Velocity bias in a LCDM model

We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are ``hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius.Comment: 13 pages, Latex, AASTeXv5 and natbi

The importance of the merging activity for the kinetic polarization of the Sunyaev-Zel'dovich signal from galaxy clusters

The polarization sensitivity of the upcoming millimetric observatories will open new possibilities for studying the properties of galaxy clusters and for using them as powerful cosmological probes. For this reason it is necessary to investigate in detail the characteristics of the polarization signals produced by their highly ionized intra-cluster medium (ICM). This work is focussed on the polarization effect induced by the ICM bulk motions, the so-called kpSZ signal, which has an amplitude proportional to the optical depth and to the square of the tangential velocity. In particular we study how this polarization signal is affected by the internal dynamics of galaxy clusters and what is its dependence on the physical modelling adopted to describe the baryonic component. This is done by producing realistic kpSZ maps starting from the outputs of two different sets of high-resolution hydrodynamical N-body simulations. The first set (17 objects) follows only non-radiative hydrodynamics, while for each of 9 objects of the second set we implement four different kinds of physical processes. Our results shows that the kpSZ signal turns out to be a very sensitive probe of the dynamical status of galaxy clusters. We find that major merger events can amplify the signal up to one order of magnitude with respect to relaxed clusters, reaching amplitude up to about 100 nuK. This result implies that the internal ICM dynamics must be taken into account when evaluating this signal because simplicistic models, based on spherical rigid bodies, may provide wrong estimates. Finally we find that the dependence on the physical modelling of the baryonic component is relevant only in the very inner regions of clusters.Comment: 13 pages, 7 figures, submitted to A&

The Structure and Dynamical Evolution of Dark Matter Halos

(Shortened) We use N-body simulations to investigate the structure and dynamical evolution of dark matter halos in galaxy clusters. Our sample consists of nine massive halos from an EdS universe with scale free power spectrum and n = -1. Halos are resolved by ~20000 particles each, with a dynamical resolution of 20-25 kpc. Large scale tidal fields are included up to L=150 Mpc using background particles. The halo formation process can be characterized by the alternation of two dynamical configurations: a merging phase and a relaxation phase, defined by their signature on the evolution of the total mass and rms velocity. Halos spend on average one 1/3 of their evolution in the merging phase and 2/3 in the relaxation phase. Using this definition, we study the density profiles and their change during the halo history. The average density profiles are fitted by the NFW analytical model with an rms residual of 17% between the virial radius Rv and 0.01 Rv. The Hernquist (1990) profiles fits the same halos with an rms residual of 26%. The trend with mass of the scale radius of these fits is marginally consistent with that found by Cole & Lacey (1996): in comparison our halos are more centrally concentrated, and the relation between scale radius and halo mass is slightly steeper. We find a moderately large scatter in this relation, due both to dynamical evolution within halos and to fluctuations in the halo population. We analyze the dynamical equilibrium of our halos using the Jeans' equation, and find that on average they are approximately in equilibrium within their virial radius. Finally, we find that the projected mass profiles of our simulated halos are in very good agreement with the profiles of three rich galaxy clusters derived from strong and weak gravitational lensing observations.Comment: 20 pages, Latex, with all figures included. Modified to match the published versio

Weakly Self-Interacting Dark Matter and the Structure of Dark Halos

We study the formation of dark halos in a $\Lambda$CDM universe under the assumption that Cold Dark Matter particles have a finite cross-section for elastic collisions. We compare evolution when CDM mean free paths are comparable to halo sizes with the collisionless and fluid limits. We show that a few collisions per particle per Hubble time at halo centre can substantially affect the central density profile. Cross-sections an order of magnitude larger produce sufficient relaxation for rich clusters to develop core radii in the range 100-200 $h^{-1}$kpc. The structural evolution of halos is a competition between collisional relaxation caused by individual particle interactions and violent relaxation resulting from the infall and merging processes by which clusters grow. Although our simulations concentrate on systems of cluster size, we can scale our results to address the halo structure expected for dwarf galaxies. We find that collision cross-sections sufficiently large to significantly modify the cores of such galaxies produce cluster cores which are too large and/or too round to be consistent with observation. Thus the simplest model for self-interacting dark matter is unable to improve fits to published dwarf galaxy rotation curves without violating other observational constraints.Comment: Revised, accepted for publication in ApJ Letters. Figure1 replace

Dark matter annihilation in the halo of the Milky Way

If the dark matter in the Universe is made of weakly self-interacting particles, they may self-annihilate and emit gamma-rays. We use high resolution numerical simulations to estimate directly the annihilation flux from the central regions of the Milky Way and from dark matter substructures in its halo. Although such estimates remain uncertain because of their strong dependence on the structure of the densest regions, our numerical experiments suggest that less direct calculations have overestimated the emission both from the centre and from halo substructure. We estimate a maximal enhancement of at most a factor of a few with respect to a smooth spherical halo of standard Navarro-Frenk-White (NFW) structure. We discuss detection strategies for the next generation of gamma-ray detectors and find that the annihilation flux may be detectable, regardless of uncertainties about the densest regions, for the annihilation cross-sections predicted by currently popular elementary particle models for the dark matter.Comment: 10 pages, 8 figures, replaced with version accepted by MNRAS (very minor changes

The Population of Dark Matter Subhaloes: Mass Functions and Average Mass Loss Rates

Using a cosmological N-Body simulation and a sample of re-simulated cluster-like haloes, we study the mass loss rates of dark matter subhaloes, and interpret the mass function of subhaloes at redshift zero in terms of the evolution of the mass function of systems accreted by the main halo progenitor. When expressed in terms of the ratio between the mass of the subhalo at the time of accretion and the present day host mass the unevolved subhalo mass function is found to be universal. However, the subhalo mass function at redshift zero clearly depends on $M_0$, in that more massive host haloes host more subhaloes. To relate the unevolved and evolved subhalo mass functions, we measure the subhalo mass loss rate as a function of host mass and redshift. We find that the average, specific mass loss rate of dark matter subhaloes depends mainly on redshift. These results suggest a pleasingly simple picture for the evolution and mass dependence of the evolved subhalo mass function. Less massive host haloes accrete their subhaloes earlier, which are thus subjected to mass loss for a longer time. In addition, their subhaloes are typically accreted by denser hosts, which causes an additional boost of the mass loss rate. To test the self-consistency of this picture, we use a merger trees constructed using the extended Press-Schechter formalism, and evolve the subhalo populations using the average mass loss rates obtained from our simulations, finding the subhalo mass functions to be in good agreement with the simulations. [abridged]Comment: 12 pages, 12 figures; submitted to MNRA

A reassessment of the evidence of the Integrated Sachs-Wolfe effect through the WMAP-NVSS correlation

We reassess the estimate of the cross-correlation of the spatial distribution of the NRAO VLA Sky Survey (NVSS) radio sources with that of Cosmic Microwave Background (CMB) anisotropies from the Wilkinson Microwave Anisotropy Probe (WMAP). This re-analysis is motivated by the fact that most previous studies adopted a redshift distribution of NVSS sources inconsistent with recent data. We find that the constraints on the bias-weighted redshift distribution, b(z)xN(z), of NVSS sources, set by the observed angular correlation function, w(theta), strongly mitigate the effect of the choice of N(z). If such constraints are met, even highly discrepant redshift distributions yield NVSS-WMAP cross-correlation functions consistent with each other within statistical errors. The models favoured by recent data imply a bias factor, b(z), decreasing with increasing z, rather than constant, as assumed by most previous analyses. As a consequence, the function b(z)xN(z) has more weight at z<1, i.e. in the redshift range yielding the maximum contribution to the ISW in a standard LambdaCDM cosmology. On the whole, the NVSS turns out to be better suited for ISW studies than generally believed, even in the absence of an observational determination of the redshift distribution. The NVSS-WMAP cross-correlation function is found to be fully consistent with the prediction of the standard LambdaCDM cosmology.Comment: 6 pages, 2 figures, submitted to MNRA

Density profiles and substructure of dark matter halos: converging results at ultra-high numerical resolution

Can N-body simulations reliably determine the structural properties of dark matter halos? Focussing on a Virgo-sized galaxy cluster, we increase the resolution of current ``high resolution simulations'' by almost an order of magnitude to examine the convergence of the important physical quantities. We have 4 million particles within the cluster and force resolution 0.5 kpc/h (0.05% of the virial radius). The central density profile has a logarithmic slope of -1.5, as found in lower resolution studies of the same halo, indicating that the profile has converged to the ``physical'' limit down to scales of a few kpc. Also the abundance of substructure is consistent with that derived from lower resolution runs; on the scales explored, the mass and circular velocity functions are close to power laws of exponents ~ -1.9 and -4. Overmerging appears to be globally unimportant for suhalos with circular velocities > 100 km/s. We can trace most of the cluster progenitors from z=3 to the present; the central object (the dark matter analog of a cD galaxy)is assembled between z=3 and 1 from the merging of a dozen halos with v_circ \sim 300 km/s. The mean circular velocity of the subhalos decreases by ~ 20% over 5 billion years, due to tidal mass loss. The velocity dispersions of halos and dark matter globally agree within 10%, but the halos are spatially anti-biased, and, in the very central region of the cluster, they show positive velocity bias; however, this effect appears to depend on numerical resolution.Comment: 19 pages, 13 figures, ApJ, in press. Text significantly clarifie

Self-similar collapse and the structure of dark matter halos: A fluid approach

We explore the dynamical restrictions on the structure of dark matter halos through a study of cosmological self-similar gravitational collapse solutions. A fluid approach to the collisionless dynamics of dark matter is developed and the resulting closed set of moment equations are solved numerically including the effect of halo velocity dispersions (both radial and tangential), for a range of spherically averaged initial density profiles. Our results highlight the importance of tangential velocity dispersions to obtain density profiles shallower than $1/r^2$ in the core regions, and for retaining a memory of the initial density profile, in self-similar collapse. For an isotropic core velocity dispersion only a partial memory of the initial density profile is retained. If tangential velocity dispersions in the core are constrained to be less than the radial dispersion, a cuspy core density profile shallower than $1/r$ cannot obtain, in self-similar collapse.Comment: 25 pages, 7 figures, submitted to Ap

Numerical study of halo concentrations in dark-energy cosmologies

We study the concentration parameters, their mass dependence and redshift evolution, of dark-matter halos in different dark-energy cosmologies with constant and time-variable equation of state, and compare them with "standard'' Lambda-CDM and OCDM models. We find that previously proposed algorithms for predicting halo concentrations can be well adapted to dark-energy models. When centred on the analytically expected values, halo concentrations show a log-normal distribution with a uniform standard deviation of ~0.2. The dependence of averaged halo concentrations on mass and redshift permits a simple fit of the form (1+z) c=c0 (M/M0)^a, with a~-0.1 throughout. We find that the cluster concentration depends on the dark energy equation of state at the cluster formation redshift z_{coll} through the linear growth factor D_+(z_{coll}). As a simple correction accounting for dark-energy cosmologies, we propose scaling c0 from Lambda-CDM with the ratio of linear growth factors, c0 -> c0 D_+(z_{coll})/D_{+,Lambda-CDM}(z_{coll}).Comment: 11 pages, submitted to Astronomy & Astrophysic