Measuring the galaxy power spectrum with multiresolution decomposition -- II. diagonal and off-diagonal power spectra of the LCRS galaxies

Abstract

The power spectrum estimator based on the discrete wavelet transform (DWT) for 3-dimensional samples has been studied. The DWT estimator for multi-dimensional samples provides two types of spectra with respect to diagonal and off-diagonal modes, which are very flexible to deal with configuration-related problems in the power spectrum detection. With simulation samples 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 power spectrum with ``slice-like'' mode; (2) the Poisson sampling with the LCRS selection function doesn't cause more than 1-$\sigma$ error in the DWT power spectrum; and (3) the powers of peculiar velocity fluctuations, which cause the redshift distortion, are approximately scale-independent. These results insure 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. It is less than 1-$\sigma$ of the cosmic variance of mock samples 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 has been significantly measured. This indicates that the off-diagonal power spectra are capable of providing information about the power spectrum of galaxy velocity field.

AAS LaTeX file, 41 pages, 10 figures included, accepted for publication in ApJ

Cited by in corpus (13)

• An ideal mass assignment scheme for measuring the Power Spectrum with FFTs
• Measuring the galaxy power spectrum with multiresolution decomposition -- III. velocity field analysis
• Non-Gaussian Features of Transmitted Flux of QSO's Ly$\alpha$ Absorption: Intermittent Exponent
• Power spectrum and intermittency of the transmitted flux of QSOs Ly-alpha absorption spectra
• On the Normalization of the QSO's Lyman alpha Forest Power Spectrum
• The continuous wavelet derived by smoothing function and its application in cosmology
• Measuring the galaxy power spectrum with multiresolution decomposition -- IV. redshift distortion
• Estimating Power Spectrum of Sunyaev-Zeldovich Effect from the Cross-Correlation between WMAP and 2MASS
• One-point Statistics of the Cosmic Density Field in Real and Redshift Spaces with A Multiresolutional Decomposition
• A Parameter-free Statistical Measurement of Halos with Power Spectra
• Pair Counting without Binning -- A New Approach to Correlation Functions in Clustering Statistics
• Three-Dimensional Filamentation Analysis of SDSS DR5 Survey
• An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions