Universality of Halo Shape and its Morphological Evolution across Cosmic Time

We investigate the evolution of dark matter halo shapes in cosmological N-body simulations both in scale free Einstein-De Sitter (EdS) and $\Lambda$CDM cosmologies. We compute the axis ratios ($q=b/a,s=c/a$) of well resolved central halos using the shape tensor. These halos are identified using two different halo finding algorithms, SUBFIND and ROCKSTAR. We find that at fixed mass, halos become more spherical with decreasing redshift. The distribution $P(q,s)$ along with their median values ($q$ and $s$) shows self-similar behaviour as a function of mass scaled by the non-linear mass, $(M/M_{nl})$ across power-law spectral indices for scale free EdS models. However the median $q$ and $s$ show a tighter self-similar evolution as a function of peak height $\nu=\delta_c/\sigma(M,z)$. We find that the median $q(\nu)$ and $s(\nu)$ are consistent with an evolution along a universal curve described by $y=\alpha-\delta \tanh \left[ \omega \left(\log_{10}(\nu) - \mu\right)\right]$ across the spectral indices ranging from $n=-1.0$ to $n=-2.2$. Our results hold for both SUBFIND and ROCKSTAR, although there are some differences between them. The universality of the evolution of median $q(\nu)$ and $s(\nu)$ also holds for the $\Lambda$CDM runs, although with a different behaviour at small $\nu$ compared to the scale free models. The width of the distributions of $P(q)$ and $P(s)$ in both, scale-free and $\Lambda$CDM, classes of simulations can be reduced further by classifying halos as oblate, triaxial and prolate, each of which also follows a universal behaviour. Although oblate halos are relatively rare at all redshifts, their fraction increases over time at the expense of the other two populations.