Spherical Harmonic Analysis of the PSCz Galaxy Catalogue: Redshift distortions and the real-space power spectrum

Abstract

We apply the formalism of spherical harmonic decomposition to the galaxy density field of the IRAS PSCz redshift survey. The PSCz redshift survey has almost all-sky coverage and includes IRAS galaxies to a flux limit of 0.6 Jy. Using maximum likelihood methods to examine (to first order) the distortion of the galaxy pattern due to redshift coordinates, we have measured the parameter β= Ω^{0.6}/b. We also simultaneously measure (a) the undistorted amplitude of perturbations in the galaxy distribution when a parameterised power spectrum is assumed, or (b) the shape and amplitude of the real-space power spectrum if the band-power in a set of passbands is measured in a step- wise fashion. These methods are extensively tested on a series of CDM, ΛCDM and MDM simulations and are found to be unbiased. We obtain consistent results for the subset of the PSCz catalogue with flux above 0.75 Jy but inclusion of galaxies to the formal flux limit of the catalogue gives variations which are larger than our internal errors. For the 0.75 Jy catalogue we find, in the case of a parameterised power spectrum, β=0.58\pm0.26 and the amplitude of the real space power measured at wavenumber k=0.1 h/Mpc is Δ_{0.1}=0.42 \pm 0.03. Freeing the shape of the power spectrum we find that β=0.47\pm 0.16 (conditional error), and Δ_{0.1}=0.47 \pm 0.03. The shape of the real-space power spectrum is consistent with a Γ= 0.2 CDM-like shape parameter, but does not strongly rule out a number of other models. Finally by combining our estimate of the amplitude of galaxy clustering and the distortion parameter we find the amplitude of mass fluctuations on a scale k=0.1 \hmpc is Δ_ρ= 0.24 Ω_0^{-0.6}$, with an uncertainty of 50%.