Density profiles in a spherical infall model with non-radial motions

A generalized version of the Spherical Infall Model (SIM) is used to study the effect of angular momentum on the final density profile of a spherical structure. The numerical method presented is able to handle a variety of initial density profiles (scale or not scale free) and no assumption of self-similar evolution is required. The realistic initial overdensity profiles used are derived by a CDM power spectrum. We show that the amount of angular momentum and the initial overdensity profile affect the slope of the final density profile at the inner regions. Thus, a larger amount of angular momentum or shallower initial overdensity profiles lead to shallower final density profiles at the inner regions. On the other hand, the slope at the outer regions is not affected by the amount of angular momentum and has an almost constant value equal to that predicted in the radial collapse case

The velocity field of collapsing spherical structures. Limitations of the spherical infall model in mass estimation

We assume that the amplitude of the caustics in redshift space is a sum of two components: the first one can be predicted by the spherical infall model with no random motion, and the second is due to the random motion distribution. Smooth model curves are used to estimate the maximum values of the first component for the Coma cluster. Then, an approximation of the radial component of the infall velocity --based on the above curves-- is derived and a mass profile of the cluster is calculated. This mass profile, that is an upper limit for the spherical infall model, combined with estimations given by other authors provides an approximation of a lower limit for the mass of the system

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.Comment: 29 pages, 9 figure

Modelling elliptical galaxies: phase-space constraints on two-component (gamma1,gamma2) models

In the context of the study of the properties of the mutual mass distribution of the bright and dark matter in elliptical galaxies, present a family of two-component, spherical, self-consistent galaxy models, where one density distribution follows a gamma_1 profile, and the other a gamma_2 profile [(gamma_1,gamma_2) models], with different total masses and ``core'' radii. A variable amount of Osipkov-Merritt (radial) orbital anisotropy is allowed in both components. For these models, I derive analytically the necessary and sufficient conditions that the model parameters must satisfy in order to correspond to a physical system. Moreover, the possibility of adding a black hole at the center of radially anisotropic gamma models is discussed, determining analytically a lower limit of the anisotropy radius as a function of gamma. The analytical phase-space distribution function for (1,0) models is presented, together with the solution of the Jeans equations and the quantities entering the scalar virial theorem. It is proved that a globally isotropic gamma=1 component is consistent for any mass and core radius of the superimposed gamma=0 model; on the contrary, only a maximum value of the core radius is allowed for the gamma=0 model when a gamma=1 density distribution is added. The combined effects of mass concentration and orbital anisotropy are investigated, and an interesting behavior of the distribution function of the anisotropic gamma=0 component is found: there exists a region in the parameter space where a sufficient amount of anisotropy results in a consistent model, while the structurally identical but isotropic model would be inconsistent.Comment: 29 pages, LaTex, plus 5 .eps figures and macro aaspp4.sty - accepted by ApJ, main journa

Non-radial motion and the NFW profile

The self-similar infall model (SSIM) is normally discussed in the context of radial orbits in spherical symmetry. However it is possible to retain the spherical symmetry while permitting the particles to move in Keplerian ellipses, each having the squared angular momentum peculiar to their 'shell'. The spherical 'shell', defined for example by the particles turning at a given radius, then moves according to the radial equation of motion of a 'shell' particle. The 'shell' itself has no physical existence except as an ensemble of particles, but it is convenient to sometimes refer to the shells since it is they that are followed by a shell code. In this note we find the distribution of squared angular momentum as a function of radius that yields the NFW density profile for the final dark matter halo. It transpires that this distribution is amply motivated dimensionally. An effective 'lambda' spin parameter is roughly constant over the shells. We also study the effects of angular momentum on the relaxation of a dark matter system using a three dimensional representation of the relaxed phase space.Comment: accepted for publication in Astronomy and Astrophysics. date received: 31-03-03 date accepted: 10-06-0

On the spin distributions of Λ\LambdaCDM haloes

We used merger trees realizations, predicted by the extended Press-Schechter theory, in order to study the growth of angular momentum of dark matter haloes. Our results showed that: 1) The spin parameter $\lambda'$ resulting from the above method, is an increasing function of the present day mass of the halo. The mean value of $\lambda'$ varies from 0.0343 to 0.0484 for haloes with present day masses in the range of $10^9\mathrm{h}^{-1}M_{\odot}$ to $10^{14}\mathrm{h}^{-1}M_{\odot}$. 2)The distribution of $\lambda'$ is close to a log-normal, but, as it is already found in the results of N-body simulations, the match is not satisfactory at the tails of the distribution. A new analytical formula that approximates the results much more satisfactorily is presented. 3) The distribution of the values of $\lambda'$ depends only weakly on the redshift. 4) The spin parameter of an halo depends on the number of recent major mergers. Specifically the spin parameter is an increasing function of this number.Comment: 10 pages, 8 figure

On the reliability of merger-trees and the mass growth histories of dark matter haloes

We have used merger trees realizations to study the formation of dark matter haloes. The construction of merger-trees is based on three different pictures about the formation of structures in the Universe. These pictures include: the spherical collapse (SC), the ellipsoidal collapse (EC) and the non-radial collapse (NR). The reliability of merger-trees has been examined comparing their predictions related to the distribution of the number of progenitors, as well as the distribution of formation times, with the predictions of analytical relations. The comparison yields a very satisfactory agreement. Subsequently, >.........Comment: A&SS Accepte

Axisymmetric galactic models in spherical potentials

We study projected kinematic characteristics of a class of axisymmetric models for the luminous components of galaxies. Models of this class are known as extended Osipkov-Merritt models and have been studied first by Arnold (1990). The line-of-sight velocity dispersions are given and the profiles of the projected velocity distribution are described using their Gauss-Hermite moments. © 1995 Kluwer Academic Publishers