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

ABSTRACT We use high-resolution N-body simulations to develop a new, exible, empirical ap-proach for measuring the growth rate from redshift-space distortions (RSD) in the2-point galaxy correlation function. We quantify the systematic error in measuringthe growth rate in a 1h 3 Gpc volume over a range of redshifts, from the darkmatter particle distribution and a range of halo-mass catalogues with a number den-sity comparable to the latest large-volume galaxy surveys such as the WiggleZ DarkEnergy Survey and the Baryon Oscillation Spectroscopic Survey (BOSS). Our sim-ulations allow us to span halo masses with bias factors ranging from unity (probedby 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 thesmall-scale real-space correlation function, and in particular that the \standard" as-sumption of a power-law correlation function can result in a signi cant systematicerror in the growth rate determination. We introduce a new, empirical tting func-tion that produces results with a lower (5-10%) amplitude of systematic error. Wealso introduce a new technique which permits the galaxy pairwise velocity distribu-tion, the quantity which drives the non-linear growth of structure, to be measuredas a non-parametric stepwise function. Our (model-independent) results agree wellwith an exponential pairwise velocity distribution, expected from theoretical consid-erations, and are consistent with direct measurements of halo velocity di erences fromthe parent catalogues. In a companion paper we present the application of our newmethodology to the WiggleZ Survey dataset.Key words: large-scale structure of Universe, cosmological parameters, cosmology:theory