Biasing and Genus Statistics of Dark Matter Halos in the Hubble Volume Simulation

We present a numerical analysis of genus statistics for dark matter halocatalogs from the Hubble volume simulation. The huge box-size of the Hubblevolume simulation enables us to carry out a reliable statistical analysis ofthe biasing properties of halos at a Gaussian smoothing scale of R_G>30Mpc/hwith a cluster-mass scale of between 7*10^{13}Msolar/h and 6*10^{15}Msolar/h. Adetailed comparison of the genus for dark matter halos with that for the massdistribution shows that the non-Gaussianity induced by the halo biasing iscomparable to that by nonlinear gravitational evolution, and both the shape andthe amplitude of the genus are almost insensitive to the halo mass atR_G>30Mpc/h. In order to characterize the biasing effect on the genus, we applya perturbative formula developed by Matsubara (1994). We find that theperturbative formula well describes the simulated halo genus at R_G>50Mpc/h.The result indicates that the biasing effect on the halo genus is wellapproximated by nonlinear deterministic biasing up to the second-order term inthe mass density fluctuation. The two parameters describing the linear andquadratic terms in the nonlinear biasing accurately specify the genus forgalaxy clusters.Comment: 10 pages, 7 figures, accepted for publication in PASJ (Vol.55, No.2, 2003