Spiral structure in galaxies can arise from both dynamic and non dynamic phenomena: spiral density waves and stochastic selfpropagating star formation. The relative importance of these effects is still not known. Deficiences of the original selfpropagating star formation model (where only stars are taken into account) are overcome by explicitly considering the stars embedded in and interacting with a two-component gas (Seiden and Gerola, 1979; Seiden, Schulman and Feitzinger, 1982; Seiden and Gerola, 1982). The two-component gas is essential because it is the means by which we get feedback in the interaction between stars and gas. The coupling between stars and gas regulates and stabilizes star formation in a galaxy. Under proper conditions this model can give good grand design spirals (Fig. 1).

Yuan and Wallace (1973) explained the “Rolling motion” in galactic spiral arms by geometrical means as apparent, but not actual motions. Strauss and Poeppel (1976), however, could demonstrate, that these geometrical effects are not sufficiently large to produce the rolling motions. The aim of this investigation is to explain the remaining part of the rolling motion effect with the galactic fountain model (Bregman 1980).

Numerical calculations of spiral shocks in the gas discs of galaxies (1,2,3) usually assume that the disc is flat, i.e. the gas motion is purely horizontal. However there is abundant evidence that the discs of galaxies are warped and corrugated (4,5,6) and it is therefore of interest to consider the effect of the consequent vertical motion on the structure of spiral shocks. If one uses the tightly wound spiral approximation to calculate the gas flow in a vertical cut around a circular orbit (i.e the ⊝ -z plane, see Nelson & Matsuda (7) for details), then for a gas disc with Gaussian density profile in the z-direction and initially zero vertical velocity a doubly periodic spiral potential modulation produces the steady shock structure shown in Fig. 1. The shock structure is independent of z, and only a very small vertical motion appears with anti-symmetry about the mid-plane.

Preliminary Hα observations with the TAURUS imaging spectrometer confirm a pattern of systematic radial motions in a section of spiral arm in M83. The velocity gradients are not consistent with those predicted for the neutral gas.

Non-circular motions have also been discovered in the central regions of the galaxy.

In a previous paper, (Comte and Duquennoy, 1982), we have reported observations of the distribution and kinematics of the ionized hydrogen in the large southern spiral NGC 1566 (SAB(r?s)bc I). We found evidence for a severe warping of the galactic disk, and discussed the spiral distribution of 477 detected HII regions. The observed spiral structure, deduced from the positions of the regions deprojected in a (ln r, θ) diagram, shows a four-armed design (Fig. 1):

An objective method involving a Fourier analysis is applied to seven galaxies for measuring the strength of spiral and bar components.

Fourier analysis of the observed distribution of spiral tracers (e.g. HII regions) can yield a wealth of information about the spiral structure of a given galaxy. A description of the method has been given by Kalnajs (1975) and, in brief, involves decomposing the observed distribution into components with given angular periodicity m. Component m = 0 corresponds to the axisymmetric part, m = 1 to either a one-armed spiral or an asymmetry, m = 2 to a spiral or a bar, etc. Each component is then analysed into a superposition of logarithmic spirals. This does not imply that the observed spirals are assumed to be logarithmic, but rather that logarithmic spirals are convenient building blocks.

A magnetohydrodynamical result is deduced, which could contribute to our understanding of spiral and ring structures in galaxies. The usual expressions for the continuity, momentum and induction equations are adopted for the gas of a galaxy, and the following simplifying hypotesis are made : a) Steady state conditions, b) Axisymmetry, c) A velocity field given by (π=0, θ=θ(r), Z=0) for the interstellar gas (where π,θ and Z are the radial, azimuthal and vertical to the galactic plane components and r is the distance from the galactic center). Then, the direction of magnetic field must be azimuthal and the plasma distribution is compatible with ring structures.

Interstellar magnetic fields are known to be a constraint for star formation, but their influence on the formation of spiral structures and the evolution of galaxies is generally neglected. Structure, strength and degree of uniformity of interstellar magnetic fields can be determined by measuring the linearly polarised radio continuum emission at several frequencies (e.g. Beck, 1982). Results for 7 galaxies observed until now with the Effelsberg and Westerbork radio telescopes are given in the table. The Milky Way is also included for comparison.

Recent studies (Frenk and White 1980, 1982) of the (x, y, z) and (Π, θ) distributions of the Galactic globular cluster population have given Ro = 6.8±0.8 kpc and Π = 51±26 kms−1 for the inner halo. The observations leading to these solutions are well illustrated by the ρ vs. x plot in figure 1 (Clube and Watson (CW), 1979) for the globulars with the best determined data within |l|, |b| < 20°. The independently determined Ro value clearly divides the distribution in such a way that most of the objects on the nearside of the G.C. approach the Sun while those on the farside recede, the probability that this arrangement arises by chance from a “stationary” distribution being ~ 0.002.

This is a critical and selective review of current theoretical and observational work related to spiral structure in disk galaxies. Productive future areas of research are suggested.

The large-scale warps of disk galaxies remain a challenge for theorists. Recent speculations about their origins or longevity have tended to focus on the possible benefits of halos. After some remarks about modes, this review will do likewise. It will conclude that any applause even there can as yet be only scattered rather than thunderous.

The current suggestions for the origin of warps in disk galaxies (see Toomre, this volume) find difficulties in explaining their frequent occurrence and an external driving mechanism seems to be required in order to maintain long-lived warps. Such a mechanism can be provided by an extended dark halo if a) it dominates the gravity at large radii while the inner disk is self-gravitating, b) it is slightly flattened and becomes flatter at larger radii, and c) it is tilted relative to the inner disk. Such a configuration may be formed as a result of tidal encounters, or of clouds infalling into halos.

Orbit calculations were done in a rotating triaxial system with a density distribution in accordance with recent observations of spiral galaxies. A search was made for simple closed orbits which are tilted with respect to the plane of the galaxy. A family of stable prograde tilted orbits was found which can explain warps as stationary phenomena.

A brief review is given of the morphology of barred galaxies, following Kormendy (1981, 1982). The features illustrated include bulges, bars, disks, lenses, and inner and outer rings.

Most of the paper is devoted to a detailed discussion of the absorption-line velocity field of the prototypical SBO galaxy NGC 936. The stars in the bar region show systematic non-circular streaming motions, with average orbits which are elongated parallel to the bar. Beyond the end of the bar, the data are consistent with circular orbits. The bar region also shows large random motions: the velocity dispersion at one-half of the radius of the bar is 1/2–2/3 as large as the maximum circular velocity. The observed kinematics are qualitatively and quantitatively similar to the behavior of n-body models by Miller and Smith (1979) and by Hohl and Zang (1979). The galaxy and the models show similar radial dependences of simple dimensionless parameters that characterize the dynamics. These include the local ratio of rotation velocity to velocity dispersion, which measures the relative importance of the ordered and random motions discussed above. Also similar are the residual streaming motions (relative to the circular velocity) in a frame of reference rotating with the bar. Circulation is in the same direction as rotation in all galaxies studied to date. Thus, except for the fact that NGC 936 has a slightly larger velocity dispersion, both n-body models are good first-order approximations to bars. Thus bars are different from elliptical galaxies, which in general are also triaxial, but which rotate slowly. This study of NGC 936 will be published in Kormendy (1983).

A brief discussion is given of the kinematics of lens components. In both barred and unbarred galaxies, the velocity dispersions in the inner parts of lenses are large. The ratio of rotational to random kinetic energy is ∼ 1/2 at 1/3–1/2 of the radius of the lens. This ratio then decreases to small values at the rim of the lens. Thus at least some kinds of disk components have large stellar velocity dispersions, even in unbarred galaxies.

What has prevented the formation of a strong bar in the majority of disc galaxies? No truly satisfactory answer has yet been given to this question and the difficulty remains a major obstacle to our understanding of the dynamics of these systems. In this review, I will discuss the implications of recent studies of this problem.

We use computer simulations to determine the dominant unstable modes of stellar discs having the surface density distribution of Toomre's (1963) model 1 and large random motions in the plane. Particles in the models have their initial coordinates chosen from distribution functions to ensure that the configurations would, in the limit of infinitely many particles, be stationary solutions of the Vlasov and Poisson equations. The 40,000 particles in our simulations are constrained to move on a plane and we use a polar grid based Fourier method to determine the force field (Sellwood 1982). The surface density is smoothly tapered to zero at six scale lengths and the softening length is 1/30th of the outer radius of the disc.

Massive “dark” halos are currently believed to surround individual galaxies and systems of galaxies primarily because: (a) individual galaxies exhibit “flat” rather than Keplerian rotation curves (see the review by Faber and Gallagher 1979); (b) the measured ratio of mass to light in systems of galaxies continues to increase roughly linearly with radius as one observes larger and larger systems (Rood 1982); and (c) rapidly spinning “cold” stellar disks are not dynamically stable if they are fully self-gravitating (Ostriker and Peebles 1973). It can be shown, however, that properties (a) and (b) of galaxies and systems of galaxies can be explained without invoking dark halos if one assumes that the force of gravity has the form where r is the distance between the attracting bodies of masses M and m, and the scale “a” must assume a value a ∼ 1 kpc. (See Milgrom 1982 and Bekenstein, these proceedings, for a discussion along similar lines.) Newton's Law is retrieved on scales « a but the force is proportional to 1/r on scales » a. Equation (1) should not be adopted in place of Newtonian gravity to explain the dynamical properties of galaxies unless it also explains property (c) without invoking the presence of dark halos.

As a generating mechanism of spiral structure, we have recently studied the driving of density waves in the stellar component of disk galaxies by growing barlike perturbations or oval distortions. Numerical experiments (Thielheim and Wolff 1981, 1982) as well as analytical calculations using the first-order epicyclic approximation (Thielheim 1981; Thielheim and Wolff 1982) have been performed, demonstrating that this mechanism is capable of producing two-armed trailing spiral density waves in disks of noninteracting stars. These regular, global spiral structures are similar to those found in N-body experiments on self-consistent stellar disks that show bar instabilities which are weak enough to allow spiral patterns to persist (e.g., Hohl 1978; Berman and Mark 1979; Sellwood 1981). On account of this similarity, we take the view that the spiral structure observed in N-body experiments is primarily not an effect of the self-gravity of the stellar disk but a response phenomenon, caused by the formation of a weak central bar and its subsequent growth due to angular momentum extraction by interaction with the spiral as described by Lynden-Bell and Kalnajs (1972).

A preliminary step towards the construction of self-consistent models for barred galaxies consists in understanding the stellar orbital behaviour in a given axisymmetrical + bar-like potential and, in particular, the influence of various parameters characterizing the bar on the different kinds of possible motions. To do this we undertook a systematic study of the main periodic and quasi-periodic orbits in a two-component mass model: An axisymmetrical part characterized by a rotation curve V(r) = Vo (r/ro)1-δ and a prolate bar-like perturbation whose density distribution is ρ = ρo (1-(x2+z2)/b2-y2/a2)2(a>b). This rather realistic choice for the bar is in agreement with the available photometric data and has several advantages, i.e. all cos(mθ) terms are included and the physical parameters such as the length of the bar a or its eccentricity e are explicitly included in the formulae. The ratio of bar to disk mass measured up to the outer Lindblad Resonance (ε) and the angular velocity (ωs) are also free parameters.