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

Jamkhedkar

et al. 2002

ApJ

Self Cite

Recently, it has been found that the field traced by QSO's Lyα forests is intermittent on small scales. Intermittent behavior is essential for understanding the statistics and dynamics of cosmic gravitational clustering in the nonlinear regime. The most effective method of describing intermittency uses the structure functions and the intermittent exponent, which measure the scale-and order-dependencies of the ratio between the higher order to second order moments of the field. These properties can be used not only to confirm the non-gaussianity of fields, but also to detect the type of non-gaussianity.In this paper, we calculate the structure function and intermittent exponent of 1.) Keck data, which consists of 28 high resolution, high signal to noise ratio (S/N) QSO Lyα absorption spectra, and 2.) Lyα forest simulation samples produced via the pseudo hydro scheme for the low density cold dark matter (LCDM) model and warm dark matter (WDM) model with particle mass m W = 300, 600, 800 and 1000 eV. Aside from the WDM model with m W = 300 eV, the simulation samples are in agreement with observations in the context of the power spectrum. We find, however, that the intermittent behavior of all the simulation samples is substantially inconsistent, both quantitatively and qualitatively, with the Keck data. Specifically, 1.) the structure functions of the simulation samples are significantly larger than that of Keck data on scales k ≥ 0.1 km −1 s, 2.) the intermittent exponent of the simulation samples is more negative than that of Keck data on all redshifts considered, 3.) the order-dependence of the structure functions of simulation samples are closer to the intermittency of hierarchical clustering on all scales, while the Keck data are closer to a lognormal field on small scales. These differences are independent of noise and show that the intermittent evolution modeled by the pseudo-hydro simulation is substantially different from observations, even though they are in good agreement with each other in terms of second and lower order statistics. This result also shows that "weakly" clustered samples, like high resolution Lyα absorption spectrum, are effective in testing dynamical models of structure formation if their intermittent features are considered.Subject headings: cosmology: theory -large-scale structure of the universe

Section: The Intermittent Exponent In the Dwt Basismentioning

confidence: 97%

Non‐Gaussian Features of Transmitted Flux of QSOs' Lyα Absorption: Intermittent Exponent

Pando

Jamkhedkar

et al. 2002

ApJ

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“…The algorithm of the power spectrum for both P n ( k ) or P ( k ) in the DWT representation has been developed (Pando & Fang 1998; Fang & Feng 2000; Yang et al 2001a,b; Jamkhedkar, Bi & Fang 2001). We will study only the unnormalized power spectrum P ( k ) below.…”

Section: Dwt Algorithm For the Power Spectrum Of Lyα Transmitted Fluxmentioning

confidence: 99%

Power spectrum and intermittency of the transmitted flux from the Lyman absorption spectra of quasi-stellar objects

Jamkhedkar

Monthly Notices of the Royal Astronomical Society

Zheng

et al. 2003

Using a set of 28 high‐resolution, high signal‐to‐noise ratio quasi‐stellar object Lyα absorption spectra, we investigate the non‐Gaussian features of the transmitted flux fluctuations and their effect upon the power spectrum of this field. We find that the spatial distribution of the local power of the transmitted flux on scales k≥ 0.05 s km−1 is highly spiky or intermittent. The probability distribution functions of the local power are long‐tailed. The power on small scales is dominated by small probability events, and consequently, the uncertainty in the power spectrum of the transmitted flux field is generally large. This uncertainty arises owing to the slow convergence of an intermittent field to a Gaussian limit required by the central limit theorem (CLT). To reduce this uncertainty, it is common to estimate the error of the power spectrum by selecting subsamples with an ‘optimal’ size. We show that this conventional method actually does not calculate the variance of the original intermittent field but of a Gaussian field. Based on the analysis of intermittency, we propose an algorithm to calculate the error. It is based on a bootstrap resampling among all independent local power modes. This estimation does not require any extra parameter such as the size of the subsamples and is sensitive to the intermittency of the fields. This method effectively reduces the uncertainty in the power spectrum when the number of independent modes matches the condition for CLT convergence.

“…Recently, we developed the method of measuring the galaxy power spectrum with a space-scale (multiresolution) decomposition, i.e. measuring power spectrum in the representation of discrete wavelet transform (DWT) , Yang et al 2001). Unlike eq.…”

Section: Introductionmentioning

confidence: 99%

Measuring the Galaxy Power Spectrum with Multiresolution Decomposition. III. Velocity Field Analysis

Yang

Chu

et al. 2001

ApJ

Self Cite

In this paper, we develop the method of analyzing the velocity field of cosmic matter with a multiresolution decomposition. This is necessary in calculating the redshift distortion of power spectrum in the discrete wavelet transform (DWT) representation. We show that, in the DWT analysis, the velocity field can be described by discrete variables, which are given by assignment of the number density and velocity into the DWT modes. These DWT variables are complete and not redundant. In this scheme, the peculiar velocity and pairwise velocity of galaxies or particles are given by field variables. As a consequence, the velocity dispersion (VD) and pairwise velocity dispersion (PVD) are no longer measured by number-counting or pair-counting statistic, but with the ensemble of the field variables, and therefore, they are free from the bias due to the number-counting and pair-counting. We analyzed the VD and PVD of the velocity fields given by the N-body simulation for models of the SCDM, τ CDM and ΛCDM. The spectrum (scale-dependence) of the VD and PVD show that the length scale of the two-point correlation of the velocity field is as large as few tens h −1 Mpc. Although the VD and PVD show similar behavior in some aspects, they are substantially different from each other. The VD-to-PVD ratio shows the difference between the scale-dependencies of the VD and PVD. More prominent difference between the VD and PVD is shown by probability distribution function.The one-point distribution of peculiar velocity is approximately exponential, while the pairwise velocity's is lognormal, i.e. of long tail. This difference indicates that the cosmic velocity field is typically intermittent.Subject headings: cosmology: theory -large-scale structure of universe Recently, we developed the method of measuring the galaxy power spectrum with a space-scale