Determining accurate measurements of the growth rate from the galaxy correlation function in simulations

We use high-resolution N-body simulations to develop a new, flexible, empirical approach for measuring the growth rate from redshift-space distortions (RSD) in the 2-point galaxy correlation function. We quantify the systematic error in measuring the growth rate in a $1 \, h^-3$ Gpc$^3$ volume over a range of redshifts, from the dark matter particle distribution and a range of halo-mass catalogues with a number density comparable to the latest large-volume galaxy surveys such as the WiggleZ Dark Energy Survey and the Baryon Oscillation Spectroscopic Survey (BOSS). Our simulations allow us to span halo masses with bias factors ranging from unity (probed by emission-line galaxies) to more massive haloes hosting Luminous Red Galaxies. We show that the measured growth rate is sensitive to the model adopted for the small-scale real-space correlation function, and in particular that the "standard" assumption of a power-law correlation function can result in a significant systematic error in the growth rate determination. We introduce a new, empirical fitting function that produces results with a lower (5-10%) amplitude of systematic error. We also introduce a new technique which permits the galaxy pairwise velocity distribution, the quantity which drives the non-linear growth of structure, to be measured as a non-parametric stepwise function. Our (model-independent) results agree well with an exponential pairwise velocity distribution, expected from theoretical considerations, and are consistent with direct measurements of halo velocity differences from the parent catalogues. In a companion paper we present the application of our new methodology to the WiggleZ Survey dataset.