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 distribution of triaxial dark matter halos driven from physical principles. Adopting the picture of triaxial collapse based on the Zel'dovich approximation, we derive analytically both the minor-to-major and the conditional intermediate-to-major axis ratio distributions, and examine how they depend on the halo mass, redshift, and cosmology. Our analytic model is tested against the simulation data given by Jing & Suto in 2002, and found to reproduce the conditional intermediate-to-major axis ratio distribution successfully and the minor-to-major axis ratio distribution approximately. However, the trends of our analytic axis-ratio distributions with mass and redshift are opposite to what is found in N-body simulations. This failure of our analytic model puts a limitation on analytic approaches based on the Lagrangian theory to the halo ellipticity. Given the overall agreement with the simulation results, our model provides a new theoretical step toward using the axis-ratio distribution of dark halos as a cosmological probe. We also discuss several possibilities to improve the model. 
Jounghun Lee (KIAS/SNU), Yipeng Jing (SAO), Yasushi Suto (U.Tokyo)