The age dependence of halo clustering

TL;DR

The paper analyzes halo clustering in the Millennium Simulation to test whether environment and assembly history influence bias. It shows that for haloes with $M \lesssim M_*$, the large-scale bias correlates with formation time, with early-forming haloes exhibiting substantially stronger clustering than late-forming ones, a result that contradicts standard excursion-set independence. Comparisons with analytic bias models (e.g., $b(\nu,z)=1+(\nu^2-1)/\delta_c$, where $\nu=\delta_c/\sigma(M,z)$) indicate broad agreement but notable scatter, reinforcing that the effect is real and systematic rather than a numerical artifact. The findings imply that common halo occupation approaches, which ignore formation history, may mispredict galaxy clustering, underscoring the need for assembly-history-aware modeling or direct baryonic simulations to capture the age-dependent clustering signal.

Abstract

We use a very large simulation of the concordance LCDM cosmogony to study the clustering of dark matter haloes. For haloes less massive than about 1e13Msun/h, the amplitude of the two-point correlation function on large scales depends strongly on halo formation time. Haloes that assembled at high redshift are substantially more clustered than those that assembled more recently. The effect is a smooth function of halo formation time and its amplitude increases with decreasing halo mass. At 1e11 Msun/h the ``oldest'' 10% of haloes are more than 5 times more strongly correlated than the ``youngest'' 10%. This unexpected result is incompatible with the standard excursion set theory for structure growth, and it contradicts a fundamental assumption of the halo occupation distribution models often used to study galaxy clustering, namely that the galaxy content of a halo of given mass is statistically independent of its larger scale environment.

Figures (5)

• Figure 1: Halo bias as a function of peak height, $\nu=\delta_c/\sigma(M,z)$. Individual symbols are the bias factors measured from the Millennium Simulation; different symbols refer to different redshifts as indicated. The red and blue lines are analytic predictions from Mo & White (1996) and Sheth, Mo & Tormen (2000). The magenta and black lines are the fitting formulae given by Jing (1998) and Mandelbaum et al. (2005). The latter are plotted only over the parameter range covered directly by the numerical data.
• Figure 2: Two-point correlation functions for haloes in four mass ranges. Each panel gives results for haloes in the mass range indicated in the label. The dotted black line, repeated in all panels, is the correlation function of the underlying mass distribution. Dashed black lines give the correlation functions for the full sample of haloes in each mass range. The red and blue curves give correlation functions for the 20% oldest and 20% youngest of these haloes, respectively. Error bars are based on Poisson uncertainties in the pair counts. Note that halo exclusion effects are visible on small scales for the two most massive samples.
• Figure 3: Bias at $z=0$ as a function of halo mass and formation time. Halo mass is given in units of the characteristic mass ${\rm M_*} = 6.15\times 10^{12}h^{-1} {\rm M_\odot}$. The dotted black curve is the mean bias for all haloes in the given mass bin. The solid red and blue curves are for the 20% oldest and 20% youngest haloes, respectively. The red and blue dashed curves refer to the 10% oldest and 10% youngest haloes.
• Figure 4: Images comparing the distribution of "young" haloes, "old" haloes and dark matter. The region plotted is a $30 h^{-1} {\rm Mpc}$ slice through the Millennium Simulation. All haloes plotted contain between 100 and 200 particles. The top row shows the 20% youngest (left) and 20% oldest (middle) of these haloes, together with an equal number of randomly selected dark matter particles (right). The bottom row shows corresponding plots for the 10% tails of the halo formation time distribution.
• Figure 5: Bias as a function of halo formation time. We divide haloes with particle number in the range $[100,200]$ into ten equal-sized subsamples as a function of their formation time. For each subsample we compute a mean formation redshift and a bias factor. The figure plots these two quantities against each other. Vertical and horizontal dotted lines show the mean formation redshift and the mean bias for the sample as a whole.