Power spectrum multipoles on the curved sky: an application to the 6-degree Field Galaxy Survey

The peculiar velocities of galaxies cause their redshift-space clustering to depend on the angle to the line of sight, providing a key test of gravitational physics on cosmological scales. These effects may be described using a multipole expansion of the clustering measurements. Focussing on Fourier-space statistics, we present a new analysis of the effect of the survey window function, and the variation of the line of sight across a survey, on the modelling of power spectrum multipoles.We determine the joint covariance of the Fourier-space multipoles in a Gaussian approximation, and indicate how these techniques may be extended to studies of overlapping galaxy populations via multipole cross-power spectra.We apply our methodology to one of the widest area galaxy redshift surveys currently available, the 6-degree Field Galaxy Survey, deducing a normalized growth rate fσ₈(z = 0.06) = 0.38 ± 0.12 in the low-redshift Universe, in agreement with previous analyses of this data set using different techniques. Our framework should be useful for processing future wide-angle galaxy redshift surveys.