Given the failure of existing models for redshift-space distortions to provide a highly accurate measure of the \beta -parameter , and the ability of forthcoming surveys to obtain data with very low random errors , it becomes necessary to develop better models for these distortions .
Here we review the failures of the commonly-used velocity dispersion models and present an empirical method for extracting \beta from the quadrupole statistic that has little systematic offset over a wide range of \beta and cosmologies .
This empirical model is then applied to an ensemble of mock 2dF southern strip surveys , to illustrate the technique and see how accurately we can recover the true value of \beta .
We compare this treatment with the error we expect to find due only to the finite volume of the survey .
We find that non-linear effects reduce the range of scales over which \beta can be fitted , and introduce covariances between nearby modes in addition to those introduced by the convolution with the survey window function .
The result is that we are only able to constrain \beta to a 1 - \sigma accuracy of 25 \% ( \beta = 0.55 \pm 0.14 for the cosmological model considered ) .
We explore one possible means of reducing this error , that of cluster collapse , and show that accurate application of this method can greatly reduce the effect of non-linearities , improving the determination of \beta .
We conclude by demonstrating that , when the contaminating effects of clusters are dealt with , this simple analysis of the full 2dF survey yields \beta = 0.55 \pm 0.04 .
For this model this represents a determination of \beta to an accuracy of 8 \% and hence an important constraint on the cosmological density parameter \Omega _ { 0 } .