# Topology of Large-Scale Structures of Galaxies in Two Dimensions - Systematic Effects

## TL;DR

This study analyzes how various systematic effects influence the two-dimensional topology of galaxy distributions, using simulation data to improve the reliability of genus statistics for cosmological studies.

## Contribution

It models and quantifies the impact of systematics like shot noise, galaxy bias, and redshift space distortion on the 2D genus statistic, aiding its use in cosmological parameter estimation.

## Key findings

- Finite pixel effects can be minimized with smaller pixels.
- Nonlinear evolution causes small amplitude changes in genus over time.
- Redshift space distortions affect genus shape and amplitude.

## Abstract

We study the two-dimensional topology of the galactic distribution when projected onto two-dimensional spherical shells. Using the latest Horizon Run 4 simulation data, we construct the genus of the two-dimensional field and consider how this statistic is affected by late-time nonlinear effects -- principally gravitational collapse and redshift space distortion (RSD). We also consider systematic and numerical artifacts such as shot noise, galaxy bias, and finite pixel effects. We model the systematics using a Hermite polynomial expansion and perform a comprehensive analysis of known effects on the two-dimensional genus, with a view toward using the statistic for cosmological parameter estimation. We find that the finite pixel effect is dominated by an amplitude drop and can be made less than $1\%$ by adopting pixels smaller than $1/3$ of the angular smoothing length. Nonlinear gravitational evolution introduces time-dependent coefficients of the zeroth, first, and second Hermite polynomials, but the genus amplitude changes by less than $1\%$ between $z=1$ and $z=0$ for smoothing scales $R_{\rm G} > 9 {\rm Mpc/h}$. Non-zero terms are measured up to third order in the Hermite polynomial expansion when studying RSD. Differences in shapes of the genus curves in real and redshift space are small when we adopt thick redshift shells, but the amplitude change remains a significant $\sim {\cal O}(10\%)$ effect. The combined effects of galaxy biasing and shot noise produce systematic effects up to the second Hermite polynomial. It is shown that, when sampling, the use of galaxy mass cuts significantly reduces the effect of shot noise relative to random sampling.