Shapes and orientations of massive halos in the statistically anisotropic universe

TL;DR

Statistical anisotropy (SA) in the matter density field, parameterized by the quadrupolar magnitude $g_*$ and a preferred direction $\hat{\mathbf{d}}$, may imprint observable signatures in cluster-scale halos. The authors implement SA in initial conditions as $P_m(\boldsymbol{k})=\left[1+\tfrac{2}{3}g_*\mathcal{L}_2(\mu)\right]\bar{P}_m(k)$ and analyze halos identified by Rockstar in cosmological $N$-body simulations, across several mass bins. They find that halo shapes, quantified by $s=c/a$ and $T$, are largely insensitive to SA, while halo orientations $\hat{\mathbf{A}}$ exhibit a pronounced SA-driven alignment that strengthens with halo mass and reverses with the sign of $g_*$. The SA-induced alignment is perpendicular to $\hat{\mathbf{d}}$ for $g_*>0$ and parallel for $g_*<0$, suggesting that measurements of projected halo ellipticity from cluster-galaxy lensing could provide a new constraint on SA, complementing CMB and galaxy-clustering probes.

Abstract

We investigate how statistical anisotropy (SA) in matter distributions affects the distributions of shapes and orientations of cluster-sized halos, using cosmological $N$-body simulations that incorporate SA. While the three-dimensional halo shape parameters show little dependence on SA, we find that halo orientations are significantly influenced, with halos tending to align either perpendicular or parallel to the SA direction. This SA-induced alignment becomes more prominent for more massive halos. We also study other vector quantities associated with the dynamics of halos, such as bulk velocity and angular momentum vectors. We find that their dependences on the SA are smaller than those of the orientation vectors. Our findings suggest that observational measurements of projected halo shapes derived from galaxy cluster-galaxy lensing could provide a novel probe of SA in the universe.

Figures (9)

• Figure 1: Visualizations of the matter distributions at the redshift $z=0$ in the $x$-$z$ plane, in the simulated universes with $g_*= +1$ (left), $0$ (middle), and $-1$ (right). Each panel shows a $50~h^{-1}{\rm Mpc}$-thick slice along the $y$-direction taken from the realization with the same initial random seed in the L05 run. The SA direction $\hat{\mathbf{d}}$ is shown in each panel.
• Figure 2: Left: PDFs of $s$, $P(s)$, for the three halo mass ranges of $\log_{10}[M_{\rm 200b}/(h^{-1}M_\odot)]\in(13,~13.5],~(14,~14.5]$ and $(15,~15.5]$ obtained from the L05, L2, and L4 runs, respectively. Each color line shows the result for $g_* =0$ (blue), $\pm 0.1$ (green), and $\pm 1.0$ (orange), and the dashed (solid) lines are for the cases with the positive (negative) sign. We note that all five curves almost overlap. Right: Same as the left panel but for the PDFs of $T$, $P(T)$. The vertical dashed line in each panel indicates the boundaries between halo shape categories: "oblate" for $T < 1/3$, "triaxial" for $1/3 < T < 2/3$, and "prolate" for $2/3 < T < 1$. Similar to the left panel, all five curves almost overlap.
• Figure 3: PDFs of $\hat{A}_x,~\hat{A}_y$ and $\hat{A}_z$, i.e., the halo orientations, for the halos with masses of $14<\log_{10}[M_{\rm 200b}/(h^{-1}M_\odot)]\leq14.5$ from the L2 run. Each color line shows the result for $g_* =0$ (blue), $\pm 0.1$ (green), $\pm 0.5$ (red), and $\pm 1.0$ (orange), and the dashed (solid) lines are for the cases with the positive (negative) sign.
• Figure 4: Left: PDFs of $\hat{A}_x$, $P(\hat{A}_x)$, for the halo mass ranges of $\log_{10}[M_{\rm 200b}/(h^{-1}M_\odot)]\in(13,~13.5],~(14,~14.5]$ and $(15,~15.5]$. Each line shows the results for $g_*=0$ and $\pm0.1$. Right: Same as the left panel but for the PDFs of $\hat{A}_z$, $P(\hat{A}_z)$.
• Figure 5: PDFs of $\hat{A}_z$ for the high- and low-$c_{\rm vir}$ halos of $14<\log_{10}[M_{\rm 200b}/(h^{-1}M_\odot)]\leq14.5$ from the L2 run with $g_*=\pm0.1$.