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.

3. […]

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.