Statement of the problem

Most studies of light scattering in planetary rings have assumed layers which are many particles thick, plane parallel, and homogeneous. However, real rings may be thin, vertically warped, and clumpy. We have developed a ray tracing code which calculates the light scattered by an arbitrary distribution of particles. This approach promises to clarify a number of puzzling observations of the Saturnian and Uranian rings.

(1) Many studies have concluded that Saturn's rings are many particles thick (e.g. Lumme et al. 1983), whereas dynamical calculations predict that optically thick rings should be physically thin (Wisdom & Tremaine 1988 and references therein). Lumme et al. argue that the particles in Saturn's B Ring fill only 2% of the volume of the ring, while Wisdom and Tremaine predict a filling factor of 20% or more.

The claim that Saturn's rings are thick is based on their observed opposition surge, a rapid brightening (0.3 mag in the V band) which occurs at phase angles below about 1.5°. The surge is attributed to particles covering their own shadows near opposition. Shadowing can occur either between discrete particles, or within the surface structure of a particle. The range in phase angle over which the brightening takes place is proportional to the volume filling factor of the ring or surface. Thus the very narrow opposition effect of Saturn's rings implies a very porous ring, unless individual particles backscatter extremely strongly.

Simulation

A videomovie, showing a simulation of a disc galaxy perturbed by a companion, has been made. It is easy to see some time-dependent phenomena in the movie that would have been hard to discover on paper plots.

The videomovie shows results from a 2-dimensional N-body simulation with 60 000 particles using a polar coordinate code. The disc is self-gravitating and surrounded by an inert spherical halo. It has Mestel's density distribution, which gives a flat rotation curve, and the companion is represented by a point mass which passes on an initially parabolic orbit.

The initially stable disc evolves as follows: A very sharply defined material arm quickly appears. After some time a counter arm is formed due to self-gravitation. Soon after the appearance of the counter arm, a third arm forms from the remains of the first material arm. This third arm has a higher radial velocity than the counter arm which makes it pass, or expand, through the latter. Some time later, after the passage of the companion, a density wave pattern, much more long lived than the material arms, is formed. The density waves first appear between the material arms giving the impression of a fork in the arm, such as has been observed in several galaxies. As the material arms are decaying when this happens, a fork would be a short lived phenomenon.

Introduction

In two contexts, this talk revisited an old idea – that any concentrated mass orbiting within a shearing disc tends to create an inclined and sometimes quite intense wavelike wake amidst the material that flows past it. More exactly, as actually delivered, this talk began with a fairly lengthy review of such swing-amplified wake-making in the gorgeous global setting of Zang's V = const disc, and only then did it proceed to my two main contexts.

Polarisation in the shearing sheet

One context was the idealized shearing sheet composed of thousands of identical softened mass points, with which I have been conducting a long series of numerical experiments in recent years. As I illustrated with slides and even with a homemade (!) movie, the typical impression there is one of an ever-changing kaleidoscope of “spiral” features, very much suggesting some sort of a recurrent strong instability in a system that really ought not to have any. Appearances aside, it turns in fact that those features are no instabilities. Instead, they are logically just superpositions of the separate wakes of the many random particles, each of which in this sense keeps acting simultaneously as both an aggressor and a victim. It is the collection of these wakes that forever keeps shifting in location and appearance as the individual particles constantly drift in this shear flow, but each particle in turn always carries along a wake of its own.

Introduction

High resolution (≤ 10 km s−1) spectra of a selection of symbiotic stars have been obtained using the Manchester Echelle Spectrograph and IPCS on the 2.5 m Isaac Newton Telescope on La Palma, as a preliminary to a high resolution survey of all known symbiotic stars now being conducted from the INT and ESO. In several cases, the [OIII] 5007 Å region shows complex structure, probably originating in extended outflows. However, the Hα line in many objects shows a well-known double-peaked profile (see e.g. Anderson et al. 1980). This is very reminiscent of those associated with dwarf novae, where observations through eclipse indicate that the emission originates in the accretion disc surrounding the white dwarf component of the semi-detached binary (see e.g. King, this volume).

If this were also the case with symbiotic systems, then theoretical modelling of the line profiles would enable us to constrain the all-important binary parameters. Our preliminary aim, however, is to determine whether such line profiles can be reconciled with emission from accretion discs at all. Anderson et al. (1980) concluded that the case still remained ambiguous.

The model

In order to construct theoretical line profiles from accretion discs, we have adapted the optically thick disc model of Home & Marsh (1986) producing double-peaked profiles which have a deep “V”-shaped central reversal. These match the observed profiles more closely than earlier (optically thin) models (e.g. Smak 1969).

Introduction

There is growing evidence for circumstellar discs associated with young stellar objects (YSOs). Motivated by observational evidence suggesting that these discs produce significant luminosity, LD ∼ L⋆, and have moderate masses, MD ∼ M⋆, (Adams, Lada & Shu 1988), we explore the possibility that the accretion mechanism ultimately owes its origin to the growth of spiral gravitational instabilities. As a start, we study the growth and structure of linear, global, gravitational disturbances in star/disc systems.

The physics of m = 1 modes

For simplicity, we take the unperturbed discs to be infinitesimally thin and in centrifugal equilibrium; we characterize the surface density and temperature profiles in the disc as power-laws in radial distance from the star. Since the potential well of the star dominates that of the disc everywhere except near the disc's outer edge, the rotation curve is nearly Keplerian throughout most of the disc's radial extent.

Our study concentrates on modes with azimuthal wave number m = 1, since these modes can be global in extent and may also be the most difficult modes to suppress in unstable protostellar discs. Modes with m = 1 correspond to elliptic streamlines (i.e. eccentric particle orbits), which play a unique role in Keplerian potentials, a fundamental point explicitly recognized by Kato (1983). In an exactly Keplerian potential, circular streamlines of zero pressure are neutrally stable to kinematic perturbations that make them ellipses.

Observations

While NGC 1068 has received much attention in recent years, little is known of the large-scale dynamics of the ionized gas in this nearby Seyfert galaxy. We have used the Hawaii Imaging Fabry-Perot Interferometer (HIFI, Bland & Tully 1989) at the CFHT to obtain detailed spectrophotometry at 65 km s−1 FWHM resolution for Hα and the [NII]λλ6548, 6583 lines. The final maps are derived from ∼ 100 000 fits to spectra taken at 0.4″ increments over a 200″ field-of-view. The flux-weighted Hα + [NII] velocity field is presented in Figure 1.

Deep images of NGC 1068 reveal an outer θ-shaped ring lying roughly east-west which encompasses a visibly bright, inner disc with diameter ∼ 20 kpc (230″), orthogonal to the outer ring. The Hα line flux is dominated by a luminous, elliptic ring of HII regions with diameter 3 kpc and major axis 45°. The “3 kpc ring” is aligned with an oval, bar-like distortion recently discovered at λ2µ (Scoville et al. 1988). The inner disc is marked by high concentrations of atomic and molecular gas (∼ 1010M⊙) which is thought to fuel the rapid star formation that characterizes the 3 kpc ring (Scoville et al. 1983). Most of the ring bolometric luminosity (1.5 × 1011L°), which is comparable to that of the active nucleus, emerges in the far-infrared as re-radiation from dust heated by young stars (Telesco et al. 1984).

From Figure 1, the large-scale disc appears to undergo flat rotation with V(Rmax) = 170/ sin i where Rmax ≈ 30″.

Introduction

A two stage mechanism for fuelling AGN is proposed which makes use of stellar dynamical and gas dynamical instabilities (Shlosman et al. 1989). First, a stellar bar sweeps the interstellar material inwards as a consequence of the gas losing angular momentum to the bar. In a second stage, the gaseous disc accumulated in the nuclear region of the host galaxy, goes bar unstable again and the material flows further in. The main criterion for the occurence of the second instability is that the mass of the gaseous disc must exceed some critical fraction of the total mass of the host galaxy. This critical mass fraction is of the order of a tenth or so according to our estimates. The inflowing gas may eventually join a viscosity-driven accretion disc if a black hole was already present or lead to its formation. If the host galaxy is relatively gas rich, but the disc formed during the first stage does not exceed the critical mass, or if the inflow of gas is halted around resonances, a nuclear starburst may follow. This mechanism may explain the association of bars and rings with nuclear activity and the dichotomy between AGN and starburst nuclei.

Gas in galaxies

The atomic and molecular gas content of spiral galaxies is observed to be in the range 108 – 1010 M⊙ and to peak at Hubble types Sb-Sbc (Haynes & Giovanelli 1984, Verter 1987).

Introduction

Large-scale magnetic fields could play an important role in the dynamics of astrophysical discs. Here we report some results showing how the structure of non-axisymmetric magnetic fields is affected by differential rotation. A turbulent disc is likely to be surrounded by a gaseous corona. We shall study in particular how the field structure in the disc is affected by surrounding gas.

We are interested in the question of the origin of galactic magnetic fields. It appears that an appreciable fraction of galactic fields are bisymmetric, i.e. the field in alternate spiral arms is in opposite directions (Sofue et al. 1988). This poses a problem, since on general grounds one expects that non-axisymmetric fields should be destroyed by differential rotation on a fairly short timescale. This difficulty would be avoided if it could be shown that a non-spherically symmetric distribution of turbulent diffusivity could actually lead to dynamo generation of non-axisymmetric fields, as was suggested by Rädler (1983) and Skaley (1985). For this reason, and also in order to avoid the uncertainties involved in assuming some specific model, we have not included an α-effect in these computations. Unfortunately, we have not found any growing field modes yet, but the decaying modes are of some interest in their own right.

Method and results

The evolution of the magnetic field is governed by the induction equation. We solve for the eigenmodes in a system consisting of a high-conductivity disc embedded in a low-conductivity corona using the so-called Bullard-Gellman formalism. For details of the model and numerical methods, see Donner & Brandenburg (1989) and references therein.

Introduction

It is known from stellar kinematics in the solar neighbourhood that the velocity dispersions of old populations are significantly higher than those of young populations. This implies a heating rate which seems hard to reconcile with known heating mechanisms such as stellar encounters or interactions between stars and molecular clouds, spiral structure etc… Our information elsewhere in the disc comes from fairly limited and biased samples that include line of sight velocities and, in some cases, distances (Lewis & Freeman 1989). This is insufficient to infer a velocity dispersion profile reliably. In this contribution we use a dynamical model and a large database of radial velocities of OH/IR stars to deduce the velocity dispersions as function of Galactic distance.

The data

Our catalogue of OH/IR stars is a compilation of the 1612 MHz maser surveys by teLintel Hekkert et al. (1989), Eder et al. (1988) and Sivagnanam & le Squeren (1986). The compilation yielded a total of 1600 positions and radial velocities. The positional information for these surveys was taken from the IRAS Point Source Catalogue (PSC).

In order to obtain an approximately constant BC1 (on average BC = 3.4), we selected only those stars from the OH/IR catalogue with an R212 between 0.0 and 0.9. Although the 1612 MHz surveys have been made with different radio telescopes, the catalogue has a well denned detection limit of 3 Jy (12µm), or 8 kpc assuming a luminosity of 5000 L⊙ for a given OH/IR star. We used Habing's (1986) luminosity distribution of the OH/IR stars for our modelling, recalculated for the above R21 range.

Abstract The observational evidence for the presence of discs around protostars and young stars consists of spectral and polarimetric data from which the existence of circum-stellar discs are indirectly inferred and data in which discs are directly imaged. A review of both the direct and indirect evidence for discs is presented as well as summary of the properties of these discs and their relationship to bipolar outflows and stellar jets.

Introduction

This review of discs associated with protostars and young stars stars is limited to two types of young stellar objects (YSOs): infrared sources (objects that emit only at infrared wavelengths) and optically visible T Tauri and FU Orionis stars. Current star formation models suggest that discs should commonly be associated with protostars and young stars. In fact, the flattened nature of our Solar system provides strong circumstantial evidence that discs have played a role in the formation of at least one star and planetary system.

Interest in circum-stellar discs has been heightened by the recent discovery of bipolar molecular outflows and stellar jets associated with many YSOs. An attractive model for the collimation and generation of energetic outflows assumes that accretion of material onto a young star through a viscous disc ultimately powers this energetic phenomenon. Unfortunately, direct imaging of these discs has proven difficult and only a few circumstellar discs have been unambiguously detected. Instead the efforts to detect circumstellar discs have frequently uncovered evidence for much larger structures, often called “interstellar discs”, surrounding YSOs.

Abstract Observed infrared and ultraviolet excesses have widely been interpreted as signatures for accretion discs around young stellar objects. Analyses of the observed properties of these discs are important for the investigation of star formation as well as the dynamics of the protoplanetary disc out of which the solar system was formed. Accretion disc theories suggest that evolution of protoplanetary discs is determined by the efficiency of angular momentum transport. During the formation stages, the disc dynamics are regulated by mixing of infalling material and disc gas. In the outermost regions of the disc, self-gravity may promote the growth of non-axisymmetric perturbations which can transfer angular momentum outwards. After infall has ceased, convectively driven turbulence can redistribute angular momentum with an evolutionary time-scale of the order 105−6 yr. Convection in protoplanetary discs may eventually be stabilized by surface heating as the disc material is depleted. Once the grains in the disc have settled to the midplane region, the disc can neither generate its own energy through viscous dissipation nor reflect radiation from the central star. Consequently, the infrared excess vanishes and the young stellar objects become “naked T Tauri stars.” Protoplanetary formation modifies the structure and evolution of the disc when giant protoplanets acquire sufficient mass to truncate the disc. In this case, a protoplanet's tidal torque opens up a gap in disc. Gap formation also leads to the termination of protoplanetary growth by accretion. The condition for a proto-Jupiter to acquire its present mass implies that the viscous evolution time-scale for the disc is of the order 105−6 yr which is comparable to the age of typical T Tauri stars with circumstellar protoplanetary discs.

Introduction

We apply the technique of smoothed particle hydrodynamics (SPH), a gas-dynamical Lagrangian numerical scheme, to analyse the non-linear response of a gaseous disc to an imposed potential. For the first time, we compare SPH and semi-analytical results for a galaxy model with small spiral pitch angles. Density amplitudes, phases and general density profile shapes, including the subtle effects of the n = 2 ultra-harmonic resonance, are in good agreement throughout the disc. We therefore establish the applicability of SPH to wide range of problems involving density waves in galactic discs.

The SPH scheme, which is based on kernel estimates of the physical parameters of the gas, has been described elsewhere (e. g. Gingold & Monaghan 1982, Monaghan & Lattanzio 1985). In SPH, gradients of physical quantities, such as pressure, are expressed as gradients of the kernel alone through an integration by parts. The resulting SPH fluid equations contain bulk flow parameters, such as the gas sound speed and viscosity, which are explicitly specified. This helps constrain the problem and permits a stringent test of the technique. SPH has some major advantages over the familiar grid-based schemes: first, there is no need to solve the continuity equation separately; second, the convective terms in the momentum equations are represented exactly; third, the mesh is adaptive – it becomes dense wherever the gas density becomes large – which is important in the highly non-linear flows often found in galaxies.

Introduction

We present a simple analytic description of the evolution of a captured galactic gas disc as it settles into a preferred orientation. These discs, which often display warps and twists (e.g. Cen A), are widely believed to arise from the tidal capture of gas from a nearby galaxy or the accretion of a gas rich companion. The newly formed disc will initially be unstable and evolve on both the precessional and viscous timescales. Differential precession causes a smooth continuous twist to develop. Cloud-cloud collisions within this twisted disc lead to the transport of angular momentum, causing changes in the orientations of cloud orbits and the inflow of material. Ultimately, the disc settles into a preferred orientation.

Steiman-Cameron & Durisen (1988) (hereafter SCD) derived three coupled differential equations governing the evolution of annular mass elements of a fluid disc including the effects of both orbit precession and viscosity. These equations, which describe the transport of angular momentum by Navier-Stokes stresses, describe the motion of orbit-averaged annular fluid elements. In general these equations must be solved numerically. However, analytic solutions are possible when: (1) disc precession is dominated by gravitational forces, with viscous forces being a minor perturbation. This condition is generally met. (2) The viscous timescale for inflow is much longer than the timescale for disc settling. This is true if condition four is met. (3) Settling takes place in an axisymmetric galaxy. However, if the initial disc inclination relative to a preferred orientation is small, then this condition is often approximately met even in triaxial potentials.

Observations

X-ray observations of the spectrum and variability of the Seyfert galaxy NGC 5548 were obtained with 2 instruments aboard the European X-ray satellite EXOSAT. The low energy (LE) experiment was an imaging device with a spatial resolution of 18″ (FWHM) on axis. It operated in the energy range of 0.05 – 2 KeV and has no intrinsic energy resolution, but multi-colour photometry was possible using different filters. We used data obtained with the 300 nm Lexan (3Lx), 400 nm Lexan (4Lx), Aluminium-Parylene (Al/Pa) and Boron (B) filter. The 3Lx and B filters in particular, have distinctly different spectral responses to AGN spectra. The medium energy (ME) experiment consisted of an array of 8 passively collimated proportional counters. It had no intrinsic position resolution, but spectra with moderate energy resolution in the energy range 1 – 50 KeV could be obtained.

The data set consists of 3 long observations in 1984 and 1986. Both components show correlated variability on a typical time scale of half a day. The variability amplitude is low: a few tenths. There is evidence for a delay of the hard X-rays with respect to the soft X-rays of 1 – 2 hour.

Spectral fit

The spectra were fitted by a power law plus a soft excess, which we modelled by a modified blackbody spectrum. In fact, other two-parameter models for the soft excess (like a simple blackbody or thermal radiation) also yield acceptable fits; the modified blackbody is chosen in order to be consistent with the disc model to be discussed below.

Introduction

Low-mass X-ray binaries (LMXB) are semi-detached binary systems consisting of a mass-losing late-type star and a compact object (neutron star or black hole) which is surrounded by an accretion disc fed by mass loss from the late-type companion. Soft X-ray transients are unique in this group by showing outbursts with recurrence time of 0.5 – 50 years, rise time scale 2 – 10 days, and decline time scale of order of a month (for recent reviews, see e.g. White et al. 1984; van Paradijs & Verbunt 1984; Priedhorsky & Holt 1987). Two models are proposed for outbursts of soft X-ray transients: the disc instability model (Cannizzo et al. 1985), and the mass-transfer burst model (Hameury et al. 1986).

Thermal Instability of Accretion Discs

As the first step, we integrate the vertical structure of the disc in LMXB following the method described in Mineshige & Osaki (1983). We scale the viscosity parameter α = α0(h/r)n, where α0 and n are numerical constants and h represents the semithickness of the disc. We also assume that the effects of X-ray illumination of the outer disc by the central disc are negligible. We find that for relevant accretion rates, the disc suffers a thermal instability due to the ionization and recombination of the hydrogen and the helium, leading to intermittent accretion onto the central compact object, similar to models for the outbursts in dwarf novae (Osaki 1974; Meyer & Meyer-Hofmeister 1981)

Description of simulation

In an effort to better understand disc galaxies, we have developed a Cartesian, 2-D, N-body and hydrodynamic computer code. The results presented here use only the N-body portion of the code. To accommodate the variable time-step length required by the Courant condition for hydrodynamic flows, we use a second order predictorcorrector integration scheme (Schroeder & Comins 1989) with the same accuracy as the more familiar time-centred leap frog scheme.

The particles are distributed as a Kuz'min disc, and we add a fixed ‘halo’, having between 65% and 75% of the total gravitational potential, to stabilize the system against bar-mode instabilities. Tangential and radial velocity dispersions establish an initial Toomre Q of 1.0 over the disc. The resulting disc appears to be stable to nonaxisymmetric perturbations.

We add a rotating, logarithmic, two-armed, spiral perturbation to the potential. The amplitude of this spiral is ramped up and down as a Gaussian (Toomre 1981). This spiral perturbation grows from 2% of its maximum amplitude to full strength in 1/2 a rotation period and then decays in the same manner. Both trailing arm spirals (TASs) and leading arm spirals (LASs) are used with varieties of pitch angles and pattern speeds. All such perturbations lead to strong non-axisymmetric responses in the disc. Unless indicated otherwise, the pattern speed of the perturbation is 1/2 the co-rotation speed of the particles at the half-mass radius. Final Qs range between 1.1 in the interior and 3.5 near the disc edge.

Physical processes

We distinguish between the two possibilities indicated in the title by analysing the physical process operating in the β Pic system. Based on recent models of the disc (Artymowicz et al. 1989) and the information on gaseous constituents of the disc (Vidal-Madjar et al. 1986, Lagrange-Henri et al. 1988) we consider the following processes, which we expect to determine the size distribution of grains and influence the disc appearance:

1. 1 Inter-particle collisions. In the densest parts of the disc (∼ 20 to 50 AU from the star) grains collide typically once in several hundred orbits (∼ 103 yr). At 100 AU, the time-scale is 105 yr and at 1000 AU of order 108 yr. The outcome of a typical collision, which from our knowledge of the disc geometry occurs at impact speeds ∼ 0.1 times the local Keplerian velocity, is the erosional cratering of larger particles and the destructive shattering of smaller ones. No agglomeration through grain sticking is possible.

2. 2 Poynting-Robertson (P-R) effect. In most previous work, the P-R drag was suggested to play a dominant role. This is not correct. The P-R time-scale for even the smallest (∼ 2 µm-sized) particles is too long, ∼ 4 × 106 yr at 100 AU and increasing with the square of the radius. Whenever collisions act on shorter time-scales, the P-R drag effectively acts on the total mass of the disc, not just the smallest grains, hence the time-scales given are merely lower limits.

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