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We revisit the non-sphericity of cluster-mass scale halos from cosmologicalN-body simulation on the basis of triaxial modelling. In order to understandthe difference between the simulation results and the conventional ellipsoidalcollapse model (EC), we first consider the evolution of individual simulatedhalos. The major difference between EC and the simulation becomes appreciableafter the turn-around epoch. Moreover, it is sensitive to the individualevolution history of each halo. Despite such strong dependence on individualhalos, the resulting nonsphericity of halos exhibits weak but robust massdependence in a statistical fashion; massive halos are more spherical up to theturn-around, but gradually become less spherical by z = 0. This is clearlyinconsistent with the EC prediction; massive halos are usually more spherical.In addition, at z=0, inner regions of the halos are less spherical than outerregions, i.e., the density distribution inside the halos is highlyinhomogeneous and therefore not self-similar. Since most of previous fittingformulae for the PDF of axis ratio of triaxial ellipsoids have been constructedunder the self-similarity assumption, they are not accurate. Indeed, we computethe PDF of projected axis ratio a1/a2 directly from the simulation data withoutthe self-similarity assumption, and find that it is very sensitive to theassumption. The latter needs to be carefully taken into account in directcomparison with observations, and therefore we provide an empirical fittingformula for the PDF of a1/a2. Our preliminary analysis suggests that thederived PDF of a1/a2 roughly agrees with the current weak-lensing observations.More importantly, the present results will be useful in future exploration ofthe non-sphericity of clusters in X-ray and optical observations.

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