Evolution and Statistics of Non-Sphericity of Dark Matter Halos from Cosmological N-Body Simulation

Abstract: We revisit the non-sphericity of cluster-mass scale halos from cosmological N-body simulation on the basis of triaxial modelling. In order to understand the difference between the simulation results and the conventional ellipsoidal collapse model (EC), we first consider the evolution of individual simulated halos. The major difference between EC and the simulation becomes appreciable after the turn-around epoch. Moreover, it is sensitive to the individual evolution history of each halo. Despite such strong dependence on individual halos, the resulting nonsphericity of halos exhibits weak but robust mass dependence in a statistical fashion; massive halos are more spherical up to the turn-around, but gradually become less spherical by z = 0. This is clearly inconsistent with the EC prediction; massive halos are usually more spherical. In addition, at z=0, inner regions of the halos are less spherical than outer regions, i.e., the density distribution inside the halos is highly inhomogeneous and therefore not self-similar. Since most of previous fitting formulae for the PDF of axis ratio of triaxial ellipsoids have been constructed under the self-similarity assumption, they are not accurate. Indeed, we compute the PDF of projected axis ratio a1/a2 directly from the simulation data without the self-similarity assumption, and find that it is very sensitive to the assumption. The latter needs to be carefully taken into account in direct comparison with observations, and therefore we provide an empirical fitting formula for the PDF of a1/a2. Our preliminary analysis suggests that the derived PDF of a1/a2 roughly agrees with the current weak-lensing observations. More importantly, the present results will be useful in future exploration of the non-sphericity of clusters in X-ray and optical observations.