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

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