantly from those predicted with the standard assumption of complete stripping of the hot coronae.     

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.     

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or the hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error ≲0.3 per cent, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses  ∼10¹⁵ M_⊙  , the effect of the gravitomagnetic term is ≲0.04 per cent on strong lensing estimates and ≲0.5 per cent in the weak-lensing analyses. The total kinematic effect on the mass estimate is then ≲1 per cent, which is negligible in current statistical studies. In the weak-lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow, in principle, a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current technological capabilities.     

Clustering of galaxy clusters in cold dark matter universes

We use very large cosmological N -body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model ( τ CDM) and a flat low density model with a cosmological constant (ΛCDM). Our simulations each use 10⁹ particles to follow the mass distribution within cubes of side 2  h ⁻¹ Gpc ( τ CDM) and 3  h ⁻¹ Gpc (ΛCDM) with a force resolution better than 10⁻⁴ of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from     for samples with mean separation     to     for samples with     The lower value here corresponds to τ CDM and the upper to ΛCDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10 per cent using the simple model of Sheth, Mo & Tormen. This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the automated plate measurement (APM) cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for ΛCDM. The observed power spectrum (for a cluster sample of mean separation     ) lies significantly above the predictions of both models.     

X-ray clusters of galaxies in conformal gravity

We run adiabatic N -body/hydrodynamical simulations of isolated self-gravitating gas clouds to test whether conformal gravity, an alternative theory to general relativity, is able to explain the properties of X-ray galaxy clusters without resorting to dark matter. We show that the gas clouds rapidly reach equilibrium with a density profile which is well fitted by a β-model whose normalization and slope are in approximate agreement with observations. However, conformal gravity fails to yield the observed thermal properties of the gas cloud: (i) the mean temperature is at least an order of magnitude larger than the observed and (ii) the temperature profiles increase with the square of the distance from the cluster centre, in clear disagreement with real X-ray clusters. These results depend on a gravitational potential whose parameters reproduce the velocity rotation curves of spiral galaxies. However, this parametrization stands on an arbitrarily chosen conformal factor. It remains to be seen whether a different conformal factor, specified by a spontaneous breaking of the conformal symmetry, can reconcile this theory with observations.     

Adiabatic scaling relations of galaxy clusters

The aim of this work is to show that, contrary to popular belief, galaxy clusters are not expected to be self-similar, even when the only energy sources available are gravity and shock-wave heating. In particular, we investigate the scaling relations between mass, luminosity and temperature of galaxy groups and clusters in the absence of radiative processes. Theoretical expectations are derived from a polytropic model of the intracluster medium and compared with the results of high-resolution adiabatic gasdynamical simulations. It is shown that, in addition to the well-known relation between the mass and concentration of the dark matter halo, the effective polytropic index of the gas also varies systematically with cluster mass, and therefore neither the dark matter nor the gas profiles are exactly self-similar. It is remarkable, though, that the effects of concentration and polytropic index tend to cancel each other, leading to scaling relations whose logarithmic slopes roughly match the predictions of the most-basic self-similar models. We provide a phenomenological fit to the relation between polytropic index and concentration, as well as a self-consistent scheme to derive the non-linear scaling relations expected for any cosmology and the best-fitting normalizations of the M – T , L – T and F – T relations appropriate for a Λ cold dark matter universe. The predicted scaling relations reproduce observational data reasonably well for massive clusters, where the effects of cooling and star formation are expected to play a minor role.     

Enhanced mergers of galaxies in low-redshift clusters

An ensemble cluster has been formed from a data set comprising a complete magnitude-limited sample of 680 giant galaxies  ( M ⁰ _B ≲−19)  in eight low-redshift clusters, normalized by the velocity dispersions and virial radii for the early-type cluster populations. Distinct galaxy populations have been identified, including an infall population. A majority (50–70 per cent or greater) of the infall population are found to be in interacting or merging systems characterized by slow gravitational encounters. The observed enhancement of galaxy–galaxy encounters in the infall population compared to the field can be explained by gravitational shocking. It is shown that disc galaxy mergers in the infall population integrated over the estimated lifetime of the cluster (∼10 Gyr) can readily account for the present cluster S0 population.