Dynamical evolution of primordial dark matter haloes through mergers (original) (raw)
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Monthly Notices of the Royal Astronomical Society, 2012
Using a statistical sample of dark matter haloes drawn from a suite of cosmological Nbody simulations of the Cold Dark Matter (CDM) model, we quantify the impact of a simulated halo's mass accretion and merging history on two commonly used measures of its dynamical state, the virial ratio η and the centre of mass offset ∆r. Quantifying this relationship is important because the degree to which a halo is dynamically equilibrated will influence the reliability with which we can measure characteristic equilibrium properties of the structure and kinematics of a population of haloes. We begin by verifying that a halo's formation redshift z form correlates with its virial mass M vir and we show that the fraction of its recently accreted mass and the likelihood of it having experienced a recent major merger increases with increasing M vir and decreasing z form . We then show that both η and ∆r increase with increasing M vir and decreasing z form , which implies that massive recently formed haloes are more likely to be dynamically unrelaxed than their less massive and older counterparts. Our analysis shows that both η and ∆r are good indicators of a halo's dynamical state, showing strong positive correlations with recent mass accretion and merging activity, but we argue that ∆r provides a more robust and better defined measure of dynamical state for use in cosmological N -body simulations at z ≃ 0. We find that ∆r 0.04 is sufficient to pick out dynamically relaxed haloes at z=0. Finally, we assess our results in the context of previous studies, and consider their observational implications.
Merger versus Accretion and the Structure of Dark Matter Halos
The Astrophysical Journal, 1998
High-resolution N-body simulations of hierarchical clustering in a wide variety of cosmogonies show that the density profiles of dark matter halos are universal, with low mass halos being denser than their more massive counterparts. This mass-density correlation is interpreted as reflecting the earlier typical formation time of less massive objects. We investigate this hypothesis in the light of formation times defined as the epoch at which halos experience their last major merger. Such halo formation times are calculated by means of a modification of the extended Press & Schechter formalism which includes a phenomenological frontier, ∆ m , between tiny and notable relative mass captures leading to the distinction between merger and accretion. For ∆ m ∼ 0.6, we confirm that the characteristic density of halos is essentially proportional to the mean density of the universe at their time of formation. Yet, proportionality with respect to the critical density yields slightly better results for open universes. In addition, we find that the scale radius of halos is also essentially proportional to their virial radius at the time of formation. We show that these two relations are consistent with the following simple scenario. Violent relaxation caused by mergers rearranges the structure of halos leading to the same density profile with universal values of the dimensionless characteristic density and scale radius. Between mergers, halos grow gradually through the accretion of surrounding layers by keeping their central parts steady and expanding their virial radius as the critical density of the universe diminishes.
Evolution of the phase-space density of dark matter haloes and mixing effects in merger events
Monthly Notices of the Royal Astronomical Society, 2006
Cosmological N-body simulations were performed to study the evolution of the phase-space density Q = ρ/σ 3 of dark matter halos. No significant differences in the scale relations Q ∝ σ −2.1 or Q ∝ M −0.82 are seen for "cold" or "warm" dark matter models. The follow up of individual halos from z = 10 up to the present time indicate the existence of two main evolutionary phases: an early and fast one (10 > z > 6.5), in which Q decreases on the average by a factor of 40 as a consequence of the randomization of bulk motions and a late and long one (6.5 > z ≥ 0), in which Q decreases by a factor of 20 because of mixing induced by merger events. The study of these halos has also evidenced that rapid and positive variations of the velocity dispersion, induced by merger episods, are related to a fast decrease of the phase density Q.
On the reliability of merger-trees and the mass growth histories of dark matter haloes
We have used merger trees realizations to study the formation of dark matter haloes. The construction of merger-trees is based on three different pictures about the formation of structures in the Universe. These pictures include: the spherical collapse (SC), the ellipsoidal collapse (EC) and the non-radial collapse (NR). The reliability of merger-trees has been examined comparing their predictions related to the distribution of the number of progenitors, as well as the distribution of formation times, with the predictions of analytical relations. The comparison yields a very satisfactory agreement. Subsequently, the mass growth histories (MGH) of haloes have been studied and their formation scale factors have been derived. This derivation has been based on two different definitions that are: (a) the scale factor when the halo reaches half its present day mass and (b) the scale factor when the mass growth rate falls below some specific value. Formation scale factors follow approximately power laws of mass. It has also been shown that MGHs are in good agreement with models proposed in the literature that are based on the results of N-body simulations. The agreement is found to be excellent for small haloes but, at the early epochs of the formation of large haloes, MGHs seem to be steeper than those predicted by the models based on N-body simulations. This rapid growth of mass of heavy haloes is likely to be related to a steeper central density profile indicated by the results of some N-body simulations.
The merger rates and mass assembly histories of dark matter haloes in the two Millennium simulations
Monthly Notices of The Royal Astronomical Society, 2010
We construct merger trees of dark matter haloes and quantify their merger rates and mass growth rates using the joint dataset from the Millennium and Millennium-II simulations. The finer resolution of the Millennium-II Simulation has allowed us to extend our earlier analysis of halo merger statistics to an unprecedentedly wide range of descendant halo mass (10^10 < M0 < 10^15 Msun), progenitor mass ratio (10^-5 < xi < 1), and redshift (0 < z < 15). We update our earlier fitting form for the mean merger rate per halo as a function of M_0, xi, and z. The overall behavior of this quantity is unchanged: the rate per unit redshift is nearly independent of z out to z~15; the dependence on halo mass is weak (M0^0.13); and it is nearly a power law in the progenitor mass ratio (xi^-2). We also present a simple and accurate fitting formula for the mean mass growth rate of haloes as a function of mass and redshift. This mean rate is 46 Msun/yr for 10^12 Msun haloes at z=0, and it increases with mass as M^{1.1} and with redshift as (1+z)^2.5 (for z > 1). When the fit for the mean mass growth rate is integrated over a halo's history, we find excellent match to the mean mass assembly histories of the simulated haloes. By combining merger rates and mass assembly histories, we present results for the number of mergers over a halo's history and the statistics of the redshift of the last major merger.
The structure and dynamical evolution of dark matter haloes
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.
Predicting the Number, Spatial Distribution, and Merging History of Dark Matter Halos
The Astrophysical Journal, 2002
We present a new algorithm (PINOCCHIO, PINpointing Orbit-Crossing Collapsed HIerarchical objects) to predict accurately the formation and evolution of individual dark matter haloes in a given realization of an initial linear density field. Compared with the halo population formed in a large (360 3 particles) collisionless simulation of a CDM universe, our method is able to predict to better than 10 per cent statistical quantities such as the mass function, two-point correlation function and progenitor mass function of the haloes. Masses of individual haloes are estimated accurately as well, with errors typically of order 30 per cent in the mass range well resolved by the numerical simulation. These results show that the hierarchical formation of dark matter haloes can be accurately predicted using local approximations to the dynamics when the correlations in the initial density field are properly taken into account. The approach allows one to automatically generate a large ensemble of accurate merging histories of haloes with complete knowledge of their spatial distribution. The construction of the full merger tree for a 256 3 realisation requires a few hours of CPU-time on a personal computer, orders of magnitude faster than the corresponding N -body simulation would take, and without needing any extensive post-processing. The technique can be efficiently used, for instance, for generating the input for galaxy formation modeling.
Phase-Space Evolution of Dark Matter Halos
2007
(Context) In a Universe dominated by dark matter, halos are continuously accreting mass (violently or not) and such mechanism affects their dynamical state. (Aims) The evolution of dark matter halos in phase-space, and using the phase-space density indicator Q=rho/sigma^3 as a tracer, is discussed. (Methods) We have performed cosmological N-body simulations from which we have carried a detailed study of the evolution of ~35 dark halos in the interval 0<z<10. (Results)The follow up of individual halos indicates two distinct evolutionary phases. First, an early and fast decrease of Q associated to virialization after the gravitational collapse takes place. The nice agreement between simulated data and theoretical expectations based on the spherical collapse model support such a conjecture. The late and long period where a slow decrease of the phase-space density occurs is related to accretion and merger episodes. The study of some merger events in the phase-space (radial velocity versus radial distance) reveals the formation of structures quite similar to caustics generated in secondary infall models of halo formation. After mixing in phase-space, halos in quasi-equilibrium have flat-topped velocity distributions (negative kurtosis) with respect to Gaussians. The effect is more noticiable for captured satellites and/or substructures than for the host halo.
The nearly universal merger rate of dark matter haloes in LambdaCDM cosmology
Monthly Notices of The Royal Astronomical Society, 2008
We construct merger trees from the largest data base of dark matter haloes to date provided by the Millennium Simulation to quantify the merger rates of haloes over a broad range of descendant halo mass (1012≲M0≲ 1015 MȮ), progenitor mass ratio (10−3≲ξ≤ 1), and redshift (0 ≤z≲ 6). We find the mean merger rate per halo, B/n, to have very simple dependence on M0, ξ, and z, and propose a universal fitting form for B/n that is accurate to 10–20 per cent. Overall, B/n depends very weakly on the halo mass (∝M0.080) and scales as a power law in the progenitor mass ratio (∝ξ−2) for minor mergers (ξ≲ 0.1) with a mild upturn for major mergers. As a function of time, we find the merger rate per Gyr to evolve roughly as (1 +z) with nm= 2–2.3, while the rate per unit redshift is nearly independent of z. Several tests are performed to assess how our merger rates are affected by e.g. the time interval between Millennium outputs, binary versus multiple progenitor mergers, and mass conservat...
Scale radii and aggregation histories of dark haloes
Monthly Notices of the Royal Astronomical Society, 2005
Relaxed dark-matter haloes are found to exhibit the same universal density profiles regardless of whether they form in hierarchical cosmologies or via spherical collapse. Likewise, the shape parameters of haloes formed hierarchically do not seem to depend on the epoch in which the last major merger took place. Both findings suggest that the density profile of haloes does not depend on their aggregation history. Yet, this possibility is apparently at odds with some correlations involving the scale radius r s found in numerical simulations. Here we prove that the scale radius of relaxed, nonrotating, spherically symmetric haloes endowed with the universal density profile is determined exclusively by the current values of four independent, though correlated, quantities: mass, energy and their respective instantaneous accretion rates. Under this premise and taking into account the inside-out growth of haloes during the accretion phase between major mergers, we build a simple physical model for the evolution of r s along the main branch of halo merger trees that reproduces all the empirical trends shown by this parameter in N-body simulations. This confirms the conclusion that the empirical correlations involving r s do not actually imply the dependence of this parameter on the halo aggregation history. The present results give strong support to the explanation put forward in a recent paper by Manrique et al. (2003) for the origin of the halo universal density profile.