Evolution of the degree of substructures in simulated galaxy clusters

We study the evolution of substructure in the mass distribution with mass, redshift and radius in a sample of simulated galaxy clusters. The sample, containing $1226$ objects, spans the mass range $M_{200} = 10^{14} - 1.74 \times 10^{15} \ {\rm M_{\odot}} \ h^{-1}$ in six redshift bins from $z=0$ to $z=1.179$. We consider three different diagnostics: 1) subhalos identified with SUBFIND; 2) overdense regions localized by dividing the cluster into octants; 3) offset between the potential minimum and the center of mass. The octant analysis is a new method that we introduce in this work. We find that none of the diagnostics indicate a correlation between the mass of the cluster and the fraction of substructures. On the other hand, all the diagnostics suggest an evolution of substructures with redshift. For SUBFIND halos, the mass fraction is constant with redshift at $R_{\mathrm{vir}}$, but shows a mild evolution at $R_{200}$ and $R_{500}$. Also, the fraction of clusters with at least a subhalo more massive than one thirtieth of the total mass is less than $20 \%$. Our new method based on the octants returns a mass fraction in substructures which has a strong evolution with redshift at all radii. The offsets also evolve strongly with redshift. We also find a strong correlation for individual clusters between the offset and the fraction of substructures identified with the octant analysis. Our work puts strong constraints on the amount of substructures we expect to find in galaxy clusters and on their evolution with redshift.