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We construct merger trees based on the extended Press-Schechter theory (EPS)in order to study the merger rates of dark matter haloes over a range ofpresent day mass ($10^{10}M_{\sun}\leq M_0 \leq10^{15}M_{\sun}$), progenitormass $(5\times10^{-3}\leq \xi \leq1$) and redshift ($0\leq z\leq 3$). We usedthe first crossing distribution of a moving barrier of the form$B(S,z)=p(z)+q(z)S^{\gamma}$, proposed by Sheth & Tormen, to take into accountthe ellipsoidal nature of collapse. We find that the mean merger rate per halo$B_m/n$ depends on the halo mass $M$ as $M^{0.2}$ and on the redshift as$(\mathrm{d}\delta_c(z)/\mathrm{d}z)^{1.1}$. Our results are in agreement withthe predictions of N-body simulations and this shows the ability ofmerger-trees based on EPS theory to follow with a satisfactory agreement theresults of N-body simulations and the evolution of structures in a hierarchicalUniverse.

Merger rates of dark matter haloes from merger trees in the extended Press-Schechter theory