The Stromlo-APM Redshift Survey. III. Redshift Space Distortions, Omega, and Bias

Galaxy redshift surveys provide a distorted picture of the universe due tothe non-Hubble component of galaxy motions. By measuring such distortions inthe linear regime one can constrain the quantity $\beta = \Omega^{0.6}/b$ where$\Omega$ is the cosmological density parameter and $b$ is the (linear) biasfactor for optically-selected galaxies. In this paper we apply two techniquesfor estimating $\beta$ from the Stromlo-APM redshift survey --- (1) measuringthe anisotropy of the redshift space correlation function in sphericalharmonics and (2) comparing the amplitude of the direction-averaged redshiftspace correlation function to the real space correlation function. We test thevalidity of these techniques, particularly whether the assumption of lineartheory is justified, using two sets of large $N$-body simulations. We find thatthe first technique is affected by non-linearities on scales up to $\sim 30\hMpc$. The second technique is less sensitive to non-linear effects and so ismore useful for existing redshift surveys. The Stromlo-APM survey data favoursa low value for $\beta$, with $\beta \simlt 0.6$. A bias parameter $b \approx2$ is thus required if $\Omega \equiv 1$. However, higher-order correlationsmeasured from the APM galaxy survey (Gazta\~{n}aga and Frieman 1994) indicate alow value for the bias parameter $b \approx 1$, requiring that $\Omega \simlt0.5$. We also measure the relative bias for samples of galaxies of variousluminosity and morphological type and find that low-luminosity galaxies areroughly three times less biased than $L^*$ galaxies. For the galaxy populationas a whole, we measure a real space variance of galaxy counts in $8 \hMpc$spheres of $(\sigma^2_8)_g = 0.89 \pm 0.05$.Comment: Revised to accommodate referee's comments (added MDM simulation); accepted by ApJ 29 Feb 96. 32 pages, uuencoded, gzipped tar archive, includes all figure