The real-space power spectrum of IRAS galaxies on large scales and the redshift distortion

Galaxy redshift surveys contain valuable cosmological information on the power spectrum of galaxy clustering, but the information is not easily obtained because of distortion of the map arising from the use of redshift as a distance indicator. The distortion arises because of peculiar velocities, the magnitude of which depends on the mean density of the Universe. Using a spherical transform of the data which correctly accounts for the radial nature of the distortion, we calculate simultaneously the real-space power spectrum and the distortion, for the near-all-sky Infrared Astronomical Satellite (IRAS) 1. 2-Jy survey. For the distortion, we find |=1. 040. 3|⁠, where |^0. 6₀/b|⁠, and b is the IRAS linear bias parameter. We constrain the power spectrum on large scales with wavenumbers 0. 01 ≲ k ≲ 0. 1 h Mpc−1 where the ‘distant-observer’ Fourier approximation should not be used. Power is not convincingly detected at wavenumbers less than 0. 03 h Mpc−1, but the power spectrum is consistent with a change in slope from the k−1. 5 behaviour observed on smaller scales to Zeldovich spectrum on large scales. In the wavenumber range considered, we find somewhat less power than in the optically selected APM survey.