We study the statistical properties of mergers between central and satellite galaxies in galaxy clusters in the redshift range $0<z<1$, using a sample of dark-matter only cosmological N-body simulations from Le SBARBINE dataset. Using a spherical overdensity algorithm to identify dark-matter haloes, we construct halo merger trees for different values of the over-density $Delta_c$. While the virial overdensity definition allows us to probe the accretion of satellites at the cluster virial radius $r_{vir}$, higher overdensities probe satellite mergers in the central region of the cluster, down to $approx 0.06 r_{vir}$, which can be considered a proxy for the accretion of satellite galaxies onto central galaxies. We find that the characteristic merger mass ratio increases for increasing values of $Delta_c$: more than $60%$ of the mass accreted by central galaxies since $zapprox 1$ comes from major mergers. The orbits of satellites accreting onto central galaxies tend to be more tangential and more bound than orbits of haloes accreting at the virial radius. The obtained distributions of merger mass ratios and orbital parameters are useful to model the evolution of the high-mass end of the galaxy scaling relations without resorting to hydrodynamic cosmological simulations.
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