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

Abstract

We study the power spectrum estimator based on the discrete wavelet transform (DWT) for three-dimensional samples. The DWT estimator for higher than one-dimensional samples provides two types of spectra with respect to diagonal and off-diagonal modes, respectively. The two types of modes have different spatial invariance, and therefore the diagonal and off-diagonal DWT power spectra are very flexible for dealing with configuration-related problems in power spectrum detection. With simulation samples and the mock catalogs of the Las Campanas Redshift Survey (LCRS), we show that (1) the geometry of the LCRS does not affect the off-diagonal power spectrum with a slicelike mode; (2) the Poisson sampling with the LCRS selection function does not cause more than 1 sigma error in the DWT power spectrum; and (3) the powers of the mass or galaxy random velocity fluctuations, which cause the redshift distortion, are approximately scale-independent. These results ensure that the uncertainties of the power spectrum measurement are under control. The scatter of the DWT power spectra of the six strips of the LCRS survey is found to be rather small, less than 1 sigma of the cosmic variance of the mock sample in the wavenumber range 0.1< k<2 h Mpc(-1). To fit the detected LCRS diagonal DWT power spectrum with CDM models, we find that the best-fitting redshift distortion parameter beta is about the same as that obtained from the Fourier power spectrum. The velocity dispersions sigma (v) for SCDM and Lambda CDM models are also consistent with other sigma (v) detections with the LCRS. A systematic difference between the best-fitting parameters of diagonal and off-diagonal power spectra have been significantly measured. This indicates that the off-diagonal power spectra are capable of providing information about the power spectrum of the galaxy velocity field.