Adding Long Wavelength Modes to an NN-Body Simulation

We present a new method to add long wavelength power to an evolved $N$-body simulation, making use of the Zel'dovich (1970) approximation to change positions and velocities of particles. We describe the theoretical framework of our technique and apply it to a P$^3$M cosmological simulation performed on a cube of $100$ Mpc on a side, obtaining a new ``simulation'' of $800$ Mpc on a side. We study the effect of the power added by long waves by mean of several statistics of the density and velocity field, and suggest possible applications of our method to the study of the large-scale structure of the universe.Comment: Revised version, shortened. 15 pages without figures. Accepted for publication in the Astrophysical Journal. Paper and 11 Figures available as .ps.gz files by anonymous ftp at ftp://ftp.mpa-garching.mpg.de/pub/bepi/MA

Hydrodynamic Simulations of Galaxy Formation

This review is a short introduction to numerical hydrodynamics in a cosmological context, intended for the non specialist. The main processes relevant to galaxy formation are first presented. The fluid equations are then introduced, and their implementation in numerical codes by Eulerian grid based methods and by Smooth Particle Hydrodynamics is sketched. As an application, I finally show some results from an SPH simulation of a galaxy cluster.Comment: uuencoded gzipped latex file, 8 pages with 2 figures. Invited talk to appear in the Proceedings of the XXXIst Rencontres de Moriond "Dark Matter in Cosmology, Quantum Measurements, Experimental Gravitation" held in Les Arcs, January 1996. Editions Frontiere

Constraining the distribution of dark matter in dwarf spheroidal galaxies with stellar tidal streams

We use high-resolution N-body simulations to follow the formation and evolution of tidal streams associated to dwarf spheroidal galaxies (dSphs). The dSph models are embedded in dark matter (DM) haloes with either a centrally-divergent 'cusp', or an homogeneous-density 'core'. In agreement with previous studies, we find that as tides strip the galaxy the evolution of the half-light radius and the averaged velocity dispersion follows well-defined tracks that are mainly controlled by the amount of mass lost. Crucially, the evolutionary tracks behave differently depending on the shape of the DM profile: at a fixed remnant mass, dSphs embedded in cored haloes have larger sizes and higher velocity dispersions than their cuspy counterparts. The divergent evolution is particularly pronounced in galaxies whose stellar component is strongly segregated within their DM halo and becomes more disparate as the remnant mass decreases. Our analysis indicates that the DM profile plays an important role in defining the internal dynamics of tidal streams. We find that stellar streams associated to cored DM models have velocity dispersions that lie systematically above their cuspy counterparts. Our results suggest that the dynamics of streams with known dSph progenitors may provide strong constraints on the distribution of DM on the smallest galactic scales.Comment: 5 pages, 4 figure

Survival of Substructure within Dark Matter Haloes

Using high resolution cosmological N-body simulations, we investigate the survival of dark matter satellites falling into larger haloes. Satellites preserve their identity for some time after merging. We compute their loss of mass, energy and angular momentum as dynamical friction, tidal forces and collisions with other satellites dissolve them. We also analyse the evolution of their internal structure. Satellites with less than a few per cent the mass of the main halo may survive for several billion years, whereas larger satellites rapidly sink into the center of the main halo potential well and lose their identity. Penetrating encounters between satellites are frequent and may lead to significant mass loss and disruption. Only a minor fraction of cluster mass (10 per cent on average) is bound to substructure at most redshifts of interest. We discuss the application of these results to the survival and extent of dark matter haloes associated with cluster galaxies, and to interactions between galaxies in clusters. We find that 35-40 per cent of galaxy dark matter haloes are disrupted by the present time. The fraction of satellites undergoing close encounters is similar to the fraction of interacting or merging galaxies in clusters at moderate redshift.Comment: 16 pages, Latex, 14 Postscript figures. Submitted to MNRAS. Postscript version also available at http://www.mpa-garching.mpg.de/~bep

The Rise and Fall of Satellites in Galaxy Clusters

We use N-body simulations to study the infall of dark matter haloes onto rich clusters of galaxies. After identification of all cluster progenitors in the simulations, we select those haloes which accrete directly onto the main cluster progenitor. We construct the mass function of these merging satellites, and calculate the main orbital parameters for the accreted lumps. The average circularity of the orbits is epsilon = 0.5, while either radial or almost circular orbits are equally avoided. More massive satellites move along slightly more eccentric orbits, with lower specific angular momentum and a smaller pericentre. We find that the infall of satellites onto the main cluster progenitor has a very anisotropic distribution. This anisotropy is to a large extent responsible for the shape and orientation of the final cluster and of its velocity ellipsoid. At the end of the simulations, the major axis of the cluster is aligned both with that of its velocity ellipsoid, and with the major axis of the ellipsoid defined by the satellite infall pattern, to 30 degrees on average. We also find that, in lower mass clusters, a higher fraction of the final virial mass is provided by small, dense satellites. These sink to the centre of the parent cluster and so enhance its central density. This mechanism is found to be partially responsible for the correlation between halo masses and characteristic overdensities, recently highlighted by Navarro, Frenk & White (1996).Comment: Revised to match the published versio

Ellipsoidal halo finders and implications for models of triaxial halo formation

We describe an algorithm for identifying ellipsoidal haloes in numerical simulations, and quantify how the resulting estimates of halo mass and shape differ with respect to spherical halo finders. Haloes become more prolate when fit with ellipsoids, the difference being most pronounced for the more aspherical objects. Although the ellipsoidal mass is systematically larger, this is less than 10% for most of the haloes. However, even this small difference in mass corresponds to a significant difference in shape. We quantify these effects also on the initial mass and deformation tensors, on which most models of triaxial collapse are based. By studying the properties of protohaloes in the initial conditions, we find that models in which protohaloes are identified in Lagrangian space by three positive eigenvalues of the deformation tensor are tenable only at the masses well-above $M_*$. The overdensity $\delta$ within almost any protohalo is larger than the critical value associated with spherical collapse (increasing as mass decreases); this is in good qualitative agreement with models which identify haloes requiring that collapse have occured along all three principal axes, each axis having turned around from the universal expansion at a different time. The distributions of initial values are in agreement with the simplest predictions associated with ellipsoidal collapse, assuming initially spherical protohaloes, collapsed around random positions which were sufficiently overdense. However, most protohaloes are not spherical and departures from sphericity increase as protohalo mass decreases. [Abridged]Comment: 18 pages, 17 figures, accepted for publication in MNRA

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

The galaxy velocity field and CDM models

It is generally accepted that some kind of non-baryonic dark matter accounts for most of the mass density of the universe. Considering such a component has become, in the last decade, a key ingredient in current theories of structure formation. In particular, the Cold Dark Matter (CDM) scenario has proven to be quite successful in explaining most of the observed properties of galaxies and of their large-scale distribution. The standard CDM model is characterized by a primordial Zel'dovich spectrum, of random-phase adiabatic perturbations in a universe with density parameter omega sub 0 = 1 and vanishing cosmological constant. This poster paper presents an analysis of observational data on peculiar motion of optical galaxies in comparison to the predictions of CDM models where the assumptions of the standard scenario: omega sub 0 = 1, n = 1, and bias parameter b = 1 are relaxed. In particular, CDM models with 0 less than n less than 1 and 0.4 less than omega sub 0 less than 1 are considered