Stellar orbits in the plane of a strong bar potential demonstrate the breakdown of the second integral of motion well inside corotation (Sanders(1980) and more recently Contopoulos (1982), Athanassoula et. al. (1983), Sanders and Teuben (1982)).

One way of approaching the problem of a selfconsistent bar, is to examine the orbits of the stars which make up the bar. Given that there are 1010 such stars and therefore 1010 such orbits, one has to devise a way of studying and classifying them. Once one knows the most important types of orbits which appear in a system and when they appear, can proceed in constructing a selfconsistent bar.

We know far more about the velocity and density distributions of gas in ordinary spirals than in barred spirals. There are several reasons for this : the absence of a nearby barred spiral, the circumstance that several of the best objects lie rather far south, the necessity to map in two dimensions, and the surprisingly low intensity of the emission lines, except in the nucleus and near the ends of the bar. The older literature contains several investigations of radial velocities measured along the bars of barred spirals (cf. Burbidge, Burbidge and Prendergast, 1960 a,b for NGC 7479 and NGC 3504), and it has been known for some time that rotation curves taken in different position angles through the nuclei of barred spirals are not compatible with simple circular motion. It was not until recently, however, that attempts were made to map the velocity fields of barred spirals in two dimensions. Chevalier and Furenlid (1978) studied NGC 7723, NGC 5383 has been mapped by Peterson, Rubin, Ford and Thonnard (1978) in the optical and by Sancisi, Allen and Sullivan (1979) in neutral hydrogen, and NGC 1300 has been mapped by Peterson and Huntley (1980). The most striking result of these observations is that the isovelocity contours are elongated in the direction of the bars, or, put differently, there is no straight line through the center of a barred spiral along which the radial velocity is constant. This is clear proof that significant non-circular motions are present in these galaxies. However, as it is impossible to reconstruct a non-axisymmetric velocity field from radial velocity data alone, there is no analog for barred spirals of the reduction models which are used to estimate local mass densities for ordinary spirals from observed rotation curves.

One purpose for studying the gas flow in barred spiral galaxies is to use the observed distribution and kinematics of the gas as a tracer of the underlying gravitational field. By comparing model hydrodynamical calculations with observations of actual systems, one would like to define three basic properties of barred galaxies:

1. 1) The bar strength. How significant is the deviation from axial symmetry in the region of the bar, measured by some parameter such as qt, maximum aximuthal force in terms of the mean radial force (Sanders and Tubbs, 1980).

2. 2) The mean radial distribution of matter. Clearly in a system with large deviations from circular motion, the “rotation curve” gives no direct information on the radial mass distribution.

3. 3) The angular velocity of the bar. Where is the co-rotation radius (or Lagrange points) with respect to the bar axes? Are other principal resonances present?

How a bar potential can force a spiral structure in the gas component is now well understood. This response is due to the dissipative character of the gas. Results of the computations of the response differ greatly with the numerical code adopted, either particle (Schwarz 1981), or hydrodynamic (e.g. Sanders and Huntley, 1976) and within a given code, with the spatial resolution used, since the artificial viscosity is thus varied (see e.g. van Albada et al 1981). According to observations, the gas component is mostly cloudy. Hence our aim is to compute the response to a bar potential of the ensemble of molecular clouds for which collision rate (and therefore dissipation rate) is relatively well-known. Using a particle code and explicitly treating the collisions between clouds, the viscosity parameter is more easily controlled and less artificial. Also, since the mass transfer between clouds is taken into account, we will obtain insight into the formation of large molecular clouds, which are the preferential sites of active star formation.

This paper is a progress report on a research project studying the gas flow in barred spirals. The parametrization of the potential and the gasdynamics code being used are described in section 1, some preliminary conclusions and a sample result are presented in section 2.

NGC 5383 has often been used as a prototype of SB(s)b type galaxies, particulary in studies of gas flow. We have therefore set out to complement the existing data with surface photometry, velocity measurements in the bar and a dynamical model.

NGC 1365 is a galaxy which has lately received a lot of attention from people studying the structure and dynamics of barred galaxies. This is not surprising since it is one of the best suited objects in the sky. We have obtained a number of long-slit spectra in the red region (Hα, [NII], [SII]) with the ESO 3.6 m (Lindblad and Jörsäter) and with the CTIO 4 m (Peterson) telescopes. In addition, a couple of Fabry-Perot Hα interferograms have kindly been given to us by G. Comte and Y. Georgelin. Some preliminary results are presented here. Fig. 1 shows the positions of measured velocity points. The digits along the vertical axis indicate distance from the nucleus in seconds of arc. The dashed line at P.A. 48 deg indicates the line of nodes as determined from photometry of the outer features of the galaxy (Lindblad 1978). An arbitrary isophote has been sketched to aid the orientation. The emission lines in the bar are surprisingly weak which is the reason for the scarcity of velocity points there. Fig. 2 shows a rotation curve based on the P.A. of the line of nodes of 48 deg and an inclination of 55 deg (Lindblad 1978). Only velocity measurements within 50 deg of the line of nodes have been used in this diagram in order to avoid large projection errors. The distance used is 20 Mpc. The spread is quite large indicating a significant amount of non-circular motion.

In this paper we present preliminary results from 21-cm line observations with the Very Large Array (VLA) of the southern barred spiral galaxies NGC 1365 and NGC 1097. Despite a wealth of theoretical models describing the gas flow in a non-axisymmetric bar potential (see Prendergast this volume), few observations of the HI distribution and motions in barred spiral galaxies exist. A notable exception is NGC 5383 (Sancisi et al. 1979). The observations we performed with the VLA are described below. The velocity resolution is 25 km sec−1. The angular resolution is 28″x20″, p.a. 20° for NGC 1365 and 30″x25″, p.a. 20° for NGC 1097. Velocities are heliocentric.

We report observations of the atomic hydrogen properties of the barred spiral galaxies NGC 3992 and NGC 4731. These systems were observed in 1980 and 1981 with the VLA telescope of the National Radio Astronomy Observatory. In Table 1 we list the systemic parameters of interest.

The type of this galaxy (SB(s)cd) is intermediate between symmetrical early type galaxies and asymmetric late-type barred spirals. Three different components are clearly seen: a bar (B), a central disk (c) and an extended disk (d).

We have studied the flow of gas in barred spirals in which the centers of the bar and the disk do not coincide. This is often observed in late type galaxies like the L.M.C., NGC 1313, NGC 4618 etc…

In continuation of former work (Feitzinger 1980) the morphological structure of 68 SB(s)m systems, greater than 2!5 on ESO/SRC survey plates, was investigated. Three morphological features should be mentioned:

1. 1. Stellar bars located asymmetrically with respect to the disk are found in 70% of the cases; the displacement relative to the disk diameter is Λ = 0.1 − 0.35.

2. 2. The disk is populated in 45 % of the cases by chains of HII regions (spiral arm filaments).

3. 3. Though not very frequent nearly 25 % of the SBm systems have a dominating HII region near the outer periphery and predominantly near one end of the bar.

Both inner rings and outer rings are frequently observed in disk galaxies (de Vaucouleurs, 1963 and 1975). As an example, Fig. 1 shows NGC 2217 in which both occur. Further examples, e.g. NGC 2859 and NGC 3081, can be found in the Hubble Atlas (Sandage, 1961), the Revised Shapley Ames Catalogue (Sandage and Tammann, 1981), and in the morphological study of nearby barred spirals by Kormendy (1979). In this talk I will concentrate on some theoretical questions concerning rings, and in particular on their formation.

The 21.65-“law” for disk galaxies has been debated ever since Freeman's (1970) paper in which he found that for 28 out of 36 galaxies the extrapolated central surface brightness of the exponential disk component I0, follows this rule with little intrinsic scatter. Some people think it significant, while others invoke selection effects. Bosma and Freeman (1982) made a new attempt to clarify this problem by studying ratios of diameters of disk galaxies on the various Sky Surveys in a region of overlap. The limiting surface brightness levels were calibrated to be 24.6 and 25.6 magn/arcsec2 for the Palomar blue prints and the SRC J films, resp. The distribution of the ratio Γ = diameter (SRC) / diameter (PAL) gives a measure of the true distribution of Io if the galaxy has an exponential disk in the brightness interval 24.6 to 25.6; e.g. Io = 21.6 corresponds to Γ = 1.32, Io = 22.6 to Γ = 1.50 and Io = 23.6 to Γ = 1.90, etc.

The form of the velocity and velocity dispersion profiles in elliptical galaxies, and their implications for anisotropy and mass-to-light ratio changes in ellipticals are discussed. Recent results on the luminosity dependence of the rotational properties of ellipticals are summarized, as are questions concerning the shapes of ellipticals. The relation of bulges to ellipticals, in the light of these new data, is considered.

The following discussion is based on a paper of the same title co-authored with Allan Sandage in the January 1, 1983 Astrophysical Journal.

During the last seven years we have become much more aware of the importance of velocity anisotropy in spheroidal components. There were never any sound arguments for assuming that the velocity ellipsoids in spheroidal components would be spherical, but the mathematical convenience of this assumption is such that velocity anisotropy was either absent from or unimportant in the models that seemed so promising at the last Besancon meeting in 1974. With the advent of accurate velocity information from absorption-line studies of early-type systems, it became apparent that the real world is a good deal more complex than it might have been, and the theoretical situation is now less satisfactory than it seemed in 1974. All I can do here is to report on our somewhat painful efforts to pick ourselves up from the floor to which the observers knocked us in 1975–7.

The possible equilibrium configurations for elliptical galaxies and the bulges of spiral galaxies are no longer thought to be confined to the small class of axisymmetric systems with isotropic velocity dispersions. Many of these systems are not supported by rotation but instead by anisotropic velocity dispersions which are maintained by nonclassical integrals of motion (e.g., Binney 1978), and may be triaxial. Few theoretical models for such systems exist (Schwarzschild 1981). Here we discuss some axisymmetric models that we have constructed by means of Schwarzschild's (1979) selfconsistent method, and in particular their stability.

Many elliptical galaxies may be slowly rotating, moderately triaxial systems. Their dynamics are probably characteristic of a 1:1:1-resonance between the frequencies of oscillation along the three principal axes.