Accurate Universal Models for the Mass Accretion Histories and Concentrations of Dark Matter Halos

Abstract

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...

Structure formation with suppressed small-scale perturbations

“…In Fig. 7 we show that this is indeed the case: the average collapse redshift measured in CDM simulations (solid grey stars, obtained from Jiang & van den Bosch (2014), based on simulations from Zhao et al 2009) is about a factor of 1.5 larger than the one predicted by our simplified model. It is, however, interesting to realise that the slope of the CDM zc-mass relation described by Eq.…”

Galaxy groups in the low-redshift Universe

“…with the concentration, c180 = r180/rs, given by the model of Zhao et al (2009). Finally, we calculate PM (R, ∆z) for each of all the galaxy-group pairs.…”

Characterizing strong lensing galaxy clusters using the Millennium-XXL and moka simulations

“…We do so because, even if the M-XXL simulation has been run with a different set of cosmological parameters, we assume to be able to rescale those clusters at z = 1 from a M-XXL cosmology to a sample at z = 0.5 in a Planck13 cosmology. This is supported by the fact that the halo properties at z = 1 in the M-XXL cosmology are very similar to those at z = 0.5 in a Planck13 cosmology (Sheth & Tormen 1999;Macciò et al 2008;Zhao et al 2009;Giocoli et al 2012b;Despali et al 2015); even if the two mass functions for haloes more massive than 3 × 10 14 M /h may be different by more than 50%, the two concentration-mass relations deviate by less than 5%.…”

“…In modelling the subhalo density profiles we account for tidal stripping due to close interactions with the main halo smooth component and to close encounters with other clumps, gravitational heating, and dynamical friction (Hayashi et al 2003;van den Bosch et al 2005;Choi et al 2007;Giocoli et al 2008) using a truncated singular isothermal sphere (Metcalf & Madau 2001). For the halo concentration-mass relation we use the Zhao et al (2009) model which links the concentration of a given halo with the time (t0.04) at which its main progenitor assembles 4 percent of its mass -each halo mass accretion history is computed using the results by Giocoli et al (2012b). Haloes may also be populated by galaxies according to a HOD approach (Wang et al 2006) and once settled the central galaxy, with a given stellar mass profile, the surrounding dark matter distribution can adiabatically contract (Blumenthal et al 1986;Keeton 2001;Gnedin et al 2011).…”

“…On the left we show the differential distributions normalised to the total number of clusters while on the right the cumulative ones. To be consistent with the numerical simulation, MOKA haloes have been generated without a Bright Central Galaxy (BCG) and have a c-M relation as for the M-XXL cosmology at z = 1, computed using the Zhao et al (2009) model adopting the Giocoli et al (2012b) halo mass accretion history model. The blue and the cyan histograms show the measurements from the M-XXL considering only the three random projections and considering all the six onesrandom plus peculiar projections, respectively.…”