A Model for the Formation and Evolution of Cosmological Halos
Paul Shapiro2002, arXiv (Cornell University)
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Abstract
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This paper presents a model for the formation and evolution of cosmological halos, utilizing adaptive smoothed particle hydrodynamics (SPH) and N-body simulations to analyze dark matter halo dynamics resulting from gravitational instability in cosmological pancakes. The study identifies three distinct mass evolution stages in halos—initial collapse, intermediate infall, and a tapering off of accretion—demonstrating that fundamental properties of halo collapse and evolution are consistent across various initial conditions, ultimately resembling those observed in cold dark matter (CDM) scenarios.
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The Equilibrium Structure of CDM Halos
Arxiv preprint astro-ph/ …, 2004
Dark-matter (DM) halos are the scaffolding around which galaxies and clusters are built. They form when the gravitational instability of primordial density fluctuations causes regions which are denser than average to slow their cosmic expansion, recollapse, and virialize. Understanding the equilibrium structure of these halos is thus a prerequisite for understanding galaxy and cluster formation. Numerical N-body simulations of structure formation from Gaussian-random-noise initial conditions in the Cold Dark Matter (CDM) universe find a universal internal structure for halos. Objects as different in size and mass as dwarf spheroidal galaxies and galaxy clusters are predicted to have halos with the same basic structure when properly rescaled, independent of halo mass, of the shape of the power spectrum of primordial density fluctuations, and of the cosmological background parameters. This remarkable universality is a fundamental prediction of the CDM model, but our knowledge is limited to the "empirical" N-body simulation results, with little analytical understanding. We summarize here our attempts to fill this gap, in an effort to derive and give physical insight to the numerical results and extend them beyond the range of numerical simulation: (1) Simulated halos which form from highly simplified initial conditions involving gravitational instability in a cosmological pancake show that many of the universal properties of CDM halos are generic to cosmological gravitational collapse and do not require Gaussian-random-noise density fluctuations or hierarchical clustering. (2) A fluid approximation derived from the Boltzmann equation yields an analytical theory of halo dynamics which can explain many of the N-body results if the complex mass assembly history of individual halos is approximated by continuous spherical infall. The universal mass growth history reported for CDM N-body halos corresponds to a time-varying infall rate which self-consistently determines the shape of the equilibrium halo profile and its evolution without regard for the complicated details of the merger process.
The Structure and Dynamical Evolution of Dark Matter Halos
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 Gas Accretion History of Low-mass Halos within the Cosmic Web from Cosmological Simulations
The Astrophysical Journal
Using high resolution hydrodynamical cosmological simulations, we study the gas accretion history of low mass halos located in a field-like, low density environment. We track their evolution individually from the early, pre-reionization era, through reionization, and beyond until z = 0. Before reionization, low mass halos accrete cool cosmic web gas at a very rapid rate, often reaching the highest gas mass they will ever have. But when reionization occurs, we see that almost all halos lose significant quantities of their gas content, although some respond less quickly than others. We find that the response rate is influenced by halo mass first, and secondarily by their internal gas density at the epoch of reionization. Reionization also fully ionises the cosmic web gas by z∼6. As a result, the lowest mass halos (M∼10 6 h −1 M ⊙ at z = 6) can never again re-accrete gas from the cosmic web, and by z ∼ 5 have lost all their internal gas to ionisation, resulting in a halt in star formation at this epoch. However, more massive halos can recover from their gas mass loss, and re-accrete ionised cosmic web gas. We find the efficiency of this re-accretion is a function of halo mass first, followed by local surrounding gas density. Halos that are closer to the cosmic web structure can accrete denser gas more rapidly. We find that our lower mass halos have a sweet spot for rapid, dense gas accretion at distances of roughly 1-5 virial radii from the most massive halos in our sample (>10 8 h −1 M ⊙), as these tend to be embedded deeply within the cosmic web.
Characterizing dark interactions with the halo mass accretion history and structural properties
Monthly Notices of the Royal Astronomical Society, 2013
ABSTRACT We study the halo mass accretion history (MAH) and its correlation with the internal structural properties in coupled dark energy cosmologies (cDE). To accurately predict all the non-linear effects caused by dark interactions, we use the COupled Dark Energy Cosmological Simulations (CoDECS). We measure the halo concentration at z=0 and the number of substructures above a mass resolution threshold for each halo. Tracing the halo merging history trees back in time, following the mass of the main halo, we develope a MAH model that accurately reproduces the halo growth in term of M_{200} in the {\Lambda}CDM Universe; we then compare the MAH in different cosmological scenarios. For cDE models with a weak constant coupling, our MAH model can reproduce the simulation results, within 10% of accuracy, by suitably rescaling the normalization of the linear matter power spectrum at z=0, {\sigma}_8. However, this is not the case for more complex scenarios, like the "bouncing" cDE model, for which the numerical analysis shows a rapid growth of haloes at high redshifts, that cannot be reproduced by simply rescaling the value of {\sigma}_8. Moreover, at fixed value of {\sigma}_8, cold dark matter (CDM) haloes in these cDE scenarios tend to be more concentrated and have a larger amount of substructures with respect to {\Lambda}CDM predictions. Finally, we present an accurate model that relates the halo concentration to the time at which it assembles half or 4% of its mass. Combining this with our MAH model, we show how halo concentrations change while varying only {\sigma}_8 in a {\Lambda}CDM Universe, at fixed halo mass.
The dynamical state of dark matter haloes in cosmological simulations - I. Correlations with mass assembly history
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.
The ultimate halo mass in a LambdaCDM universe
Monthly Notices of the Royal Astronomical Society: Letters, 2005
In the far future of an accelerating ΛCDM cosmology, the cosmic web of largescale structure consists of a set of increasingly isolated halos in dynamical equilibrium. We examine the approach of collisionless dark matter to hydrostatic equilibrium using a large N-body simulation evolved to scale factor a = 100, well beyond the vacuummatter equality epoch, a eq = 0.75, and 53h −1 Gyr into the future for a concordance model universe (Ω m = 0.3, Ω Λ = 0.7). The radial phase-space structure of haloscharacterized at a < ∼ a eq by a pair of zero-velocity surfaces that bracket a dynamically active accretion region -simplifies at a > ∼ 10a eq when these surfaces merge to create a single zero-velocity surface, clearly defining the halo outer boundary, r halo , and its enclosed mass, M halo . This boundary approaches a fixed physical size encompassing a mean interior density ∼ 5 times the critical density, similar to the turnaround value in a classical Einstein-deSitter model. We relate M halo to other scales currently used to define halo mass (M 200 , M vir , M 180b ) and find that M 200 is approximately half of the total asymptotic cluster mass, while M 180b follows the evolution of the inner zero velocity surface for a < ∼ 2 but becomes much larger than the total bound mass for a > ∼ 3. The radial density profile of all bound halo material is well fit by a truncated Hernquist profile. An NFW profile provides a somewhat better fit interior to r 200 but is much too shallow in the range r 200 < r < r halo .
The physical origin of the universal accretion history of dark matter halos
Understanding the universal accretion history of dark matter halos is the first step towards determining the origin of their universal structure. In this work, we begin by using the extended Press-Schechter (EPS) formalism to show that the halo mass accretion history is determined by the growth rate of initial density perturbations, and that it follows the expression M(z)=M0(1+z)^{af(M0)}e^{-f(M0)z}, where M0=M(z=0), a depends on cosmology and f(M0) depends only on the matter power spectrum. We then explore the relation between the structure of the inner dark matter halo and halo mass history using a suite of cosmological, hydrodynamical simulations. We confirm that the formation time, defined as the time when the virial mass of the main progenitor equals the mass enclosed within the scale radius, correlates strongly with concentration. We provide a fitting formula for the relation between concentration and formation time, from which we show analytically that the scatter in formatio...
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.
Formation and Structure of Halos in a Warm Dark Matter Cosmology
Astrophysical Journal, 2001
Using high-resolution cosmological N-body simulations, we study how the density profiles of dark matter halos are affected by the filtering of the density power spectrum below a given scale length and by the introduction of a thermal velocity dispersion. In the warm dark matter (WDM) scenario, both the free-streaming scale, R f , and the velocity dispersion, v w th , are determined by the mass m W of the WDM particle. We found that v w th is too small to affect the density profiles of WDM halos. Down to the resolution attained in our simulations (∼ 0.01 virial radii), there is not any significant difference in the density profiles and concentrations of halos obtained in simulations with and without the inclusion of v w th . Resolved soft cores appear only when we increase artificially the thermal velocity dispersion to a value which is much higher than v w th . We show that the size of soft cores in a monolithic collapse is related to the tangential velocity dispersion. The density profiles of the studied halos with masses down to ∼ 0.01 the filtering mass M f can be described by the Navarro-Frenk-White shape; soft cores are not formed. Nevertheless, the concentrations of these halos are lower than those of the CDM counterparts and are approximately independent of mass. The cosmogony of halos with masses ∼ < M f is not hierarchical: they form through monolithic collapse and by fragmentation of larger structures. The formation epoch of these halos is slightly later than that of halos with masses ≈ M f . The lower concentrations of WDM halos with respect to their CDM counterparts can be accounted for their late formation epoch.
Prepared for submission to JCAP The Non-Gaussian Halo Mass Function and Non-Spherical Halo Collapse: Theory vs. Simulations
2016
The mass distribution of dark matter halos is a sensitive probe of primordial non-Gaussianity (NG). We derive an analytical formula of the halo mass function by perturbatively computing the excursion set path-integrals for a non-Gaussian density field with non-vanishing skewness, f N L. We assume a stochastic barrier model which captures the main features of the ellipsoidal collapse of halos. Contrary to previous results based on extensions of the Press-Schechter formalism to NG initial conditions, we find that the non-spherical collapse of halos directly alter the signature of primordial NG. This points toward a potential degeneracy between the effect of primordial non-Gaussianity and that of non-linear halo collapse. The inferred mass function is found to be in remarkable agreement with N-body simulations of NG local type. Deviations are well within numerical uncertainties for all values of −80 < f loc N L < 300 in the range of validity of the perturbative calculation. Moreover, the comparison with simulation results suggests that for f N L > 150 or f N L < −50 the non-linear collapse of halos, as described by our barrier model, strongly deviates from that of Gaussian initial conditions. This is not surprising since the effect of non-linear gravitational processes may be altered by initially large NG. Hence, in the lack of prior theoretical knowledge, halo collapse model parameters should be included in statistical halo mass function data analysis which aim to constrain the signature of primordial NG.
Related papers
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.
The evolution of dark-matter dominated cosmological halos
2001
Adaptive SPH and N-body simulations were carried out to study the evolution of the equilibrium structure of dark matter halos that result from the gravitational instability and fragmentation of cosmological pancakes. Such halos resemble those formed by hierarchical clustering from realistic initial conditions in a CDM universe and, therefore, serve as a test-bed model for studying halo dynamics. The dark
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 EFFECTS OF VARYING COSMOLOGICAL PARAMETERS ON HALO SUBSTRUCTURE
The Astrophysical Journal, 2014
We investigate how different cosmological parameters, such as those delivered by the WMAP and Planck missions, affect the nature and evolution of dark matter halo substructure. We use a series of flat Λ cold dark matter (ΛCDM) cosmological N -body simulations of structure formation, each with a different power spectrum but the same initial white noise field. Our fiducial simulation is based on parameters from the WMAP 7th year cosmology. We then systematically vary the spectral index, n s , matter density, Ω M , and normalization of the power spectrum, σ 8 , for 7 unique simulations. Across these, we study variations in the subhalo mass function, mass fraction, maximum circular velocity function, spatial distribution, concentration, formation times, accretion times, and peak mass. We eliminate dependence of subhalo properties on host halo mass and average over many hosts to reduce variance. While the "same" subhalos from identical initial overdensity peaks in higher σ 8 , n s , and Ω m simulations accrete earlier and end up less massive and closer to the halo center at z = 0, the process of continuous subhalo accretion and destruction leads to a steady state distribution of these properties across all subhalos in a given host. This steady state mechanism eliminates cosmological dependence on all properties listed above except subhalo concentration and V max , which remain greater for higher σ 8 , n s and Ω m simulations, and subhalo formation time, which remains earlier. We also find that the numerical technique for computing scale radius and the halo finder used can significantly affect the concentration-mass relationship computed for a simulation.
THE CONTRIBUTION OF HALOS WITH DIFFERENT MASS RATIOS TO THE OVERALL GROWTH OF CLUSTER-SIZED HALOS
The Astrophysical Journal, 2013
We provide a new observational test for a key prediction of the ΛCDM cosmological model: the contributions of mergers with different halo-to-main-cluster mass ratios to cluster-sized halo growth. We perform this test by dynamically analyzing seven galaxy clusters, spanning the redshift range 0.13 < z c < 0.45 and caustic mass range 0.4 − 1.5 10 15 h −1 0.73 M ⊙ , with an average of 293 spectroscopically-confirmed bound galaxies to each cluster. The large radial coverage (a few virial radii), which covers the whole infall region, with a high number of spectroscopically identified galaxies enables this new study. For each cluster, we identify bound galaxies. Out of these galaxies, we identify infalling and accreted halos and estimate their masses and their dynamical states. Using the estimated masses, we derive the contribution of different mass ratios to cluster-sized halo growth. For mass ratios between ∼ 0.2 and ∼ 0.7, we find a ∼ 1σ agreement with ΛCDM expectations based on the Millennium simulations I and II. At low mass ratios, 0.2, our derived contribution is underestimated since the detection efficiency decreases at low masses, ∼ 2 × 10 14 h −1 0.73 M ⊙ . At large mass ratios, 0.7, we do not detect halos probably because our sample, which was chosen to be quite X-ray relaxed, is biased against large mass ratios. Therefore, at large mass ratios, the derived contribution is also underestimated.
MultiDark simulations: the story of dark matter halo concentrations and density profiles
Accurately predicting structural properties of dark matter halos is one of the fundamental goals of modern cosmology. We use the new suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies. The MultiDark simulations cover a large range of masses 10 10 − 10 15 M ⊙ and volumes ranging from ∼ 0.05 Gpc 3 to ∼ 50 Gpc 3 . The total number of dark matter halos in all the simulations and redshifts exceeds 60 billion. We find that in order to understand the structure of dark matter halos and to make 1-2% accurate predictions for density profiles, one needs to realize that halo concentration is more complex than the traditionally accepted ratio of the virial radius to the core radius as in the Navarro-Frenk-White (NFW) profile. For massive halos the average density profile is far from the NFW shape and the concentration is defined by both the core radius and the shape parameter α in the Einasto approximation. Combining results from different redshifts, masses and cosmologies, we show that halos progress through three stages of evolution. They start as rare density peaks that experience very fast and nearly radial infall. This radial infall brings mass closer to the center, producing a highly concentrated halo. At this stage the halo concentration increases with increasing halo mass and the concentration is defined by the α parameter with a nearly constant core radius. Later halos slide into the plateau regime where the accretion becomes less radial, but frequent mergers still affect even the central region. At this stage the concentration does not depend on halo mass. Once the rate of accretion and merging slows down, halos move into the domain of declining concentration-mass relation because new accretion piles up mass close to the virial radius while the core radius is staying constant. Accurate analytical fits to the numerical results for halo density profiles and concentrations are also provided.
The Growth of Dark-Matter Halos. The Effects of Accretion and Mergers
arXiv (Cornell University), 1998
High resolution cosmological N-body simulations show that the density profiles of dark matter halos in hierarchical cosmogonies are universal, with low mass halos typically denser than more massive ones. This mass-density correlation is interpreted as reflecting the earlier formation 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. We find that the characteristic density and the scale radius of halos are essentially proportional, respectively, to the critical density of the universe and the virial radius at the time of their formation. These two relations are consistent with the following simple evolutionary picture. Violent relaxation caused by major mergers rearrange the structure of halos leading to a universal dimensionless density profile. Between major mergers, halos gradually grow through the accretion of surrounding layers by keeping the central part steady and only expanding their virial radius as the critical density of the universe diminishes.
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.
Evolution of Characteristic Quantities for Dark Matter Halo Density Profiles
The Astrophysical Journal, 2007
We have investigated the effect of an assembly history on the evolution of galactic dark matter (DM) halos of 10 12 h −1 M ⊙ using Constrained Realizations of random Gaussian fields. Five different realizations of a DM halo with distinct merging histories were constructed and have been evolved using collisionless high-resolution N -body simulations. Our main results are: A halo evolves via a sequence of quiescent phases of a slow mass accretion intermitted by violent episodes of major mergers. In the quiescent phases, the density is well fitted by an NFW profile, the inner scale radius R s and the mass enclosed within it remain constant, and the virial radius (R vir ) grows linearly with the expansion parameter a. Within each quiescent phase the concentration parameter (c) scales as a, and the mass accretion history (M vir ) is well described by the Tasitsiomi et al. fitting formula. In the violent phases the halos are not in a virial dynamical equilibrium and both R s and R vir grow discontinuously. The violent episodes drive the halos from one NFW dynamical equilibrium to another. The final structure of a halo, including c, depends on the degree of violence of the major mergers and the number of violent events. Next, we find a distinct difference between the behavior of various NFW parameters taken as averages over an ensemble of halos and those of individual halos. Moreover, the simple scaling relations c−M vir do not apply to the entire evolution of individual halos, and so is the common notion that late forming halos are less concentrated than early forming ones. The entire evolution of the halo cannot be fitted by single analytical expressions.
The accretion history of dark matter halos III: A physical model for the concentration-mass relation
We present a semi-analytic, physically motivated model for dark matter halo concentration as a function of halo mass and redshift. The semi-analytic model is intimately based on hierarchical structure formation. It uses an analytic model for the halo mass accretion history, based on extended Press Schechter (EPS) theory, and an empirical relation between concentration and an appropriate definition of formation time obtained through fits to the results of numerical simulations. The resulting concentration-mass relations are tested against the simulations and do not exhibit an upturn at high masses or high redshifts as claimed by recent works. Because our semi-analytic model is based on EPS theory, it can be applied to wide ranges in mass, redshift and cosmology. We predict a change of slope in the z=0 concentration-mass relation at a mass scale of $10^{11}\rm{M}_{\odot}$, that is caused by the varying power in the density perturbations. We provide best-fitting expressions of the $c-M...
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