Measuring the galaxy power spectrum with multiresolution decomposition. II. Diagonal and off-diagonal power spectra of the Las Campanas Redshift Survey galaxies

We study the power spectrum estimator based on the discrete wavelet transfo rm (DWT) for three-dimensional samples. The DWT estimator for higher than o ne-dimensional samples provides two types of spectra with respect to diagon al and off-diagonal modes, respectively. The two types of modes have differ ent spatial invariance, and therefore the diagonal and off-diagonal DWT pow er spectra are very flexible for dealing with configuration-related problem s in power spectrum detection. With simulation samples and the mock catalog s of the Las Campanas Redshift Survey (LCRS), we show that (1) the slicelik e geometry of the LCRS does not affect the off-diagonal power spectrum with a "slicelike" mode; (2) the Poisson sampling with the LCRS selection funct ion 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 cau se the redshift distortion, are approximately scale-independent. These resu lts ensure that the uncertainties of the power spectrum measurement are und er control. The scatter of the DWT power spectra of the six strips of the L CRS survey is found to be rather small, less than 1 sigma of the cosmic var iance 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 tha t the best-fitting redshift distortion parameter beta is about the same as that obtained from the Fourier power spectrum. The velocity dispersions sig ma (v) for SCDM and Lambda CDM models are also consistent with other sigma (v) detections with the LCRS. A systematic difference between the best-fitt ing parameters of diagonal and off-diagonal power spectra have been signifi cantly measured. This indicates that the off-diagonal power spectra are cap able of providing information about the power spectrum of the galaxy veloci ty field.