Measuring the Galaxy Power Spectrum with Multiresolution Decomposition. II. Diagonal and Off‐Diagonal Power Spectra of the Las Campanas Redshift Survey Galaxies

The power spectrum estimator based on the discrete wavelet transform (DWT)for 3-dimensional samples has been studied. The DWT estimator formulti-dimensional samples provides two types of spectra with respect todiagonal and off-diagonal modes, which are very flexible to deal withconfiguration-related problems in the power spectrum detection. With simulationsamples and mock catalogues of the Las Campanas redshift survey (LCRS), we show(1) the slice-like geometry of the LCRS doesn't affect the off-diagonal powerspectrum with ``slice-like'' mode; (2) the Poisson sampling with the LCRSselection function doesn't cause more than 1-$\sigma$ error in the DWT powerspectrum; and (3) the powers of peculiar velocity fluctuations, which cause theredshift distortion, are approximately scale-independent. These results insurethat the uncertainties of the power spectrum measurement are under control. Thescatter of the DWT power spectra of the six strips of the LCRS survey is foundto be rather small. It is less than 1-$\sigma$ of the cosmic variance of mocksamples in the wavenumber range $0.1 < k < 2$ h Mpc$^{-1}$. To fit the detectedLCRS diagonal DWT power spectrum with CDM models, we find that the best-fittingredshift distortion parameter $\beta$ is about the same as that obtained fromthe Fourier power spectrum. The velocity dispersions $\sigma_v$ for SCDM and$\Lambda$CDM models are also consistent with other $\sigma_v$ detections withthe LCRS. A systematic difference between the best-fitting parameters ofdiagonal and off-diagonal power spectra has been significantly measured. Thisindicates that the off-diagonal power spectra are capable of providinginformation about the power spectrum of galaxy velocity field.Comment: AAS LaTeX file, 41 pages, 10 figures included, accepted for publication in Ap