Cosmological redshift distortion: deceleration, bias and density parameters from future redshift surveys of galaxies

The observed two-point correlation functions of galaxies in redshift space become anisotropic due to the geometry of the universe as well as due to the presence of the peculiar velocity field. On the basis of linear perturbation theory, we expand the induced anisotropies of the correlation functions with respect to the redshift $z$, and obtain analytic formulae to infer the deceleration parameter $q_0$, the density parameter $\Omega_0$ and the derivative of the bias parameter $d\ln b/dz$ at $z=0$ in terms of the observable statistical quantities. The present method does not require any assumption of the shape and amplitude of the underlying fluctuation spectrum, and thus can be applied to future redshift surveys of galaxies including the Sloan Digital Sky Survey. We also evaluate quantitatively the systematic error in estimating the value of $\beta_0 \equiv \Omega_0^{0.6}/b$ from a galaxy redshift survey on the basis of a conventional estimator for $\beta_0$ which neglects both the geometrical distortion effect and the time evolution of the parameter $\beta(z)$. If the magnitude limit of the survey is as faint as 18.5 (in B-band) as in the case of the Sloan Digital Sky Survey, the systematic error ranges between -20% and 10% depending on the cosmological parameters. Although such systematic errors are smaller than the statistical errors in the current surveys, they will dominate the expected statistical error for future surveys.Comment: 9 pages, 5 figs, aastex, ApJ in press, replaced version includes minor correction

Wide Angle Redshift Distortions Revisited

We explore linear redshift distortions in wide angle surveys from the point of view of symmetries. We show that the redshift space two-point correlation function can be expanded into tripolar spherical harmonics of zero total angular momentum $S_{l_1 l_2 l_3}(\hat x_1, \hat x_2, \hat x)$. The coefficients of the expansion $B_{l_1 l_2 l_3}$ are analogous to the $C_l$'s of the angular power spectrum, and express the anisotropy of the redshift space correlation function. Moreover, only a handful of $B_{l_1 l_2 l_3}$ are non-zero: the resulting formulae reveal a hidden simplicity comparable to distant observer limit. The $B_{l_1 l_2 l_3}$ depend on spherical Bessel moments of the power spectrum and $f = \Omega^{0.6}/b$. In the plane parallel limit, the results of \cite{Kaiser1987} and \cite{Hamilton1993} are recovered. The general formalism is used to derive useful new expressions. We present a particularly simple trigonometric polynomial expansion, which is arguably the most compact expression of wide angle redshift distortions. These formulae are suitable to inversion due to the orthogonality of the basis functions. An alternative Legendre polynomial expansion was obtained as well. This can be shown to be equivalent to the results of \cite{SzalayEtal1998}. The simplicity of the underlying theory will admit similar calculations for higher order statistics as well.Comment: 6 pages, 1 figure, ApJL submitte

Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.Comment: AAS Latex file, 44 pages, accepted for publication in Ap

The motion of bubbles inside drops in containerless processing

A theoretical model of thermocapillary bubble motion inside a drop, located in a space laboratory, due to an arbitrary axisymmetric temperature distribution on the drop surface was constructed. Typical results for the stream function and temperature fields as well as the migration velocity of the bubble were obtained in the quasistatic limit. The motion of bubbles in a rotating body of liquid was studied experimentally, and an approximate theoretical model was developed. Comparison of the experimental observations of the bubble trajectories and centering times with theoretical predictions lends qualified support to the theory

Sensitivity of Redshift Distortion Measurements to Cosmological Parameters

The multipole moments of the power spectrum of large scale structure, observed in redshift space, are calculated for a finite sample volume including the effects of both the linear velocity field and geometry. A variance calculation is also performed including the effects of shot noise. The sensitivity with which a survey with the depth and geometry of the Sloan Digital Sky Survey (SDSS) can measure cosmological parameters $\Omega_0$ and $b_0$ (the bias) or $\lambda_0$ (the cosmological constant) and $b_0$ is derived through fitting power spectrum moments to the large scale structure in the linear regime in a way which is independent of the evolution of the galaxy number density. We find that for surveys of the approximate depth of the SDSS no restrictions can be placed on $\Omega_0$ at the 99% confidence limit when a fiducial open, $\Omega_0 = 0.3$ model is assumed and bias is unconstrained. At the 95% limit, $\Omega_{0} < .85$ is ruled out. Furthermore, for this fiducial model, both flat (cosmological constant) and open models are expected to reasonably fit the data. For flat, cosmological constant models with a fiducial $\Omega_{0} = 0.3$, we find that models with $\Omega_{0} > 0.48$ are ruled out at the 95% confidence limit regardless of the choice of the bias parameter, and open models cannot fit the data even at the 99% confidence limit.Comment: We correct an error which which caused us to overestimate the cosmic variance of our statistics. We also include shot noise in the new variace calculation. In our fitting proceedure, we now include $\sigma$, the non-linear velocity dispersion, as a free parameter. Our conclusions are modifed as a result, with $\Omega_0=0.3$ open models now nominaly excluding $\Omega_0 = 1$ at the 95% but not 99% confidence limi

The synergistic effects of slip ring-brush design and materials

Synergistic effects of slip ring-brush design and fabrication for vacuum application determined by friction, wear, electrical noise, and dielectric strength dat

The synergistic effects of slip ring-brush design and materials

The design, fabrication, and subsequent testing of four power slip rings for synchronous orbit application are described. The synergistic effects of contact materials and slip ring-brush design are studied by means of frequent and simultaneous recording of friction, wear, and electrical noise. Data generated during the test period are presented along with post test analysis data

Unusually Large Fluctuations in the Statistics of Galaxy Formation at High Redshift

We show that various milestones of high-redshift galaxy formation, such as the formation of the first stars or the complete reionization of the intergalactic medium, occurred at different times in different regions of the universe. The predicted spread in redshift, caused by large-scale fluctuations in the number density of galaxies, is at least an order of magnitude larger than previous expectations that argued for a sharp end to reionization. This cosmic scatter in the abundance of galaxies introduces new features that affect the nature of reionization and the expectations for future probes of reionization, and may help explain the present properties of dwarf galaxies in different environments. The predictions can be tested by future numerical simulations and may be verified by upcoming observations. Current simulations, limited to relatively small volumes and periodic boundary conditions, largely omit cosmic scatter and its consequences. In particular, they artificially produce a sudden end to reionization, and they underestimate the number of galaxies by up to an order of magnitude at redshift 20.Comment: 8 ApJ pages, 4 figures, ApJ. Minor changes in revised version. Originally first submitted for publication on Aug. 29, 200

Intracluster Comptonization of the CMB: Mean Spectral Distrortion and Cluster Number Counts

The mean sky-averaged Comptonization parameter, y, describing the scattering of the CMB by hot gas in clusters of galaxies is calculated in an array of flat and open cosmological and dark matter models. The models are globally normalized to fit cluster X-ray data, and intracluster gas is assumed to have evolved in a manner consistent with current observations. We predict values of y lower than the COBE/FIRAS upper limit. The corresponding values of the overall optical thickness to Compton scattering are < 10^{-4} for relevant parameter values. Of more practical importance are number counts of clusters across which a net flux (with respect to the CMB) higher than some limiting value can be detected. Such number counts are specifically predicted for the COBRAS/SAMBA and BOOMERANG missions.Comment: 23 pages, Latex, 11 PostScript figures, 5 PostScript tables, to appear in Ap

Comparing the Evolution of the Galaxy Disk Sizes with CDM Models: The Hubble Deep Field

The intrinsic sizes of the field galaxies with I<26 in the Hubble and ESO-NTT Deep Fields are shown as a function of their redshifts and absolute magnitudes using photometric redshifts derived from the multicolor catalogs and are compared with the CDM predictions. Extending to lower luminosities and to higher z our previous analysis performed on the NTT field alone, we find that the distribution of the galaxy disk sizes at different cosmic epochs is within the range predicted by typical CDM models. However, the observed size distribution of faint (M_B>-19) galaxies is skewed with respect to the CDM predictions and an excess of small-size disks (R_d<2 kpc) is already present at z~ 0.5. The excess persists up to z~3 and involves brighter galaxies . Such an excess may be reduced if luminosity-dependent effects, like starburst activity in interacting galaxies, are included in the physical mechanisms governing the star formation history in CDM models.Comment: 9 pages, 3 figures, ApJ Letters in pres