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We identify voids as maximal non-overlapping spheres within the haloes of the Uchuu simulation and three smaller halo simulation boxes with smaller volume and different $\sigma_{8}$ values, and galaxies with redshift in the range $0.02

We study the concentration of dark matter halos and its evolution in N-body simulations of the standard LCDM cosmology. The results presented in this paper are based on 4 large N-body simulations with about 10 billion particles each: the Millennium-I and II, Bolshoi, and MultiDark simulations. The MultiDark (or BigBolshoi) simulation is introduced in this paper. This suite of simulations with high mass resolution over a large volume allows us to compute with unprecedented accuracy the concentration over a large range of scales (about six orders of magnitude in mass), which constitutes the state-of-the-art of our current knowledge on this basic property of dark matter halos in the LCDM cosmology. We find that there is consistency among the different simulation data sets. We confirm a novel feature for halo concentrations at high redshifts: a flattening and upturn with increasing mass. The concentration c(M,z) as a function of mass and the redshift and for different cosmological parameters shows a remarkably complex pattern. However, when expressed in terms of the linear rms fluctuation of the density field sigma(M,z), the halo concentration c(sigma) shows a nearly-universal simple U-shaped behaviour with a minimum at a well defined scale at sigma=0.71. Yet, some small dependences with redshift and cosmology still remain. At the high-mass end (sigma < 1) the median halo kinematic profiles show large signatures of infall and highly radial orbits. This c-sigma(M,z) relation can be accurately parametrized and provides an analytical model for the dependence of concentration on halo mass. When applied to galaxy clusters, our estimates of concentrations are substantially larger -- by a factor up to 1.5 -- than previous results from smaller simulations, and are in much better agreement with results of observations. (abridged), Comment: Submitted to MNRAS

We provide a set of general tools for studying the alignments of dark matter halos and galaxies with respect to the large scale structure. The statistics of the positioning of these objects is represented by a Probability Distribution Function (PDF) of their Euler angles. The PDF corresponding to halos located in the shells of the cosmic voids is inferred from previous results. This PDF is used to show how to recover the outcomes found for the alignments of the axes of these halos in simulations. We also explore the orientation of the angular momentum of the halos, both with respect to the halo axes and with respect to the large scale structure. We present an expression which describes well numerical results for the alignment of the angular momentum of the halo with respect to the halo axes for randomly chosen halos. We also propose a model that relates the orientation of the angular momentum with the halos axes accounting for the orientation of the halo axes with the large scale structure. This model is shown to recover accurately the observed PDF of the halo angular momentum with respect to the void radial direction. In addition, we give an expression for determining the degradation of the angular momentum intrinsic alignment when observational errors are accounted. This expression is also used to determine the departure of the observed value of the alignment from the initial expectation (as provided by the tidal torque theory) due to the rotation of the angular momentum of the halo with respect to the initial torque. For voids, we find that the strength of the alignment is reduced to half the original value. We discuss how to adapt the void results to other cosmic large scale structures (i.e. filaments, walls, etc)., Comment: 18 pages, 5 figures, submitted to MNRAS

It has recently been shown that the correct halo mass function high mass behaviour may be obtained by an appropriate treatment of the all-mass-at-center problem. Here we show that the treatment of this problem leads to an accumulated mass fraction, F, which is not a universal function of the linear variance of the density contrast, but depends also on the shape of the power spectrum. For relevant power spectra F is a universal function of two quantities: the linear variance and a quantity related to the local shape (at the given mass scale) of the power spectrum. This implies, for a given shape of the power spectrum, a redshift dependence of the mass function, which is quite important for a cold dark matter power spectrum. Our results are in good agreement with numerical simulations.

We claim that the discrepancy found between theoretical predictions for the cosmic mass function and those found in numerical simulations is due to the fact that in deriving the former all mass elements are assumed to be at the center of the object they belong to (the all-mass-at-center problem). By an appropriate treatment of this problem, using the spherical collapse model (which is not a bad approximation in the high mass limit), we obtain both the high mass behaviour found in simulations and the true assymptotic behaviour of the mass function (for arbitrarily high masses). Therefore, we conclude that by combining ellipsoidal dynamics with a suitable treatment of the all-mass-at-center problem (that we will show in a follow up work) a theoretical prediction for the cosmic mass function in full agreement with simulations may be obtained., Comment: 4 pages, 2 figures, ApJ letters Accepted

In the present work we describe the formalism necessary to derive the properties of dark matter halos beyond two virial radius using the spherical collapse model (without shell crossing), and provide the framework for the theoretical prediction presented in Prada et al. (2005). We show in detail how to obtain within this model the probability distribution for the spherically-averaged enclosed density at any radii P(delta,r). Using this probability distribution, we compute the most probable and mean density profiles, which turns out to differ considerably from each other. We also show how to obtain the typical profile, as well as the probability distribution and mean profile for the spherically averaged radial velocity. Two probability distributions are obtained: a first one is derived using a simple assumption, that is, if Q is the virial radius in Lagrangian coordinates, then the enclosed linear contrast delta_l(q,Q) must satisfy the condition that delta_l(q=Q) = delta_vir, where delta_vir is the linear density contrast within the virial radius Rvir at the moment of virialization. Then we introduce an additional constraint to obtain a more accurate P(delta,r) which reproduces to a higher degree of precision the distribution of the spherically averaged enclosed density found in the simulations. This new constraint is delta_l(q,Q) < delta_vir for all q > Q, which means that there are no radii larger than Rvir where the density contrast is larger than that used to define the virial radius. Finally, we compare in detail our theoretical predictions for the probability distributions with the results found in the simulations., Comment: 12 pages, 8 figures, 1 table, replaced to match the published version

We present a general analytical procedure for computing the number density of voids with radius above a given value within the context of gravitational formation of the large scale structure of the universe out of Gaussian initial conditions. To this end we develop an accurate (under generally satisfied conditions) extension of unconditional mass function to constrained environments, which allowes us both to obtain the number density of collapsed objects of certain mass at any distance from the center of the void, and to derive the number density of voids defined by those collapsed objects. We have made detailed calculations for the spherically averaged mass density and halo number density profiles for individual voids. We also present a formal expression for the number density of voids defined by galaxies of a given type and luminosity. This expression contains the probability for a collapsed object of certain mass to host a galaxy of that type and luminosity as a function of the environmental density. We propose a procedure to infer this function, which may provide useful clues as to the galaxy formation process, from the observed void densities., Comment: 14 pages, 7 figures, MNRAS in press