Profiles of dark haloes: evolution, scatter, and environment

TL;DR

The paper investigates dark-matter halo density profiles in a high-resolution $\Lambda$CDM N-body simulation, focusing on two-parameter NFW profiles and halo concentration $c_{ m vir}$. It introduces a revised toy model that links the concentration to the collapse epoch and a contraction factor, enabling accurate reproduction of median $c_{ m vir}(M_{ m vir},z)$ and its redshift evolution across cosmologies. The authors quantify a significant intrinsic scatter in $\log c_{ m vir}$ (about $0.18$ for distinct haloes and $0.24$ for subhaloes) and demonstrate environmental enhancements in concentration, with dense regions and subhaloes being more concentrated. These results imply substantial consequences for disc-size predictions, TF scatter, and the origin of the Hubble sequence, and they emphasize the need to treat $c_{ m vir}$ as a fundamental parameter in semi-analytic galaxy formation models.

Abstract

We study dark-matter halo density profiles in a high-resolution N-body simulation of an LCDM cosmology. Our statistical sample contains ~5000 haloes in the range 10^{11}-10^{14} M_sun. The profiles are parameterized by an NFW form with two parameters, an inner radius r_s and a virial radius r_v, and we define the halo concentration c_v = r_v/r_s. First, we find that, for a given halo mass, the redshift dependence of the median concentration is c_v ~ 1/(1+z), corresponding to a roughly constant r_s with redshift. We present an improved analytic treatment of halo formation that fits the measured relations between halo parameters and their redshift dependence. The implications are that high-redshift galaxies are predicted to be more extended and dimmer than expected before. Second, we find that the scatter in log(c_v) is ~0.18, corresponding to a scatter in maximum rotation velocities of dV/V ~ 0.12. We discuss implications for modelling the Tully-Fisher relation, which has a smaller reported intrinsic scatter. Third, haloes in dense environments tend to be more concentrated than isolated haloes. These results suggest that c_v is an essential parameter for the theory of galaxy modelling, and we briefly discuss implications for the universality of the Tully-Fisher relation, the formation of low surface brightness galaxies, and the origin of the Hubble sequence.

Figures (13)

• Figure 1: Maximum velocity versus concentration. The maximum rotation velocity for an NFW halo in units of the rotation velocity at its virial radius as a function of halo concentration.
• Figure 2: Convergence test for an $M_{\rm vir} = 2 \times 10^{12} h^{-1}M_{\odot}{\ }$ halo simulated with $2,000$ and $120,000$ particles respectively. When the fit is restricted to $0.02 R_{\rm vir} - R_{\rm vir}$ the best-fit $c_{\rm vir}$ values show no significant difference.
• Figure 3: Convergence test for $c_{\rm vir}$ evolution and scatter. Shown is a comparison of $M_{\rm vir} = 3-10 \times 10^{11} h^{-1}M_{\odot}{\ }$ haloes simulated using our main simulation (thick lines) and a second simulation with $8$ times the mass resolution (thin lines). The solid lines and errors reflect the median and Poisson uncertainty respectively. The dashed lines reflect the estimated intrinsic scatter. There is no evidence for significant deviations in either the measured median or scatter as the mass resolution is increased.
• Figure 4: Concentration versus mass for distinct haloes at $z=0$. The thick solid curve is the median at a given $M_{\rm vir}$. The error bars represent Poisson errors of the mean due to the sampling of a finite number of haloes per mass bin. The outer dot-dashed curves encompass $68\%$ of the $c_{\rm vir}$ values as measured in the simulations. The inner dashed curves represent only the true, intrinsic scatter in $c_{\rm vir}$, after eliminating both the Poisson scatter and the scatter due to errors in the individual profile fits due, for example, to the finite number of particles per halo. The central and outer thin solid curves are the predictions for the median and $68\%$ values by the toy model outlined in the text, for $F=0.01$ and three different values of $K$. The thin dot-dashed line shows the prediction of the toy model of NFW97 for $f=0.01$ and $k=3.4\times10^3$.
• Figure 5: Concentration versus mass for subhaloes at $z=0$. The curves and errors are the same as in Figure \ref{['fig:c.vs.mass.distinct']}.