An Analytic Model for the Axis-Ratio Distribution of Dark Matter Halos from the Primordial Gaussian Density Field

We present an analytic expression for the axis ratio distributions of triaxial dark matter halos. The ellipticity of a dark halo develops as a consequence of the filamentary nature of the cosmic web induced by the initial coherent tidal interactions. Adopting the picture, we derive both the minor-to-major and the conditional intermediate-to-major axis ratio distributions, and examine how they depend on the halo mass, redshifts, and cosmology. We find a reasonable overall agreement between our analytic model and the previous findings from numerical simulations on a qualitative level, confirming that the halo ellipticity is originated from the cosmic filaments of the initial density field. Thus our analytic model will provide a useful theoretical footing for studying the filamentary nature of structure formation. We also discuss several possibilities to improve the present model. Subject headings: cosmology:theory — large-scale structure of universe