Accurate universal models for the mass accretion histories and concentrations of dark matter halos

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 varies with mass scale dramatically in the so-called concordance Lambda CDM 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 Lambda CDM) to study the mass accretion histories (MAHs), 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. According to two simple but tight correlations we find from the simulation results, we develop new empirical models for both the MAHs 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 the model predictions are highly accurate even when the histories are traced to very high redshift. These models are also simple and easy to implement. A web calculator and a user-friendly code to make the relevant calculations are available from http://www.shao.ac.cn/dhzhao/mandc.html . We explain why Lambda CDM halos on nearly all mass scales show two distinct phases in their evolution histories.

A fitting formula for the merger timescale of galaxies in hierarchical clustering

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 1/2ln [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 epsilon is much weaker than the widely adopted power-law epsilon^{0.78}, whereas 0.94*{epsilon}^{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.