Effects of Gravitational Evolution, Biasing, and Redshift Space Distortion on Topology

We have studied the dependence of topology of large-scale structure on tracer, gravitational evolution, redshift space distortion, and cosmology. A series of large N-body simulations of the (lambda)CDM and SCDM models that have evolved 1.1 or 8.6 billion particles are used in the study. Evolution of the genus statistic, used as a topology measure, from redshift 8 to 0 is accurately calculated over a wide range of smoothing scales using the simulations. The tracers of large-scale structure considered are the cold dark matter (CDM), biased peaks in the initial density field, dark halos, and "galaxies" populating the dark halos in accordance with a halo occupation distribution (HOD) model. We have found that the effects of biasing, gravitational evolution, and initial conditions on topology of large-scale structure are all comparable. The redshift space distortion effects are relatively small down to about 5 h-1 Mpc for all tracers except for the high-threshold part of the genus curve. The gravitational effects are found to be well modeled by analytic perturbation theory when the CDM distribution is considered. But the direction of gravitational evolution of topology can be even reversed for different tracers. For example, the shift parameter of the genus curve evolves in opposite directions for matter and HOD galaxies at large scales. At small scales, there are interesting deviations of the genus curve of dark halos and galaxies from that of matter in our initially Gaussian simulations. The deviations should be understood as due to combined effects of gravitational evolution and biasing. This fact gives us an important opportunity: topology of large-scale structure can be used as a strong constraint on galaxy formation mechanisms. At scales larger than 20 h-1 Mpc all the above effects gradually decrease. With good knowledge of the effects of nonlinear gravitational evolution and galaxy biasing on topology, one can also constrain the Gaussian random phase initial conditions hypothesis to high accuracy.