Systematic Effects on the Genus Topology of Large Scale Structure of the
  Universe
  Large-scale structure of the universe is a useful cosmological probe of the
primordial non-Gaussianity and the expansion history of the universe because
its topology does not change with time in the linear regime in the standard
paradigm of structure formation. However, when the topology of iso-density
contour surfaces is measured from an observational data, many systematic
effects are introduced due to the finite size of pixels used to define the
density field, non-linear gravitational evolution, redshift-space distortion,
shot noise (discrete sampling), and bias in the distribution of the density
field tracers. We study the various systematic effects on the genus curve to a
great accuracy by using the Horizon Run 2 simulation of a {\Lambda}CDM
cosmology. We numerically measure the genus curve from the gravitationally
evolved matter and dark matter halo density fields. It is found that all the
non-Gaussian deviations due to the systematic effects can be modeled by using a
few low-order Hermite polynomials from H0 to H4. We compare our results with
the analytic theories whenever possible, and find many new terms in the Hermite
series that are making significant contributions to the non-Gaussian
deviations. In particular, it is found that the amplitude drop of the genus
curve due to the non-linear gravitational evolution can be accurately modeled
by two terms H0 and H2 with coefficients both proportional to \sigma_0^2, the
mean-square density fluctuation.
