Path integral approach for merger rates of dark matter haloes

We use path integrals in order to estimate 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. A detailed comparison between these models is presented. Path approach gives a better agreement with the exact solutions for constrained distributions than the approach of \cite{shto02}. Although this improvement seems not to be very large, our results show that the path approach is a step to the right direction. Differences between the two widely used barriers, spherical and ellipsoidal, depend crucially on the mass of the descendant halo. These differences become larger for decreasing mass of the descendant halo. The use of additional terms in the expansion used in the path approach, other improvements as well as detailed comparisons with the predictions of N-body simulations, that could improve our understanding about the important issue of structure formation, are under study.Comment: 32 pages, 6 figures, Accepted for publication in Astrophysics & Space Scienc

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

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

Extended Press-Schechter theory and the density profiles of dark matter haloes

An inside-out model for the formation of haloes in a hierarchical clustering scenario is studied. The method combines the picture of the spherical infall model and a modification of the extended Press-Schechter theory. The mass accretion rate of a halo is defined to be the rate of its mass increase due to minor mergers. The accreted mass is deposited at the outer shells without changing the density profile of the halo inside its current virial radius. We applied the method to a flat $\Lambda CDM$ Universe. The resulting density profiles are compared to analytical models proposed in the literature, and a very good agreement is found. A trend is found of the inner density profile becoming steeper for larger halo mass, that also results from recent N-body simulations. Additionally, present-day concentrations as well as their time evolution are derived and it is shown that they reproduce the results of large cosmological N-body simulations.Comment: 9 pages, 7 figures, accepted for publication in MNRA

Dark matter density profiles from the Jeans equation

We make a simple analytical study of radial profiles of dark matter structures, with special attention to the question of the central radial density profile. We let our theoretical assumptions be guided by results from numerical simulations, and show that at any radius where both the radial density profile, rho, and the phase-space-like density profile, rho/sigma^epsilon, are exact power laws, the only allowed density slopes in agreement with the spherical symmetric and isotropic Jeans equation are in the range 1< beta <3, where beta = - dln(rho)/dln(r). We also allow for a radial variation of these power laws, as well as anisotropy, and show how this allows for more shallow central slopes.Comment: 4 pages, no figures, minor typos correcte

Merger as Intermittent Accretion

The Self-Similar Secondary Infall Model (SSIM) is modified to simulate a merger event. The model encompass spherical versions of tidal stripping and dynamical friction that agrees with the Syer & White merger paradigm's behaviour. The SSIM shows robustness in absorbing even comparable mass perturbations and returning to its original state. It suggests the approach to be invertible and allows to consider accretion as smooth mass inflow merging and mergers as intermittent mass inflow accretion.Comment: letter accepted by A&A 29/09/08, 4 pages, colour figure