  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.
