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

Galaxy Clustering Around Nearby Luminous Quasars

We examine the clustering of galaxies around a sample of 20 luminous low redshift (z<0.30) quasars observed with the Wide Field Camera-2 on the Hubble Space Telescope. The HST resolution makes possible galaxy identification brighter than V=23.5 and as close as 2'' to the quasar. We find a significant enhancement of galaxies within a projected separation of < 100 kpc/h of the quasars. If we model the qso/galaxy correlation function as a power law with a slope given by the galaxy/galaxy correlation function, we find that the ratio of the qso/galaxy to galaxy/galaxy correlation functions is $3.8\pm 0.8$. The galaxy counts within r<15 kpc/h of the quasars are too high for the density profile to have an appreciable core radius ( > 100 kpc). Our results reinforce the idea that low redshift quasars are located preferentially in groups of 10-20 galaxies rather than in rich clusters. We see no significant difference in the clustering amplitudes derived from radio-loud and radio-quiet subsamples.Comment: 16 pages, 3 figures (included), 2 tables, Apj in pres

Fourier Analysis of Redshift Space Distortions and the Determination of Omega

The peculiar velocities of galaxies distort the pattern of galaxy clustering in redshift space, making the redshift space power spectrum anisotropic. In the linear regime, the strength of this distortion 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. We derive a linear theory estimator for $\beta$ based on the harmonic moments of the redshift space power spectrum. Using N-body simulations, we examine the impact of non-linear gravitational clustering on the power spectrum anisotropy and on our $\beta$-estimator. Non-linear effects can be important out to wavelengths $\lambda \sim 50$Mpc/h or larger; in most cases, they lower the quadrupole moment of the power spectrum and thereby depress the estimate of $\beta$ below the true value. With a sufficiently large redshift survey, the scaling of non-linear effects may allow separate determinations of $\Omega$ and $b$. We describe a practical technique for measuring the anisotropy of the power spectrum from galaxy redshift surveys, and we test the technique on mock catalogues drawn from the N-body simulations. Preliminary application of our methods to the 1.2 Jy IRAS galaxy survey yields $\beta_{est} \sim 0.3-0.4$ at wavelengths $\lambda \sim 30-40$Mpc/h . Non-linear effects remain important at these scales, so this estimate of $\beta$ is probably lower than the true value.Comment: uuencoded compressed postscript fil

Size-scaling of clump instabilities in turbulent, feedback regulated disks

We explore the scaling between the size of star-forming clumps and rotational support in massively star-forming galactic disks. The analysis relies on simulations of a clumpy galaxy at $z=2$ and the observed DYNAMO sample of rare clumpy analogs at $z\approx0.1$ to test a predictive clump size scaling proposed by \citet{Fisher2017ApJ...839L...5F} in the context of the Violent Disk Instability (VDI) theory. We here determine the clump sizes using a recently presented 2-point estimator, which is robust against resolution/noise effects, hierarchical clump substructure, clump-clump overlap and other galactic substructure. After verifying Fisher's clump scaling relation for the DYNAMO observations, we explore whether this relation remains characteristic of the VDI theory, even if realistic physical processes, such as local asymetries and stellar feedback, are included in the model. To this end, we rely on hydrodynamic zoom-simulations of a Milky Way-mass galaxy with four different feedback prescriptions. We find that, during its marginally stable epoch at $z=2$, this mock galaxy falls on the clump scaling relation, although its position on this relation depends on the feedback model. This finding implies that Toomre-like stability considerations approximately apply to large ($\sim\rm kpc$) instabilities in marginally stable turbulent disks, irrespective of the feedback model, but also emphasizes that the global clump distribution of a turbulent disk depends strongly on feedback.Comment: Accepted by ApJ, no changes made. 11 pages, 4 figure

A Discotic Disguised as a Smectic: A Hybrid Columnar Bragg Glass

We show that discotics, lying deep in the columnar phase, can exhibit an x-ray scattering pattern which mimics that of a somewhat unusual smectic liquid crystal. This exotic, new glassy phase of columnar liquid crystals, which we call a ``hybrid columnar Bragg glass'', can be achieved by confining a columnar liquid crystal in an anisotropic random environment of e.g., strained aerogel. Long-ranged orientational order in this phase makes {\em single domain} x-ray scattering possible, from which a wealth of information could be extracted. We give detailed quantitative predictions for the scattering pattern in addition to exponents characterizing anomalous elasticity of the system.Comment: 4 RevTeX pgs, 2 eps figures. To appear in PR