C. Fedeli

Strong lensing in the MARENOSTRUM UNIVERSE I. Biases in the cluster lens population

Context. Strong lensing is one of the most direct probes of mass distribution in the inner regions of galaxy clusters. It can be used to constrain the density profiles and to measure the mass of the lenses. Moreover, the abundance of strong lensing events can be used to constrain structure formation and cosmological parameters through the so-called “arc-statistics” approach. However, several issues related to the use of strong lensing clusters in cosmological applications are still controversial, leading to the suspicion that several biases may affect this very peculiar class of objects. Aims. With this study we aim a better understanding of the properties of galaxy clusters that can potentially act as strong lenses. Methods. We do so by investigating the properties of a large sample of galaxy clusters extracted from the N-body/hydrodynamical simulation MareNostrum Universe. We perform ray-tracing simulations with each of them and identify those objects capable of producing strong lensing effects. We explore the correlation between the cross section for lensing and many properties of clusters, such as mass, three-dimensional and projected shapes, their concentrations, the X-ray luminosity, and the dynamical activity. Results. We quantify the minimal cluster mass required for producing both multiple images and large distortions. While we do not measure a significant excess of triaxiality in strong lensing clusters, we find that the probability of strong alignments between the major axes of the lenses and the line of sight is a growing function of the lensing cross section. In projection, the strong lenses appear rounder within R200, but we find that their cores tend to be more elliptical as the lensing cross section increases. As a result of the orientation bias, we also find that the cluster concentrations estimated from the projected density profiles tend to be biased high. The X-ray luminosity of strong lensing clusters tend to be higher than for normal lenses of similar mass and redshift. This is particularly significant for the least massive lenses. Finally, we find that the strongest lenses generally exhibit an excess of kinetic energy within the virial radius, thus indicating that they are more dynamically active than the usual clusters. Conclusions. We conclude that strong lensing clusters are a very peculiar class of objects, affected by many selection biases that need to be properly modeled when using them to study the inner structure of galaxy clusters or to constrain the cosmological parameters.

Comparison of an X-ray-selected sample of massive lensing clusters with the MareNostrum Universe ΛCDM simulation

Context. A long-standing problem of strong-lensing by galaxy clusters is the observed high rate of giant gravitational arcs that are not predicted in the framework of the “standard” cosmological model. This is known as the “arc statistics problem”. Recently, several other inconsistencies between the theoretical expectations and observations have been claimed regarding the large size of the Einstein rings and the high concentrations of few clusters with strong-lensing features. All these problems consistently indicate that observed galaxy clusters may be stronger gravitational lenses than expected. Aims. We aim at better understanding these problems by comparing the lensing properties of well defined cluster samples with those of a large set of numerically simulated objects. Methods. We use clusters extracted from the MareNostrum Universe to build up mock catalogs of galaxy clusters selected through their X-ray flux. We use these objects to estimate the probability distributions of lensing cross sections, Einstein rings, and concentrations for a sample of 12 MACS clusters at z > 0.5 from the literature. Results. We find that three clusters in the MACS sample have lensing cross sections and Einstein ring sizes larger than any simulated cluster in the MareNostrum Universe. We use the lensing cross sections of simulated and real clusters to estimate the number of giant arcs that should arise from lensed sources at z = 2. We find that simulated clusters produce ∼50% less arcs than observed clusters do. The medians of the distributions of the Einstein ring sizes differ by ∼25% between simulations and observations. We estimate that the concentrations of the individual MACS clusters inferred from the lensing analysis should be up to a factor of ∼2 larger than expected from the ΛCDM model because of cluster triaxiality and orientation biases that affect the lenses with the largest cross sections. In particular, we predict that for ∼20% of the clusters in the MACS sample the lensing-derived concentrations should be higher than expected by more than ∼40%. Conclusions. The arc statistics, the Einstein ring, and the concentration problems in strong lensing clusters are mitigated but not solved on the basis of our analysis. Nevertheless, owing to the lack of redshifts for most of the multiple image systems used for modeling the MACS clusters, the results of this work will need to be verified with additional data. The upcoming CLASH program will provide an ideal sample for extending our comparison.

The potential of X‐ray cluster surveys to constrain primordial non‐Gaussianity

We present forecasts for constraints on deviations from Gaussian distribution of primordial density perturbations from future high‐sensitivity X‐ray surveys of galaxy clusters. Our analysis is based on computing the Fisher‐Matrix for number counts and large-scale power spectrum of clusters. The surveys that we consider have high‐sensitivity and wide‐area to detect about 2: 5�10 5 extended sources, and to provide reliable measurements of robust mass proxies for about 2�10 4 clusters. Based on the so-called self-calibration approac h, and including Planck priors in our analysis, we constrain at once nine cosmological parameters and four nuisance parameters, which define the relation between cluster mass and X‐ray flux. Because of the scale dependence of large‐scale bias induced by local‐shape non‐Gaussianity, we find that the power spectrum provides strong constraints on the non‐Gaussianity fNL parameter, which complement the stringent constraints on the power spectrum normalization,� 8, from the number counts. To quantify the joint constraints on the two parameters,� 8 and fNL, that specify the timing of structure formation for a fixed background expa nsion, we define the figure-of� � :

Observing the clustering properties of galaxy clusters in dynamical dark-energy cosmologies

We study the clustering properties of galaxy clusters expected to be observed by various forthcoming surveys both in the X-ray and sub-mm regimes by the thermal Sunyaev-Zel’dovich effect. Several different background cosmological models are assumed, including the concordance ΛCDM and various cosmologies with dynamical evolution of the dark energy. Particular attention is paid to models with a significant contribution of dark energy at early times which affects the process of structure formation. Past light cone and selection effects in cluster catalogs are carefully modeled by realistic scaling relations between cluster mass and observables and by properly taking into account the selection functions of the different instruments. The results show that early dark-energy models are expected to produce significantly lower values of effective bias and both spatial and angular correlation amplitudes with respect to the standard ΛCDM model. Among the cluster catalogs studied in this work, it turns out that those based on eRosita, Planck, and South Pole Telescope observations are the most promising for distinguishing between various dark-energy models.

Next Generation Cosmology: Constraints from the Euclid Galaxy Cluster Survey

We study the characteristics of the galaxy cluster samples expected from the European Space Agencys Euclid satellite and forecast constraints on parameters describing a variety of cosmological models. In this paper we use the same method of analysis already adopted in the Euclid Red Book, which is based on the Fisher matrix approach. Based on our analytical estimate of the cluster selection function in the photometric Euclid survey, we forecast the constraints on cosmological parameters corresponding to different extensions of the standard I \textgreater cold dark matter model. Using only Euclid clusters, we find that the amplitude of the matter power spectrum will be constrained to Delta sigma(8) = 0.0014 and the mass density parameter to Delta Omega(m) = 0.0011. The dynamical evolution of dark energy will be constrained to Delta w(0) = 0.03 and Delta w(a) = 0.2 with free curvature Omega(k), resulting in a (w(0), w(a)) figure of merit (FoM) of 291. In combination with Planck cosmic microwave background (CMB) constraints, the amplitude of primordial non-Gaussianity will be constrained to Delta f(NL) a parts per thousand integral 6.6 for the local shape scenario. The growth factor parameter gamma, which signals deviations from general relativity, will be constrained to Delta gamma = 0.02, and the neutrino density parameter to Delta Omega(nu) = 0.0013 (or Delta am(nu) = 0.01). Including the Planck CMB covariance matrix improves dark energy constraints to Delta w(0) = 0.02, Delta w(a) = 0.07, and a FoM = 802. Knowledge of the observable-cluster mass scaling relation is crucial to reach these accuracies. Imaging and spectroscopic capabilities of Euclid will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies, supported by external cluster surveys.

The clustering of galaxies and galaxy clusters: constraints on primordial non-Gaussianity from future wide-field surveys

We investigate the constraints on primordial non-Gaussianity with varied bispectrum shapes that can be derived from the power spectrum of galaxies and clusters of galaxies detected in future wide field optical/near-infrared surveys. Having in mind the proposed ESA space mission Euclid as a specific example, we combine the spatial distribution of spectroscopically selected galaxies with that of weak lensing selected cluste rs. We use the physically motivated halo model in order to represent the correlation function of arbitrary tracers of the Large Scale Structure in the Universe. As naively expected, we find that g alaxies are much more effective in jointly constrain the level of primordial non-Gaussiani ty fNL and the amplitude of the matter power spectrumσ8 than clusters of galaxies, due to the much lower abundance of the latter that is not adequately compensated by the larger effe ct on the power spectrum. Nevertheless, combination of the galaxy power spectrum with the cluster-galaxy cross spectrum can decrease the error on the determination of fNL by up to a factor of∼ 2. This decrement is particularly evident for the less studied non-Gaussian bispec trum shapes, the so-called enfolded and the orthogonal ones. Setting constraints on these models can shed new light on various aspects of the physics of the early Universe, and it is hence o f extreme importance. By combining the power spectra of clusters and galaxies with the cl uster-galaxy cross spectrum we

Strong lensing statistics and the power spectrum normalisation

We use semi-analytic modelling of the galaxy-cluster population and its strong lensing efficiency to explore how the expected abundance of large gravitational arcs on the sky depends on σ 8 . Our models take all effects into account that have been shown to affect strong cluster lensing substantially, in particular cluster asymmetry, substructure, merging, and variations in the central density concentrations. We show that the optical depth for long and thin arcs increases by approximately one order of magnitude when σ 8 increases from 0.7 to 0.9, owing to a constructive combination of several effects. Models with high σ 8 are also several orders of magnitude more efficient in producing arcs at intermediate and high redshifts. Finally, we use realistic source number counts to quantitatively predict the total number of arcs brighter than several magnitude limits in the R and I bands. We confirm that, while σ 8 ∼ 0.9 may come close to the known abundance of arcs, even σ 8 ∼ 0.8 falls short by almost an order of magnitude in reproducing known counts. We conclude that, should σ 8 ∼ 0.8 be confirmed, we would fail to understand the strong-lensing efficiency of the galaxy cluster population, and in particular the abundance of arcs in high-redshift clusters. We argue that early-dark energy or non-Gaussian density fluctuations may indicate one way out of this problem.

A fast method for computing strong-lensing cross sections: application to merging clusters

Astronomy & Astrophysics, submitted Abstract. Strong gravitational lensing by irregular mass distributi ons, such as galaxy clusters, is generally not well quantifie d by cross sections of analytic mass models. Computationally expensive ray-tracing methods have so far been necessary for accurate cross-section calculations. We describe a fast, s emi-analytic method here which is based on surface integrals over high-magnification regions in the lens plane and demonstrat e that it yields reliable cross sections even for complex, as ymmetric mass distributions. The method is faster than ray-tracing s imulations by factors of ∼ 30 and thus suitable for large cosmological simulations, saving large amounts of computing time. We apply this method to a sample of galaxy cluster-sized dark matter haloes with simulated merger trees and show that cluster mergers approximately double the strong-lensing optical depth for lens redshifts zl & 0.5 and sources near zs = 2. We believe that this result hints at one possibility for un derstanding the recently detected high arcs abundance in clusters at moderate and high redshifts, and is thus worth further studies.

Imprints of primordial non‐Gaussianity on the number counts of cosmic shear peaks

We studied the effect of primordial non-Gaussianity with varied bispectrum shapes on the number counts of signal-to-noise ratio peaks in wide-field cosmic shear maps. The two cosmological contributions to this particular weak lensing statistic, namely the chance projection of Large Scale Structure (LSS) and the occurrence of real, cluster-sized dark matter haloes, have been modelled semianalytically, thus allowing to easily introduce the effect of nonGaussian initial conditions. We performed a Fisher matrix analysis by taking into account the full covariance of the peak counts in order to forecast the joint constraints on the level of primordial non-Gaussianity and the amplitude of the matter power spectrum that are expected from future wide-field imaging surveys. We find that positive-skewed non-Gaussianity increases the number counts of cosmic shear peaks, more so at high signal-to-noise ratio values, where the signal is mostly dominated by massive clusters as expected. The increment is at the level of ∼1 per cent for f NL = 10 and ∼10 per cent for f NL = 100 for a local shape of the primordial bispectrum, while different bispectrum shapes give generically a smaller effect. For a future survey on the model of the proposed ESA space mission Euclid and by avoiding the strong assumption of being capable of distinguishing the weak-lensing signal of galaxy clusters from the chance projection of LSSs, we forecast a 1σ error on the level of non-Gaussianity of ∼30–40 for the local and equilateral models, and of ∼100–200 for the less explored enfolded and orthogonal bispectrum shapes.

The effects of baryonic cooling on the concentration—mass relation

I re-examine the relation between virial mass and concentration for groups and clusters of galaxies as measured in a number of recent works. As previously noted by several authors, low-mass clusters and groups of galaxies display systematically larger concentrations than simple prescriptions based on pure N-body simulations would predict. This implies an observed concentration–mass relation with a substantially larger slope/normalization than expected from theoretical investigations. Additionally, this conclusion seems to be quite independent of selection effects, holding for both lensing based and X-ray based cluster samples. In order to shed new light on this issue I employ a simple spherical halo model containing, in addition to dark matter, also stars and hot diffuse gas in proportions and with distributions in agreement with the most recent observations. Moreover, I include the contraction effect experienced by dark matter due to the cooling of baryons in the very central part of the structure itself. The resulting modified concentration–mass relation is steeper than the theoretical input one, because star formation is fractionally more efficient in low-mass objects. However, the effect is non-vanishing at all masses, thus resulting also in a larger normalization. Overall the new relation provides a better representation of the observed one for almost all catalogues considered in this work, although the specific details depend quite significantly on the baryon fraction prescription adopted. Specifically, the observed concentration–mass relation seems to favour a scenario where the stellar mass fraction in large clusters of galaxies is substantially lower than several works have found. Anyhow, the same effect could also be produced by a redistribution of baryons within the structure. Moreover, the concentration of a number of high-mass objects seems to be significantly lower even than the predictions based on pure N-body simulations, and they are hence unaccounted for in the modified scenario that is proposed here. Finally I use this simple model to show how the estimated concentration of cosmic structures is expected to be overestimated as a function of the radial range covered by the analysis.