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 Bispectrum of IRAS Galaxies

We compute the bispectrum for the galaxy distribution in the IRAS QDOT, 2Jy, and 1.2Jy redshift catalogs for wavenumbers 0.05<k<0.2 h/Mpc and compare the results with predictions from gravitational instability in perturbation theory. Taking into account redshift space distortions, nonlinear evolution, the survey selection function, and discreteness and finite volume effects, all three catalogs show evidence for the dependence of the bispectrum on configuration shape predicted by gravitational instability. Assuming Gaussian initial conditions and local biasing parametrized by linear and non-linear bias parameters b_1 and b_2, a likelihood analysis yields 1/b_1 = 1.32^{+0.36}_{-0.58}, 1.15^{+0.39}_{-0.39} and b_2/b_1^2=-0.57^{+0.45}_{-0.30}, -0.50^{+0.31}_{-0.51}, for the for the 2Jy and 1.2Jy samples, respectively. This implies that IRAS galaxies trace dark matter increasingly weakly as the density contrast increases, consistent with their being under-represented in clusters. In a model with chi^2 non-Gaussian initial conditions, the bispectrum displays an amplitude and scale dependence different than that found in the Gaussian case; if IRAS galaxies do not have bias b_1> 1 at large scales, \chi^2 non-Gaussian initial conditions are ruled out at the 95% confidence level. The IRAS data do not distinguish between Lagrangian or Eulerian local bias.Comment: 30 pages, 11 figure

Power Spectrum of Velocity Fluctuations in the Universe

We investigate the power spectrum of velocity fluctuations in the universe, $V^2(k)$, starting from four different measures of velocity: (1) the power spectrum of velocity fluctuations from peculiar velocities of galaxies; (2) the rms peculiar velocity of galaxy clusters; (3) the power spectrum of velocity fluctuations from the power spectrum of density fluctuations in the galaxy distribution; (4) and the bulk velocity from peculiar velocities of galaxies. We show that measures (1) and (2) are not consistent with each other and either the power spectrum from peculiar velocities of galaxies is overestimated or the rms cluster peculiar velocity is underestimated. The amplitude of velocity fluctuations derived from the galaxy distribution (measure 3) depends on the parameter $\beta$. We estimate the parameter $\beta$ on the basis of measures (2) and (4). The power spectrum of velocity fluctuations from the galaxy distribution in the Stromlo-APM redshift survey is consistent with the observed rms cluster velocity and with the observed large-scale bulk flow when the parameter $\beta$ is in the range 0.4-0.5. In this case the value of the function $V(k)$ at wavelength $\lambda=120h^{-1}$Mpc is $\sim 350$ km s$^{-1}$ and the rms amplitude of the bulk flow at the radius $r=60h^{-1}$ Mpc is $\sim 340$ km s$^{-1}$. The velocity dispersion of galaxy systems originates mostly from the large-scale velocity fluctuations with wavelengths $\lambda >100h^{-1}$ Mpc.Comment: Astrophysical Journal, Vol. 493, in press: 23 pages, uses AAS Latex, and 14 separate postscript figure

Lithium overdose and delayed severe neurotoxicity:timing for renal replacement therapy and restarting of lithium

This is a case report of a man in his 60s who presented to an English hospital following a significant lithium overdose. He was monitored for 24 hours, and then renal replacement therapy was initiated after assessment by the renal team. As soon as the lithium level returned to normal therapeutic levels (from 4.7 mEq/L to 0.67 mEq/L), lithium was restarted by the medical team. At this point, the patient developed new slurred speech and later catatonia. In this case report, we discuss the factors that could determine which patients are at risk of neurotoxicity following lithium overdose and the appropriate decision regarding when and how to consider initiation of renal replacement therapy and restarting of lithium

Steps toward the power spectrum of matter. I.The mean spectrum of galaxies

We calculate the mean power spectrum of galaxies using published power spectra of galaxies and clusters of galaxies. On small scales we use the power spectrum derived from the 2-dimensional distribution of APM galaxies, on large scales we use power spectra derived from 3-dimensional data for galaxy and cluster samples. Spectra are reduced to real space and to the amplitude of the power spectrum of APM galaxies. Available data indicate the presence of two different populations in the nearby Universe. Clusters of galaxies sample a relatively large region in the Universe where rich, medium and poor superclusters are well represented. Their mean power spectrum has a spike on scale 120 h^{-1}Mpc, followed by an approximate power-law spectrum of index n = -1.9 towards small scales. The power spectrum found from LCRS and IRAS 1.2 Jy surveys is flatter around the maximum, which may represent regions of the Universe with medium-rich and poor superclusters.Comment: LaTex (sty files added), 35 pages, 5 PostScript figures and Table with mean power spectrum embedded, Astrophysical Journal (accepted

Constraining the Cosmological Density of Compact Objects with the Long-Term Variability of Quasars

By comparing the results from numerical microlensing simulations to the observed long-term variability of quasars, strong upper limits on the cosmological density of compact objects in the 0.0001-1 solar mass range may in principle be imposed. Here, this method is generalized from the Einstein-de Sitter universe to the currently favored Omega_M=0.3, Omega_Lambda=0.7 cosmology and applied to the latest observational samples. We show that the use of high-redshift quasars from variability-selected samples has the potential to substantially improve current constraints on compact objects in this mass range. We also investigate to what extent the upper limits on such hypothetical dark matter populations are affected by assumptions concerning the size of the optical continuum-emitting region of quasars and the velocity dispersion of compact objects. We find that mainly due to uncertainties in the typical value of the source size, cosmologically significant populations of compact objects cannot safely be ruled out with this method at the present time.Comment: 10 pages, 7 figures, accepted for publication in A&

An Inversion Method for Measuring Beta in Large Redshift Surveys

A precision method for determining the value of Beta= Omega_m^{0.6}/b, where b is the galaxy bias parameter, is presented. In contrast to other existing techniques that focus on estimating this quantity by measuring distortions in the redshift space galaxy-galaxy correlation function or power spectrum, this method removes the distortions by reconstructing the real space density field and determining the value of Beta that results in a symmetric signal. To remove the distortions, the method modifies the amplitudes of a Fourier plane-wave expansion of the survey data parameterized by Beta. This technique is not dependent on the small-angle/plane-parallel approximation and can make full use of large redshift survey data. It has been tested using simulations with four different cosmologies and returns the value of Beta to +/- 0.031, over a factor of two improvement over existing techniques.Comment: 16 pages including 6 figures Submitted to The Astrophysical Journa