Using six high‐resolution dissipationless simulations with a varying box size in a flat Lambda cold dark matter (ΛCDM) universe, we study the mass and redshift dependence of dark matter halo shapes for Mvir= 9.0 × 1011− 2.0 × 1014 h−1 M⊙, over the redshift range z= 0–3, and for two values of σ8= 0.75 and 0.9. Remarkably, we find that the redshift, mass and σ8 dependence of the mean smallest‐to‐largest axis ratio of haloes is well described by the simple power‐law relation 〈s〉= (0.54 ± 0.02)(Mvir/M*)−0.050±0.003, where s is measured at 0.3Rvir, and the z and σ8 dependences are governed by the characteristic non‐linear mass, M*=M*(z, σ8). We find that the scatter about the mean s is well described by a Gaussian with σ∼ 0.1, for all masses and redshifts. We compare our results to a variety of previous works on halo shapes and find that reported differences between studies are primarily explained by differences in their methodologies. We address the evolutionary aspects of individual halo shapes by following the shapes of the haloes through ∼100 snapshots in time. We determine the formation scalefactor ac as defined by Wechsler et al. and find that it can be related to the halo shape at z= 0 and its evolution over time.

We study galaxy mergers using a high-resolution cosmological hydro/N-body simulation with star formation, and compare the measured merger timescales with theoretical predictions based on the Chandrasekhar formula. In contrast to Navarro et al., our numerical results indicate, that the commonly used equation for the merger timescale given by Lacey and Cole, systematically underestimates the merger timescales for minor mergers and overestimates those for major mergers. This behavior is partly explained by the poor performance of their expression for the Coulomb logarithm, ln(m pri /m sat ). The two alternative forms ln(1 + m pri /m sat ) and 1/2 ln[1 + (m pri /m sat ) 2 ] for the Coulomb logarithm can account for the mass dependence of merger timescale successfully, but both of them underestimate the merger time scale by a factor 2. Since ln(1 + m pri /m sat ) represents the mass dependence slightly better we adopt this expression for the Coulomb logarithm. Furthermore, we find that the dependence of the merger timescale on the circularity parameter ǫ is much weaker than the widely adopted power-law ǫ 0.78 , whereas 0.94ǫ 0.60 + 0.60 provides a good match to the data. Based on these findings, we present an accurate and convenient fitting formula for the merger timescale of galaxies in cold dark matter models.

Clusters, filaments, sheets and voids are the building blocks of the cosmic web. Forming dark matter halos respond to these different large-scale environments, and this in turn affects the properties of galaxies hosted by the halos. It is therefore important to understand the systematic correlations of halo properties with the morphology of the cosmic web, as this informs both about galaxy formation physics and possible systematics of weak lensing studies. In this study, we present and compare two distinct algorithms for finding cosmic filaments and sheets, a task which is far less well established than the identification of dark matter halos or voids. One method is based on the smoothed dark matter density field, the other uses the halo distributions directly. We apply both techniques to one high resolution N-body simulation and reconstruct the filamentary/sheet like network of the dark matter density field. We focus on investigating the properties of the dark matter halos inside these structures, in particular on the directions of their spins and the orientation of their shapes with respect to the directions of the filaments and sheets. We find that both the spin and the major axes of filament-halos with masses 10 13 h −1 M ⊙ are preferentially aligned with the direction of the filaments. The spins and major axes of halos in sheets tend to lie parallel to the sheets. There is an opposite mass dependence of the alignment strengths for the spin (negative) and major (positive) axes, i.e. with increasing halo mass the major axis tends to be more strongly aligned with the direction of the filament whereas the alignment between halo spin and filament becomes weaker with increasing halo mass. The alignment strengths as a function of distance to the most massive node halo indicate that there is a transit large scale environment impact: from the 2-D collapse phase of the filament to the 3-D collapse phase of the cluster/node halo at small separation. Overall, the two algorithms for filament/sheet identification investigated here agree well with each other. The method based on halos alone can be easily adapted for use with observational data sets. Subject headings: methods: data analysis -dark matter -large-scale structure of universe -galaxies: halos

Using constrained simulations of the local Universe for generic cold dark matter and for 1 keV warm dark matter, we investigate the difference in the abundance of dark matter halos in the local environment. We find that the mass function within 20 h −1 Mpc of the Local Group is ∼ 2 times larger than the universal mass function in the 10 9 − 10 13 h −1 M ⊙ mass range. Imposing the field of view of the on-going HI blind survey ALFALFA in our simulations, we predict that the velocity function in the Virgo-direction region exceeds the universal velocity function by a factor of 3. Furthermore, employing a scheme to translate the halo velocity function into a galaxy velocity function, we compare the simulation results with a sample of galaxies from the early catalog release of ALFALFA. We find that our simulations are able to reproduce the velocity function in the 80 − 300 km s −1 velocity range, having a value ∼ 10 times larger than the universal velocity function in the Virgo-direction region. In the low velocity regime, 35 − 80 km s −1 , the warm dark matter simulation reproduces the observed flattening of the velocity function. On the contrary, the simulation with cold dark matter predicts a steep rise in the velocity function towards lower velocities; for V max = 35 km s −1 , it forecasts ∼ 10 times more sources than the ones observed. If confirmed by the complete ALFALFA survey, our results indicate a potential problem for the cold dark matter paradigm or for the conventional assumptions about energetic feedback in dwarf galaxies.