Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur

Distances from the Correlation between Galaxy Luminosities and Rotation Rates

A large luminosity--linewidth template sample is now available, improved absorption corrections have been derived, and there are a statistically significant number of galaxies with well determined distances to supply the zero point. A revised estimate of the Hubble Constant is H_0=77 +-4 km/s/Mpc where the error is the 95% probability statistical error. Systematic uncertainties are potentially twice as large.Comment: 21 pages, 9 figures. Invited chapter for the book `Post-Hipparcos Cosmic Candles', Eds. F. Caputo and A. Heck (Kluwer Academic Publishers, Dordrecht

On the kinematics of the Local cosmic void

We collected the existing data on the distances and radial velocities of galaxies around the Local Void in the Aquila/Hercules to examine the peculiar velocity field induced by its underdensity. A sample of 1056 galaxies with distances measured from the Tip of the Red Giant Branch, the Cepheid luminosity, the SNIa luminosity, the surface brightness fluctuation method, and the Tully-Fisher relation has been used for this purpose. The amplitude of outflow is found to be ~300 km/s. The galaxies located within the void produce the mean intra-void number density about 1/5 of the mean external number density of galaxies. The void's population has a lower luminosity and a later morphological type with the medians: M_B = -15.7^m and T = 8 (Sdm), respectively.Comment: Version 1. 14 pages, 8 figures, 2 tables. Accepted to Astrophysics, Volume 54, Issue

The origin of galaxy scaling laws in LCDM

It has long been recognized that tight relations link the mass, size, and characteristic velocity of galaxies. These scaling laws reflect the way in which baryons populate, cool, and settle at the center of their host dark matter halos; the angular momentum they retain in the assembly process; as well as the radial distribution and mass scalings of the dark matter halos. There has been steady progress in our understanding of these processes in recent years, mainly as sophisticated N-body and hydrodynamical simulation techniques have enabled the numerical realization of galaxy models of ever increasing complexity, realism, and appeal. These simulations have now clarified the origin of these galaxy scaling laws in a universe dominated by cold dark matter: these relations arise from the tight (but highly non-linear) relations between (i) galaxy mass and halo mass, (ii) galaxy size and halo characteristic radius; and (iii) from the self-similar mass nature of cold dark matter halo mass profiles. The excellent agreement between simulated and observed galaxy scaling laws is a resounding success for the LCDM cosmogony on the highly non-linear scales of individual galaxies.Comment: Contribution to the Proceedings of the Simons Conference "Illuminating Dark Matter", held in Kruen, Germany, in May 2018, eds. R. Essig, K. Zurek, J. Fen

Galaxy Harassment and the Evolution of Clusters of Galaxies

Disturbed spiral galaxies with high rates of star formation pervaded clusters of galaxies just a few billion years ago, but nearby clusters exclude spirals in favor of ellipticals. ``Galaxy harassment" (frequent high speed galaxy encounters) drives the morphological transformation of galaxies in clusters, provides fuel for quasars in subluminous hosts and leaves detectable debris arcs. Simulated images of harassed galaxies are strikingly similar to the distorted spirals in clusters at $z \sim 0.4$ observed by the Hubble Space Telescope.Comment: Submitted to Nature. Latex file, 7 pages, 10 photographs in gif and jpeg format included. 10 compressed postscript figures and text available using anonymous ftp from ftp://ftp-hpcc.astro.washington.edu/pub/hpcc/moore/ (mget *) Also available at http://www-hpcc.astro.washington.edu/papers

Blueshifted galaxies in the Virgo Cluster

We examine a sample of 65 galaxies in the Virgo cluster with negative radial velocities relative to the Local Group. Some features of this sample are pointed out. All of these objects are positioned compactly within a virial zone of radius 6{\deg} in the cluster, but their centroid is displaced relative to the dynamic center of the cluster, M87, by 1.1{\deg} to the northwest. The dwarf galaxies in this sample are clumped on a scale of ~10' (50 kpc). The observed asymmetry in the distribution of the blueshifted galaxies may be caused by infall of a group of galaxies around M86 onto the main body of the cluster. We offer another attempt to explain this phenomenon, assuming a mutual tangential velocity of ~300 km/s between the Local Group and the Virgo cluster owing to their being repelled from the local cosmological void.Comment: 10 pages, 4 figures, 1 table. Published in Astrophysics, Vol. 53, No. 1, pp. 32-41, 201

A 120-Mpc Periodicity in the Three-Dimensional Distribution of Galaxy Superclusters

Using a new compilation of available data on galaxy clusters and superclusters we present evidence for a quasiregular three-dimensional network of rich superclusters and voids, with the regions of high density separated by about 120 Mpc. We calculate the power spectrum for clusters of galaxies; it has a peak on the wavelength equal to the step of the network; the excess in the amplitude of the spectrum over that of the cold dark matter model is by a factor of 1.4. The probability that the spectrum can be formed within the framework of the standard cosmogony is very small. If the cluster distribution reflects the distribution of all matter (luminous and dark), then there must exists some hithero unknown process that produces regular structure on large scales.Comment: Tex, 6 pages, 2 PostScript figures embedded, accepted by Nature on November 19, 199

Rotation Curves of Spiral Galaxies

Rotation curves of spiral galaxies are the major tool for determining the distribution of mass in spiral galaxies. They provide fundamental information for understanding the dynamics, evolution and formation of spiral galaxies. We describe various methods to derive rotation curves, and review the results obtained. We discuss the basic characteristics of observed rotation curves in relation to various galaxy properties, such as Hubble type, structure, activity, and environment.Comment: 40 pages, 6 gif figures; Ann. Rev. Astron. Astrophys. Vol. 39, p.137, 200

High star formation rates as the origin of turbulence in early and modern disk galaxies

High spatial and spectral resolution observations of star formation and kinematics in early galaxies have shown that two-thirds are massive rotating disk galaxies with the remainder being less massive non-rotating objects. The line of sight averaged velocity dispersions are typically five times higher than in today's disk galaxies. This has suggested that gravitationally-unstable, gas-rich disks in the early Universe are fuelled by cold, dense accreting gas flowing along cosmic filaments and penetrating hot galactic gas halos. However these accreting flows have not been observed, and cosmic accretion cannot power the observed level of turbulence. Here we report on a new sample of rare high-velocity-dispersion disk galaxies we have discovered in the nearby Universe where cold accretion is unlikely to drive their high star-formation rates. We find that the velocity dispersion is most fundamentally correlated with their star-formation rates, and not their mass nor gas fraction, which leads to a new picture where star formation itself is the energetic driver of galaxy disk turbulence at all cosmic epochs.Comment: 9 pages, 2 figures, Supplimentary Info available at: http://pulsar.swin.edu.au/~agreen/nature/sigma_mean_arXiv.pdf. Accepted for publication in Natur

The Hubble Constant

I review the current state of determinations of the Hubble constant, which gives the length scale of the Universe by relating the expansion velocity of objects to their distance. There are two broad categories of measurements. The first uses individual astrophysical objects which have some property that allows their intrinsic luminosity or size to be determined, or allows the determination of their distance by geometric means. The second category comprises the use of all-sky cosmic microwave background, or correlations between large samples of galaxies, to determine information about the geometry of the Universe and hence the Hubble constant, typically in a combination with other cosmological parameters. Many, but not all, object-based measurements give $H_0$ values of around 72-74km/s/Mpc , with typical errors of 2-3km/s/Mpc. This is in mild discrepancy with CMB-based measurements, in particular those from the Planck satellite, which give values of 67-68km/s/Mpc and typical errors of 1-2km/s/Mpc. The size of the remaining systematics indicate that accuracy rather than precision is the remaining problem in a good determination of the Hubble constant. Whether a discrepancy exists, and whether new physics is needed to resolve it, depends on details of the systematics of the object-based methods, and also on the assumptions about other cosmological parameters and which datasets are combined in the case of the all-sky methods.Comment: Extensively revised and updated since the 2007 version: accepted by Living Reviews in Relativity as a major (2014) update of LRR 10, 4, 200