Shapes and Alignments of Galaxy Cluster Halos

Abstract

We present distribution functions and mark correlations of the shapes of massive dark matter halos derived from Hubble volume simulations of a ÃCDM 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 ; 10 14 h À1 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 minoraxis ratio in position follows hc/ai(M ; z) ¼ c 15;0 ½1 À ln (M/10 15 h À1 M ) (1 þ z) À , with c 15;0 ¼ 0:631 AE 0:001, ¼ 0:023 AE 0:002, and ¼ 0:086 AE 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 À1 Mpc, while a filamentary statistic exhibits nonrandom alignment extending to scales $200 h À1 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.

Weak lensing observations of potentially X-ray underluminous galaxy clusters

“…Shaw et al (2006), for example, found that prolate halos, i.e., those halos that according to Corless & King (2007) lead to higher additional errors in weak lensing measurements, are much more common than oblate halos. Kasun & Evrard (2005) presented a fitting function for the minor-axis (2007), we found that in the extreme cases of the major (minor) axis being aligned with the line of sight, the weak-lensing mass for this axis ratio will be overestimated (underestimated) by 16% (10%). Because the results of Corless & King (2007) cannot be convolved with the full halo-shape distribution, we adopt this combination of mean axis ratio and extreme alignment as additional error from halo triaxiality.…”

“…Corless & King (2007) investigated the influence of halo triaxiality on weak-lensing mass estimates and found that very oblate or prolate halos with axis ratio 1:3 decrease or increase weak-lensing mass estimates by as much as 40%, depending on their orientation with respect to the line of sight. These are, however, extreme cases, which occur in less than 1% of all halos (Kasun & Evrard 2005) and a realistic estimation of the contribution to the total error budget must take the halo-shape distribution into account. Shaw et al (2006), for example, found that prolate halos, i.e., those halos that according to Corless & King (2007) lead to higher additional errors in weak lensing measurements, are much more common than oblate halos.…”

The 400d Galaxy Cluster Survey weak lensing programme

“…Applying the Kasun & Evrard (2005) fitting formula for the largest-to-smallest axis ratio of a triaxial halo as a function of mass to all our eight clusters, we arrive at expectation values of 0.60 < η < 0.64 for the largest-to-smallest axis ratio. Hence, considering the triaxiality biases of Corless & King (2007), we use σ + proj = 0.16 M wl for the error M wl induced by overestimation and σ − proj = 0.10 M wl for the one induced by underestimation caused by the projection of triaxial halos.…”

The400dGalaxy Cluster Survey weak lensing programme

“…Inspired by cosmological simulations, Kasun & Evrard (2005) devised a fitting formula for the largest-to-smallest axis ratio η of triaxial haloes as a function of redshift and mass maximal biases from : for a complete alignment of the major cluster axis with the line of sight, mass is overestimated by 16%, while complete alignment with the minor axis results in a 10% underestimation. The projection of physically unrelated large-scale structure can lead to a significant underestimation of the statistical errors in M 200 and c NFW (Hoekstra 2003(Hoekstra , 2007.…”