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.

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.