MultiDark simulations: the story of dark matter halo concentrations and density profiles

TL;DR

MultiDark simulations address how dark matter halos acquire their internal structure, focusing on density profiles and concentrations across a vast mass range and cosmic time. The study shows that halo concentration cannot be captured by the simple $C\propto R_{\rm vir}/r_{-2}$ ratio for massive halos; instead, Einasto profiles with a mass- and redshift-dependent $\alpha$ must be used, with the concentration tied to both $r_{-2}$ and $\alpha$ and tracked via $V_{\max}/V_{\rm vir}$. It identifies three evolutionary regimes—rapid infall, plateau, and slow accretion—and explains the upturn of the concentration–mass relation in terms of peak-height statistics and radial infall, not equilibrium artifacts. The authors provide accurate analytic fits for densities and concentrations and practical methods to estimate profiles from simulation outputs across redshift and cosmology.

Abstract

Accurately predicting structural properties of dark matter halos is one of the fundamental goals of modern cosmology. We use the new suite of MultiDark cosmological simulations to study the evolution of dark matter halo density profiles, concentrations, and velocity anisotropies. The MultiDark simulations cover a large range of masses 1e10-1e15Msun and volumes upto 50Gpc**3. The total number of dark matter halos in all the simulations exceeds 60 billion. We find that in order to understand the structure of dark matter halos and to make ~1% accurate predictions for density profiles, one needs to realize that halo concentration is more complex than the traditional ratio of the virial radius to the core radius in the NFW profile. For massive halos the averge density profile is far from the NFW shape and the concentration is defined by both the core radius and the shape parameter alpha in the Einasto approximation. Combining results from different redshifts, masses and cosmologies, we show that halos progress through three stages of evolution. (1) They start as rare density peaks that experience very fast and nearly radial infall. This radial infall brings mass closer to the center producing a high concentrated halo. Here, the halo concentration increases with the increasing halo mass and the concentration is defined by the alpha parameter with nearly constant core radius. Later halos slide into (2) the plateau regime where the accretion becomes less radial, but frequent mergers still affect even the central region. Now the concentration does not depend on halo mass. (3) Once the rate of accretion slows down, halos move into the domain of declining concentration-mass relation because new accretion piles up mass close to the virial radius while the core radius is staying constant. We provide accurate analytical fits to the numerical results for halo density profiles and concentrations.

Figures (23)

• Figure 1: Evolution of the dark matter power spectrum in simulations with the Planck cosmological parameters for redshifts indicated in the plot. The error bars show errors assuming poissonian noise due to the finite number of independent harmonics in each bin. The full (blue) curves show the linear power spectra. Different symbols show BigMDPL (circles), MDPL (triangles), and SMDPL (squares) simulations. The plot shows that there are three regimes of growth of perturbations: (1) Linear growth of perturbations on long waves gradually shrinks as indicated by the point where the non-linear power spectrum starts to deviate upward from the linear theory prediction, (2) Mildly non-linear regime where fluctuations grow substantially faster than the linear growth, (3) Strongly non-linear regime where fluctuations start to approach relatively slow self-similar clustering, and the power spectrum is the power-law with slope $\sim -2$ indicated by the dashed line in the plot.
• Figure 2: Power spectra (bottom panel) and halo bias (top panel) at redshift $z=1$. Different symbols show BigMDPL (circles), MDPL (triangles), and SMDPL (squares) simulations. Bottom panel: Power spectra for dark matter (lower curves) and halos (top curves). The power spectra are multiplied by factor $k^{1.5}$ to see more clearly the BAO peaks. The full curves show the linear power spectrum and the linear power spectrum scaled up with bias factor $b=1.95$. Top set of symbols are for dark matter halos with circular velocities $\hbox{$v_{\rm max }$}>250 {\rm km/s}$. Top panel: Bias factor $b(k) =\sqrt{P_{\rm halos}/P_{\rm nonlin DM}}$.
• Figure 3: Evolution of the halo mass function in simulations with the Planck cosmological parameters. Different symbols show results from different simulations. The full curves correspond to the Tinker2008 mass function. It gives an excellent fit to $z=0$ results and slightly underestimates the mass function at high redshifts.
• Figure 4: Distribution of the offset $X_{\rm off}$ and spin $\lambda$ parameters for halos in the MDPL simulation at $z=0$ (bottom panels) and $z=3$ (top panels), for masses indicated in the plot. Dashed lines show the selection of relaxed halos: only halos in the low left quadrants are considered to be candidates for relaxed halos. In addition to $\lambda$ and $X_{\rm off}$ we also use the virial parameter $2K/|W|-1$.
• Figure 5: Distribution of virial parameters $2K/|W|-1$ for halos in the MDPL simulation at $z=0$ (bottom panels) and $z=3$ (top panels). Points show a fraction of all halos to avoid crowding. The full curves show average $2K/|W|-1$ values for all halos with the error bars indicating the r.m.s. deviations. Right panels show uncorrected data for all halos. Left panels show halos satisfying selection conditions given by eq.(\ref{['eq:select']}), which were corrected for the surface pressure effect eq.(\ref{['eq:Sp']}). Note that the correction brings halos closer to equilibrium.