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.

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.