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

Cold gas accretion in galaxies

Evidence for the accretion of cold gas in galaxies has been rapidly accumulating in the past years. HI observations of galaxies and their environment have brought to light new facts and phenomena which are evidence of ongoing or recent accretion: 1) A large number of galaxies are accompanied by gas-rich dwarfs or are surrounded by HI cloud complexes, tails and filaments. It may be regarded as direct evidence of cold gas accretion in the local universe. It is probably the same kind of phenomenon of material infall as the stellar streams observed in the halos of our galaxy and M31. 2) Considerable amounts of extra-planar HI have been found in nearby spiral galaxies. While a large fraction of this gas is produced by galactic fountains, it is likely that a part of it is of extragalactic origin. 3) Spirals are known to have extended and warped outer layers of HI. It is not clear how these have formed, and how and for how long the warps can be sustained. Gas infall has been proposed as the origin. 4) The majority of galactic disks are lopsided in their morphology as well as in their kinematics. Also here recent accretion has been advocated as a possible cause. In our view, accretion takes place both through the arrival and merging of gas-rich satellites and through gas infall from the intergalactic medium (IGM). The infall may have observable effects on the disk such as bursts of star formation and lopsidedness. We infer a mean ``visible'' accretion rate of cold gas in galaxies of at least 0.2 Msol/yr. In order to reach the accretion rates needed to sustain the observed star formation (~1 Msol/yr), additional infall of large amounts of gas from the IGM seems to be required.Comment: To appear in Astronomy & Astrophysics Reviews. 34 pages. Full-resolution version available at http://www.astron.nl/~oosterlo/accretionRevie

AN HI STUDY OF URSA-MAJOR SPIRALS

This is a progress report on a survey of detailed HI synthesis observations of galaxies in the Ursa Major cluster. Two preliminary conclusions are presented. First, the scatter in the H band Tully-Fisher relation can be reduced by using the maximum rotational velocity taken from the rotation curves. Second, there is no indication of an HI deficiency in galaxies near the cluster center.</p

The Ursa Major Cluster of galaxies:Tully-Fisher relations and dark matter in spirals.

A brief overview is presented of some results from ongoing research on the properties of a complete sample of spiral galaxies in the Ursa Major cluster. Optical and near infrared photometric imaging is combined with HI 21cm-line synthesis mapping. These observations allow to study in great detail the Tully-Fisher relations in various passbands with different kinematic measures and to investigate the properties of the dark matter halos as a function of the global properties of the luminous matter.</p

The ursa major cluster of galaxies - IV. HI synthesis observations

In this data paper we present the results of an extensive 21 cm-line synthesis imaging survey of 43 spiral galaxies in the nearby Ursa Major cluster using the Westerbork Synthesis Radio Telescope. Detailed kinematic information in the form of position-velocity diagrams and rotation curves is presented in an atlas together with HI channel maps, 21 cm continuum maps, global HI profiles, radial HI surface density profiles, integrated HI column density maps, and HI velocity fields. The relation between the corrected global HI linewidth and the rotational velocities V-max and V-flat as derived from the rotation curves is investigated. Inclination angles obtained from the optical axis ratios are compared to those derived from the inclined HI disks and the HI velocity fields. The galaxies were not selected on the basis of their HI content but solely on the basis of their cluster membership and inclination which should be suitable for a kinematic analysis. The observed galaxies provide a well-defined, volume limited and equidistant sample, useful to investigate in detail the statistical properties of the Tully-Fisher relation and the dark matter halos around them

HI column density distribution function at z=0: Connection to damped Ly alpha statistics

We present a measurement of the HI column density distribution function f(N-HI) at the present epoch for column densities > 10(20) cm(-2). These high column densities compare to those measured in damped Ly alpha lines seen in absorption against background quasars. Although observationally rare, it appears that the bulk of the neutral gas in the Universe is associated with these damped Ly alpha systems. In order to obtain a good anchor point at z = 0 we determine f(N-HI) in the local Universe by using 21 cm synthesis observations of a complete sample of spiral galaxies. We show that f(N-HI) for damped Ly alpha systems has changed significantly from high z to the present and that change is greatest for the highest column densities. The measurements indicate that low surface brightness galaxies make a minor contribution to the cross section for HI, especially for N-HI > 10(21) cm(-2)