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

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.Comment: AAS LaTeX file, 41 pages, 10 figures included, accepted for publication in Ap

Nonlinear Gravitational Clustering: dreams of a paradigm

We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$ to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.Comment: 32 Pages, Submitted to Ap

A technique for correcting ERTS data for solar and atmospheric effects

The author has identified the following significant results. Based on processing ERTS CCTs and ground truth measurements collected on Michigan test site for January through June 1973 the following results are reported: (1) atmospheric transmittance varies from: 70 to 85% in band 4, 77 to 90% in band 5, 80 to 94% in band 6, and 84 to 97% in band 7 for one air mass; (2) a simple technique was established to determine atmospheric scattering seen by ERTS-1 from ground-based measurements of sky radiance. For March this scattering was found to be equivalent to that produced by a target having a reflectance of 11% in band 4, 5% in band 5, 3% in band 6, and 1% in band 7; (3) computer ability to classify targets under various atmospheric conditions was determined. Classification accuracy on some targets (i.e. bare soil, tended grass, etc.) hold up even under the most severe atmospheres encountered, while performance on other targets (trees, urban, rangeland, etc.) degrades rapidly when atmospheric conditions change by the smallest amount

Hall Effect and Specific Resistance in Thin Evaporated Film of Fe, Co, Ni, Pd, and Pt

Further investigation of the Hall effect and specific resistance in thin films of iron, cobalt, nickel , palladium, and platinum give the following results: (1) the specific resistances of films deposited on a cool surface range from 4 to 30 times the accepted values for the corresponding bulk metals; (2) the Hall coefficients for the paramagnetic metals palladium and platinum are slightly smaller than bulk values: (3) the Hall coefficients for iron, cobalt, and nickel deposited on a cool surface are respectively 1.8 times, 5 times, and 7 times, the bulk values; (4) heating films of iron, cobalt, and nickel during deposition causes both the Hall coefficients and specific resistances to decrease almost to bulk values; (5) saturation of the Hall effect occurs for iron at a slightly lower magnetic field than for bulk values, for cobalt at 12500 as compared with 13500 for bulk, and for nickel at 2500 as compared with 6000 for bulk; and (6) microscopic investigation of nickel and cobalt shows some evidence of crystal structure

The cosmological light-cone effect on the power spectrum of galaxies and quasars in wide-field redshift surveys

We examine observational consequences of the cosmological light-cone effect on the power spectrum of the distribution of galaxies and quasars from upcoming redshift surveys. First we derive an expression for the power spectrum of cosmological objects in real space on a light cone, $P^{\rm LC}_{\rm R,lin}(k)$, which is exact in linear theory of density perturbations. Next we incorporate corrections for the nonlinear density evolution and redshift-space distortion in the formula in a phenomenological manner which is consistent with recent numerical simulations. On the basis of this formula, we predict the power spectrum of galaxies and quasars on the light cone for future redshift surveys taking account of the selection function properly. We demonstrate that this formula provides a reliable and useful method to compute the power spectrum on the light cone given an evolution model of bias.Comment: 18 pages, 3 figures, to be published in the Astrophysical Journa

The Hall Effect and Specific Resistance in Evaporated Films of Nickel, Cobalt, Palladium and Platinum

Steinberg has shown that in the case of a thin film of metal formed by evaporation from a heated filament in a high vacuum the specific resistance and Hall coefficient are not the same as for the bulk metal. The metals investigated were silver, copper and iron, and in all of these the specific resistance was found to be about 1000% greater than in the metals in bulk. The Hall coefficients were slightly smaller for silver and copper than for the bulk metals, but for iron this coefficient was about 600% greater than the value generally accepted for iron. Also, the magnetic field necessary to produce saturation in the Hall electromotive force was considerably smaller for evaporated iron than for bulk iron. These differences he explained on the belief that evaporated films consist of granules not in such intimate contact as in the bulk metals which has the effect of increasing the resistance and changing the magnetic properties of the metal. On account of the bearing which this work might have on theories of magnetism and electric conduction, it seemed desirable to extend this investigation to other metals

The Attenuation Factors in Acoustic Wave Filters

A theory has been formulated by Dr. G. W. Stewart by which it is possible to determine the selective transmission in three types of specially constructed acoustic wave filters. The theoretical attenuation factor also has been worked out and shows fair agreement with experimental results. Theoretical values of the attenuation were computed for one filter of each type and, from these values, the theoretical transmission curves were determined. The types of filters were the low-frequency and high-frequency— pass, and the single band

The finite size effect of galaxies on the cosmic virial theorem and the pairwise peculiar velocity dispersions

We discuss the effect of the finite size of galaxies on estimating small-scale relative pairwise peculiar velocity dispersions from the cosmic virial theorem (CVT). Specifically we evaluate the effect by incorporating the finite core radius $r_c$ in the two-point correlation function of mass, i.e. $\xi_\rho(r) \propto (r+r_c)^{-\gamma}$ and the effective gravitational force softening $r_s$ on small scales. We analytically obtain the lowest-order correction term for $\gamma <2$ which is in quantitative agreement with the full numerical evaluation. With a nonzero $r_s$ and/or $r_c$ the cosmic virial theorem is no longer limited to the case of $\gamma<2$. We present accurate fitting formulae for the CVT predicted pairwise velocity dispersion for the case of $\gamma>2$. Compared with the idealistic point-mass approximation ($r_s=r_c=0$), the finite size effect can significantly reduce the small-scale velocity dispersions of galaxies at scales much larger than $r_s$ and $r_c$. Even without considering the finite size of galaxies, nonzero values for $r_c$ are generally expected, for instance, for cold dark matter (CDM) models with a scale-invariant primordial spectrum. For these CDM models, a reasonable force softening r_s\le 100 \hikpc would have rather tiny effect. We present the CVT predictions for the small-scale pairwise velocity dispersion in the CDM models normalized by the COBE observation. The implication of our results for confrontation of observations of galaxy pair-wise velocity dispersions and theoretical predictions of the CVT is also discussed.Comment: 18 pages. LaTeX text and 8 postcript figures. submitted to Ap