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Register a new userHalo Assembly Bias in the Quasi-linear Regime
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We address the question of whether or not assembly bias arises in the absence of highly non-linear effects such as tidal stripping of halos near larger mass concentrations. Therefore, we use a simplified dynamical scheme where these effects are not modeled. We choose the punctuated Zeldovich (PZ) approximation, which prevents orbit mixing by coalescing particles coming within a critical distance of each other. A numerical implementation of this approximation is fast, allowing us to run a large number of simulations to study assembly bias. We measure an assembly bias from 60 PZ simulations, each with 512^3 cold particles in a 128h^-1 Mpc cubic box. The assembly bias estimated from the correlation functions at separations < 5h^-1 Mpc for objects (halos) at z=0 is comparable to that obtained in full N-body simulations. For masses 4x10^11 h^-1 Mo the oldest 10% haloes are 3-5 times more correlated than the youngest 10%. The bias weakens with increasing mass, also in agreement with full N-body simulations. We find that that halo ages are correlated with the dimensionality of the surrounding linear structures as measured by the parameter (lambda_1+lambda_2+lambda_3)/ (lambda_1^2+lambda_2^2+lambda_3^2)^{1/2} where lambda_i are proportional to the eigenvalues of the velocity deformation tensor. Our results suggest that assembly bias may already be encoded in the early stages of the evolution.
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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.
The two-point clustering of dark matter halos is influenced by halo properties besides mass, a phenomenon referred to as halo assembly bias. Using the depth of the gravitational potential well, $V_{rm max}$, as our secondary halo property, in this paper we present the first study of the scale-dependence assembly bias. In the large-scale linear regime, $rgeq10h^{-1}{rm Mpc},$ our findings are in keeping with previous results. In particular, at the low-mass end ($M_{rm vir}<M_{rm coll}approx10^{12.5}{rm M}_{odot}$), halos with high-$V_{rm max}$ show stronger large-scale clustering relative to halos with low-$V_{rm max}$ of the same mass, this trend weakens and reverses for $M_{rm vir}geq M_{rm coll}.$ In the nonlinear regime, assembly bias in low-mass halos exhibits a pronounced scale-dependent bump at $500h^{-1}{rm kpc}-5h^{-1}{rm Mpc},$ a new result. This feature weakens and eventually vanishes for halos of higher mass. We show that this scale-dependent signature can primarily be attributed to a special subpopulation of ejected halos, defined as present-day host halos that were previously members of a higher-mass halo at some point in their past history. A corollary of our results is that galaxy clustering on scales of $rsim1-2h^{-1}{rm Mpc}$ can be impacted by up to $sim15%$ by the choice of the halo property used in the halo model, even for stellar mass-limited samples.
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 present significant evidence of halo assembly bias for SDSS redMaPPer galaxy clusters in the redshift range $[0.1, 0.33]$. By dividing the 8,648 clusters into two subsamples based on the average member galaxy separation from the cluster center, we first show that the two subsamples have very similar halo mass of $M_{rm 200m}simeq 1.9times 10^{14}~h^{-1}M_odot$ based on the weak lensing signals at small radii $R<sim 10~h^{-1}{rm Mpc}$. However, their halo bias inferred from both the large-scale weak lensing and the projected auto-correlation functions differs by a factor of $sim$1.5, which is a signature of assembly bias. The same bias hypothesis for the two subsamples is excluded at 2.5$sigma$ in the weak lensing and 4.4$sigma$ in the auto-correlation data, respectively. This result could bring a significant impact on both galaxy evolution and precision cosmology.
We derive a simple prescription for including beyond-linear halo bias within the standard, analytical halo-model power spectrum calculation. This results in a corrective term that is added to the usual two-halo term. We measure this correction using data from $N$-body simulations and demonstrate that it can boost power in the two-halo term by a factor of $sim2$ at scales $ksim0.7,h Mpc^{-1}$, with the exact magnitude of the boost determined by the specific pair of fields in the two-point function. How this translates to the full power spectrum depends on the relative strength of the one-halo term, which can mask the importance of this correction to a greater or lesser degree, again depending on the fields. Generally we find that our correction is more important for signals that arise from lower-mass haloes. When comparing our calculation to simulated data we find that the under-prediction of power in the transition region between the two- and one-halo terms, which typically plagues halo-model calculations, is almost completely eliminated when including the full non-linear halo bias. We show improved results for the auto and cross spectra of galaxies, haloes and matter. In the specific case of matter-matter or matter-halo power we note that a large fraction of the improvement comes from the non-linear biasing between low- and high-mass haloes. We envisage our model being useful in the analytical modelling of cross correlation signals. Our non-linear bias halo-model code is available at https://github.com/alexander-mead/BNL
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