It has been recently shown that any halo velocity bias present in the initial conditions does not decay to unity, in agreement with predictions from peak theory. However, this is at odds with the standard formalism based on the coupled fluids approximation for the coevolution of dark matter and halos. Starting from conservation laws in phase space, we discuss why the fluid momentum conservation equation for the biased tracers needs to be modified in accordance with the change advocated in Baldauf, Desjacques & Seljak (2014). Our findings indicate that a correct description of the halo properties should properly take into account peak constraints when starting from the Vlasov-Boltzmann equation.
We explore the phenomenon commonly known as halo assembly bias, whereby dark matter halos of the same mass are found to be more or less clustered when a second halo property is considered, for halos in the mass range $3.7 \times 10^{11} \; h^{-1} \mathrm{M_{\odot}} - 5.0 \times 10^{13} \; h^{-1} \mathrm{M_{\odot}}$. Using the Large Suite of Dark Matter Simulations (LasDamas) we consider nine commonly used halo properties and find that a clustering bias exists if halos are binned by mass or by any other halo property. This secondary bias implies that no single halo property encompasses all the …
Secondary halo bias, commonly known as 'assembly bias,' is the dependence of halo clustering on a halo property other than mass. This prediction of the Lambda-Cold Dark Matter cosmology is essential to modelling the galaxy distribution to high precision and interpreting clustering measurements. As the name suggests, different manifestations of secondary halo bias have been thought to originate from halo assembly histories. We show conclusively that this is incorrect for cluster-size haloes. We present an up-to-date summary of secondary halo biases of high-mass haloes due to various halo proper…
Primordial non-Gaussianity can lead to a scale-dependent bias in the density of collapsed halos relative to the underlying matter density. The galaxy power spectrum already provides constraints on local-type primordial non-Gaussianity complementary those from the cosmic microwave background (CMB), while the bispectrum contains additional shape information and has the potential to outperform CMB constraints in future. We develop the bias model for the halo density contrast in the presence of local-type primordial non-Gaussianity, deriving a bivariate expansion up to second order in terms of the…
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, $Δ$. 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 $Δ$. For conventional halo definitions ($Δ\sim 200\mathrm{m}-600\mathrm{m}$), concentration-dependent cluste…
In the Halo Model, galaxies are hosted by dark matter halos, while the halos themselves are biased tracers of the underlying matter distribution. Measurements of galaxy correlation functions include contributions both from galaxies in different halos, and from galaxies in the same halo (the so-called 1-halo terms). We show that, for highly biased tracers, the 1-halo term of the power spectrum obeys a steep scaling relation in terms of bias. We also show that the 1-halo term of the trispectrum has a steep scaling with bias. The steepness of these scaling relations is such that the 1-halo terms …
We study halo assembly bias for cluster-sized halos. Previous work has found little evidence for correlations between large-scale bias and halo mass assembly history for simulated cluster-sized halos, in contrast to the significant correlation found between bias and concentration for halos of this mass. This difference in behavior is surprising, given that both concentration and assembly history are closely related to the same properties of the linear-density peaks that collapse to form halos. Using publicly available simulations, we show that significant assembly bias is indeed found in the m…
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 combinati…
The bias of dark matter halos and galaxies is a crucial quantity in many cosmological analyses. In this work, using large cosmological simulations, we explore the halo mass function and halo bias within cosmic voids. For the first time to date, we show that they are scale-dependent along the void profile, and provide a predictive theoretical model of both the halo mass function and halo bias inside voids, recovering for the latter and 1% accuracy against simulated data. These findings may help shed light on the dynamics of halo formation within voids and improve the analysis of several void st…
We develop a novel approach in exploring the joint dependence of halo bias on multiple halo properties using Gaussian process regression. Using a $Λ$CDM $N$-body simulation, we carry out a comprehensive study of the joint bias dependence on halo structure, formation history and environment. We show that the bias is a multivariate function of halo properties that falls into three regimes. For massive haloes, halo mass explains the majority of bias variation. For early-forming haloes, bias depends sensitively on the recent mass accretion history. For low-mass and late-forming haloes, bias depend…
We determine the error introduced in a joint halo model analysis of galaxy-galaxy lensing and galaxy clustering observables when adopting the standard approximation of linear halo bias. Considering the Kilo-Degree Survey, we forecast that ignoring the non-linear halo bias would result in up to 5$σ$ offsets in the recovered cosmological parameters describing structure growth, $S_8$, and the matter density parameter, $Ω_{\mathrm{m}}$. We include the scales $10^{-1.3}<r_{\rm{p}} \ / h^{-1}\, \mathrm{Mpc}<10$ in the data vector, and the direction of these offsets are shown to depend on the freedom…
We present estimates of the nonlinear bias of cosmological halo formation, spanning a wide range in the halo mass from $\sim 10^{5} M_\odot$ to $\sim 10^{12} M_\odot$, based upon both a suite of high-resolution cosmological N-body simulations and theoretical predictions. The halo bias is expressed in terms of the mean bias and stochasticity as a function of local overdensity ($δ$), under different filtering scales, which is realized as the density of individual cells in uniform grids. The sampled overdensities span a range wide enough to provide the fully nonlinear bias effect on the formation…
We use $N$-body simulations to study halo assembly bias (i.e., the dependence of halo clustering on properties beyond total mass) in the density and primordial non-Gaussianity (PNG) linear bias parameters $b_1$ and $b_ϕ$, respectively. We consider concentration, spin and sphericity as secondary halo properties, for which we find a clear detection of assembly bias for $b_1$ and $b_ϕ$. At fixed total mass, halo spin and sphericity impact $b_1$ and $b_ϕ$ in a similar manner, roughly preserving the shape of the linear $b_ϕ(b_1)$ relation satisfied by the global halo population. Halo concentration,…
We investigate the role of angular momentum in the clustering of dark matter haloes. We make use of data from two high-resolution N-body simulations spanning over four orders of magnitude in halo mass, from $10^{9.8}$ to $10^{14}\ h^{-1}\ \text{M}_\odot$. We explore the hypothesis that mass accretion in filamentary environments alters the angular momentum of a halo, thereby driving a correlation between the spin parameter $λ$ and the strength of clustering. However, we do not find evidence that the distribution of matter on large scales is related to the spin of haloes. We find that a halo's s…
We study the halo-matter cross bispectrum in the presence of primordial non-Gaussianity of the local type. We restrict ourselves to the squeezed limit, for which the calculation are straightforward, and perform the measurements in the initial conditions of N-body simulations, to mitigate the contamination induced by nonlinear gravitational evolution. Interestingly, the halo-matter cross bispectrum is not trivial even in this simple limit as it is strongly sensitive to the scale-dependence of the quadratic and third-order halo bias. Therefore, it can be used to test biasing prescriptions. We co…
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 $k\sim0.7\,h Mpc^{-1}$, 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-hal…
The standard formalism for the co-evolution of halos and dark matter predicts that any initial halo velocity bias rapidly decays to zero. We argue that, when the purpose is to compute statistics like power spectra etc., the coupling in the momentum conservation equation for the biased tracers must be modified. Our new formulation predicts the constancy in time of any statistical halo velocity bias present in the initial conditions, in agreement with peak theory. We test this prediction by studying the evolution of a conserved halo population in N-body simulations. We establish that the initial…
We present direct measurements of cubic bias parameters of dark matter halos from the halo-matter-matter-matter trispectrum. We measure this statistic efficiently by cross-correlating the halo field measured in N-body simulations with specific third-order nonlocal transformations of the initial density field in the same simulation. Together with the recent Abidi & Baldauf (2018), these are the first measurements of halo bias using the four-point function that have been reported to date. We also obtain constraints on the quadratic bias parameters. For all individual cubic parameters involving t…
We present precise measurements of the assembly bias of dark matter halos, i.e. the dependence of halo bias on other properties than the mass, using curved "separate universe" N-body simulations which effectively incorporate an infinite-wavelength matter overdensity into the background density. This method measures the LIMD (local-in-matter-density) bias parameters $b_n$ in the large-scale limit. We focus on the dependence of the first two Eulerian biases $b^E_1$ and $b^E_2$ on four halo properties: the concentration, spin, mass accretion rate, and ellipticity. We quantitatively compare our re…
We use the forward modeling approach to galaxy clustering combined with the likelihood from the effective-field theory of large-scale structure to measure assembly bias, i.e. the dependence of halo bias on properties beyond the total mass, in the linear ($b_1$) and second order bias parameters ($b_2$ and $b_{K^2}$) of dark matter halos in $N$-body simulations. This is the first time that assembly bias in the tidal bias parameter $b_{K^2}$ is measured. We focus on three standard halo properties: the concentration $c$, spin $λ$, and sphericity $s$, for which we find an assembly bias signal in $b…
Halo bias is the one of the key ingredients of the halo models. It was shown at a given redshift to be only dependent, to the first order, on the halo mass. In this study, four types of cosmic web environments: clusters, filaments, sheets and voids are defined within a state of the art high resolution $N$-body simulation. Within those environments, we use both halo-dark matter cross-correlation and halo-halo auto correlation functions to probe the clustering properties of halos. The nature of the halo bias differs strongly among the four different cosmic web environments we describe. With resp…
The large-scale distribution of cold dark matter halos is generally assumed to trace the large-scale distribution of matter. In a universe with multiple types of matter fluctuations, as is the case with massive neutrinos, the relation between the halo field and the matter fluctuations may be more complicated. We develop a method for calculating the bias factor relating fluctuations in the halo number density to fluctuations in the mass density in the presence of multiple fluctuating components of the energy density. In the presence of massive neutrinos we find a small but pronounced feature in…
We study the role of the local tidal environment in determining the assembly bias of dark matter haloes. Previous results suggest that the anisotropy of a halo's environment (i.e, whether it lies in a filament or in a more isotropic region) can play a significant role in determining the eventual mass and age of the halo. We statistically isolate this effect using correlations between the large-scale and small-scale environments of simulated haloes at $z=0$ with masses between $10^{11.6}\lesssim (m/h^{-1}M_{\odot})\lesssim10^{14.9}$. We probe the large-scale environment using a novel halo-by-ha…
We use bootstrapping to estimate the bias of concentration estimates on N-body dark matter halos as a function of particle number. We find that algorithms based on the maximum radial velocity and radial particle binning tend to overestimate the concentration by 15%-20% for halos sampled with 200 particles and by 7% - 10% for halos sampled with 500 particles. To control this bias at low particle numbers we propose a new algorithm that estimates halo concentrations based on the integrated mass profile. The method uses the full particle information without any binning, making it reliable in cases…
It is common practice for methods that use galaxy clustering to constrain the galaxy-halo relationship, such as the halo occupation distribution (HOD) and/or conditional luminosity function (CLF), to assume that halo mass alone suffices to determine a halo's resident galaxy population. Yet, the clustering strength of cold dark matter halos depends upon halo properties in addition to mass, such as formation time, an effect referred to as assembly bias. If galaxy characteristics are correlated with any of these auxiliary halo properties, the basic assumption of HOD/CLF methods is violated. We es…
The connection between galaxies and dark matter halos is often inferred from data using probabilistic models, such as the Halo Occupation Distribution (HOD). Conventional HOD formulations assume that only halo mass governs the galaxy-halo connection. Violations of this assumption, known as galaxy assembly bias, threaten the HOD program. We introduce decorated HODs, a new, flexible class of models designed to account for assembly bias. Decorated HODs minimally expand the parameter space and maximize the independence between traditional and novel HOD parameters. We use decorated HODs to quantify…
Halo bias is the main link between the matter distribution and dark matter halos. In its simplest form, halo bias is determined by halo mass, but there are known additional dependencies on other halo properties which are of consequence for accurate modeling of galaxy clustering. Here we present the most precise measurement of these secondary-bias dependencies on halo age, concentration, and spin, for a wide range of halo masses spanning from 10$^{10.7}$ to 10$^{14.7}$ $h^{-1}$ M$_{\odot}$. At the high-mass end, we find no strong evidence of assembly bias for masses above M$_{vir}$ $\sim10^{14}…
We present a calibration of halo assembly bias using the Separate Universe technique. Specifically, we measure the response of halo abundances at fixed mass and concentration to the presence of an infinite-wavelength initial perturbation. We develop an analytical framework for describing the concentration dependence of this peak-background split halo bias -- a measure of assembly bias -- relying on the near-Lognormal distribution of halo concentration at fixed halo mass. The combination of this analytical framework and the Separate Universe technique allows us to achieve very high precision in…
Linear halo bias is the response of dark matter halo number density to a long wavelength fluctuation in the dark matter density. Using abundance matching between separate universe simulations which absorb the latter into a change in the background, we test the consistency relation between the change in a one point function, the halo mass function, and a two point function, the halo-matter cross correlation in the long wavelength limit. We find excellent agreement between the two at the $1-2\%$ level for average halo biases between $1 \lesssim \bar b_1 \lesssim 4$ and no statistically significa…
We present a non-parametric Lagrangian biasing model and fit the ratio of the halo and mass densities at the field level using the mass-weighted halo field in the AbacusSummit simulations at $z=0.5$. Unlike the perturbative halo bias model widely used in interpreting the observed large-scale structure traced by galaxies, we find a non-negative halo-to-mass ratio that increases monotonically with the linear overdensity $δ_1$ in the initial Lagrangian space. The bias expansion, however, does not guarantee non-negativity of the halo counts, and may give rising halo number counts at negative overd…
The clustering of dark matter halos depends on the assembly history of halos at fixed halo mass; a phenomenon referred to as \textit{halo assembly bias}. Halo assembly bias is readily observed in cosmological simulations of dark matter. However, it is difficult to detect it in observations. The identification of galaxy or cluster properties correlated with the formation time of the halo at fixed halo mass and the ability to select galaxy clusters free from projection effects are the two most significant hurdles in the observational detection of halo assembly bias. The latter, in particular, ca…
We present a detailed analysis of the physical processes that cause halo assembly bias -- the dependence of halo clustering on proxies of halo formation time. We focus on the origin of assembly bias in the mass range corresponding to the hosts of typical galaxies and use halo concentration as our chief proxy of halo formation time. We also repeat our key analyses across a broad range of halo masses and for alternative formation time definitions. We show that splashback subhaloes are responsible for two thirds of the assembly bias signal, but do not account for the entire effect. After splashba…
One of the main predictions of excursion set theory is that the clustering of dark matter haloes only depends on halo mass. However, it has been long established that the clustering of haloes also depends on other properties, including formation time, concentration, and spin; this effect is commonly known as halo assembly bias. We use a suite of gravity-only simulations to study the dependence of halo assembly bias on cosmology; these simulations cover cosmological parameters spanning 10$σ$ around state-of-the-art best-fitting values, including standard extensions of the $Λ$CDM paradigm such a…
Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method
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, $r\geq10h^{-1}{\rm Mpc},$ 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 relat…
Clustering of dark matter halos has been shown to depend on halo properties beyond mass such as halo concentration, a phenomenon referred to as halo assembly bias. Standard halo occupation models (HOD) in large scale structure studies assume that halo mass alone is sufficient in characterizing the connection between galaxies and halos. Modeling of galaxy clustering can face systematic effects if the number of galaxies within a halo is correlated with other halo properties. Using the Small MultiDark-Planck high resolution $N$-body simulation and the clustering measurements of the Sloan Digital …
The simplest analyses of halo bias assume that halo mass alone determines halo clustering. However, if the large scale environment is fixed, then halo clustering is almost entirely determined by environment, and is almost completely independent of halo mass. We show why. Our analysis is useful for studies which use the environmental dependence of clustering to constrain cosmological and galaxy formation models. It also shows why many correlations between galaxy properties and environment are merely consequences of the underlying correlations between halos and their environments, and provides a…
We use the improved IllustrisTNG300 magneto-hydrodynamical cosmological simulation to revisit the effect that secondary halo bias has on the clustering of the central galaxy population. With a side length of 205 $h^{-1}$Mpc and significant improvements on the sub-grid model with respect to the previous Illustris boxes, IllustrisTNG300 allows us to explore the dependencies of galaxy clustering over a large cosmological volume and wide halo-mass range. We show, at high statistical significance, that the halo assembly bias signal (i.e., the secondary dependence of halo bias on halo formation reds…
Using two sets of large $N$-body simulations, we study the origin of the correlations of halo assembly time ($z_{\rm f}$), concentration ($v_{\rm max}/v_{\rm 200}$) and spin ($λ$) with the large-scale evolved density field at given halo mass, i.e. the secondary bias. We find that the secondary bias is the secondary effect of the correlations of halo properties with the linear density estimated at the same comoving scale. Using the linear density on different scales, we find two types of correlations. The internal correlation, which reflects the correlation of halo properties with the mean line…
We propose a simple model that elucidates the generation of halo velocity bias. The fluid equation approximation is often adopted in modelling the evolution of the halo density field. In this approach, halos are often taken to be point particles even though in reality they are finite-sized objects. In this paper, we generalize the fluid equation approximation to halos to include the finite extent of halos by taking into account the halo profile. We compute the perturbation of the halo density and velocity field to second order and find that the profile correction gives rise to $k^2$ correction…
