POWER-SPECTRUM ANALYSIS OF 3-DIMENSIONAL REDSHIFT SURVEYS

We develop a general method for power-spectrum analysis of three-dimen sional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power, and we are able to derive a rigorous optimal weighting scheme under the reasonable (and largely em pirically verified) assumption that the long-wavelength Fourier compon ents are Gaussian-distributed. We apply the formalism to the updated o ne-in-six QDOT IRAS redshift survey and compare our results with data from other probes: APM angular correlations and the CfA and the Berkel ey 1.2 Jy IRAS redshift surveys. Our results bear out and further quan tify the impression from, e.g., counts-in-cells analysis that there is extra power on large scales as compared to the standard cold dark mat ter (CDM) model with OMEGAh congruent-to 0.5. We apply likelihood anal ysis using the CDM spectrum with OMEGAh as a free parameter as a pheno menological family of models; we find the best-fitting parameters in r edshift space and transform the results to real space. Finally, we cal culate the distribution of the estimated long-wavelength power. This a grees remarkably well with the exponential distribution expected for G aussian fluctuations, even out to powers of 10 times the mean. Our res ults thus reveal no trace of periodicity or other non-Gaussian behavio r.