The Gigaparsec WiggleZ Simulations: Characterising scale dependant bias and associated systematics in growth of structure measurements

Abstract

We use the Gigaparsec WiggleZ (GiggleZ) simulations to characterise galaxy bias and its scale dependence for a range of redshifts and halo masses in a standard $\Lambda$LCDM cosmology. Assuming bias converges to a scale independent form at large scales, we develop a phenomenological model which fully expresses the mass and redshift dependence of bias and its scale dependence in real or redshift space. We then use this to illustrate how scale-dependent bias can systematically skew measurements of the growth-rate of cosmic structure obtained from redshift-space distortion measurements. When data is fit only to scales $k_{\rm max}{\le}0.1$ $[h^{-1} \rm{Mpc}]^{-1}$, we find that these effects are significant only for large biases ($b{\gtrsim}3$) at large redshifts ($z{\gtrsim}1$). However, when smaller scales are incorporated ($k_{\rm max}{\le}0.2$ $[h^{-1} \rm{Mpc}]^{-1}$) to increase measurement precision, the combination of reduced statistical uncertainty and increased scale dependent bias can result in highly significant systematics for most large halos across all redshifts. We identify several new interesting aspects of bias, including a significant large-scale bias boost for small halos at low-redshifts due to substructure effects ($\sim$20\% for Milky Way-like systems) and a nearly redshift-independent halo mass (corresponding to a redshift-space bias of ${\sim}1.5$) for which halo bias has little-or-no scale dependence on scales greater than $3$ $[h^{-1} {\rm Mpc}]$. This suggests an optimal strategy of targeting bias ${\sim}{1.5}$ systems for clustering studies which are dominated by systematic uncertainties in how observed halo (or galaxy) distributions map to their underlying mass distribution, such as cosmological measurements of neutrino masses. Code for generating our fitting formula is publicly available at http://gbpoole.github.io/Poole_2014a_code/ (Abridged)