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Shapes and Alignments of Galaxy Cluster Halos

We present distribution functions and mark correlations of the shapes of massive dark matter halos derived from Hubble volume simulations of a ΛCDM universe. We measure both position and velocity shapes within spheres that encompass a mean density 200 times the critical value and calibrate small-N systematic errors using Poisson realizations of isothermal spheres and higher resolution simulations. For halos more massive than 3 × 1014 h-1 M☉, the shape distribution function peaks at (minor/major, intermediate/major) axial ratios of (0.64, 0.76) in position and is rounder in velocity, peaking at (0.72, 0.82). Halo shapes are rounder at lower mass and/or redshift; the mean minor-axis ratio in position follows ⟨c/a⟩(M,z) = c15,0[1 - α ln(M/1015 h-1 M☉)](1 + z)-ϵ, with c15,0 = 0.631 ± 0.001, α = 0.023 ± 0.002, and ϵ = 0.086 ± 0.004. Position and velocity principal axes are well aligned in direction, with median alignment angle 22°, and the axial ratios in these spaces are correlated in magnitude. We investigate mark correlations of halo pair orientations using two measures: a simple scalar product shows ≥1% alignment extending to 30 h-1 Mpc, while a filamentary statistic exhibits nonrandom alignment extending to scales ~200 h-1 Mpc, 10 times the sample two-point correlation length and well into the regime of negative two-point correlation. Shapes of cluster halos are little affected by the large-scale environment; the distribution of supercluster member minor-axis ratios differs from that of the general population at only the few percent level.