We use the recently completed one billion particle Via Lactea II LambdaCDM simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the central relaxed regions but spans four orders of magnitude in the outskirts, both because of the presence of subhaloes as well as of underdense regions and holes in the matter distribution. In the inner regions the local velocity dispersion ellipsoid is aligned with the shape ellipsoid of the halo. This is not true in the outer parts where the orientation becomes more isotropic. The clumpy structure in local velocity space of the outer halo can not be well described by a smooth multivariate normal distribution. Via Lactea II also shows the presence of cold streams made visible by their high 6D phase space density. Generally, the structure of dark matter haloes shows a high degree of graininess in phase space that cannot be described by a smooth distribution function.
High-resolution, numerical simulations of 17 cluster-sized dark-matter haloes in eight different cosmologies with and without dynamical dark energy confirm the picture that core halo densities are imprinted early during their formation by the mean cosmological density. Quite independent of cosmology, halo concentrations have a log-normal distribution with a scatter of ~0.2 about the mean. We propose a simple scaling relation for halo concentrations in dark-energy cosmologies.
Recent observations indicate that dark matter haloes have flat central density profiles. Cosmological simulations with non-baryonic dark matter predict however self similar haloes with central density cusps. This contradiction has lead to the conclusion that dark matter must be baryonic. Here it is shown that the dark matter haloes of dwarf spiral galaxies represent a one parameter family with self similar density profiles. The observed global halo parameters are coupled with each other through simple scaling relations which can be explained by the standard cold dark matter model if one assume…
A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the dark matter itself, the model allows one to describe the evolution of the Eulerian space distribution of the haloes. It can also be used to describe density profiles, on scales larger than the virial radius, of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the init…
HD molecules can be an important cooling agent of the primordial gas behind the shock waves originated through mergings of the dark matter haloes at epochs when first luminous objects were to form. We study the necessary conditions for the HD cooling to switch on in the low temperature range $T<200$ K. We show that these conditions are fulfiled in merging haloes with the total (dark matter and baryon) mass in excess of $M_{\rm cr}\sim 10^7[(1+z)/20]^{-2}\msun$. Haloes with masses $M>M_{\rm cr}$ may be the sites of low-mass star formation.
We develop a simple analytic model for the gravitational clustering of dark haloes. The statistical properties of dark haloes are determined from the initial density field (assumed to be Gaussian) through an extension of the Press-Schechter formalism. Gravitational clustering is treated by a spherical model which describes the concentration of dark haloes in collapsing regions. We test this model against results from a variety of N-body simulations. The autocorrelation function of dark haloes in such simulations depends significantly on how haloes are identified. Our predictions agree well wit…
Virial mass is used as an estimator for the mass of a dark matter halo. However, the commonly used constant overdensity criterion does not reflect the dynamical structure of haloes. Here we analyze dark matter cosmological simulations in order to obtain properties of haloes of different masses focusing on the size of the region with zero mean radial velocity. Dark matter inside this region is stationary, and thus the mass of this region is a much better approximation for the virial mass.
We have constructed realistic, self-consistent models of triaxial elliptical galaxies embedded in triaxial dark matter haloes. We examined three different models for the shape of the dark matter halo: (i) the same axis ratios as the luminous matter (0.7:0.86:1); (ii) a more prolate shape (0.5:0.66:1); (iii) a more oblate shape (0.7:0.93:1). The models were obtained by means of the standard orbital superposition technique introduced by Schwarzschild. Self-consistent solutions were found in each of the three cases. Chaotic orbits were found to be important in all of the models,and their presence…
Much evidence suggests that we live in a flat Cold Dark Matter universe with a cosmological constant. Accurate analytic formulae are now available for many properties of the dark halo population in such a Universe. Assuming current ``concordance'' values for the cosmological parameters, we plot halo abundance against redshift as a function of halo mass, of halo temperature, of the fraction of cosmic matter in haloes, of halo clustering strength, and of the clustering strength of the z=0 descendants of high redshift haloes. These plots are useful for understanding how nonlinear structure grows …
Caustics are formally singular structures, with infinite density, that form in collisionless media. The non-negligible velocity dispersion of dark matter particles renders their density finite. We evaluate the maximum density of the caustics within the framework of secondary infall model of formation of dark matter haloes. The result is then used to demonstrate that caustics can be probed by properly stacking the weak-lensing signal of about 600 haloes. CFHTLS accompanied by X-ray observations and the space-based experiments like SNAP or DUNE can provide us with the required statistics and hen…
We estimate the two-point correlation function of dark matter haloes, with masses >10^{13} h^{-1} Mo, that have or not significant substructure. The haloes are identified with a friends of friends algorithm in a large LCDM simulation at two redshift snapshots (z=0 and 1), while halo substructure is determined using an observationally driven method. We find in both epochs a clear and significant signal by which haloes with substructure are more clustered than those with no-substructure. This is true for all the considered halo mass ranges, although for the highest halo masses the signal is nois…
In hierarchical models of gravitational clustering, virialized haloes are biased tracers of the matter distribution. As discussed by Mo & White (1996), this bias is nonlinear and stochastic. They developed a model which allows one to write down analytic expressions for the mean of the bias relation, in the initial Lagrangian, and the evolved, Eulerian spaces. We provide analytic expressions for the higher order moments as well. We also show how the Mo-White approach can be extended to compute the evolution, not just of the haloes, but of the dark matter distribution itself. The model predictio…
The MMF technique is used to segment the cosmic web as seen in a cosmological N-body simulation into wall-like and filament-like structures. We find that the spins and shapes of dark matter haloes are significantly correlated with each other and with the orientation of their host structures. The shape orientation is such that the halo minor axes tend to lie perpendicular to the host structure, be it a wall or filament. The orientation of the halo spin vector is mass dependent. Low mass haloes in walls and filaments have a tendency to have their spins oriented within the parent structure, while…
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 agree…
Models of structure formation based on cold dark matter predict that most of the small dark matter haloes that first formed at high redshift would have merged into larger systems by the present epoch. Substructure in present-day haloes preserves the remains of these ancient systems, providing the only direct information we may ever have about the low-mass end of the power spectrum. I describe some recent attempts to model halo substructure down to very small masses, using a semi-analytic model of halo formation. I make a preliminary comparison between the model predictions, observations of sub…
An overview is presented of the main properties of dark matter haloes, as we know them from observations, essentially from rotation curves around spiral and dwarf galaxies. Detailed rotation curves are now known for more than a thousand galaxies, revealing that they are not so flat in the outer parts, but rising for late-types, and falling for early-types. A well established result now is that most bright galaxies are not dominated by dark matter inside their optical disks. Only for dwarfs and LSB (Low Surface Brightness galaxies) dark matter plays a dominant role in the visible regions. The 3…
Thanks to the ever increasing computational power and the development of more sophisticated algorithms, numerical N-body simulations are now uncovering several phenomenological relations between the physical properties of dark matter haloes in position and velocity space. It is the aim of the present work to investigate in detail the dynamical structure of dark matter haloes, as well as its possible dependence on mass and its evolution with redshift up to z=5. We use high-resolution cosmological simulations of individual objects to compute the radially-averaged profiles of several quantities, …
This paper uses numerical simulations to test the formation time distribution of dark matter haloes predicted by the analytic excursion set approaches. The formation time distribution is closely linked to the conditional mass function and this test is therefore an indirect probe of this distribution. The excursion set models tested are the extended Press-Schechter (EPS) model, the ellipsoidal collapse (EC) model, and the non-spherical collapse boundary (NCB) model. Three sets of simulations (6 realizations) have been used to investigate the halo formation time distribution for halo masses rang…
The effects of merging histories of proto-objects on the angular momentum distributions of the present-time dark matter haloes are analysed. An analytical approach to the analysis of the angular momentum distributions assumes that the haloes are initially homogeneous ellipsoids and that the growth of the angular momentum of the haloes halts at their maximum expansion time. However, the maximum expansion time cannot be determined uniquely, because in the hierarchical clustering scenario each progenitor, or subunit, of the halo has its own maximum expansion time. Therefore the merging history of…
In several interacting systems, gas accumulations as massive as 10^9 solar masses are observed near the tip of tidal tails, and are thought to be possible progenitors of Tidal Dwarf Galaxies. Using N-body simulations of galaxy interactions, we show that the existence of such features requires that dark matter haloes around spiral galaxies extend at least ten times further than the stellar disks. The massive gas clouds formed in our simulations have a kinematical origin and gravitationally collapse into dwarf galaxies that often survive for a few billion years.
We investigate whether a correlation exists between the concentration and spin parameters of dark matter haloes forming in LCDM N-body simulations. In particular, we focus on haloes with virial masses characteristic of the hosts of Low Surface Brightness (LSB) and High Surface Brightness (HSB) galaxies. Our analysis demonstrates that concentration and spin are anti-correlated. If we assume that a galaxy disk forms in one of these haloes from baryons that approximately conserved angular momentum during their dissipation into the rotationally supported disk, then it is possible to estimate the d…
We use an extremely large volume ($2.4h^{-3}{\rm Gpc}^{3}$), high resolution N-body simulation to measure the higher order clustering of dark matter haloes as a function of mass and internal structure. As a result of the large simulation volume and the use of a novel ``cross-moment'' counts-in-cells technique which suppresses discreteness noise, we are able to measure the clustering of haloes corresponding to rarer peaks than was possible in previous studies; the rarest haloes for which we measure the variance are 100 times more clustered than the dark matter. We are able to extract, for the f…
Using the Millennium N-body simulation we explore how the shape and angular momentum of galaxy dark matter haloes surrounding the largest cosmological voids are oriented. We find that the major and intermediate axes of the haloes tend to lie parallel to the surface of the voids, whereas the minor axis points preferentially in the radial direction. We have quantified the strength of these alignments at different radial distances from the void centres. The effect of these orientations is still detected at distances as large as 2.2 R_void from the void centre. Taking a subsample of haloes expecte…
We develop a simple analytic model for the gravitational clustering of dark matter haloes to understand how their spatial distribution is biased relative to that of the mass. The statistical distribution of dark haloes within the initial density field (assumed Gaussian) is determined by an extension of the Press-Schechter formalism. Modifications of this distribution caused by gravitationally induced motions are treated using a spherical collapse approximation. We test this model against results from a variety of N-body simulations, and find that it gives an accurate description of a bias func…
(Abridged) We study the outer density profiles of dark matter haloes predicted by a generalized secondary infall model and observed in a N-body cosmological simulation of a ΛCDM model. We find substantial systematic variations in shapes and concentrations of the halo profiles as well as a strong correlation of the profiles with the environment. In the N-body simulation, the average outer slope of the density profiles, β(ρ\propto r^{-β}), of isolated haloes is \approx 2.9; 68% of these haloes have values of βbetween 2.5 and 3.8. Haloes in dense environments of clusters are more concentrated and…
We present a new fast method for simulating pencil-beam type light-cones, using the MLAPM-code (Multi Level Adaptive Particle Mesh) with light-cone additions. We show that by a careful choice of the light-cone orientation, it is possible to avoid extra periodicities in the light-cone. As an example, we apply the method to simulate a 6 Gpc deep light-cone, create the dark matter halo catalogue for the light-cone and study the evolution of haloes from $z=6$ up to the present time. We determine the spatial density of the haloes, their large-scale correlation function, and study the evolution of t…
Using the high resolution cosmological N-body simulation MareNostrum Universe we study the orientation of shape and angular momentum of galaxy-size dark matter haloes around large voids. We find that haloes located on the shells of the largest cosmic voids have angular momenta that tend to be preferentially perpendicular to the direction that joins the centre of the halo and the centre of the void. This alignment has been found in spiral galaxies around voids using galaxy redshift surveys. We measure for the first time the strength of this alignment, showing how it falls off with increasing di…
Using cosmological N-body simulations we study the radial velocity distribution in dark matter haloes focusing on the lowest-order even moments, dispersion and kurtosis. We determine the properties of ten massive haloes in the simulation box approximating their density distribution by the NFW formula characterized by the virial mass and concentration. We also calculate the velocity anisotropy parameter of the haloes and find it mildly radial and increasing with distance from the halo centre. The radial velocity dispersion of the haloes shows a characteristic profile with a maximum, while the r…
Recent high-resolution simulations together with theoretical studies of the dynamical evolution of galactic disks have shown that contrary to wide-held beliefs a `live', dynamically responsive, dark halo surrounding a disk does not stabilize the disk against dynamical instabilities. We generalize Toomre's Q stability parameter for a disk-halo system and show that if a disk, which would be otherwise stable, is embedded in a halo, which is too massive and cold, the combined disk-halo system can become locally Jeans unstable. The good news is, on the other hand, that this will not happen in real …
In this paper, we analyse in detail the mass-accretion histories and structural properties of dark haloes in high-resolution N-body simulations. Modeling the density distribution in individual haloes with the NFW profile, we find, for all main progenitors of a given halo, there is a tight correlation between its inner scale radius $r_s$ and the mass within it, $M_s$, which is the basic reason why halo structural properties are closely related to their mass-accretion histories. This correlation can be used to predict accurately the structural properties of a dark halo at any time from its mass-…
Integral measures of weak gravitational lensing by dark-matter haloes, like the aperture mass, are sensitive to different physical halo properties dependent on the halo mass density profile. For isothermal profiles, the relation between aperture mass and virial mass is steeper than for haloes with the universal NFW profile. Consequently, the halo mass range probed by the aperture mass is much wider for NFW than for isothermal haloes. We use recent modifications to the Press-Schechter mass function in CDM models normalised to the local abundance of rich clusters, to predict the properties of th…
We present measurements of the spatial clustering of ultraluminous infrared galaxies in two redshift intervals, 1.5<z<2.0 and 2<z<3. Both samples cluster strongly, with r_0=14.40+/-1.99 h^-1 Mpc for the 2<z<3 sample, and r_0=9.40+/-2.24 h^-1 Mpc for the 1.5<z<2.0 sample, making them among the most biased galaxies at these epochs. These clustering amplitudes are consistent with both populations residing in dark matter haloes with masses of ~6x10^13 solar masses. We infer that a minimum dark matter halo mass is an important factor for all forms of luminous, obscured activity in galaxies at z>1. …
(Abridged) Virial mass is used as an estimator for the mass of a dark matter halo. However, the commonly used constant overdensity criterion does not reflect the dynamical structure of haloes. Here we analyze dark matter cosmological simulations in order to obtain properties of haloes of different masses focusing on the size of the region with zero mean radial velocity. Dark matter inside this region is stationary, and thus the mass of this region is a much better approximation for the virial mass. We call this mass the static mass to distinguish from the commonly used constant overdensity mas…
We discuss the tight interconnection between microlensing optical depths, flattening of dark haloes and low-to-intermediate redshift baryonic census. By analysing plots of the microlensing optical depth as a function of galactic coordinates for different values of axis ratio $q$ of the galactic MACHO halo, we have shown that observations are best described by a flattened halo with $q \simeq 0.6$. There is no dynamical obstacle for such a choice of global halo shape. Both extremely flattened $q \simeq 0.2$ and spherical $q \simeq 1$ haloes have several difficulties, although not of equal severi…
Using high resolution cosmological N-body simulations, we investigate the survival of dark matter satellites falling into larger haloes. Satellites preserve their identity for some time after merging. We compute their loss of mass, energy and angular momentum as dynamical friction, tidal forces and collisions with other satellites dissolve them. We also analyse the evolution of their internal structure. Satellites with less than a few per cent the mass of the main halo may survive for several billion years, whereas larger satellites rapidly sink into the center of the main halo potential well …
(abridged) We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press-Schechter (EPS) formalism, (ii) numerical simulations, and (iii) the Lagrangian perturbation code PINOCCHIO. We show that the PINOCCHIO MAHs are in excellent agreement with those obtained using numerical simulations. Using a suite of 55 PINOCCHIO simulations, with 256^3 particles each, we study the MAHs of 12,924 cold dark matter haloes in a \LambdaCDM concordance cosmology. We show that haloes less massive than the characteristic non-li…
We test the Secondary Infall Model (SIM) by direct comparison with the results of N-body simulations. Eight cluster-size and six galactic-size dark matter haloes have been selected at $z=0$ and re-simulated with high resolution. Based on their density profiles at the initial redshift, we compute their evolution by the SIM, assuming a simple prescription for the angular momentum. A comparison of the density profiles obtained by the SIM and the numerical experiments at $z=5$, 1 and 0 shows that, for most of the haloes at most epochs, the SIM reproduces the simulated mater distribution with a typ…
Cold dark matter haloes are populated by high-density structures with sharply-peaked profiles known as caustics which have not yet been resolved by 3-dimensional numerical simulations. Here, we derive semi-analytic expressions for the density profiles near caustics in haloes which form by self-similar accretions of dark matter with infinitesimal velocity dispersion. A simple rescaling shows that similarly to the case of absolutely cold medium these profiles are universal: they are valid for all caustics and irrespective of physical parameters of the halo. We derive the maximum density of the c…
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, wi…
One of the predictions of the standard CDM is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark matter dominated dwarf and low surface brightness galaxies and the inner mass profiles…
We present an approximation for the average density profile of dark matter haloes in the LambdaCDM cosmological model, which is accurate to within 10--15% even for large radial distances from 0.05R_{vir} up to 10R_{vir} for halo masses ranging from 10^{11.5} to 10^{15.0} h^{-1}M_{Sun}. We propose a modified form of the Navarro, Frenk & White (NFW) approximation: ρ(r)=ρ_{NFW}(r)+ A (r/R_{vir})^{-1}+B (1+r/R_{vir})^{-1}. This generalized expression, which is applicable to the external regions of dark matter haloes, only very slightly affects the density in the inner regions of haloes. The strong…
I study the evolution of haloes density profiles as a function of time in the SCDM and LCDM cosmologies. Following Del Popolo et al. (1999), I calculate the concentration parameter c=r_v/a and study its time evolution. For a given halo mass, I find that c(z) ~1/(1+z) both in the LCDM and SCDM cosmology, in agreement with Bullock et al. (1999) analytic model and N-body simulations. In both models, a(z) is roughly constant. The present model predicts a stronger evolution of c(z) with respect to Navarro et al. (1997) model. Finally I show some consequences of the result on galaxy modelling.
We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the `excursion set' approach by Bond et al., which automatically accounts for the `cloud-in-cloud' problem in the identification of bound systems. Our method allows to calculate correlation functions of haloes in Lagrangian space using either a multi-dimensional Fokker-Planck equation with suitable boundary conditions or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical …
We investigate the impact finite simulation box size has on the structural and kinematic properties of Cold Dark Matter haloes forming in cosmological simulations. Our approach involves generating a single realisation of the initial power spectrum of density perturbations and studying how truncation of this power spectrum on scales larger than L_cut affects the structure of dark matter haloes at z=0. In particular, we have examined the cases of L_cut = f_cut L_box with f_cut=1 (i.e. no truncation), 1/2, 1/3 and 1/4. In common with previous studies, we find that the suppression of long waveleng…
Simulated dark matter haloes are fitted by self-similar, universal density profiles, where the scaled parameters depend only on a scaled (truncation) radius which, in turn, is supposed to be independent on the mass and the formation redshift. A criterion for the choice of the best fitting density profile is proposed, with regard to a set of high-resolution simulations, where some averaging procedure on scaled density profiles has been performed, in connection with a number of fitting density profiles. An application is made to a pair of sets each made of a dozen of high-resolution simulations,…
The cold dark matter (CDM) scenario generically predicts the existence of triaxial dark matter haloes which contain notable amounts of substructure. However, analytical halo models with smooth, spherically symmetric density profiles are routinely adopted in the modelling of light propagation effects through such objects. In this paper, we address the biases introduced by this procedure by comparing the surface mass densities of actual N-body haloes against the widely used analytical model suggested by Navarro, Frenk and White (1996) (NFW). We conduct our analysis in the redshift range of 0.0 -…
Cold dark matter haloes are populated by caustics, which are yet to be resolved in N-body simulations or observed in the Universe. Secondary infall model provides a paradigm for the study of caustics in "typical" haloes assuming that they have had no major mergers and have grown only by smooth accretion. This is a particular characteristic of the smallest dark matter haloes of about 10^{-5} Mo, which although "atypical" contain no substructures and could have survived until now with no major mergers. Thus using this model as the first guidline, we evaluate the neutralino self-annihilation flux…
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 da…
The distortion of the images of faint high-redshift galaxies can be used to probe the intervening mass distribution. This weak gravitational lensing effect has been used recently to study the (projected) mass distribution of several clusters at intermediate and high redshifts. In addition, the weak lensing effect can be employed to detect (dark) matter concentrations in the Universe, based on their mass properties alone. Thus it is feasible to obtain a mass-selected sample of `clusters', and thereby probe the full range of their mass-to-light ratios. We study the expected number density of suc…
We test the ability of the numerical action method (NAM) to recover the individual orbit histories of mass tracers in an expanding universe in a region of radius 26Mpc/h, given the masses and redshift-space coordinates at the present epoch. The mass tracers are represented by dark matter haloes identified in a high resolution N-body simulation of the standard LCDM cosmology. Since previous tests of NAM at this scale have traced the underlying distribution of dark matter particles rather than extended haloes, our study offers an assessment of the accuracy of NAM in a scenario which more closely…
The microlensing optical depth to Baade's Window constrains the minimum total mass in baryonic matter within the Solar circle to be greater than 3.9 x 10^{10} solar masses, assuming the inner Galaxy is barred with viewing angle of roughly 20 degrees. From the kinematics of solar neighbourhood stars, the local surface density of dark matter is about 30 +/- 15 solar masses per square parsec. We construct cuspy haloes normalised to the local dark matter density and calculate the circular-speed curve of the halo in the inner Galaxy. This is added in quadrature to the rotation curve provided by the…
We investigate statistically the dynamical consequences of cosmological fluxes of matter and related moments on progenitors of today's dark matter haloes. Their dynamics is described via canonical perturbation theory which accounts for two types of perturbations: the tidal field corresponding to fly-bys and accretion of dark matter through the halo's outer boundary. he dynamical equations are solved linearly, order by order, projecting on a biorthogonal basis to consistently satisfy the field equation. Since our solution of the Boltzmann Poisson equations is explicit, it allows statistical pre…
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, non-rot…
In the standard model of cosmic structure formation, dark matter haloes form by gravitational instability. The process is hierarchical: smaller systems collapse earlier, and later merge to form larger haloes. The galaxy clusters, hosted by the largest dark matter haloes, are at the top of this hierarchy representing the largest as well as the last structures formed in the universe, while the smaller and first haloes are those Earth-sized dark subhaloes which have been both predicted by theoretical considerations and found in numerical simulations, though it does not exist any observational hin…
We study the ability of PINOCCHIO (PINpointing Orbit-Crossing Collapsed HIerarchical Objects) to predict the merging histories of dark matter (DM) haloes, comparing the PINOCCHIO predictions with the results of two large N-body simulations run from the same set of initial conditions. We focus our attention on quantities most relevant to galaxy formation and large-scale structure studies. PINOCCHIO is able to predict the statistics of merger trees with a typical accuracy of 20 per cent. Its validity extends to higher-order moments of the distribution of progenitors. The agreement is valid also …
(Abridged) We develop the halo model of large-scale structure to include triaxial dark matter haloes and their intrinsic alignments. As a direct application we derive general expressions for the power spectrum. This we calculate for two different triaxial density profiles. The first is a toy-model that allows us to isolate the dependence of clustering on halo shape alone and the second is the more realistic model of Jing & Suto (2002). In both cases, we find that the effects of triaxiality are manifest as a suppression of power at the level of ~5% on scales k~1-10 h/Mpc. When considered by mas…
We present new velocity dispersion measurements for a set of 12 spiral galaxies and use them to derive a more accurate V_c - sigma relation which holds for a wide morphological range of galaxies. Combined with the M_BH - sigma relation, this relation can be used as a tool to estimate supermassive black hole (SMBH) masses by means of the asymptotic circular velocity. Together with the Tully-Fisher relation, it serves as a constraint for galaxy formation and evolution models.
The most commonly used definition of halo formation is the time when a halo's most massive progenitor first contains at least half the final mass of its parent. Reasonably accurate formulae for the distribution of formation times of haloes of fixed mass have been available for some time. We use numerical simulations of hierarchical gravitational clustering to test the accuracy of formulae for the mass at formation. We also derive and test a formula for the joint distribution of formation masses and times. The structure of a halo is expected to be related to its accretion history. Our tests sho…
Using a series of high-resolution N-body simulations of the concordance cosmology we investigate how the formation histories, shapes and angular momenta of dark-matter haloes depend on environment. We first present a classification scheme that allows to distinguish between haloes in clusters, filaments, sheets and voids in the large-scale distribution of matter. This method is based on a local-stability criterion for the orbits of test particles and closely relates to the Zel'dovich approximation. Applying this scheme to our simulations we then find that: i) Mass assembly histories and formati…
This paper presents a stochastic approach to the clustering evolution of dark matter haloes in the Universe. Haloes, identified by a Press-Schechter-type algorithm in Lagrangian space, are described in terms of `counting fields', acting as non-linear operators on the underlying Gaussian density fluctuations. By ensemble averaging these counting fields, the standard Press-Schechter mass function as well as analytic expressions for the halo correlation function and corresponding bias factors of linear theory are obtained, thereby extending the recent results by Mo and White. The non-linear evolu…
The effects of spatial correlations of density fluctuations on merger histories of dark matter haloes (so-called `{\it merger trees}') are analysed. We compare the mass functions of dark haloes derived by a new method for calculating merger trees, that proposed by Rodrigues \& Thomas (RT), with those given by other methods such as the Block model, the Press-Schechter formula and our own formula in which the mass functions are analytically expressed in a way that takes into consideration the spatial correlations. It is found that the mass functions given by the new method are well fit by those …
