Shellflow. I. The Convergence of the Velocity Field at 6000 km/s

We present the first results from the Shellflow program, an all-sky Tully-Fisher (TF) peculiar velocity survey of 276 Sb-Sc galaxies with redshifts between 4500 and 7000 km/s. Shellflow was designed to minimize systematic errors between observing runs and between telescopes, thereby removing the possibility of a spurious bulk flow caused by data inhomogeneity. A fit to the data yields a bulk flow amplitude V_bulk = 70{+100}{-70} km/s (1 sigma error) with respect to the Cosmic Microwave Background, i.e., consistent with being at rest. At the 95% confidence level, the flow amplitude is < 300 km/s. Our results are insensitive to which Galactic extinction maps we use, and to the parameterization of the TF relation. The larger bulk motion found in analyses of the Mark III peculiar velocity catalog are thus likely to be due to non-uniformities between the subsamples making up Mark III. The absence of bulk flow is consistent with the study of Giovanelli and collaborators and flow field predictions from the observed distribution of IRAS galaxies.Comment: Accepted version for publication in ApJ. Includes an epitaph for Jeffrey Alan Willick (Oct 8, 1959 - Jun 18, 2000

An HI survey of the Bootes Void. II. The Analysis

We discuss the results of a VLA HI survey of the Bootes void and compare the distribution and HI properties of the void galaxies to those of galaxies found in a survey of regions of mean cosmic density. The Bootes survey covers 1100 Mpc$^{3}$, or $\sim$ 1\% of the volume of the void and consists of 24 cubes of typically 2 Mpc * 2 Mpc * 1280 km/s, centered on optically known galaxies. Sixteen targets were detected in HI; 18 previously uncataloged objects were discovered directly in HI. The control sample consists of 12 cubes centered on IRAS selected galaxies with FIR luminosities similar to those of the Bootes targets and located in regions of 1 to 2 times the cosmic mean density. In addition to the 12 targets 29 companions were detected in HI. We find that the number of galaxies within 1 Mpc of the targets is the same to within a factor of two for void and control samples, and thus that the small scale clustering of galaxies is the same in regions that differ by a factor of $\sim$ 6 in density on larger scales. A dynamical analysis of the galaxies in the void suggests that on scales of a few Mpc the galaxies are gravitationally bound, forming interacting galaxy pairs, loose pairs and loose groups. One group is compact enough to qualify as a Hickson compact group. The galaxies found in the void are mostly late-type, gas rich systems. A careful scrutiny of their HI and optical properties shows them to be very similar to field galaxies of the same morphological type. This, combined with our finding that the small scale clustering of the galaxies in the void is the same as in the field, suggests that it is the near environment that mostly affects the evolution of galaxies.Comment: Latex file of abstract. The postscript version of the complete paper (0.2 Mb in gzipped format) including all the figures can be retrieved from http://www.astro.rug.nl:80/~secr/ To appear in the February 1996 issue of the Astronomical Journa

Well-posedness, energy and charge conservation for nonlinear wave equations in discrete space-time

We consider the problem of discretization for the U(1)-invariant nonlinear wave equations in any dimension. We show that the classical finite-difference scheme used by Strauss and Vazquez \cite{MR0503140} conserves the positive-definite discrete analog of the energy if the grid ratio is $dt/dx\le 1/\sqrt{n}$, where $dt$ and $dx$ are the mesh sizes of the time and space variables and $n$ is the spatial dimension. We also show that if the grid ratio is $dt/dx=1/\sqrt{n}$, then there is the discrete analog of the charge which is conserved. We prove the existence and uniqueness of solutions to the discrete Cauchy problem. We use the energy conservation to obtain the a priori bounds for finite energy solutions, thus showing that the Strauss -- Vazquez finite-difference scheme for the nonlinear Klein-Gordon equation with positive nonlinear term in the Hamiltonian is conditionally stable.Comment: 10 page