A spherical harmonic approach to redshift distortion and a measurement of $\Omega_0$ from the 1.2-Jy IRAS Redshift Survey

We examine the nature of galaxy clustering in redshift space, using a method based on an expansion of the galactic density field in spherical harmonics and linear theory. Our approach provides a compact and self-consistent expression for the distortion when applied to flux-limited redshift surveys. The amplitude of the distortion is controlled by the combination of the density and bias parameters, beta = OMEGA0(0.6)/b; we exploit this fact to derive a maximum-likelihood estimator for beta. We check our formalism using N-body simulations, and demonstrate that it provides an unbiased estimate of beta when the amplitude and shape of the galaxy power spectrum are known. Application of the technique to the 1.2-Jy IRAS Redshift Survey yields beta almost-equal-to 1.0; both random errors (from counting statistics and the uncertainties in the power-spectrum normalization) and systematic errors (from the uncertainty in the shape of the power spectrum) individually contribute 20 per cent uncertainties in this estimate. This estimate of beta is comparable (both in amplitude and uncertainty) with previous measurements based on comparisons of the IRAS density field with direct measurements of peculiar velocities and analyses of the acceleration of the Local Group, but the spherical harmonic analysis has the advantage of being easy to implement and largely free of systematic errors.