Universality of Halo Shape and its Morphological Evolution across Cosmic Time

Abstract

We investigate the evolution of dark matter halo shapes in cosmological N-body simulations both in scale free Einstein-De Sitter (EdS) and $Λ$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 $ν=δ_c/σ(M,z)$. We find that the median $q(ν)$ and $s(ν)$ are consistent with an evolution along a universal curve described by $y=α-δ\tanh \left[ ω\left(\log_{10}(ν) - μ\right)\right]$ 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 $q(ν)$ and $s(ν)$ also holds for the $Λ$CDM runs, although with a different behaviour at small $ν$ compared to the scale free models. The width of the distributions of $P(q)$ and $P(s)$ in both, scale-free and $Λ$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.

Figures (17)

• Figure 1: The dimensionless power spectrum($\Delta^2$) as a function of $k/k_{\mathrm{nl}}$ for the six scale-free models listed in table \ref{['tab_scalefree']}. Lighter colours represent earlier epochs. The black dashed line is the linear spectrum, $P(k) \propto k^n$ used in the simulation for the initial condition.
• Figure 2: The figure shows the abundance of halo mass generated from SUBFIND (solid dashed red) and ROCKSTAR (solid dashed dotted red) algorithm. The brown and cyan solid lines are the analytical Press-Schechter and Sheth-Tormen mass function respectively. The vertical lines corresponds to the $1000 \,\,\textrm{\&}\,\, 3000$ particles (left-right). 32 particles is the minimum FOF resolution of halos. The 1000-3000 particle count is the minimum requirement to accurately identify shapes. Numbers in the square bracket represent the number of central halos in each of the halo finder with $N_{\mathrm{part}}\geq100$.
• Figure 3: The top (bottom) panels show particle distributions in a massive cluster-sized halo using the SUBFIND ( ROCKSTAR ) algorithms. Particle distributions for the FOF and central halos are plotted in the left and right panels respectively. The yellow and green circles are the virial radii of the FOF and central halos respectively. The mass of the FOF, $M_{\mathrm{vir}}^{\textrm{h}}$, and central, $M_{\mathrm{vir}}^{\textrm{c}}$, halos are indicated in the corresponding panels. The pixels are colour-coded by projected density, with lighter colours representing denser regions. The projected density is more spherical compared to the next example in figure \ref{['fig_SFRS_ex2']}.
• Figure 4: Another example of a cluster sized halo but is more elliptical in compared to figure \ref{['fig_SFRS_ex1']} in projection. The labels, colours, markers are the same as in figure \ref{['fig_SFRS_ex1']}
• Figure 5: The figure shows the distribution $P(q)$ and $P(s)$ of axis ratios $q$ and $s$ in the left and right panels for the $D_1$ (unweighted), $D_2$ ($r^2$-weighted) and $D_3$ ($r^2_{\textrm{ell}}$-weighted) definitions of the shape tensor represented in the solid, dashed and dotted lines respectively. This is done for the scale-free $n=-1.0$ model at $x_{nl}=49.4$ for halos in the mass range of $1000-10000$ particles. There are about 60,000 halos in this mass range. The top row is for the $A_{\textrm{fix}}$ (major-axis fixed) method and the bottom row is for the $V_{\textrm{fix}}$ (volume fixed) method. The vertical lines are the mean (thick) and median (thin) of the respective distributions.