Structural properties of dark matter halos

2009

I use N-body simulations to investigate the morphology and the dynamical evolution and properties of dark matter halos in clusters of galaxies. My sample consists of nine massive halos, coming from an Einstein-De Sitter universe with scale free power spectrum and spectral index n = 1. Halos are resolved by 20,000 particles each, on average, and have a dynamical resolution of 20-25 kpc, as shown by extensive tests. I nd that the average density pro les of the halos are tted by the Navarro, Frenk and White (1995) analytical t with a root mean square (rms) residual of 20% within the Virial radius. The Hernquist (1990) analytical density pro les ts the same halos with an rms residual of 30%. The projected mass pro les of the simulated halos are in very good agreement with the pro les of rich galaxy clusters derived from strong and weak gravitational lensing observations.

Monthly Notices of the Royal Astronomical Society, 1998

We examine the properties of dark matter halos within a rich galaxy cluster using a high resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 halos with circular velocities larger than 80 km s −1 within the cluster's virial radius of 2 Mpc. This enables an unprecedented study of the statistical properties of a large sample of dark matter halos evolving in a dense environment. The cumulative fraction of mass attached to these halos varies from 0% at 200 kpc, to 13% at the virial radius. Even at this resolution the overmerging problem persists; halos that pass within 200 kpc of the cluster center are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor halos. The median ratio of apocentric to pericentric radii is 6:1; the orbital distribution is close to isotropic, circular orbits are rare, radial orbits are common. The orbits of halos are unbiased with respect to both position within the cluster and with the orbits of the smooth dark matter background and no velocity bias is detected. The tidal radii of surviving halos are generally well-fit using the simple analytic prediction applied to their orbital pericenters. Halos within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other halos that cause significant mass loss -"galaxy harassment". Mergers between halos do not occur inside the clusters virial radius.

Monthly Notices of the Royal Astronomical Society, 1996

We use a set of large cosmological N-body simulations to study the internal structure of dark matter haloes which form in scale-free hierarchical clustering models (initial power spectra P (k) ∝ k n with n = 0,−1 and −2) in an Ω = 1 universe. We find that the radius r 178 in a halo corresponding to a mean interior overdensity of 178 accurately delineates the quasi-static halo interior from the surrounding infalling material, in agreement with the simple spherical collapse model. The interior velocity dispersion correlates with mass, again in good agreement with the spherical collapse model. Interior to the virial radius r 178 , the spherically averaged density, circular velocity and velocity dispersion profiles are well fit by a simple two-parameter analytical model proposed by Navarro et al. (1995a). This model has ρ ∝ r −1 at small radii, steepening to ρ ∝ r −3 at large radii, and fits our haloes to the resolution limit of the simulations. The two model parameters, scalelength and mass, are tightly correlated. Lower mass haloes are more centrally concentrated, and so have scalelengths which are a smaller fraction of their virial radius than those of their higher mass counterparts. This reflects the earlier formation times of low mass haloes. The haloes are moderately aspherical, with typical axial ratios 1 : 0.8 : 0.65 at their virial radii, becoming gradually more spherical towards their centres. The haloes are generically triaxial, but with a slight preference for prolate over oblate configurations, at least for n = −1 and 0. These shapes are maintained by an anisotropic velocity dispersion tensor. The median value of the spin parameter is λ ≈ 0.04, with a weak trend for lower λ at higher halo mass. We also investigate how the halo properties depend on the algorithm used to identify them in the simulations, using both friends-of-friends and spherical overdensity methods. We find that for groups selected at mean overdensities ∼ 100 − 400 by either method, the properties are insensitive to how the haloes are selected, if the halo centre is taken as the position of the most bound particle.

Monthly Notices of the Royal Astronomical Society, 1997

We use N -body simulations to investigate the structure and dynamical evolution of dark matter halos in clusters of galaxies. Our sample consists of nine massive halos from an Einstein-De Sitter universe with scale free power spectrum and spectral index n = −1. Halos are resolved by 20000 particles each, on average, and have a dynamical resolution of 20-25 kpc, as shown by extensive tests. Large scale tidal fields are included up to a scale L = 150 Mpc using background particles. We find that 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 root mean square (rms) velocity. Halos spend on average one third of their evolution in the merging phase and two thirds in the relaxation phase. Using this definition, we study the density profiles and show how they change during the halo dynamical history. In particular, we find that the average density profiles of our halos are fitted by the Navarro, Frenk & White (1995) analytical model with an rms residual of 17% between the virial radius R v and 0.01R v . The Hernquist (1990) analytical density 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 : compared to their results 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.

The Astrophysical Journal, 2003

We measure the average gravitational shear profile of 6 massive clusters (M vir ∼ 10 15 M ⊙ ) at z = 0.3 out to a radius ∼ 2h −1 Mpc. The measurements are fitted to a generalized NFW-like halo model ρ(r) with an arbitrary r → 0 slope α. The data are well fitted by such a model with a central cusp with α ∼ 0.9 − 1.6 (68% confidence interval). For the standard-NFW case α = 1.0, we find a concentration parameter c vir that is consistent with recent predictions from high-resolution CDM N-body simulations. Our data are also well fitted by an isothermal sphere model with a softened core. For this model, our 1σ upper limit for the core radius corresponds to a limit σ ⋆ ≤ 0.1cm 2 g −1 on the elastic collision cross-section in a self-interacting dark matter model.

High resolution N-body simulations have all but converged on a common empirical form for the shape of the density profiles of halos, but the full understanding of the underlying physics of halo formation has eluded them so far. We investigate the formation and structure of dark matter halos using analytical and semi-analytical techniques. Our halos are formed via an extended secondary infall model (ESIM); they contain secondary perturbations and hence random tangential and radial motions which affect the halo's evolution at it undergoes shell-crossing and virialization. Even though the density profiles of NFW and ESIM halos are different their phase-space density distributions are the same: ρ/σ 3 ∝ r −α , with α = 1.875 over ∼ 3 decades in radius. We use two approaches to try to explain this "universal" slope: (1) The Jeans equation analysis yields many insights, however, does not answer why α = 1.875. (2) The secondary infall model of the 1960's and 1970's, augmented by "thermal motions" of particles does predict that halos should have α = 1.875. However, this relies on assumptions of spherical symmetry and slow accretion. While for ESIM halos these assumptions are justified, they most certainly break down for simulated halos which forms hierarchically. We speculate that our argument may apply to an "on-average" formation scenario of halos within merger-driven numerical simulations, and thereby explain why α = 1.875 for NFW halos. Thus, ρ/σ 3 ∝ r −1.875 may be a generic feature of violent relaxation.

The Astrophysical Journal, 2013

Dark-matter-dominated cluster-scale halos act as an important cosmological probe and provide a key testing ground for structure formation theory. Focusing on their mass profiles, we have carried out (gravity-only) simulations of the concordance ΛCDM cosmology, covering a mass range of 2 × 10 12 to 2 × 10 15 h −1 M and a redshift range of z = 0-2, while satisfying the associated requirements of resolution and statistical control. When fitting to the Navarro-Frenk-White profile, our concentration-mass (c-M) relation differs in normalization and shape in comparison to previous studies that have limited statistics in the upper end of the mass range. We show that the flattening of the c-M relation with redshift is naturally expressed if c is viewed as a function of the peak height parameter, ν. Unlike the c-M relation, the slope of the c-ν relation is effectively constant over the redshift range z = 0-2, while the amplitude varies by ∼30% for massive clusters. This relation is, however, not universal: using a simulation suite covering the allowed wCDM parameter space, we show that the c-ν relation varies by about ±20% as cosmological parameters are varied. At fixed mass, the c(M) distribution is well fit by a Gaussian with σ c / c 1/3, independent of the radius at which the concentration is defined, the halo dynamical state, and the underlying cosmology. We compare the ΛCDM predictions with observations of halo concentrations from strong lensing, weak lensing, galaxy kinematics, and X-ray data, finding good agreement for massive clusters (M vir > 4 × 10 14 h −1 M ), but with some disagreements at lower masses. Because of uncertainty in observational systematics and modeling of baryonic physics, the significance of these discrepancies remains unclear.

The Astrophysical Journal, 2000

Can dissipationless N-body simulations be used to reliably determine the structural and substructure properties of dark matter halos? A large simulation of a galaxy cluster in a cold dark matter universe is used to increase the force and mass resolution of current "high resolution simulations" by almost an order of magnitude to examine the convergence of the important physical quantities. The cluster contains ∼ 5 million particles within the final virial radius, R vir ≃ 2 Mpc (with H 0 = 50 Km s −1 Mpc −1 ), and is simulated using a force resolution of 1.0 kpc (≡ 0.05% of R vir ); the final virial mass is 4.3 10 14 M ⊙ , equivalent to a circular velocity v circ ≡ (GM/R) 1/2 ≃ 1000 km s −1 at the virial radius. The central density profile has a logarithmic slope of -1.5, identical to lower resolution studies of the same halo, indicating that the profiles measured from simulations of this resolution have converged to the "physical" limit down to scales of a few kpc (∼ 0.2% of R vir ). Also the abundance and properties of substructure are consistent with those derived from lower resolution runs; from small to large galaxy scales (v circ > 100 km s −1 , m > 10 11 M ⊙ ), the circular velocity function and the mass function of substructures can be approximated by power laws with slopes ∼ −4 and ∼ −2 respectively. At the current resolution, overmerging -a numerical effect that leads to structureless virialized halos in low-resolution N -body simulations -seems to be globally unimportant for substructure halos with circular velocities v circ > 100 km s −1 (∼ 10% of the cluster's v circ ). We can identify subhalos orbiting in the very central region of the cluster (R ∼ < 100 kpc) and we can trace most of the cluster progenitors from high redshift to the present. The object at the cluster center (the dark matter analog of a cD galaxy) is assembled between z = 3 and z = 1 from the merging of a dozen halos with v circ ∼ > 300 km s −1 . Tidal stripping and halo-halo collisions decrease the mean circular velocity of the substructure halos by ≈ 20% over a 5 billion year period. We use the sample of 2000 substructure halos to explore the possibility of biases using galactic tracers in clusters: the velocity dispersions of the halos globally agree with the dark matter within ∼ < 10%, but the halos are spatially anti-biased, and in the very central region of the cluster (R/R vir < 0.3), they show positive velocity bias (b v ≡ σ v3D,halos /σ v3D,DM ≃ 1.2-1.3); however, this effect appears to depend on numerical resolution.

Monthly Notices of The Royal Astronomical Society, 2006

Using six high-resolution dissipationless simulations with a varying box size in a flat Lambda cold dark matter (ΛCDM) universe, we study the mass and redshift dependence of dark matter halo shapes for Mvir= 9.0 × 1011− 2.0 × 1014 h−1 M⊙, over the redshift range z= 0–3, and for two values of σ8= 0.75 and 0.9. Remarkably, we find that the redshift, mass and σ8 dependence of the mean smallest-to-largest axis ratio of haloes is well described by the simple power-law relation 〈s〉= (0.54 ± 0.02)(Mvir/M*)−0.050±0.003, where s is measured at 0.3Rvir, and the z and σ8 dependences are governed by the characteristic non-linear mass, M*=M*(z, σ8). We find that the scatter about the mean s is well described by a Gaussian with σ∼ 0.1, for all masses and redshifts. We compare our results to a variety of previous works on halo shapes and find that reported differences between studies are primarily explained by differences in their methodologies. We address the evolutionary aspects of individual halo shapes by following the shapes of the haloes through ∼100 snapshots in time. We determine the formation scalefactor ac as defined by Wechsler et al. and find that it can be related to the halo shape at z= 0 and its evolution over time.

J. Royal Society Interface, 2024

The impact of inter-group conflict on population dynamics has long been debated, especially for prehistoric and non-state societies. In this work, we consider that beyond direct battle casualties, conflicts can also create a "landscape of fear" in which many non-combatants near theaters of conflict abandon their homes and migrate away. This process causes population decline in the abandoned regions and increased stress on local resources in better protected areas that are targeted by refugees. By applying analytical and computational modeling, we demonstrate that these indirect effects of conflict are sufficient to produce substantial, long-term population boom-and-bust patterns in non-state societies, such as the case of Mid-Holocene Europe. We also demonstrate that greater availability of defensible locations act to protect and maintain the supply of combatants, increasing the permanence of the landscape of fear and the likelihood of endemic warfare. (here preprint SocArXiv)