Giant cluster arcs as a constraint on the scattering cross-section of dark matter

We carry out ray tracing through five high-resolution simulations of a galaxy cluster, to study how its ability to produce giant gravitationally lensed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dark matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long ('collisionless') and short ('fluid') mean free path limits. We study the size and shape distributions of arcs and compute the cross-section for producing 'extreme' arcs of various sizes. Even a few collisions per particle modifies the core structure enough to destroy the ability of the cluster to produce long, thin arcs. For larger collision frequencies the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the 'fluid' limit) is able to produce radial arcs; even the case with the smallest scattering cross-section must be scaled to the upper limit of observed cluster masses before it produces radial arcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm² g⁻¹, to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs.     

Undistorted lensed images in galaxy clusters

To date, the study of high-magnification gravitational lensing effects of galaxy clusters has focused upon the grossly distorted, luminous arc-like features formed in massive, centrally condensed clusters. We investigate the formation of a different type of image, highly magnified yet undistorted, in two widely employed cluster mass density profiles, namely an isothermal sphere with a core, and a universal dark matter halo profile derived from the numerical simulations of Navarro et al. We examine the properties of images of extended sources produced by these two cluster profiles, paying particular attention to the undistorted images. Using simple assumptions about the source and lens population, we estimate the relative frequency of the occurrence of highly magnified, undistorted images and the more commonly known giant arcs.     

The observed concentration–mass relation for galaxy clusters

The properties of clusters of galaxies offer key insights into the assembly process of structure in the universe. Numerical simulations of cosmic structure formation in a hierarchical, dark matter dominated universe suggest that galaxy cluster concentrations, which are a measure of a halo's central density, decrease gradually with virial mass. However, cluster observations have yet to confirm this correlation. The slopes of the run of measured concentrations with virial mass are often either steeper or flatter than that predicted by simulations. In this work, we present the most complete sample of observed cluster concentrations and masses yet assembled, including new measurements for 10 strong-lensing clusters, thereby more than doubling the existing number of strong-lensing concentration estimates. We fit a power law to the observed concentrations as a function of virial mass, and find that the slope is consistent with the slopes found in simulations, though our normalization factor is higher. Observed lensing concentrations appear to be systematically larger than X-ray concentrations, a more pronounced effect than that found in simulations. We also find that at a fixed mass, the bulk of observed cluster concentrations are distributed lognormally, with the exception of a few anomalously high concentration clusters. We examine the physical processes likely responsible for the discrepancy between lensing and X-ray concentrations, and for the anomalously high concentrations in particular. The forthcoming Millennium simulation results will offer the most comprehensive comparison set to our findings of an observed concentration–mass power law relation.     

Constraints on dark matter physics from dwarf galaxies through galaxy cluster haloes

One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m _x is the mass of the dark matter particle: σ m _x ≈4×10⁻²⁵ (100 km s⁻¹  v ⁻¹) cm² GeV⁻¹.     

Detecting mass substructure in galaxy clusters: an aperture mass statistic for gravitational flexion

Gravitational flexion has been introduced as a technique by which one can map out and study substructure in clusters of galaxies. Previous analyses involving flexion have measured the individual galaxy–galaxy flexion signal, or used either parametric techniques or a Kaiser, Squires and Broadhurst (KSB)-type inversion to reconstruct the mass distribution in Abell 1689. In this paper, we present an aperture mass statistic for flexion, and apply it to the lensed images of background galaxies obtained by ray-tracing simulations through a simple analytic mass distribution and through a galaxy cluster from the Millennium Simulation. We show that this method is effective at detecting and accurately tracing structure within clusters of galaxies on subarcminute scales with high signal to noise even using a moderate background source number density and image resolution. In addition, the method provides much more information about both the overall shape and the small-scale structure of a cluster of galaxies than can be achieved through a weak lensing mass reconstruction using gravitational shear data. Lastly, we discuss how the zero-points of the aperture mass might be used to infer the masses of structures identified using this method.     

The clustering of galaxy clusters in cosmological models with non-Gaussian initial conditions: predictions for future surveys

We predict the biasing and clustering properties of galaxy clusters that are expected to be observed in the catalogues produced by two forthcoming X-ray and Sunyaev–Zel'dovich effect surveys. We study a set of flat cosmological models where the primordial density probability distribution shows deviations from Gaussianity in agreement with current observational bounds form the background radiation. We consider both local and equilateral shapes for the primordial bispectrum in non-Gaussian models. The two catalogues investigated are those produced by the e ROSITA wide survey and from a survey based on South Pole Telescope observations. It turns out that both the bias and observed power spectrum of galaxy clusters are severely affected in non-Gaussian models with local shape of the primordial bispectrum, especially at large scales. On the other hand, models with equilateral shape of the primordial bispectrum show only a mild effect at all scales, that is difficult to be detected with clustering observations. Between the two catalogues, the one performing better is the e ROSITA one, since it contains only the largest masses that are more sensitive to primordial non-Gaussianity.     

Galaxy–dark matter correlations applied to galaxy–galaxy lensing: predictions from the semi-analytic galaxy formation models

We use semi-analytic models of galaxy formation combined with high-resolution N -body simulations to make predictions for galaxy–dark matter correlations and apply them to galaxy–galaxy lensing. We analyse cross-power spectra between the dark matter and different galaxy samples selected by luminosity, colour or star formation rate. We compare the predictions with the recent detection by the Sloan Digital Sky Survey (SDSS). We show that the correlation amplitude and the mean tangential shear depend strongly on the luminosity of the sample on scales below 1  h ⁻¹ Mpc, reflecting the correlation between the galaxy luminosity and the halo mass. The cross-correlation cannot, however, be used to infer the halo profile directly because different halo masses dominate on different scales and because not all galaxies are at the centres of the corresponding haloes. We compute the redshift evolution of the cross-correlation amplitude and compare it with those of galaxies and dark matter. We also compute the galaxy–dark matter correlation coefficient and show that it is close to unity on scales above 1  h ⁻¹ Mpc for all considered galaxy types. This would allow one to extract the bias and the dark matter power spectrum on large scales from the galaxy and galaxy–dark matter correlations.     

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.     

Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z , the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N -body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.     

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.