Introduction

Nine rings of Uranus were discovered by Earth-based stellar occultations in 1977. In order of increasing semi-major axis from the planet they have been denoted 6, 5, 4, α β η γ δ and ∈. The rings are very dark, very narrow (typically < 5 km) and have extremely sharp edges. The standard theory for the confinement of narrow rings against the spreading effects of Poynting-Robertson drag and collisions (Goldreich & Tremaine 1977) proposes that each ring is bounded by a pair of Lindblad resonances from shepherding satellites. Saturn's F-ring is now known to be shepherded by the two satellites Pandora and Prometheus, and in January 1986 Voyager 2 images of the Uranian system in back scattered light showed the presence of two satellites, Cordelia and Ophelia, on either side of the ∈ ring. Eight other small satellites, all exterior to the main rings, were discovered by Voyager 2.

Porco & Goldreich (1987) showed that the inner edge of the ∈ ring is within a kilometre of the 24:25 outer Lindblad resonance with Cordelia while the outer edge is within 300 m of the 14:13 inner Lindblad resonance with Ophelia. They identified two other possible resonances between ring features and these two satellites. A series of narrow angle Voyager 2 images of the rings were taken at fixed, non-rotating positions to search for small satellites orbiting between the rings. No further satellites were found down to a detection limit of 10 km (Smith et al. 1986).

Introduction

Mass lost from stars in the central regions of galaxies may flow inwards to form both massive molecular clouds and a young, new stellar population having the form of a thick, rapidly rotating nuclear disc. Angular momentum is transferred from the clouds to the stars in the original spheroid, thereby spinning up the old bulge population within the central ≃ 1 kpc and increasing the general ‘boxiness’ of the underlying stellar density distribution. New stars formed by the collapse of massive molecular clouds in the nuclear disc also contribute towards the general boxiness of the central nuclear bulge.

Bulge-disc interaction

Following previous investigations into the fate of stellar mass loss in the central regions of galaxies (e.g. Bailey & Clube 1978, Bailey 1980, 1982, 1985), we assume that material flows inwards ultimately to form a dense, cold nuclear disc of molecular gas. We assume a disc of radius Rd ≃ 500 pc and mass Md ≈ 108M⊙, embedded within a nuclear bulge of radius Rn ≃ 1 kpc and mass Mn ≃ 1010M⊙, adopting a flat rotation curve. Over a Hubble time, the total stellar mass loss exceeds 10% of the original bulge mass, i.e. ≳ 109M⊙.

We also assume that the nuclear disc fragments into clouds with masses Mc ≃ 106M⊙, by analogy with the clouds in the disc of our Galaxy. These massive clouds, moving at the local circular velocity, suffer dynamical friction against the surrounding bulge stars, which causes them to spiral slowly into the galactic centre.

Introduction

The formation and the evolution of bars, the mutual influence of the bulge and the bar and the effects of vertical resonances, have been studied in a series of N-body simulations (105≤N≤5×105) over long time scales (T≥2000 Myr). A PM method is used with a 3-D polar grid having an exponential spacing in R (the central resolution is 0.2 kpc or less), and a linear spacing in φ and z. More detail will be given in a future paper. The particles are distributed into a bulge and a disc components in hydrostatic equilibrium (Satoh & Miyamoto 1976). The dimensionless parameters are the bulge-to-disc mass ratio µ = Mb/Md, and the bulge-to-disc scale length ratio β = b/a.

Some results

VELOCITY DISPERSION

At T = 0 the velocity ellipsoid is isotropic by construction, but it becomes rapidly anisotropic, such that σR ≥ σφ ≥ σz everywhere, and its size decreases with R. Due to heating by time-dependent perturbations, σR and σφ grow considerably, as well as σzin the bar region since vertical resonances exist. This large scale heating is more efficient than that induced by local perturbations.

BULGE EVOLUTION

The disc, and subsequently the bar, flattens the initially spherical bulge, which aligns itself with the bar, i.e. the bulge co-rotates with the bar. For example with µ = 0.18 and β = 1/12, the bulge axis ratios are 1 : 0.84 : 0.82 (T = 2000 Myr).

BAR SHAPE

The horizontal and the vertical bar ellipticity, εh and εv, are measured at the most eccentric contour line of the projected density.

Abstract Three topics are briefly discussed concerning the gas distribution and kinematics in spiral galaxies. The first concerns the relative location of neutral hydrogen, HII regions, dust, molecules and non-thermal radio continuum emission in spiral arms. The second is the asymmetrical structure and the presence of large non-circular motions in spiral galaxies, as shown by the observations of M 101. Finally, attention is drawn to the presence of spiral arm structure and to some puzzling HI features in the outermost parts of gaseous discs. Observational evidence seems to indicate that infall of gas has important effects on the kinematics of discs and on their evolution.

Structure of spiral arms

Detailed, multifrequency observations of recent years of two nearby spiral galaxies, M 51 and M 83, have led to a new picture of the relative distributions of the various ingredients of the interstellar medium. In the classical schematic picture of spiral arm structure the HI is concentrated on the inner side of spiral arms on the dust lanes, which mark the location of spiral shocks. The observations of HII and HI regions by Allen et al. (1986) and Tilanus & Allen (1989) show that both HI and HII are displaced from the dust lanes toward the outer parts of the arm, although there is no small scale agreement between the distribution of HI and HII. The radio continuum ridge in M 51 coincides with the dust lanes (Tilanus et al. 1988). Its profile across the arm is much broader than expected.

Abstract We develop the theory of instabilities in a rotating gaseous disc and in shallow water for the case where there is a break in the surface density and sound velocities, as well as the rotation rate, at a particular radius. Different instabilities of sub-sonic and supersonic flows have been investigated. We also prove the identity of the linearised dynamical equations for the gaseous disc of the Galaxy and for our rotating shallow water experiments.

Introduction

The present paper pursues two aims: (1) to prove that gradient instabilities can lead to spiral structure in galaxies, and (2) to give the theory of gradient instabilities in rotating shallow water, when viscosity effects can be neglected. The behaviour in rotating shallow water has been investigated in an experiment known as “Spiral” at the Plasma Physics Department of the Institute of Atomic Energy.

It is natural to ask why such different subjects as galactic discs and shallow water are combined in this one paper. The reason is that the dynamical behaviour of a gaseous galactic disc and rotating shallow water are described by one and the same set of differential equations. Clearly, shallow water may be considered as a 2-D gaseous dynamical system (Landau & Lifshitz 1986) similar to the gaseous disc of our galaxy. However, viscosity effects near the bottom in the experimental set-up are absent in galaxies and the latter contain forces of self-gravitation that are absent in shallow water.

Seyferts with companions

Galaxy activity is correlated with companions (Keel et al. 1985, van der Hulst et al. 1986). Using matched samples of Seyferts and controls, Dahari (1984) searched for companions, measuring the galaxy-companion separations and their sizes. He measure the tidal perturbation strength by a parameter P = (companion mass)/(separation)3 in units of the galaxy mass and radius. Dahari found that more Seyferts (37%) have companions than do normal spirals (21%), and that Seyferts with companions are perturbed more strongly. Selection effects cause companions of higher redshift Seyferts to be missed and Byrd et al. (1987) estimate that 75% to 90% of Dahari's Seyferts have companions.

Byrd et al. (1986) tested the correlation using computer models of tidally perturbed spiral galaxies. Observations require a gas mass inflow rate of > 0.5 M⊙ yr1 for Seyfert activity. We used a self-gravitating 60 000 particle disc and inert “halo” perturbed by a companion on a parabolic orbit. Tidal perturbation of the disc throws gas clouds into nucleus-crossing orbits to fuel activity. The experiments demonstrated that the inflow rate exceeded the required value at perturbation levels matching those where Dahari finds many more Seyferts than normals. We therefore conclude that observed companions of Seyferts do have tidal fields sufficient to trigger activity.

Seyferts in rich clusters

If individual gravitational encounters are responsible for activity, the incidence of activity should correlate with the enounter rate. Gavazzi & Jaffe (1987) argue that individual encounters should be less important in rich clusters than in groups.

The model

We consider the linear stability of a plane shear layer, including the effects of compressibility and viscosity, as the simplest model for viscous supersonic shear flows occurring in accretion processes. Details of this investigation can be found in Glatzel (1989). Measuring lengths and velocities in units of half of the thickness of the shear layer and the flow velocity at its edge respectively, the flow may then be described by dimensionless numbers, the influence of compressibility is described by the Mach number, M, and viscosity by two Reynolds numbers, Reν and Reµ, corresponding to shear and volume viscosity respectively.

Instabilities and critical Reynolds numbers

We distinguish two types of modes, viscous modes and sonic modes, according to their physical origin: shear viscosity and compressibility. Shear-driven pairing of viscous modes, and distortion of the pattern speed of sonic modes, leads to mode crossings among the sonic, and between viscous and sonic modes, which unfold into bands of instability. The viscous-sonic resonances provide a new example of viscous instability; the role of viscosity is merely to provide an additional discrete spectrum, while shear is needed to produce mode crossings. The instability is ultimately caused by resonant exchange of energy between the crossing modes.

Critical Reynolds numbers for some resonances are plotted in Figure 1 as a function of the Mach number, M, for zero volume viscosity (Reµ = 3Reν).

Self-absorption curves

In previous work (Friedjung & Muratorio 1987, Muratorio & Friedjung 1988), we developed methods using self-absorption curves (SACs) to study stars having Fe II emission lines in their spectra. Such a curve is obtained by plotting log(Fλ3/gf) against log(gfλ), where F is the total flux, λ the wavelength, g the lower level statistical weight, f the oscillator strength. gfλ is proportional to the optical thickness. If no selective excitation mechanisms exist for particular levels, and the levels inside a term have populations proportional to their statistical weights, such a plot for emission lines of the same multiplet will have points lying on the same self-absorption curve. The shape of the curve is characteristic of the nature of the medium where the line is formed. Shifting the curves for different multiplets (which should have the same shape) relative to each other so as to superpose them, will give at the same time the relative populations of their upper and also their lower terms. Until now, we have calculated SACs for various simplified cases, and a comparison was made with observations of luminous stars whose spectra contained many Fe II emission lines. It was found that observations of certain Magellanic cloud stars could not be fitted by spherically symmetric wind models. Another line emitting medium seemed to be present (a slab or a thin disc with constant opening angle), which is also suggested by the continuum energy distributions.