Formation Of Dark Matter Halos Research Articles

The imprint of cosmological non-Gaussianities on primordial structure formation

We study via numerical N-body/SPH chemistry simulations the effects of primordial non-Gaussianities on the formation of the first stars and galaxies, and investigate the impact of supernova feedback in cosmologies with different fnl. Density distributions are biased to higher values, so star formation and the consequent feedback processes take place earlier in high-fnl models and later in low-fnl ones. Mechanical feedback is responsible for shocking and evacuating the gas from star forming sites earlier in the highly non-Gaussian cases, because of the larger bias at high densities. Chemical feedback translates into high-redshift metal filling factors that are larger by some orders of magnitude for larger fnl, but that converge within one Gyr, for both population III and population II-I stellar regimes. The efficient enrichment process, though, leads to metallicities > 0.01 Zsun by redshift ~9, almost independently from fnl. The impact of non-Gaussianities on the formation of dark-matter haloes at high redshift is directly reflected in the properties of the gas in these haloes, as models with larger fnl show more concentrated gas profiles at early times. Non-Gaussian signatures in the gas behaviour are lost after the first feedback takes place and introduces a significant degree of turbulence and chaotic motions.

Simulation studies of dark energy clustering induced by the formation of dark matter halos

In this paper, we present a simulation method within the two-component spherical collapse model to investigate dark energy perturbations associated with the formation of dark matter halos. The realistic mass accretion history of a dark matter halo taking into account its fast and slow growth is considered by imposing suitable initial conditions and isotropized virializations for the spherical collapse process. The dark energy component is treated as a perfect fluid described by two important parameters, the equation of state parameter $w$ and the sound speed $c_s$. Quintessence models with $w>-1$ are analyzed. We adopt the Newtonian gauge to describe the spacetime which is perturbed mainly by the formation of a dark matter halo. It is found that the dark energy density perturbation $\delta_{DE}$ depends on $w$ and $c_s$, and its behavior follows closely the gravitational potential $\Phi$ of the dark matter halo with $\delta_{DE}\approx -(1+w)\Phi/c_s^2$. For $w>-1$, the dark energy perturbation presents a clustering behavior with $\delta_{DE}>0$ during the entire formation of the dark matter halo, from linear to nonlinear and virialized stages. The value of $\delta_{DE}$ increases with the increase of the halo mass. For a cluster of mass $M\sim 10^{15} M_{\odot}$, $\delta_{DE}\sim 10^{-5}$ within the virialized region for $c_s^2 \in [0.5, 1]$, and it can reach $\delta_{DE}=O(1)$ with $c_s^2=0.00001$. For a scalar-field dark energy model, we find that with suitably modeled $w$ and $c_s$, its perturbation behavior associated with the nonlinear formation of dark matter halos can well be analyzed using the fluid approach, demonstrating the validity of the fluid description for dark energy even considering its perturbation in the stage of nonlinear dark matter structure formation.

Merger rates of dark matter haloes: a comparison between EPS and N-body results

We calculate merger rates of dark matter haloes using the Extended Press-Schechter approximation (EPS) for the Spherical Collapse (SC) and the Ellipsoidal Collapse (EC) models. Merger rates have been calculated for masses in the range $10^{10}M_{\odot}\mathrm{h}^{-1}$ to $10^{14}M_{\odot}\mathrm{h}^{-1}$ and for redshifts $z$ in the range 0 to 3 and they have been compared with merger rates that have been proposed by other authors as fits to the results of N-body simulations. The detailed comparison presented here shows that the agreement between the analytical models and N-body simulations depends crucially on the mass of the descendant halo. For some range of masses and redshifts either SC or EC models approximate satisfactory the results of N-body simulations but for other cases both models are less satisfactory or even bad approximations. We showed, by studying the parameters of the problem that a disagreement --if it appears-- does not depend on the values of the parameters but on the kind of the particular solution used for the distribution of progenitors or on the nature of EPS methods. Further studies could help to improve our understanding about the physical processes during the formation of dark matter haloes.

The peaks formalism and the formation of cold dark matter haloes

We use two cosmological simulations of structure formation to study the conditions under which dark matter haloes emerge from the linear density field. Our analysis focuses on matching sites of halo collapse to local density maxima, or "peaks", in the initial conditions of the simulations and provides a crucial test of the central ansatz of the peaks formalism. By identifying peaks on a variety of smoothed, linearly extrapolated density fields we demonstrate that as many as ~70% of well-resolved dark matter haloes form preferentially near peaks whose characteristic masses are similar to that of the halo, with more massive haloes showing a stronger tendency to reside near peaks initially. We identify a small but significant fraction of haloes that appear to evolve from peaks of substantially lower mass than that of the halo itself. We refer to these as "peakless haloes" for convenience. By contrasting directly the properties of these objects with the bulk of the proto-halo population we find two clear differences: 1) their initial shapes are significantly flatter and more elongated than the predominantly triaxial majority, and 2) they are, on average, more strongly compressed by tidal forces associated with their surrounding large scale structure. Using the two-point correlation function we show that peakless haloes tend to emerge from highly clustered regions of the initial density field implying that, at fixed mass, the accretion geometry and mass accretion histories of haloes in highly clustered environments differ significantly from those in the field. This may have important implications for understanding the origin of the halo assembly bias, of galaxy properties in dense environments and how environment affects the morphological transformation of galaxies near groups and rich galaxy clusters.

The Sloan great wall. Rich clusters

We present the results of the study of the substructure and galaxy content of ten rich clusters of galaxies in three different superclusters of the Sloan Great Wall. We determine the substructure in clusters using the 'Mclust' package from the 'R' statistical environment and analyse their galaxy content. We analyse the distribution of the peculiar velocities of galaxies in clusters and calculate the peculiar velocity of the first ranked galaxy. We show that clusters in our sample have more than one component; in some clusters different components also have different galaxy content. We find that in some clusters with substructure the peculiar velocities of the first ranked galaxies are large. All clusters in our sample host luminous red galaxies. They can be found both in the central areas of clusters as well as in the outskirts, some of them have large peculiar velocities. About 1/3 of red galaxies in clusters are spirals. The scatter of colours of red ellipticals is in most clusters larger than that of red spirals. The presence of substructure in rich clusters, signs of possible mergers and infall, as well as the large peculiar velocities of the first ranked galaxies suggest that the clusters in our sample are not yet virialized. We present merger trees of dark matter haloes in an N-body simulation to demonstrate the formation of present-day dark matter haloes via multiple mergers during their evolution. In simulated dark matter haloes we find a substructure similar to that in observed clusters.

The earliest stars and their relics in the Milky Way

We have implemented a simple model to identify the likely sites of the first stars and galaxies in the high-resolution simulations of the formation of galactic dark matter halos of the Aquarius Project. The first star in a galaxy like the Milky Way formed around redshift z=35; by z=10, the young galaxy contained up to 30000 dark matter haloes capable of forming stars by molecular hydrogen cooling. These minihaloes were strongly clustered and feedback may have severely limited the actual number of Population III stars that formed. By the present day, the remnants of the first stars would be strongly concentrated to the centre of the main halo. If a second generation of long-lived stars formed near the first (the first star relics), we would expect to find half of them within 30kpc/h of the galactic centre and a significant fraction in satellites where they may be singled out by their anomalous metallicity patterns. The first halo in which gas could cool by atomic hydrogen line radiation formed at z=25; by z=10, the number of such first galaxies had increased to ~300. Feedback might have decreased the number of first galaxies at the time they undergo significant star formation, but not the number that survive to the present because near neighbours merge. Half of all the "first galaxies" that form before z=10 merge with the main halo before z~3 and most lose a significant fraction of their mass. However, today there should still be more than 20 remnants orbiting within the central ~30kpc/h of the Milky Way. These satellites have circular velocities of a few kilometers per second or more, comparable to those of known Milky Way dwarfs. They are a promising hunting ground for the remnants of the earliest epoch of star formation.

THE DYNAMICAL STRUCTURE OF DARK MATTER HALOS WITH UNIVERSAL PROPERTIES

$N$-body simulations have unveiled several apparently universal properties of dark matter halos, including a cusped density profile, a power-law pseudo phase-space density $\rho/\sigma_r^3$, and a linear $\beta-\gamma$ relation between the density slope and the velocity anisotropy. We present a family of self-consistent phase-space distribution functions $F(E,L)$, based on the Dehnen-McLaughlin Jeans models, that incorporate these universal properties very accurately. These distribution functions, derived using a quadratic programming technique, are analytical, positive and smooth over the entire phase space and are able to generate four-parameter velocity anisotropy profiles $\beta(r)$ with arbitrary asymptotic values $\beta_0$ and $\beta_\infty$. We discuss the orbital structure of six radially anisotropic systems in detail and argue that, apart from its use for generating initial conditions for $N$-body studies, our dynamical modeling provides a valuable complementary approach to understand the processes involved in the formation of dark matter halos.

The Role of the Radial Orbit Instability in Dark Matter Halo Formation and Structure

For a decade, N-body simulations have revealed a nearly universal dark matter density profile, which appears to be robust to changes in the overall density of the universe and the underlying power spectrum. Despite its universality, the physical origin of this profile has not yet been well understood. Semianalytic models by Barnes and coworkers have suggested that the density structure of dark matter halos is determined by the onset of the radial orbit instability (ROI). We have tested this hypothesis using N-body simulations of collapsing dark matter halos with a variety of initial conditions. For dynamically cold initial conditions, the resulting halo structures are triaxial in shape, due to the mild aspect of the instability. We examine how variations in initial velocity dispersion affect the onset of the instability, and find that an isotropic velocity dispersion can suppress the ROI entirely, while a purely radial dispersion does not. The quantity -->σ2/v2c is a criterion for instability, where regions with -->σ2/v2c 1 become triaxial due to the ROI or other perturbations. We also find that the radial orbit instability sets a scale length at which the velocity dispersion changes rapidly from isotropic to radially anisotropic. This scale length is proportional to the radius at which the density profile changes shape, as is the case in the semianalytic models; however, the coefficient of proportionality is different by a factor of ~2.5. We conclude that the radial orbit instability is likely to be a key physical mechanism responsible for the nearly universal profiles of simulated dark matter halos.

Quantifying the cosmic web - I. The large-scale halo ellipticity-ellipticity and ellipticity-direction correlations

The formation of dark matter halos tends to occur anisotropically along the filaments of the Cosmic Web, which induces both ellipticity-ellipticity (EE) correlations between the shapes of halos, as well as ellipticity-direction (ED) cross-correlations between halo shapes and the directions to neighboring halos. We analyze the halo catalogue and the semi-analytic galaxy catalogue of the recent Millennium Run Simulation to measure the EE and ED correlations numerically at four different redshifts (z=0, 0.5, 1 and 2). For the EE correlations, we find that (i) the major-axis correlation is strongest while the intermediate-axis correlation is weakest; (ii) the signal is significant at distances out to 10 Mpc/h; (iii) the signal decreases as z decreases; (iv) and its behavior depends strongly on the halo mass scale, with larger masses showing stronger correlations at large distances. For the ED correlations, we find that (i) the correlations are much stronger than the EE correlations, and are significant even out to distances of 50 Mpc/h; (ii) the signal also decreases as z decreases; (iii) and it increases with halo mass at all distances. We also provide empirical fitting functions for the EE and ED correlations. The EE correlations are found to scale linearly with the linear density correlation function, xi(r). While the ED cross-correlation is found to scale as xi^{1/2}(r) at large distances beyond 10 Mpc/h. The best-fit values of the fitting parameters for the EE and the ED correlations are all determined through chi^{2}-statistics. Our results may be useful for quantifying the filamentary distribution of dark matter halos over a wide range of scales.

Evidence of turbulence-like universality in the formation of galaxy-sized dark matter haloes

Although the theoretical understanding of the nonlinear gravitational clustering has greatly advanced in the last decades, in particular by the outstanding improvement on numerical N-body simulations, the physics behind this process is not fully elucidated. The main goal of this work is the study of the possibility of a turbulent-like physical process in the formation of structures, galaxies and clusters of galaxies, by the action of gravity alone. We use simulation data from the Virgo Consortium, in ten redshift snapshots (from 0 to 10). From this we identify galaxy-sized and cluster-sized dark matter haloes, by using a FoF algorithm and applying a boundedness criteria, and study the gravitational potential energy spectra. We find that the galaxy-sized haloes energy spectrum follows closely a Kolmogorov's power law, similar to the behaviour of dynamically turbulent processes in fluids. This means that the gravitational clustering of dark matter may admit a turbulent-like representation.

The Halo Mass Function: High‐Redshift Evolution and Universality

We study the formation of dark matter halos in the concordance ΛCDM model over a wide range of redshifts, from -->z = 20 to the present. Our primary focus is the halo mass function, a key probe of cosmology. By performing a large suite of nested-box N-body simulations with careful convergence and error controls (60 simulations with box sizes from 4 to 256 h−1 Mpc), we determine the mass function and its evolution with excellent statistical and systematic errors, reaching a few percent over most of the considered redshift and mass range. Across the studied redshifts, the halo mass is probed over 6 orders of magnitude (107-1013.5 h−1 M☉). Historically, there has been considerable variation in the high-redshift mass function as obtained by different groups. We have made a concerted effort to identify and correct possible systematic errors in computing the mass function at high redshift and to explain the discrepancies between some of the previous results. We discuss convergence criteria for the required force resolution, simulation box size, halo mass range, initial and final redshifts, and time stepping. Because of conservative cuts on the mass range probed by individual boxes, our results are relatively insensitive to simulation volume, the remaining sensitivity being consistent with extended Press-Schechter theory. Previously obtained mass function fits near -->z = 0, when scaled by linear theory, are in good agreement with our results at all redshifts, although a mild redshift dependence consistent with that found by Reed et al. may exist at low redshifts. Overall, our results are consistent with a universal form for the mass function at high redshifts.

Orbital Instabilities in a Triaxial Cusp Potential

This paper constructs an analytic form for a triaxial potential that describes the dynamics of a wide variety of astrophysical systems, including the inner portions of dark matter halos, the central regions of galactic bulges, and young embedded star clusters. Specifically, this potential results from a density profile of the form $\rho (m) \propto m^{-1}$, where the radial coordinate is generalized to triaxial form so that $m^2 = x^2/a^2 + y^2/b^2 + z^2/c^2 $. Using the resulting analytic form of the potential, and the corresponding force laws, we construct orbit solutions and show that a robust orbit instability exists in these systems. For orbits initially confined to any of the three principal planes, the motion in the perpendicular direction can be unstable. We discuss the range of parameter space for which these orbits are unstable, find the growth rates and saturation levels of the instability, and develop a set of analytic model equations that elucidate the essential physics of the instability mechanism. This orbit instability has a large number of astrophysical implications and applications, including understanding the formation of dark matter halos, the structure of galactic bulges, the survival of tidal streams, and the early evolution of embedded star clusters.

The spherical collapse model with shell-crossing

In this work, we study the formation and evolution of dark matter haloes by means of the spherical infalling model with shell-crossing. We present a framework to tackle this effect properly based on the numerical follow-up, with time, of that individual shell of matter that contains always the same fraction of mass with respect to the total mass. In this first step, we do not include angular momentum, velocity dispersion or triaxiality. Within this framework -named as the spherical shell tracker - we investigate the dependence of the evolution of the halo with virial mass, with the adopted mass fraction of the shell, and for different cosmologies. We find that our results are very sensitive to a variation of the halo virial mass or the mass fraction of the shell that we consider. However, we obtain a negligible dependence on cosmology. Furthermore, we show that the effect of shell-crossing plays a crucial role in the way that the halo reaches the stabilization in radius and the virial equilibrium. We find that the values currently adopted in the literature for the actual density contrast at the moment of virialization, δ vir , may not be accurate enough. In this context, we stress the problems related to the definition of a virial mass and a virial radius for the halo. The question of whether the results found here may be obtained by tracking the shells with an analytic approximation remains to be explored.

THE EXCURSION SET THEORY OF HALO MASS FUNCTIONS, HALO CLUSTERING, AND HALO GROWTH

I review the excursion set theory with particular attention toward applications to cold dark matter halo formation and growth, halo abundance, and halo clustering. After a brief introduction to notation and conventions, I begin by recounting the heuristic argument leading to the mass function of bound objects given by Press and Schechter. I then review the more formal derivation of the Press–Schechter halo mass function that makes use of excursion sets of the density field. The excursion set formalism is powerful and can be applied to numerous other problems. I review the excursion set formalism for describing both halo clustering and bias and the properties of void regions. As one of the most enduring legacies of the excursion set approach and one of its most common applications, I spend considerable time reviewing the excursion set theory of halo growth. This section of the review culminates with the description of two Monte Carlo methods for generating ensembles of halo mass accretion histories. In the last section, I emphasize that the standard excursion set approach is the result of several simplifying assumptions. Dropping these assumptions can lead to more faithful predictions and open excursion set theory to new applications. One such assumption is that the height of the barriers that define collapsed objects is a constant function of scale. I illustrate the implementation of the excursion set approach for barriers of arbitrary shape. One such application is the now well-known improvement of the excursion set mass function derived from the "moving" barrier for ellipsoidal collapse. I also emphasize that the statement that halo accretion histories are independent of halo environment in the excursion set approach is not a general prediction of the theory. It is a simplifying assumption. I review the method for constructing correlated random walks of the density field in the more general case. I construct a simple toy model to illustrate that excursion set theory (with a constant barrier height) makes a simple and general prediction for the relation between halo accretion histories and the large-scale environments of halos: regions of high density preferentially contain late-forming halos and conversely for regions of low density. I conclude with a brief discussion of the importance of this prediction relative to recent numerical studies of the environmental dependence of halo properties.

Environmental dependence of cold dark matter halo formation

We use a high-resolution N-body simulation to study how the formation of cold dark matter haloes is affected by their environments, and how such environmental effects produce the age dependence of halo clustering observed in recent N-body simulations. We estimate, for each halo selected at redshift z = 0, an 'initial' mass M-i defined to be the mass enclosed by the largest sphere which contains the initial barycentre of the halo particles and within which the mean linear density is equal to the critical value for spherical collapse at z = 0. For haloes of a given final mass, M-h, the ratio M-i/M-h has large scatter, and the scatter is larger for haloes of lower final masses. Haloes that form earlier on average have larger M-i/M-h, and so correspond to higher peaks in the initial density field than their final masses imply. Old haloes are more strongly clustered than younger ones of the same mass because their initial masses are larger. The age dependence of clustering for low-mass haloes is entirely due to the difference in the initial/final mass ratio. Low-mass old haloes are almost always located in the vicinity of big structures, and their old ages are largely due to the fact that their mass accretions are suppressed by the hot environments produced by the tidal fields of the larger structure. The age dependence of clustering is weaker for more massive haloes because the heating by large-scale tidal fields is less important.

The Asymptotic Form of Cosmic Structure: Small‐Scale Power and Accretion History

We explore the effects of small-scale structure on the formation and equilibrium of dark matter halos in a universe dominated by vacuum energy. We present the results of a suite of four N-body simulations, two with a ΛCDM initial power spectrum and two with WDM-like spectra that suppress the early formation of small structures. All simulations are run into the far future when the universe is 64 h-1 Gyr old, long enough for halos to essentially reach dynamical equilibrium. We quantify the importance of hierarchical merging on the halo mass accretion history, the substructure population, and the equilibrium density profile. We modify the mass accretion history function of Wechsler and coworkers by introducing a parameter, γ, that controls the rate of mass accretion, d ln M/d ln a ∝ a-γ, and find that this form characterizes both hierarchical and monolithic formation. Subhalo decay rates are exponential in time with a much shorter timescale for WDM halos. At the end of the simulations, we find truncated Hernquist density profiles for halos in both the CDM and WDM cosmologies. There is a systematic shift to lower concentration for WDM halos, but both cosmologies lie on the same locus relating concentration and formation epoch. Because the form of the density profile remains unchanged, our results indicate that the equilibrium halo density profile is set independently of the halo formation process.

The Role of the Radial Orbit Instability in Dark Matter Halo Formation and Structure

AbstractFor nearly a decade, N-body simulations have revealed a nearly universal dark matter density profile. This density profile appears to be robust to changes in the overall density of the universe and the underlying power spectrum. Despite its universality, however, the physical origin of this profile has not yet been well understood. Semi-analytic models have suggested that scale lengths in dark matter halos may be determined by the onset of the radial orbit instability. We have tested this theory using N-body simulations of collapsing dark matter halos. The resulting halo structures are prolate in shape, due to the mild aspect of the instability. We find that the radial orbit instability sets a scale length at which the velocity dispersion changes rapidly from isotropic to radially anisotropic. Preliminary analysis suggests that this scale length is proportional to the radius at which the density profile changes shape, as is the case in the semi-analytic models; however, the coefficient of proportionality is different by a factor of ~2. We conclude that the radial orbit instability may be a key physical mechanism responsible for the nearly universal profiles of simulated dark matter halos.

Density Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems

We investigate the connection between collisionless equilibria and the phase-space relation between density ρ and velocity dispersion σ found in simulations of dark matter halo formation, F = ρ/σ3 ∝ r-α. Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-free ρ/σ3 distributions when in equilibrium. We have also done a preliminary investigation of variables other than r that may match or supersede the correlation with F. In the same vein, we show that ρ/σm, where m = 3, is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law F distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the ρ/σ3 distributions of virialized systems.

Dimensionless constants, cosmology, and other dark matters

We identify 31 dimensionless physical constants required by particle physics and cosmology, and emphasize that both microphysical constraints and selection effects might help elucidate their origin. Axion cosmology provides an instructive example, in which these two kinds of arguments must both be taken into account, and work well together. If a Peccei-Quinn phase transition occurred before or during inflation, then the axion dark matter density will vary from place to place with a probability distribution. By calculating the net dark matter halo formation rate as a function of all four relevant cosmological parameters and assessing other constraints, we find that this probability distribution, computed at stable solar systems, is arguably peaked near the observed dark matter density. If cosmologically relevant weakly interacting massive particle (WIMP) dark matter is discovered, then one naturally expects comparable densities of WIMPs and axions, making it important to follow up with precision measurements to determine whether WIMPs account for all of the dark matter or merely part of it.

Small scale structure formation in chameleon cosmology

Chameleon fields are scalar fields whose mass depends on the ambient matter density. We investigate the effects of these fields on the growth of density perturbations on sub-galactic scales and the formation of the first dark matter halos. Density perturbations on comoving scales R<1 pc go non-linear and collapse to form structure much earlier than in standard ΛCDM cosmology. The resulting mini-halos are hence more dense and resilient to disruption. We therefore expect (provided that the density perturbations on these scales have not been erased by damping processes) that the dark matter distribution on small scales would be more clumpy in chameleon cosmology than in the ΛCDM model.