Slow modes in Keplerian disks

Low-mass disks orbiting a massive body can support "slow" normal modes, in which the eigenfrequency is much less than the orbital frequency. Slow modes are lopsided, i.e., the azimuthal wavenumber m=1. We investigate the properties of slow modes, using softened self-gravity as a simple model for collective effects in the disk. We employ both the WKB approximation and numerical solutions of the linear eigenvalue equation. We find that all slow modes are stable. Discrete slow modes can be divided into two types, which we label g-modes and p-modes. The g-modes involve long leading and long trailing waves, have properties determined by the self-gravity of the disk, and are only present in narrow rings or in disks where the precession rate is dominated by an external potential. In contrast, the properties of p-modes are determined by the interplay of self-gravity and other collective effects. P-modes involve both long and short waves, and in the WKB approximation appear in degenerate leading/trailing pairs. Disks support a finite number---sometimes zero---of discrete slow modes, and a continuum of singular modes.Comment: 32 pages, 12 figures. To be published in Astronomical Journa

Embedded discontinuous Galerkin transport schemes with localised limiters

Motivated by finite element spaces used for representation of temperature in the compatible finite element approach for numerical weather prediction, we introduce locally bounded transport schemes for (partially-)continuous finite element spaces. The underlying high-order transport scheme is constructed by injecting the partially-continuous field into an embedding discontinuous finite element space, applying a stable upwind discontinuous Galerkin (DG) scheme, and projecting back into the partially-continuous space; we call this an embedded DG scheme. We prove that this scheme is stable in L2 provided that the underlying upwind DG scheme is. We then provide a framework for applying limiters for embedded DG transport schemes. Standard DG limiters are applied during the underlying DG scheme. We introduce a new localised form of element-based flux-correction which we apply to limiting the projection back into the partially-continuous space, so that the whole transport scheme is bounded. We provide details in the specific case of tensor-product finite element spaces on wedge elements that are discontinuous P1/Q1 in the horizontal and continuous P2 in the vertical. The framework is illustrated with numerical tests

Antigenic and genetic characterization of a divergent African virus, Ikoma lyssavirus

In 2009, a novel lyssavirus (subsequently named Ikoma lyssavirus, IKOV) was detected in the brain of an African civet (Civettictis civetta) with clinical rabies in the Serengeti National Park of Tanzania. The degree of nucleotide divergence between the genome of IKOV and those of other lyssaviruses predicted antigenic distinction from, and lack of protection provided by, available rabies vaccines. In addition, the index case was considered likely to be an incidental spillover event, and therefore the true reservoir of IKOV remained to be identified. The advent of sensitive molecular techniques has led to a rapid increase in the discovery of novel viruses. Detecting viral sequence alone, however, only allows for prediction of phenotypic characteristics and not their measurement. In the present study we describe the in vitro and in vivo characterization of IKOV, demonstrating that it is (1) pathogenic by peripheral inoculation in an animal model, (2) antigenically distinct from current rabies vaccine strains and (3) poorly neutralized by sera from humans and animals immunized against rabies. In a laboratory mouse model, no protection was elicited by a licensed rabies vaccine. We also investigated the role of bats as reservoirs of IKOV. We found no evidence for infection among 483 individuals of at least 13 bat species sampled across sites in the Serengeti and Southern Kenya

Disks in Expanding FRW Universes

We construct exact solutions to Einstein equations which represent relativistic disks immersed into an expanding FRW Universe. It is shown that the expansion influences dynamical characteristics of the disks such as rotational curves, surface mass density, etc. The effects of the expansion is exemplified with non-static generalizations of Kuzmin-Curzon and generalized Schwarzschild disks.Comment: Revised version to appear in ApJ, Latex, 17 pages, 10 figures, uses aaspp4 and epsf style file

Thin-disk models in an Integrable Weyl-Dirac theory

We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in Found. Phys. 29, 1303 (1999). The main differences between these solutions and the corresponding general relativistic one are analyzed, focusing on the behavior of physical observables (rotation curves of test particles, density and pressure profiles). We consider the case in which test particles move on Weyl geodesics. The same rotation curve can be obtained from many different solutions of the Weyl-Dirac theory, although some of these solutions present strong qualitative differences with respect to the usual general relativistic model (such as the appearance a ring-like density profile). In particular, for typical galactic parameters all rotation curves of the Weyl-Dirac model present Keplerian fall-off. As a consequence, we conclude that a more thorough analysis of the problem requires the determination of the gauge function $\beta$ on galactic scales, as well as restrictions on the test-particle behavior under the action of the additional fields introduced by this theory.Comment: 18 pages, 3 figures; accepted in General Relativity and Gravitatio

Vertical stability of circular orbits in relativistic razor-thin disks

During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these systems is not yet so developed. In the present work, we propose a definite vertical stability criterion for circular equatorial timelike geodesics in static, axially symmetric thin disks, possibly surrounded by other structures preserving axial symmetry. It turns out that the strong energy condition for the disk stress-energy content is sufficient for vertical stability of these orbits. Moreover, adiabatic invariance of the vertical action variable gives us an approximate third integral of motion for oblique orbits which deviate slightly from the equatorial plane. Such new approximate third integral certainly points to a better understanding of the analytical properties of these orbits. The results presented here, derived for static spacetimes, may be a starting point to study the motion around rotating, stationary razor-thin disks. Our results also allow us to conjecture that the strong energy condition should be sufficient to assure transversal stability of periodic orbits for any singular timelike hypersurface, provided it is invariant under the geodesic flow.Comment: 13 pages, 4 figures; Accepted for publication in Physical Review