A spherical harmonic analysis of redshift space

We re-examine the effects of redshift space distortion in all-sky galaxy redshift surveys in the formalism of spherical harmonics. Within this framework we show how one can treat both the large-scale linear effects, and the small-scale nonlinear clustering, exactly to first order. The method also allows in principle a determination of the power spectrum of perturbations, requiring no assumptions beyond that of linear theory. The method therefore offers significant advantages over Fourier techniques when dealing with all-sky surveys. We apply our likelihood analysis to both simulated data, and real data, using the IRAS 1. 2-Jy galaxy catalogue, for which we find a maximum likelihood \ \ 1. 1\ 0. 3, and a real-space fluctuation amplitude corresponding to \₈, \ ₈ₑ₀ₒ = 0. 68\ 0. 05.