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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 withSUBFIND; 2) overdense regions localized by dividing the cluster into octants;3) offset between the potential minimum and the center of mass. The octantanalysis is a new method that we introduce in this work. We find that none ofthe diagnostics indicate a correlation between the mass of the cluster and thefraction of substructures. On the other hand, all the diagnostics suggest anevolution of substructures with redshift. For SUBFIND halos, the mass fractionis 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 subhalomore massive than one thirtieth of the total mass is less than $20 \%$. Our newmethod based on the octants returns a mass fraction in substructures which hasa strong evolution with redshift at all radii. The offsets also evolve stronglywith redshift. We also find a strong correlation for individual clustersbetween the offset and the fraction of substructures identified with the octantanalysis. Our work puts strong constraints on the amount of substructures weexpect to find in galaxy clusters and on their evolution with redshift.

Evolution of the degree of substructures in simulated galaxy clusters