On the nonspherical nature of halo formation

We present a new collapse condition to describe the formation of dark halos via nonspherical gravitational clustering. This new nonspherical collapse condition is obtained by the logical generalization of the spherical model to the nonspherical one. By solving a diffusion-like random matrix equation with the help of the Monte Carlo method, we show that this nonspherical co llapse condition yields the mass function derived by R. K. Sheth and G. Tor men which has been shown to be in excellent agreement with the recent N-bod y results of high resolution. We expect that this nonspherical collapse con dition might provide us a deeper insight into the structure formation and s uggest that it should be widely applied to various cosmological issues such as the galaxy merging history, the galaxy bias, and so forth.