The Dependence of Halo Clustering on Subhalo Anisotropy and Planarity

TL;DR

This paper investigates whether halo clustering in a CDM framework depends on the anisotropy and planarity of subhalo distributions. It uses a cosmological N-body simulation (SMDPL) with halo catalogs, six marks of subhalo configuration, and both two-point and marked correlation functions, incorporating mass normalization to remove simple mass effects. The key finding is a strong, environment-dependent clustering signal: haloes with less anisotropic or less planar subhalo configurations cluster more strongly, and haloes whose subhaloes are less centrally concentrated (larger $\mathrm{Med}(r_{\rm sub})$) exhibit stronger clustering, with the signal persisting after accounting for known secondary biases such as concentration, spin, and halo shape. This establishes a novel, distinct form of assembly-like bias linked to subhalo spatial distributions, with potential observational tests for satellite anisotropy in the Local Group and broader implications for CDM predictions of satellite planes and anisotropy, as discussed in the Local Group context and Holmberg-like phenomena.

Abstract

We show that host cold dark matter (CDM) haloes cluster in a manner that depends upon the anisotropy/planarity of their subhaloes, indicating an environmental dependence to subhalo anisotropy/planarity. The spatial distribution of satellite galaxies about central galaxies and correspondingly, the spatial distribution of subhaloes about host haloes have been subjects of interest for two decades. Important questions include the degree to which satellites are distributed anisotropically about their hosts or exhibit planarity in their distributions and the degree to which this anisotropy depends upon the environment of the host-satellite system. We study the spatial distributions of subhaloes in a cosmological N-body simulation. We find that CDM subhaloes are distributed in a manner that is strongly anisotropic/planar, in agreement with prior work, though our presentation is complementary. The more novel result is that this anisotropy has an environmental dependence. Systems which exhibit less (more) anisotropy and less (more) planarity cluster more strongly (weakly). Systems in which subhaloes reside further from their host centres cluster more weakly. None of these clustering effects are caused by a correlation between subhalo anisotropy/planarity and other properties on which host halo clustering is known to depend, such as concentration, spin parameter, host halo shape, or subhalo count. We discuss the impact of this result on the anisotropy of satellites as predicted by CDM, its testability, and its possible relation to anisotropy observed about the large galaxies of the Local Group.

Figures (11)

• Figure 1: The distribution of subhalo counts following the cuts made to the catalogue as discussed in Section \ref{['sec:halo_filters']}. The dashed lines show the 2.5th, 16th, 50th (i.e., median), 84th, and 97.5th percentiles of the distribution. The distribution is broad, consistent with the fact that the distribution of subhalo number at fixed halo mass is broader than Poisson ZentnerBerlind2005boylan-kolchin+2010purcell_zentner2012mao+2015.
• Figure 2: A diagram explaining the directional cosine marks as introduced in section \ref{['sec:cosine']}. The large pink ellipse represents a host halo while the blue circles represent subhaloes. The dashed line visualizes the host halo's major axis, $\vec{A}_\mathrm{host}$, while the solid vector $\vec{x}_i$ makes the angle $\theta_i$ with the major axis.
• Figure 3: A diagram showing a 2D projection of a mock system to help explain the $D_\mathrm{rms}$ and $|\cos\theta_\mathrm{plane}|$ marks as introduced in sections \ref{['sec:plane_thick']} and \ref{['sec:plane_angle']}. The large pink ellipse represents a host halo while the blue circles represent subhaloes. The thick solid line spanning the diagram represents the best-fit plane while the dashed line represented the host halo's major axis ($\vec{A}_\mathrm{host}$). The solid vector labeled $d_i$ is the distance from the subhalo to the plane used when determining the best-fit plane (Eq. \ref{['eq:plane_minimize']}) and for calculating the $D_\mathrm{rms}$ mark (Eq. \ref{['eq:plane_thickness']}). The solid vector labeled $\vec{n}$ is the normal vector of the best-fit plane and is used to find the angle $\theta_\mathrm{plane}$ when calculating the $|\cos\theta_\mathrm{plane}|$ mark (Eq. \ref{['eq:plane_angle']}).
• Figure 4: The mass dependence of subhalo spatial distribution marks and the mass normalization of our marks. Each panel shows a scatter plot of the initial mark values for each host halo (prior to mass normalization) host halo virial mass. The black lines show the median of the initial, non-mass-normalized, marks of hosts binned by mass. The error bars show the standard error of the median for each bin. The shaded regions represents a "1$\sigma$" envelope from the 16th to the 84th percentiles of the marks in each bin. The new, mass-normalized marks are represented by the color coding. The color of each point is determined by the new, mass-normalized value of the marks for each host. All of the new, mass-normalized marks by definition fall between 0 and 1. We have confirmed that our mass normalization procedure, when mass itself is used as a mark, removes all mass-dependent halo clustering as desired. This figure is based off of Figure 1 of mao2018.
• Figure 5: The global distributions of each mark type used in this work. These distributions are all normalized to integrate to 1. The blue lines show the distribution of the actual marks as calculated from the catalog. The orange lines are the distributions of marks as calculated from a mock sample of the same size as the simulation data in which subhaloes were distributed isotropically about their hosts. The vertical, dashed lines show the 16th, 50th (i.e., median), and 84th percentiles of their respective distributions. Anisotropy/planarity are indicated by the differences between the simulation data and the isotropic mock data. In the case of the median subhalo radial position, the two data sets are identical. Note that we only show this comparison for our marks prior to mass normalization (see Sec. \ref{['sec:mass_norm']}) because after mass normalization all marks are distributed on a uniform distribution on the interval $[0,1]$ by definition.