SPHERICAL HARMONIC-ANALYSIS OF THE 2-JY IRAS GALAXY REDSHIFT SURVEY

The technique of spherical harmonic analysis (SHA) retains both amplitude and phase information, and therefore provides a unified language for cosmographical and statistical studies of galaxy redshift surveys. In this work, we extend the technique of SHA to incorporate radial information and apply it to the 2-Jy Infrared Astronomical Satellite (IRAS) redshift survey. The local cosmography is illustrated in reconstructions using harmonics (Y(l)m) for l less-than-or-equal-to 10 in different radial shells. We also compare the IPAS galaxy quadrupole with the one detected by COBE, but we find no obvious correlation. The amplitude information is then considered separately and related to the power spectrum of primordial fluctuations. The effect of different radial weighting schemes on the inferred cosmological parameters is investigated. We show how to choose an optimal window, given a cosmological model, which maximizes signal-to-noise ratio, and discuss ways of discriminating between models. For the scales (less than or similar 4000 km s-1) probed by the 2-Jy survey we find that, if the power spectrum is normalized according to the rms fluctuations on an 800 km s-1 sphere, sigma8.I = 0.7, on the largest scales probed by the survey (for l less than or similar 10) a cold dark matter (CDM) model, with a shape parameter characterized by OMEGAh almost-equal-to 0.2, is favoured by the data. On smaller scales (l greater than or similar to 10), the standard CDM (OMEGAh = 0.5) model is preferred. We show, however, that the scatter induced by redshift distortions is comparable to the difference between these two power spectra over the range of scales considered. We find that either power spectrum is an acceptable fit to the data, without recourse to scale-dependent biasing.