Mass accretion history and concentration evolution history of dark matter halos

Donghai Zhao, Yipeng Jing, Houjun Mo, Gerhard Boerner

     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.

Paper with detailed appendices

The models are described in our paper appeared in the Astrophysical Journal, Zhao, Jing, Mo & Boerner (2009, ApJ, 707, 354). The paper also presents detailed appendices describing the step-by-step implementation of our models. It's available here as PDF (1.59M) and Postscript (2.68M) files, as well as from arXiv e-print (arXiv:0811.0828).

Calculator sb02.gif

Halo evolution web-calculator allows one to generate data interactively for any given cosmological model. It outputs either evolution history of mass and structural properties for final halos with given mass at given redshift or mass dependence of these structural properties at the final redshift.

Code

Version 1.00 (2008.11.02): main program version (24.7K)

Version 1.03 (2010.09.14): main program version (27.1K), subroutine version 1 (17.1K) and subroutine version 2 (17.4K). Each of the two subroutine versions performs the same as the main program version but is much easier for user to call and much faster for repeated call. For example, subroutine mc(z, m, c) returns median concentration c for halos of mass m at redshift z, and it also outputs to a file the evolution history of halo properties. When called the first time, this subroutine will spent some time to prepare some tables for further usage, and thereafter computation time of each subsequent call will be negligible.

Table

tables are coming

Relevant papers and feedback

Zhao et al. (2003, MNRAS, 339, 12) found that the MAH of a halo in general consists of two distinct phases and the faster the halo mass grows, the slower the concentration increases.

Binney & Tremaine (2008, Galactic Dynamics): "Figure 9.17 Median concentrations c = r200/a of halos of various masses at four redshifts (after Zhao et al. 2003, ApJ, 597, L9)."

Klypin, Trujillo-Gomez & Primack (2011, arXiv:1002.3660): "Zhao et al. (2003, ApJ, 597, L9) and Zhao et al. (2009, ApJ, 707, 354) were the first to find that the concentration flattens at large masses and at high redshifts. Their estimates of the minimum concentration, ~4, are compatible with our results."

Munoz-Cuartas, Maccio, Gottloeber & Dutton (2011, MNRAS, 411, 584): "When compared with the model proposed in Zhao et al. (2009, ApJ, 707, 354) our results show a very good agreement at the low mass end. For high masses we find a slightly higher difference but never exceeding few percent."

Giocoli, Tormen, Sheth & van den Bosch (2010, MNRAS, 404, 502): "Zhao et al. (2009, ApJ, 707, 354) describe an accurate model for this, in which a halo's concentration is related to the time at which its main progenitor first assembled 4% of its final mass."

More, Kravtsov, Dalal, & Gottlober (2011, arXiv:1103.0005): "The evolution of overdensity predicted by the model due to the redshift evolution of concentrations, predicted using the model of Zhao et al. (2009, ApJ, 707, 354), matches the redshift trend observed in our simulations remarkably well. The scatter of overdensities is also well reproduced by the scatter of concentrations at all redshifts. Note that enclosed overdensity for this b in the mass range probed by the simulations reaches the floor value of ≈ 400-450 by z = 2.5, as virial concentration of halos reaches a floor of cvir ≈ 4 (Zhao et al. 2003b, 2009)."

This web page is developed and maintained by Donghai Zhao (dhzhao@shao.ac.cn). Any comment or suggestion will be appreciated much!