We make use of the IllustrisTNG cosmological, hydrodynamical simulations to test fundamental assumptions of the mass-based Halo Occupation Distribution (HOD) approach to modelling the galaxy-halo connection. By comparing the clustering of galaxies measured in the 300 Mpc TNG box (TNG300) with that predicted by the standard (``basic'') HOD model, we find that, on average, the ``basic'' HOD model underpredicts the real-space correlation function in the TNG300 box by $\sim$ 15\% on scales of $1 \ {\rm Mpc}/h < r < 20 \ {\rm Mpc}/h$, which is well beyond the target precision demanded of next-generation galaxy redshift surveys. We perform several tests to establish the robustness of our findings to systematic effects, including the effect of finite box size and the choice of halo finder. In our exploration of ``secondary'' parameters with which to augment the ``basic'' HOD, we find that the local environment of the halo, the velocity dispersion anisotropy, $\beta$, and the product of the half-mass radius and the velocity dispersion, $\sigma^2 R_{\rm halfmass}$, are the three most effective measures of assembly bias that help reconcile the ``basic'' HOD-predicted clustering with that in TNG300. In addition, we test other halo properties such as halo spin, formation epoch and halo concentration. We also find that at fixed halo mass, galaxies in one type of environment cluster differently from galaxies in another. We demonstrate that a more complete model of the galaxy-halo connection can be constructed if we combine both mass and local environment information about the halo.

Limitations to the `basic' HOD model and beyond

Understanding the galaxy-halo connection is fundamental for contemporary models of galaxy clustering. The extent to which the haloes' assembly history and environment impact galaxy clustering (a.k.a. galaxy assembly bias; GAB), remains a complex and challenging problem. Using a semi-analytic galaxy formation model, we study the individual contributions of different secondary halo properties to the GAB signal. These are obtained by comparing the clustering of stellar-mass selected samples to that of shuffled samples where the galaxies are randomly reassigned to haloes of fixed mass and a specified secondary halo property. We explore a large range of internal halo properties and environmental measures. We find that commonly-used properties like the halo age or concentration amount to only 20-30% of the signal, while the smoothed matter density or the tidal anisotropy can explain the full level of GAB (though care should be given to the specific definition). For the ``successful'' measures, we examine the occupancy variations and the associated changes in the halo occupation function parameters. These are used to create mock catalogues which reproduce the full level of GAB. Finally, we propose a practical modification of the standard halo occupation distribution model, which can be tuned to any level of assembly bias. Fitting the parameters to our semi-analytic model, we demonstrate that the corresponding mock catalogue recovers the target level of GAB as well as the occupancy variations. Our results enable producing realistic mock catalogues and directly inform theoretical modelling of assembly bias and attempts to detect it in the Universe.

Dissecting and modelling galaxy assembly bias

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, Vmax; 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 & 10Mpc=h; our findings are in keeping with previous results. In particular, at the low-mass end (Mvir < Mcoll 10 12:5 M =h), halos with high-Vmax show stronger large-scale clustering relative to halos with low-Vmax of the same mass; this trend weakens and reverses for Mvir & Mcoll: In the nonlinear regime, assembly bias in low-mass halos exhibits a pronounced scale-dependent “bump” at 500kpc=h 5Mpc=h; 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 r 1 2Mpc=h can be impacted by up to 15% by the choice of the halo property used in the halo model, even for stellar mass-limited samples.

The Scale-Dependence of Halo Assembly Bias

We explore two widely used empirical models for the galaxy-halo connection, subhalo abundance matching (SHAM) and the halo occupation distribution (HOD) and compare their predictions with the hydrodynamical simulation IllustrisTNG (TNG) for a range of statistics that quantify the galaxy distribution at $n_{\rm gal}\approx1.3\times10^{-3}\,[{\rm Mpc}/h]^{-3}$. We observe that in their most straightforward implementations, both models fail to reproduce the two-point clustering measured in TNG. We find that SHAM models constructed using the relaxation velocity, $V_{\rm relax}$, and the peak velocity, $V_{\rm peak}$, perform best, and match the clustering reasonably well, although neither model captures adequately the one-halo clustering. Splitting the total sample into sub-populations, we discover that SHAM overpredicts the clustering of high-mass, blue, star-forming, and late-forming galaxies and uderpredicts that of low-mass, red, quiescent, and early-forming galaxies. We also study various baryonic effects, finding that subhalos in the dark-mater-only simulation have consistently higher values of their SHAM-proxy properties than their full-physics counterparts. We then consider a two-dimensional implementation of the HOD model augmented with a secondary parameter (environment, velocity anisotropy, $\sigma^2R_{\rm halfmass}$, and total potential) and tuned so as to match the two-point clustering of the IllustrisTNG galaxies on large scales. We analyze these galaxy populations adopting alternative statistical tools such as galaxy-galaxy lensing, void-galaxy cross-correlations and cumulants of the smoothed density field, finding that the hydrodynamical galaxy distribution disfavors $\sigma^2 R_{\rm halfmass}$ and the total potential as secondary parameters, while the environment and velocity anisotropy samples are consistent with full-physics across all statistical probes examined.

Extensions to models of the galaxy-halo connection

Abstract We review the field of collisionless numerical simulations for the large-scale structure of the Universe. We start by providing the main set of equations solved by these simulations and their connection with General Relativity. We then recap the relevant numerical approaches: discretization of the phase-space distribution (focusing on N -body but including alternatives, e.g., Lagrangian submanifold and Schrödinger–Poisson) and the respective techniques for their time evolution and force calculation (direct summation, mesh techniques, and hierarchical tree methods). We pay attention to the creation of initial conditions and the connection with Lagrangian Perturbation Theory. We then discuss the possible alternatives in terms of the micro-physical properties of dark matter (e.g., neutralinos, warm dark matter, QCD axions, Bose–Einstein condensates, and primordial black holes), and extensions to account for multiple fluids (baryons and neutrinos), primordial non-Gaussianity and modified gravity. We continue by discussing challenges involved in achieving highly accurate predictions. A key aspect of cosmological simulations is the connection to cosmological observables, we discuss various techniques in this regard: structure finding, galaxy formation and baryonic modelling, the creation of emulators and light-cones, and the role of machine learning. We finalise with a recount of state-of-the-art large-scale simulations and conclude with an outlook for the next decade. 

/pdf/large-scale-dark-matter-simulations-1rpp9h4y.pdf

Large-scale dark matter simulations

The internal properties of dark matter haloes correlate with the large-scale halo clustering strength at fixed halo mass – an effect known as assembly bias – and are also strongly affected by the local, non-linear cosmic web. Characterizing a halo’s local web environment by its tidal anisotropy α at scales approximately four times the halo radius, we demonstrate that these multiscale correlations represent two distinct statistical links: one between the internal property and α, and the other between α and large-scale (⁠|${\gtrsim}30\, h^{-1}\, {\rm Mpc}$|⁠) halo bias b_1. We focus on scalar internal properties of haloes related to formation time (concentration c_vir), shape (mass ellipsoid asphericity c/a), velocity dispersion structure (velocity ellipsoid asphericity /a_v and velocity anisotropy β), and angular momentum (dimensionless spin λ) in the mass range |$8\times 10^{11}\lesssim M_{\rm vir}/(\, h^{-1}\, \mathrm{M}_{\odot })\lesssim 5\times 10^{14}$|⁠. Using conditional correlation coefficients and other detailed tests, we show that the joint distribution of α, b_1, and any of the internal properties c ∈ {β, c_v/a_v, c/a, c_vir, λ} is consistent with p(α, b_1, c) ≃ p(α)p(b_1|α)p(c|α), at all but the largest masses. Thus, the assembly bias trends c↔b_1 reflect the two fundamental correlations c↔α and b_1↔α. Our results are unaffected by the exclusion of haloes with recent major merger events or splashback objects, although the latter are distinguished by the fact that α does not explain their assembly bias trends. The overarching importance of α provides a new perspective on the nature of assembly bias of distinct haloes, with potential ramifications for incorporating realistic assembly bias effects into mock catalogues of future large-scale structure surveys and for detecting galaxy assembly bias.

Cosmic web anisotropy is the primary indicator of halo assembly bias

We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias $b_1$ and $b_2$ on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy $\alpha$ to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work which exploits the near-Lognormal shape of the distribution of $\alpha$ and results in very high precision calibrations. We present convenient fitting functions for the dependence of $b_1$ and $b_2$ on $\alpha$ over a wide range of halo mass for redshifts $0\leq z\leq1$. Our calibration of $b_2(\alpha)$ is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results which showed that $\alpha$ is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of $b_1$ and $b_2$ on any such secondary property which has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using $\alpha$ as a segregating variable in multi-tracer analyses.

Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

Large-scale sky surveys require companion large volume simulated mock catalogs. To ensure precision cosmology studies are unbiased, the correlations in these mocks between galaxy properties and their large-scale environments must be realistic. Since galaxies are embedded in dark matter halos, an important first step is to include such correlations -- sometimes called assembly bias -- for dark matter halos. However, galaxy properties correlate with smaller scale physics in halos which large simulations struggle to resolve. We describe an algorithm which addresses and largely mitigates this problem. Our algorithm exploits the fact that halo assembly bias is unchanged as long as correlations between halo property $c$ and the intermediate-scale tidal environment $\alpha$ are preserved. Therefore, knowledge of $\alpha$ is sufficient to assign small-scale, otherwise unresolved properties to a halo in a way which preserves its large-scale assembly bias accurately. We demonstrate this explicitly for halo internal properties like formation history (concentration $c_{\rm 200b}$), shape $c/a$, dynamics $c_{v}/a_{v}$, velocity anisotropy $\beta$ and angular momentum (spin $\lambda$). Our algorithm increases a simulation's reach in halo mass and number density by an order of magnitude, with improvements in the bias signal as large as 45% for 30-particle halos, thus significantly reducing the cost of mocks for future weak lensing and redshift space distortion studies.

Mock halo catalogues: assigning unresolved halo properties using correlations with local halo environment

ABSTRACT The structural and dynamic properties of the dark matter haloes, though an important ingredient in understanding large-scale structure formation, require more conservative particle resolution than those required by halo mass alone in a simulation. This reduces the parameter space of the simulations, more severely for high redshift and large-volume mocks, which are required by the next-generation large-sky surveys. Here, we incorporate redshift and cosmology dependence into an algorithm that assigns accurate halo properties such as concentration, spin, velocity, and spatial distribution to the subresolution haloes in a simulation. By focusing on getting the right correlations with halo mass and local tidal anisotropy α measured at 4 × halo radius, our method will also recover the correlations of these small-scale structural properties with the large-scale environment, i.e. the halo assembly bias at all scales greater than 5 × halo radius. We find that the distribution of halo properties is universal with redshift and cosmology. By applying the algorithm to a large-volume simulation $(600\, h^{-1}\, {\rm Mpc})^3$, we can access the 30–500 particle haloes, thus gaining an order of magnitude in halo mass and two to three orders of magnitude in number density at z = 2–4. This technique reduces the cost of mocks required for the estimation of covariance matrices, weak lensing studies, or any large-scale clustering analysis with less massive haloes. 

Sujatha Ramakrishnan

Papers

Cosmic web anisotropy is the primary indicator of halo assembly bias

Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

Mock halo catalogues: assigning unresolved halo properties using correlations with local halo environment

Properties beyond mass for unresolved haloes across redshift and cosmology using correlations with local halo environment