On The Validity of the Streaming Model for the Redshift-Space Correlation Function in the Linear Regime

The relation between the galaxy correlation function in real and redshift-space is derived in the linear regime by an appropriate averaging of the joint probability distribution of density and velocity. The derivation recovers the familiar linear theory result on large scales but has the advantage of clearly revealing the dependence of the redshift distortions on the underlying peculiar velocity field; streaming motions give rise to distortions of ${\cal O}(\Omega^{0.6}/b)$ while variations in the anisotropic velocity dispersion yield terms of order ${\cal O}(\Omega^{1.2}/b^2)$. This probabilistic derivation of the redshift-space correlation function is similar in spirit to the derivation of the commonly used ``streaming'' model, in which the distortions are given by a convolution of the real-space correlation function with a velocity distribution function. The streaming model is often used to model the redshift-space correlation function on small, highly non-linear, scales. There have been claims in the literature, however, that the streaming model is not valid in the linear regime. Our analysis confirms this claim, but we show that the streaming model can be made consistent with linear theory {\it provided} that the model for the streaming has the functional form predicted by linear theory and that velocity distribution is chosen to be a Gaussian with the correct linear theory dispersion.Comment: 14 pages, no figures, uuencoded compressed postscrip

Constraints onOmega from the IRAS Redshift Surveys

We measure the anisotropy of the redshift-space power spectrum in the 1.2-Jy and QDOT redshift surveys of IRAS-selected galaxies. On large scales, this anisotropy is caused by coherent peculiar motions, and gravitational instability theory predicts a distortion of the power spectrum that depends only on the ratio $\beta \equiv f(\Omega)/b \approx \Omega^{0.6}/b$, where Omega is the cosmological density parameter and $b$ is the bias parameter. On small scales, the distortion is dominated by the random velocity dispersion in non-linear structures. We fit the observed anisotropy with an analytic model that incorporates two parameters, beta, and a small-scale velocity dispersion sigma_v. Tests on N-body simulations show that this model recovers beta quite accurately on the scales accessible to the existing IRAS redshift surveys. Applying our procedure to the 1.2-Jy and QDOT surveys, we find beta=0.52 +/- 0.13 and beta=0.54 +/- 0.3, respectively. These results imply Omega approximately 0.35 if galaxies trace mass, or a bias factor of about 2 if Omega=1.Comment: uufiles postscript here or plain postscript at ftp://dust0.dur.ac.uk/pub/preprints/cole_rsd.p

A Spherical Harmonic Approach to Redshift Distortion and a Measurement of Omega from the 1.2 Jy IRAS Redshift Survey

We present a formalism for analysing redshift distortions based on a spherical harmonic expansion of the density field. We use a maximum likelihood estimator for the combination of density and bias parameters, $\Omega^0.6/b$. We test the method with $N$-body simulations and apply it to the 1.2 Jy IRAS redshift survey.Comment: 8 pages--uuencoded postscript fil

Essential Strangeness in Nucleon Magnetic Moments

Effective quark magnetic moments are extracted from experimental measurements as a function of the strangeness magnetic moment of the nucleon. Assumptions made in even the most general quark model analyses are ruled out by this investigation. Ab initio QCD calculations demand a non-trivial role for strange quarks in the nucleon. The effective moments from QCD calculations are reproduced for a strangeness magnetic moment contribution to the proton of 0.11 $\mu_N$, which corresponds to $F_2^s(0) = -0.33\ \mu_N$.Comment: HYP '94 presentation. File is a uuencoded postscript file of a 2 page manuscript including figures. Also available via anonymous ftp from pacific.mps.ohio-state.edu in pub/NTG/Leinweber as StrQrkNmom.ps(.gz) OSU PP #94-063

The HELP inequality on trees

We establish analogues of Hardy and Littlewood's integro-differential equation for Schrödinger-type operators on metric and discrete trees, based on a generalised strong limit-point property of the graph Laplacian