A large amount of observations have constrained cosmological parameters and the initial density fluctuation spectrum to a very high accuracy. However, cosmological parameters change with time and the power index of the power spectrum dramatically varies with mass scale in the so-called concordance ΛCDM cosmology. Thus, any successful model for its structural evolution should work well simultaneously for various cosmological models and different power spectra. We use a large set of high-resolution N-body simulations of a variety of structure formation models (scale-free, standard CDM, open CDM, and ΛCDM) to study the mass accretion histories, the mass and redshift dependence of concentrations, and the concentration evolution histories of dark matter halos. We find that there is significant disagreement between the much-used empirical models in the literature and our simulations. Based on our simulation results, we find that the mass accretion rate of a halo is tightly correlated with a simple function of its mass, the redshift, parameters of the cosmology, and of the initial density fluctuation spectrum, which correctly disentangles the effects of all these factors and halo environments. We also find that the concentration of a halo is strongly correlated with the universe age when its progenitor on the mass accretion history first reaches 4% of its current mass. According to these correlations, we develop new empirical models for both the mass accretion histories and the concentration evolution histories of dark matter halos, and the latter can also be used to predict the mass and redshift dependence of halo concentrations. These models are accurate and universal: the same set of model parameters works well for different cosmological models and for halos of different masses at different redshifts, and in the ΛCDM case the model predictions match the simulation results very well even though halo mass is traced to about 0.0005 times the final mass, when cosmological parameters and the power index of the initial density fluctuation spectrum have changed dramatically. Our model predictions also match the PINOCCHIO mass accretion histories very well, which are much independent of our numerical simulations and our definitions of halo merger trees. These models are also simple and easy to implement, making them very useful in modeling the growth and structure of dark matter halos. We provide appendices describing the step-by-step implementation of our models. A calculator which allows one to interactively generate data for any given cosmological model is provided on the Web, together with a userfriendly code to make the relevant calculations and some tables listing the expected concentration as a function of halo mass and redshift in several popular cosmological models. We explain why ΛCDM and open CDM halos on nearly all mass scales show two distinct phases in their mass growth histories. We discuss implications of the universal relations we find in connection to the formation of dark matter halos in the cosm...

In this paper, we analyse in detail the mass-accretion histories and structural properties of dark haloes in high-resolution N-body simulations. We model the density distribution in individual haloes using the Navarro-Frenk-White (NFW) profile. For a given halo, there is a tight correlation between its inner-scale radius r s and the mass within it, M s , for all its main progenitors. Using this correlation, one can predict quite well the structural properties of a dark halo at any time in its history from its mass-accretion history, implying that the structure properties and the mass-accretion history are closely correlated. The predicted growing rate of concentration c with time tends to increase with decreasing mass-accretion rate. The build-up of dark haloes in cold dark matter (CDM) models generally consists of an early phase of fast accretion (where the halo mass M h increases with time much faster than the expansion rate of the Universe) and a late phase of slow accretion (where M h increases with time approximately as the expansion rate). These two phases are separated at a time when c ∼ 4 and the typical binding energy of the halo is approximately equal to that of a singular isothermal sphere with the same circular velocity. Haloes in the two accretion phases show systematically different properties, for example, the circular velocity v h increases rapidly with time in the fast accretion phase but remains almost constant in the slow accretion phase, the inner properties of a halo, such as r s and M s increase rapidly with time in the fast accretion phase but change only slowly in the slow accretion phase, the inner circular velocity v s is approximately equal to v h in the fast accretion phase but is larger in the slow accretion phase. The potential well associated with a halo is built up mainly in the fast accretion phase, while a large amount of mass can be accreted in the slow accretion phase without changing the potential well significantly. We discuss our results in connection with the formation of dark haloes and galaxies in hierarchical models.

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