The Size and Shape of Local Voids

We study the size and shape of low density regions in the local universe which we identify in the smoothed density field of the PSCz flux limited IRAS galaxy catalogue. After quantifying the systematic biases that enter in the detection of voids using our data set and method, we identify, using a smoothing length of 5 $h^{-1}$ Mpc, 14 voids within 80 $h^{-1}$ Mpc and using a smoothing length of 10 $h^{-1}$ Mpc, 8 voids within 130 $h^{-1}$ Mpc. We study the void size distribution and morphologies and find that there is roughly an equal number of prolate and oblate-like spheroidal voids. We compare the measured PSCz void shape and size distributions with those expected in six different CDM models and find that only the size distribution can discriminate between models. The models preferred by the PSCz data are those with intermediate values of $\sigma_{8} (\simeq 0.83)$, independent of cosmology.Comment: final version, Accepted in MNRA

Automated Detection of Voids in Redshift Surveys

We present a new void search algorithm for automated detection of voids in three-dimensional redshift surveys. Based on a model in which the main features of the LSS of the Universe are voids and walls, we classify the galaxies into wall galaxies and field galaxies and we define voids as continuous volumes that are devoid of any wall galaxies. Field galaxies are allowed within the voids. The algorithm makes no assumptions regarding the shapes of the voids and the only constraint that is imposed is that the voids are always thicker than a preset limit, thus eliminating connections between adjacent voids through smal breaches in the walls. By appropriate scaling of the parameters with the selection function this algorithm can be used to analyze flux-limited surveys. We test the algorithm on Voronoi tessellations and apply it to the SSRS2 redshift survey to derive the spectrum of void sizes and other void properties. We find that the average diameter of a void is 37\pm 8 \h Mpc. We suggest the usage of this fully automated algorithm to derive a quantitative description of the voids, as another tool in describing the large scale structure of the Universe and for comparison with numerical simulations.Comment: Accepted for publication in ApJ Letters; 13 page AAS latex file including 1 table, 3 PS figures. Complete uuencoded compressed PostScript file is available at ftp://shemesh.fiz.huji.ac.il or at http://shemesh.fiz.huji.ac.il/papers.htm

Probing the dynamics of Anderson localization through spatial mapping

We study (1+1)D transverse localization of electromagnetic radiation at microwave frequencies directly by two-dimensional spatial scans. Since the longitudinal direction can be mapped onto time, our experiments provide unique snapshots of the build-up of localized waves. The evolution of the wave functions is compared with numerical calculations. Dissipation is shown to have no effect on the occurrence of transverse localization. Oscillations of the wave functions are observed in space and explained in terms of a beating between the eigenstates

Finding Galaxy Clusters using Voronoi Tessellations

We present an objective and automated procedure for detecting clusters of galaxies in imaging galaxy surveys. Our Voronoi Galaxy Cluster Finder (VGCF) uses galaxy positions and magnitudes to find clusters and determine their main features: size, richness and contrast above the background. The VGCF uses the Voronoi tessellation to evaluate the local density and to identify clusters as significative density fluctuations above the background. The significance threshold needs to be set by the user, but experimenting with different choices is very easy since it does not require a whole new run of the algorithm. The VGCF is non-parametric and does not smooth the data. As a consequence, clusters are identified irrispective of their shape and their identification is only slightly affected by border effects and by holes in the galaxy distribution on the sky. The algorithm is fast, and automatically assigns members to structures.Comment: 11 pages, 11 figures. It uses aa.cls (included). Accepted by A&

On an Analytical Framework for Voids: Their abundances, density profiles and local mass functions

We present a general analytical procedure for computing the number density of voids with radius above a given value within the context of gravitational formation of the large scale structure of the universe out of Gaussian initial conditions. To this end we develop an accurate (under generally satisfied conditions) extension of unconditional mass function to constrained environments, which allowes us both to obtain the number density of collapsed objects of certain mass at any distance from the center of the void, and to derive the number density of voids defined by those collapsed objects. We have made detailed calculations for the spherically averaged mass density and halo number density profiles for individual voids. We also present a formal expression for the number density of voids defined by galaxies of a given type and luminosity. This expression contains the probability for a collapsed object of certain mass to host a galaxy of that type and luminosity as a function of the environmental density. We propose a procedure to infer this function, which may provide useful clues as to the galaxy formation process, from the observed void densities.Comment: 14 pages, 7 figures, MNRAS in pres

High frequency diffraction of an electromagnetic plane wave by an imperfectly conducting rectangular cylinder

Copyright @ 2011 IEEEWe shall consider the the problem of determining the scattered far wave field produced when a plane E-polarized wave is incident on an imperfectly conducting rectangular cylinder. By using the the uniform asymptotic solution for the problem of the diffraction of a plane wave by a right-angled impedance wedge, in conjunction with Keller's method, the a high frequency far field solution to the problem is given

Peculiar Velocities of Nonlinear Structure: Voids in McVittie Spacetime

As a study of peculiar velocities of nonlinear structure, we analyze the model of a relativistic thin-shell void in the expanding universe. (1) Adopting McVittie (MV) spacetime as a background universe, we investigate the dynamics of an uncompensated void with negative MV mass. Although the motion itself is quite different from that of a compensated void, as shown by Haines & Harris (1993), the present peculiar velocities are not affected by MV mass. (2) We discuss how precisely the formula in the linear perturbation theory applies to nonlinear relativistic voids, using the results in (1) as well as the previous results for the homogeneous background (Sakai, Maeda, & Sato 1993). (3) We re-examine the effect of the cosmic microwave background radiation. Contrary to the results of Pim & Lake (1986, 1988), we find that the effect is negligible. We show that their results are due to inappropriate initial conditions. Our results (1)-(3) suggest that the formula in the linear perturbation theory is approximately valid even for nonlinear voids.Comment: 12 pages, aastex, 4 ps figures separate, Fig.2 added, to appear in Ap

Voids in the Large-Scale Structure

Voids are the most prominent feature of the LSS of the universe. Still, they have been generally ignored in quantitative analysis of it, essentially due to the lack of an objective tool to identify and quantify the voids. To overcome this, we present the Void-Finder algorithm, a novel tool for objectively quantifying galaxy voids. The algorithm classifies galaxies as either wall- or field-galaxies. Then it identifies voids in the wall-galaxy distribution. Voids are defined as continuous volumes that do not contain any wall-galaxies. The voids must be thicker than an adjustable limit, which is refined in successive iterations. We test the algorithm using Voronoi tessellations. By appropriate scaling of the parameters we apply it to the SSRS2 survey and to the IRAS 1.2 Jy. Both surveys show similar properties: ~50% of the volume is filled by the voids, which have a scale of at least 40 Mpc, and a -0.9 under-density. Faint galaxies populate the voids more than bright ones. These results suggest that both optically and IRAS selected galaxies delineate the same LSS. Comparison with the recovered mass distribution further suggests that the observed voids in the galaxy distribution correspond well to under-dense regions in the mass distribution. This confirms the gravitational origin of the voids.Comment: Submitted to ApJ; 33 pages, aaspp4 LaTeX file, using epsfig and natbib, 1 table, 12 PS figures. Complete gzipped version is available at http://shemesh.fiz.huji.ac.il/hagai/; uuencoded file is available at http://shemesh.fiz.huji.ac.il/papers/ep3.uu or ftp://shemesh.fiz.huji.ac.i