Power Spectrum Analysis of the Stromlo-APM Redshift Survey

We test estimators of the galaxy power spectrum $P(k)$ against simulated galaxy catalogues constructed from N-body simulations and we derive formulae to correct for biases. These estimators are then applied to compute the power spectrum of galaxies in the Stromlo-APM redshift survey. We test whether the amplitude of $P(k)$ depends on galaxy luminosity, but find no significant luminosity dependence except at absolute magnitudes brighter than $M_{\bj} = -20.3$, ($H_{0} = 100 \kms$) where there is some evidence for a rise in the amplitude of $P(k)$. By comparing the redshift space power spectrum of the Stromlo-APM survey with the real space power spectrum determined from the parent APM Galaxy Survey, we attempt to measure the distortion in the shape of $P(k)$ caused by galaxy peculiar motions. We find some evidence for an effect, but the errors are large and do not exclude a value of $\beta = \Omega^{0.6}/b = 1$, where $\Omega$ is the cosmological density parameter and $b$ is the linear biasing parameter relating galaxy fluctuations to those in the mass, $\left(\delta \rho/\rho\right)_{gal} = b \left(\delta \rho/\rho\right)_{m}$. The shape of the Stromlo-APM power spectrum is consistent with that determined from the CfA-2 survey, but has a slightly higher amplitude by a factor of about 1.4 than the power spectrum of IRAS galaxies.