Carlo Giocoli

Lensing and x-ray mass estimates of clusters (simulations)

We present a comparison between weak-lensing and x-ray mass estimates of a sample of numerically simulated clusters. The sample consists of the 20 most massive objects at redshift z = 0.25 and M_vir > 5 × 10^(14) M_☉ h^(−1). They were found in a cosmological simulation of volume 1 h^(−3) Gpc^3, evolved in the framework of a WMAP-7 normalized cosmology. Each cluster has been resimulated at higher resolution and with more complex gas physics. We processed it through Skylens and X-MAS to generate optical and x-ray mock observations along three orthogonal projections. The final sample consists of 60 cluster realizations. The optical simulations include lensing effects on background sources. Standard observational tools and methods of analysis are used to recover the mass profiles of each cluster projection from the mock catalogue. The resulting mass profiles from lensing and x-ray are individually compared to the input mass distributions. Given the size of our sample, we could also investigate the dependence of the results on cluster morphology, environment, temperature inhomogeneity and mass. We confirm previous results showing that lensing masses obtained from the fit of the cluster tangential shear profiles with Navarro–Frenk–White functionals are biased low by ~5–10% with a large scatter (~10–25%). We show that scatter could be reduced by optimally selecting clusters either having regular morphology or living in substructure-poor environment. The x-ray masses are biased low by a large amount (~25–35%), evidencing the presence of both non-thermal sources of pressure in the intra-cluster medium (ICM) and temperature inhomogeneity, but they show a significantly lower scatter than weak-lensing-derived masses. The x-ray mass bias grows from the inner to the outer regions of the clusters. We find that both biases are weakly correlated with the third-order power ratio, while a stronger correlation exists with the centroid shift. Finally, the x-ray bias is strongly connected with temperature inhomogeneities. Comparison with a previous analysis of simulations leads to the conclusion that the values of x-ray mass bias from simulations are still uncertain, showing dependences on the ICM physical treatment and, possibly, on the hydrodynamical scheme adopted.

The substructure hierarchy in dark matter haloes

We present a new algorithm for identifying the substructure within simulated dark matter haloes. The method is an extension of that proposed by Tormen, Moscardini & Yoshida and Giocoli, Tormen & van den Bosch, which identifies a subhalo as a group of self-bound particles that prior to being accreted by the main progenitor of the host halo belonged to one and the same progenitor halo (hereafter ‘satellite’). However, this definition does not account for the fact that these satellite haloes themselves may also have substructure, which thus gives rise to sub-subhaloes, etc. Our new algorithm identifies substructures at all levels of this hierarchy, and we use it to determine the mass function of all substructure (counting subhaloes, subsubhaloes, etc.). On average, haloes which are formed more recently tend to have a larger mass fraction in substructure and to be less concentrated than average haloes of the same mass. We provide quantitative fits to these correlations. Even though our algorithm is very different from that of Gao et al., we also find that the subhalo mass function per unit mass at redshift z = 0 is universal. This universality extends to any redshift only if one accounts for the fact that host haloes of a given mass are less concentrated at higher redshifts, and concentration and substructure abundance are anticorrelated. This universality allows a simple parametrization of the subhalo mass function integrated over all host halo masses, at any given time. We provide analytic fits to this function which should be useful in halo model analyses which equate galaxies with halo substructure when interpreting clustering in large sky surveys. Finally, we discuss systematic differences in the subhalo mass function that arise from different definitions of (host) halo mass.

THE MUSIC OF CLASH: PREDICTIONS ON THE CONCENTRATION-MASS RELATION

We present an analysis of the MUSIC-2 N-body/hydrodynamical simulations aimed at estimating the expected concentration-mass relation for the CLASH (Cluster Lensing and Supernova Survey with Hubble) cluster sample. We study nearly 1,400 halos simulated at high spatial and mass resolution. We study the shape of both their density and surface-density profiles and fit them with a variety of radial functions, including the Navarro-Frenk-White (NFW), the generalized NFW, and the Einasto density profiles. We derive concentrations and masses from these fits. We produce simulated Chandra observations of the halos, and we use them to identify objects resembling the X-ray morphologies and masses of the clusters in the CLASH X-ray-selected sample. We also derive a concentration-mass relation for strong-lensing clusters. We find that the sample of simulated halos that resembles the X-ray morphology of the CLASH clusters is composed mainly of relaxed halos, but it also contains a significant fraction of unrelaxed systems. For such a heterogeneous sample we measure an average two-dimensional concentration that is ~11% higher than is found for the full sample of simulated halos. After accounting for projection and selection effects, the average NFW concentrations of CLASH clusters are expected to be intermediate between those predicted in three dimensions for relaxed and super-relaxed halos. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range [3-6], with an average value of 3.87 and a standard deviation of 0.61.

An improved model for the formation times of dark matter haloes

A dark matter halo is said to have formed when at least half its mass has been assembled into a single progenitor. With this definition, it is possible to derive a simple but useful analytic estimate of the distribution of halo formation times. The standard estimate of this distribution depends on the shape of the conditional mass function - the distribution of progenitor masses of a halo as a function of time. If the spherical collapse model is used to estimate the progenitor mass function, then the formation times one infers systematically underestimate those seen in numerical simulations of hierarchical gravitational clustering. We provide estimates of halo formation which may be related to an ellipsoidal collapse model. These estimates provide a substantially better description of the simulations. We also provide an alternative derivation of the formation time distribution which is based on the assumption that haloes increase their mass through binary mergers only. Our results are useful for models which relate halo structure to halo formation.

BINARY QUASARS AT HIGH REDSHIFT. II. SUB-Mpc CLUSTERING AT z ∼ 3-4

We present measurements of the small-scale (0.1 ≲ r ≲ 1 h^(-1) Mpc) quasar two-point correlation function at z>2.9, for a flux-limited (i < 21) sample of 15 binary quasars compiled by Hennawi et al. The amplitude of the small-scale clustering increases from z ~ 3 to z ~ 4. The small-scale clustering amplitude is comparable to or lower than power-law extrapolations (assuming a fixed slope γ = 2) from the large-scale correlation function of the i < 20.2 quasar sample from the Sloan Digital Sky Survey. Using simple prescriptions relating quasars to dark matter halos, we model the observed small-scale clustering with halo occupation models. We found that the level of small-scale clustering favors an active fraction of black holes in (M ≳ 10^(13) h^(–1) M_☉) satellite halos f_s ≳ 0.1 at z ≳ 3.

Formation times, mass growth histories and concentrations of dark matter haloes

We develop a simple model for estimating the mass growth histories of dark matter halos. The model is based on a t to the formation time distribution, where formation is dened as the earliest time that the main branch of the merger tree contains a fraction f of the nal mass M. Our analysis exploits the fact that the median formation time as a function of f is the same as the median of the main progenitor mass distribution as a function of time. When coupled with previous work showing that the concentration c of the nal halo is related to the formation time tf associated with f 0:04, our approach provides a simple algorithm for estimating how the distribution of halo concentrations may be expected to depend on mass, redshift and the expansion history of the background cosmology. We also show that one can predict log10 c with a precision of about 0.13 and 0.09 dex if only its mass, or both mass and tf are known. And, conversely, one can predict log10 tf from mass or c with a precision of 0.12 and 0.09 dex, approximately independent of f. Adding the mass to the c-based estimate does not result in further improvement. These latter results may be useful for studies which seek to compare the age of the stars in the central galaxy in a halo with the time the core was rst assembled.

Analytical approach to subhalo population in dark matter haloes

In the standard model of cosmic structure formation, dark matter haloes form by gravitational instability. The process is hierarchical: smaller systems collapse earlier, and later merge to form larger haloes. The galaxy clusters, hosted by the largest dark matter haloes, are at the top of this hierarchy and representing the largest as well as the last structures formed in the Universe, while the smaller and first haloes are those Earth-sized dark subhaloes that have been both predicted by theoretical considerations and found in numerical simulations, though there do not exist any observational hints of their existence. The probability that a halo of mass m at redshift z will be part of a larger halo of mass M at the present time can be described in the frame of the extended Press & Schecter theory making use of the progenitor (conditional) mass function. Using the progenitor mass function, we calculate analytically, at redshift zero, the distribution of subhaloes in mass, formation epoch and rarity of the peak of the density field at the formation epoch. That is done for a Milky Way size system, assuming both a spherical and an ellipsoidal collapse model. Our calculation assumes that small progenitors do not lose mass due to dynamical processes after entering the parent halo, and that they do not interact with other subhaloes. For a A cold dark matter power spectrum, we obtain a subhalo mass function dn/dm proportional to m -α with a model-independent a ∼ 2. Assuming that the dark matter is a weakly interacting massive particle, the inferred distributions are used to test the feasibility of an indirect detection in the γ-ray energy band of such a population of subhaloes with a Gamma-ray Large Area Space Telescope like satellite.

Halo model description of the non-linear dark matter power spectrum at k >> 1 Mpc―1

Accurate knowledge of the non-linear dark-matter power spectrum is important for understanding the large-scale structure of the Universe, the statistics of dark-matter haloes and their evolution, and cosmological gravitational lensing. We analytically model the dark-matter power spectrum and its cross-power spectrum with dark-matter haloes. Our model extends the halo-model formalism, including realistic substructure population within individual dark-matter haloes and the scatter of the concentration parameter at xed halo mass. We consider three prescriptions for the massconcentration relation and two for the substructure distribution in dark-matter haloes. We show that this extension of the halo model mainly increases the predicted power on the small scales, and is crucial for proper modeling the cosmological weak-lensing signal due to low-mass haloes. Our extended formalism shows how the halo model approach can be improved in accuracy as one increases the number of ingredients that are calibrated from n-body simulations.

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.

moka: a new tool for strong lensing studies

Strong gravitational lensing is a powerful tool that can be used to probe the matter distribution in the cores of massive dark matter haloes. Recent and ongoing analyses of galaxy cluster surveys – such as the Massive Cluster Survey (MACS), the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS), the Sloan Digital Sky Survey (SDSS), the Sloan Giant Arcs Survey (SGAS), the Cluster Lensing and Supernova Survey with Hubble (CLASH) and the Local Cluster Substructure Survey (LoCuSS) – have addressed the question of the nature of the dark matter distribution in clusters. Using N-body simulations of cold dark matter haloes, it is consistently found that haloes should be characterized by a concentration–mass relation, which decreases monotonically with halo mass, and that they should be populated by a large amount of substructures, representing the cores of accreted progenitor halos. It is important for our understanding of dark matter that we test these predictions. We present moka, a new algorithm for simulating the gravitational lensing signal from cluster-sized haloes. It implements the most recent results from numerical simulations to create realistic cluster-scale lenses with properties independent of numerical resolution. We perform systematic studies of the strong lensing cross-section as a function of halo structures. We find that the strong lensing cross-sections depend most strongly on the concentration and on the inner slope of the density profile of a halo, followed in order of importance by halo triaxiality and the presence of a bright central galaxy.