Introduction

Since their discovery by Papaloizou & Pringle (1984) non-axisymmetric instabilities in accretion tori have been discussed by many authors. It has been found that the instabilities are driven by shear and operate – depending on flow and perturbation parameters – through sound waves, surface waves or Kelvin-Helmholtz type modes. The spectrum of internal gravity waves which is associated with finite entropy gradients has not yet been studied and will be described in a forthcoming paper (Glatzel 1989). A brief summary of the main results is given here.

Basic assumptions

In order to allow for an analytical treatment we adopt cylindrical geometry and consider the limit of thin shells which rotate differentially in their own or an external gravitational field. The entropy distribution is required to guarantee a parabolic density stratification. Maximum density occurs when the effective gravity vanishes – its zeros determine the boundaries of the configuration. We assume incompressibility and neglect the self-gravity of the perturbations. Using an additional technical approximation, which has qualitatively no consequence for the modal structure, the perturbation equation is reduced to Whittaker's equation and the dispersion relation can be written in terms of confluent hypergeometric functions.

The modal structure

In a medium at rest a two-fold infinite set of gravity modes is found moving parallel to the boundaries in opposite directions. Modes occur in pairs corresponding to a symmetric and an anti-symmetric eigenfunction, where the symmetric mode owes its existence to the non-monotonic density stratification.

Introduction

The presence of a dust disc around the main sequence A5 star β Pic is now well established (Smith & Terrile 1984, 1987; Paresce & Burrows, 1987). Models based on the integrated thermal emission measured from IRAS and the ground (5 µm to 100 µm), as well as multi-aperture photometry and IRAS slow-scan data, have been constructed by Backman, Gillett & Witteborn (1989), who conclude that there is a dust-free zone around the star at a radius ∼ 20 AU, with a (face on) surface density of dust grains which decreases quite slowly with distance out to its outer edge at ∼ 1000 AU. However, models by Artymowicz, Burrows & Paresce (1988) based mainly on the optical images suggest that beyond 100 AU the surface density falls as r−2 or faster. A possible explanation of this discrepancy could be that there are two separate populations of grains responsible for the optical and infrared emission from the disc which have radically different spatial distributions.

Polarimetry

One valuable piece of information that could add significantly to our understanding of the disc is its optical polarization. By analogy with studies of the zodiacal light, the dependence of polarization on angular distance from the star can provide constraints on the radial dependence of grain number density, and the wavelength dependence of polarization sets limits on the size distribution.

Abstract I review recent progress in the study of accretion discs in cataclysmic variables (CVs) and X-ray binaries. Observations of CVs, especially eclipse mapping, give detailed agreement with steady-state disc theory. Coronae and winds are probably universal features of discs in such systems. Our present ignorance of the disc viscosity is the main barrier to progress in understanding time dependence and stability properties. Non-axisymmetric structure is particularly prominent in observations of low-mass X-ray binaries. This may be caused by the interaction of the mass transfer stream from the companion star with the disc.

Introduction.

Cataclysmic variables (CVs) are close binary systems, having periods of a few hours, in which a white dwarf accretes material from a main-sequence companion which fills the Roche lobe. If the white dwarf is replaced by a neutron star or black hole we have a low-mass X-ray binary (LMXB).

The formation of an accretion disc lying in the orbital plane is very likely under these circumstances since the accretion stream from the companion is highly supersonic and follows an essentially ballistic trajectory; its closest approach to the accreting object is a few ×109 cm, larger than the radius of any likely accreting object. The resulting self-collisions of the stream imply dissipation. As this can remove energy much more effectively than angular momentum the matter arranges itself into a collection of orbits of lowest energy for fixed angular momentum, i.e.

Introduction

Recent studies by Tyson (1988) and Tyson & Scalo (1988) suggest the possible existence of a large population of gas-rich dwarf irregular galaxies. Their “bursting dwarf galaxies” model would imply that a large fraction of these dwarfs remains undetected due to observational selection effects (angular diameter, surface brightness). Dekel & Silk (1986), in their cold dark matter biased galaxy formation picture, also predict that the universe is filled more uniformly with dwarf galaxies than with bright ones. Our results on DDO 154 suggest it could be a prototype gas-rich, low surface brightness, small optical diameter galaxy which happens to be relatively nearby (Δ ≤ 4 Mpc based on possible membership to the CVn I cloud and the magnitudes of the brightest blue stars; Carignan & Beaulieu 1989).

Summary of the data

DDO 154 is barely discernible on the Palomar Sky Survey. Its extrapolated central surface brightness is only B(0) = 23.5 mag arcsec−2. The colours, however, are typical of Im galaxies with (B – V) = 0.32 and (V – R) = 0.30. Its large HI gas content and extent were discovered serendipitously by Krumm & Burstein (1984). From the VLA data, it is found that the HI extends to nearly 5DHO at a level ˜ 1019 cm−2 (4DHO at a level ∼ 1020 cm−2). Despite the chaotic optical appearance, the velocity field is very regular and well-defined. The analysis shows that the closing of the isovelocity contours in the outer parts is partly due to the warp of the HI disc.

Problem under study

We study interactions between disc galaxies, in particular the case of a main system and a small perturber. Here we look at the behaviour using a responsive disturber in contrast to the more common approximation of a rigid mass distribution. It is possible to isolate the effect of the perturber's dynamics by studying the difference between simulations with and without internal motion in the disturber. One facet of extended systems is the possible stripping of cool gas from the smaller galaxy in the case when the systems do not merge. Another line of study is cloud-cloud collisions, their impact on cooling the gas and keeping the velocity dispersion down.

Numerical model

A particle-mesh code is used to simulate these systems. It is possible to evolve a 2-dimensional Cartesian grid (512 × 512 maximum) with 200K particles in a reasonable time (approximately 15s/time-step). The code is quite flexible since it does not need any description of the free populations other than their mass density and desired velocity dispersion. An option is to use a rigid potential in order to mimic a hot (spherical) component. The rigid components are moved along with the centre of mass for the respective system.

Experiments

The experiment displayed in the poster session had two galaxies with a mass ratio of 5:1. The orbit was initially parabolic and direct, as seen from the larger system's point of view.

Abstract Spiral density waves and spiral bending waves have been observed at dozens of locations within Saturn's rings. These waves are excited by resonant gravitational perturbations from moons orbiting outside the ring system. Modelling of spiral waves yields the best available estimates for the mass and the thickness of Saturn's ring system. Angular momentum transport due to spiral density waves may cause significant orbital evolution of Saturn's rings and inner moons. Similar angular momentum transfer may occur in other astrophysical systems such as protoplanetary discs, binary star systems with discs and spiral galaxies with satellites.

Introduction

Saturn's ring system was the first astrophysical disc to be discovered. When Galileo observed the rings in 1610, he believed them to be two giant moons in orbit about the planet. However, these “moons” appeared fixed in position, unlike the four satellites of Jupiter which he had previously observed. Moreover, Saturn's “moons” had disappeared completely by the time Galileo resumed his observations of the planet in 1612. Many explanations were put forth to explain Saturn's “strange appendages”, which grew, shrank and disappeared every 15 years. In 1655, Huygens finally deduced the correct explanation, that Saturn's strange appendages are a flattened disc of material in Saturn's equatorial plane, which appear to vanish when the Earth passes through the plane of the disc (Figure 1). The length of time between Galileo's first observations of Saturn's rings and Huygens' correct explanation was due in part to the poor resolution of early telescopes. However, a greater difficulty was recognition of the possibility and plausibility of astrophysical disc systems.

AbstractN-body simulations of disc galaxies that display recurrent transient spiral patterns are comparatively easy to construct, but are harder to understand. In this paper, I summarise the evidence from such experiments that the spiral patterns result from a recurrent spiral instability cycle. Each wave starts as rapidly growing, small-amplitude instability caused by a deficiency of particles at a particular angular momentum. The resulting largeamplitude wave creates, through resonant scattering, the conditions needed to precipitate a new instability.

Plan

The problem of spiral structure in galaxies has been worked on for many years but progress has been painfully slow. Most effort has been directed towards the development of an analytical (or at least semi-analytical) approach and many aspects of the problem have been discovered (see Sellwood 1989 for a review). Here, I collect the evidence from N-body simulations which indicates that the structure is continuously variable and results from a recurrent cycle of spiral instabilities.

A subsidiary purpose of this paper, is to convince the reader of the advantages of using N-body simulations in tandem with approximate analytic treatments. Without a close comparison of this nature, each separate approach is much less powerful; the limitations of the N-body experiments remain unquantified and the validity of the approximations in the analytic approach cannot be assessed.

The paper is divided into three distinct sections. In §2, I discuss swing-amplified noise in global simulations, and show that the behaviour in the Mestel (V = const.) disc is very similar to that reported by Toomre (e.g. this conference) for simulations in the shearing sheet.

Introduction

The sample of CO outflows reported in Bally & Lada (1983) was searched for OH maser emission (Prestwich 1985). The stronger OH maser sources found in this search – augmented by two other sources – were then mapped using MERLIN. The maser distributions were compared with the molecular emission from the sources.

A clear-cut case of the association between OH maser emission and a molecular disc is found in G35.2-0.7N (Brebner et al. 1987). Its bipolar outflow is well collimated and an ammonia condensation is observed, clearly elongated in a direction perpendicular to the outflow direction. The OH masers are situated at, or near the exciting source of the region, and lie in an elongated distribution with an orientation which reflects that of the larger-scale ammonia disc.

Comparison of OH maser and CO outflow distributions

Comparisons could be made for eight sources – the masers in Orion-KL were mapped by Norris (1984). As observations of a molecular disc were unclear, or had not yet been attempted in many cases, a comparison was made between the orientations of the CO outflows and the OH maser distributions. The major axis of the OH maser distribution was deduced from a least squares fit and the angular differences between maser and outflow orientations are shown in (Figure 1). The largest source of error is in the estimates of the outflow direction, many of which had to be made by eye. (A selection effect is inherent: the sample could not have face-on discs, since the CO outflow direction could not be identified in such cases.)

Introduction

The recognition that astrophysical discs exist was a major intellectual achievement. As Lissauer stressed at this meeting, it was more than 40 years after Galileo discovered peculiar appendages to Saturn (‘two servants for the old man, who help him to walk and never leave his side’) before Huygens published, as an anagram, the first correct model of the Saturn system (‘it is surrounded by a thin flat ring, nowhere touching, and inclined to the ecliptic’). The long delay was due in part to the limited angular resolution of the available telescopes, but also reflects the leap of imagination needed to grasp the true nature of the first known non-spherical celestial body.

Compared with this one example of an astrophysical disc known for over 300 years, the number and variety of discs that have been discovered or inferred in just the last 30 years is remarkable: (1) Saturn's rings have been joined by lesser ring systems around the other three giant planets, all discovered since 1977; (2) there is recent strong evidence that discs are associated with many protostars and young stars (reviewed by Snell), as well as with active galactic nuclei (reviewed by Malkan); (3) it was only in the late 1960's that accretion discs were recognized to be a central ingredient of many close binary star systems, in particular cataclysmic variables and many Galactic X-ray sources; (4) although it has long been known that the solar system formed from a disc, the analysis of realistic models of protoplanetary discs, and direct observations of similar discs (e. g. the β Pictoris disc), began only in the last few years; (5) it is likely that discs play a crucial role in collimating the jets discovered in double radio sources, SS433, and bipolar flows from young stars.

Discs occurring in a wide diversity of astronomical objects prompt similar questions about their dynamical behaviour. Astrophysicists working on problems related to just one type of disc may find that a similar problem has already been addressed in a different context. This is especially true of the dynamical behaviour: the dispersion relation for spiral density waves was originally derived for galaxies but has been applied, with more success even, to Saturn's rings, the formalism of a global mode treatment for gaseous accretions discs has some similarity to that for the collisionless stellar discs of galaxies, aspects of the dynamics of planet formation around a young stellar object are reflected in the response of a galaxy disc to a co-orbiting giant molecular cloud complex, etc.

In order to encourage thinking along these lines, the Department of Astronomy in the University of Manchester organised a four day conference in December 1988 to bring together experts on discs in a number of contexts. In rough order of increasing physical size, these are: planetary ring systems, accretion discs in cataclysmic binary stars and active galactic nuclei, protoplanetary and protostellar discs and disc galaxies.

The aim of the conference, and of these proceedings, was to present those aspects of the behaviour of each type of disc that could be of relevance to other types. To emphasise this theme, the sequence of talks was deliberately arranged so as ensure that many different disc types were discussed on any one day.