The 2dF Galaxy Redshift Survey: Spherical Harmonics analysis of fluctuations in the final catalogue

We present the result of a decomposition of the 2dFGRS galaxy overdensity field into an orthonormal basis of spherical harmonics and spherical Bessel functions. Galaxies are expected to directly follow the bulk motion of the density field on large scales, so the absolute amplitude of the observed large-scale redshift-space distortions caused by this motion is expected to be independent of galaxy properties. By splitting the overdensity field into radial and angular components, we linearly model the observed distortion and obtain the cosmological constraint Omega_m^{0.6} sigma_8=0.46+/-0.06. The amplitude of the linear redshift-space distortions relative to the galaxy overdensity field is dependent on galaxy properties and, for L_* galaxies at redshift z=0, we measure beta(L_*,0)=0.58+/-0.08, and the amplitude of the overdensity fluctuations b(L_*,0) sigma_8=0.79+/-0.03, marginalising over the power spectrum shape parameters. Assuming a fixed power spectrum shape consistent with the full Fourier analysis produces very similar parameter constraints.