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In this paper we use the ``Millennium Simulation to re-examine the mass assembly history of dark matter halos and the age dependence of halo clustering. We use eight different definitions of halo formation times to characterize the different aspects of the assembly history of a dark matter halo. We find that these formation times have different dependence on halo mass. While some formation times characterize well the hierarchical nature of halo formation, in the sense that more massive halos have later formation, the trend is reversed for other definitions of the formation time. In particular, the formation times that are likely to be related to the formation of galaxies in dark halos show strong trends of ``down-sizing, in that lower-mass halos form later. We also investigate how the correlation amplitude of dark matter halos depends on the different formation times. We find that this dependence is quite strong for some definitions of formation time but weak or absent for other definitions. In particular, the correlation amplitude of halos of a given mass is almost independent of their last major merger time. For the definitions that are expected to be more related to the formation of galaxies in dark halos, a significant assembly bias is found only for halos less massive than M_*. We discuss our results in connection to the hierarchical assembly of dark matter halos, the ``archaeological down-sizing observed in the galaxy population, and the observed color-dependence of the clustering strength of galaxy groups and clusters.
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Using dark matter haloes identified in a large $N$-body simulation, we study halo assembly bias, with halo formation time, peak maximum circular velocity, concentration, and spin as the assembly variables. Instead of grouping haloes at fixed mass into different percentiles of each assembly variable, we present the joint dependence of halo bias on the {it values} of halo mass and each assembly variable. In the plane of halo mass and one assembly variable, the joint dependence can be largely described as halo bias increasing outward from a global minimum. We find it unlikely to have a combination of halo variables to absorb all assembly bias effects. We then present the joint dependence of halo bias on two assembly variables at fixed halo mass. The gradient of halo bias does not necessarily follow the correlation direction of the two assembly variables and it varies with halo mass. Therefore in general for two correlated assembly variables one cannot be used as a proxy for the other in predicting halo assembly bias trend. Finally, halo assembly is found to affect the kinematics of haloes. Low-mass haloes formed earlier can have much higher pairwise velocity dispersion than those of massive haloes. In general, halo assembly leads to a correlation between halo bias and halo pairwise velocity distribution, with more strongly clustered haloes having higher pairwise velocity and velocity dispersion. However, the correlation is not tight, and the kinematics of haloes at fixed halo bias still depends on halo mass and assembly variables.
The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f_NL, offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ~23% and ~48% for galaxies at z=1 selected by stellar mass and star formation rate, respectively.
Dark matter halo clustering depends not only on halo mass, but also on other properties such as concentration and shape. This phenomenon is known broadly as assembly bias. We explore the dependence of assembly bias on halo definition, parametrized by spherical overdensity parameter, $Delta$. We summarize the strength of concentration-, shape-, and spin-dependent halo clustering as a function of halo mass and halo definition. Concentration-dependent clustering depends strongly on mass at all $Delta$. For conventional halo definitions ($Delta sim 200mathrm{m}-600mathrm{m}$), concentration-dependent clustering at low mass is driven by a population of haloes that is altered through interactions with neighbouring haloes. Concentration-dependent clustering can be greatly reduced through a mass-dependent halo definition with $Delta sim 20mathrm{m}-40mathrm{m}$ for haloes with $M_{200mathrm{m}} lesssim 10^{12}, h^{-1}mathrm{M}_{odot}$. Smaller $Delta$ implies larger radii and mitigates assembly bias at low mass by subsuming altered, so-called backsplash haloes into now larger host haloes. At higher masses ($M_{200mathrm{m}} gtrsim 10^{13}, h^{-1}mathrm{M}_{odot}$) larger overdensities, $Delta gtrsim 600mathrm{m}$, are necessary. Shape- and spin-dependent clustering are significant for all halo definitions that we explore and exhibit a relatively weaker mass dependence. Generally, both the strength and the sense of assembly bias depend on halo definition, varying significantly even among common definitions. We identify no halo definition that mitigates all manifestations of assembly bias. A halo definition that mitigates assembly bias based on one halo property (e.g., concentration) must be mass dependent. The halo definitions that best mitigate concentration-dependent halo clustering do not coincide with the expected average splashback radii at fixed halo mass.
We study the effect of large-scale tidal fields on internal halo properties using a set of N-body simulations. We measure significant cross-correlations between large-scale tidal fields and several non-scalar halo properties: shapes, velocity dispersion, and angular momentum. Selection effects that couple to these non-scalar halo properties can produce anisotropic clustering even in real-space. We investigate the size of this effect and show that it can produce a non-zero quadrupole similar in size to the one generated by linear redshift-space distortions (RSD). Finally, we investigate the clustering properties of halos identified in redshift-space and find enormous deviations from the standard linear RSD model, again caused by anisotropic assembly bias. These effects could contaminate the values of cosmological parameters inferred from the observed redshift-space clustering of galaxies, groups, or 21cm emission from atomic hydrogen, if their selection depends on properties affected by halo assembly bias. We briefly discuss ways in which this effect can be measured in existing and future large-scale structure surveys.
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