Correlations between Triaxial Shapes and Formation History of Dark Matter Haloes

The shape of dark matter haloes plays a critical role in constraining cosmology with upcoming large-scale structure surveys. In this paper, we study the correlations between the triaxial shapes and formation histories in dark matter haloes in the MultiDark Planck 2 N-body cosmological simulation. We find that halo ellipticity is strongly correlated with halo properties that serve as proxies of halo formation history, such as halo concentration and the peak-centroid offset. In particular, the correlation between halo ellipticity and halo concentration is nearly independent of the halo density peak height. We present a simple model for the correlation between halo ellipticity and concentration using conditional abundance matching, and provide fitting formulae for the multi-dimensional distributions of triaxial halo shape as a function of halo peak height. We apply our halo shape model to gauge the effects of halo ellipticity and orientation bias on the excess surface mass density profiles in cluster-size halos. Our model should be useful for exploring the impact of triaxial halo shape on cosmological constraints in upcoming weak lensing surveys of galaxy clusters.