Non-linear clustering in the cold plus hot dark matter model

The main aim of this work is to find out if hierarchical scaling, observed in galaxy clustering, can be dynamically explained by studying N-body simulations. Previous analyses of dark matter (DM) particle distributions indicated heavy distortions with respect to the hierarchical pattern. Here, we shall describe how such distortions are to be interpreted and why they can be fully reconciled with the observed galaxy clustering. This aim is achieved by using high-resolution (512^3 grid-points) particle-mesh (PM) N-body simulations to follow the development of non-linear clustering in a Omega=1 universe, dominated either by cold dark matter (CDM) or by a mixture of cold+hot dark matter (CHDM) with Omega_cold=0.6, and Omega_hot=0.3 and Omega_baryon=0.1 a simulation box of side 100 Mpc (h=0.5) is used. We analyse two CHDM realizations with biasing factor b=1.5 (COBE normalization), starting from different initial random numbers, and compare them with CDM simulations with b=1 (COBE-compatible) and b=1.5. We evaluate high-order correlation functions and the void probability function (VPF). Correlation functions are obtained from both counts in cells and counts of neighbours. The analysis is carried out for DM particles and for galaxies identified as massive haloes of the evolved density field. We confirm that clustering of DM particles systematically exhibits deviations from hierarchical scaling, although the deviation increases somewhat in redshift space. Deviations from the hierarchical scaling of DM particles are found to be related to the spectrum shape, in a way that indicates that such distortions arise from finite sampling effects. We identify galaxy positions in the simulations and show that, quite differently from the DM particle background, galaxies follow hierarchical scaling (S_q=xi_q/& xgr^q-1_2=consta nt) far more closely, with reduced skewness and kurtosis coefficients S_3~2.5 and S_4~7.5, in general agreement with observational results. Unlike DM, the scaling of galaxy clustering is must marginally affected by redshift distortions and is obtained for both CDM and CHDM models. Hierarchical scaling in simulations is confirmed by VPF analysis. Also in this case, we find substantial agreement with observational findings.