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The main result of our work is the finding that the simple picture of a spiral galaxy, consisting of a nuclear bulge ana an axially symmetric disk, with superimposed on it the spiral structure, is inadequate. Several large scale deviations from axial symmetry can be noted in the velocity fields. Two of them are symmetric about the centre: oval (broadly elliptical) distortions and.warps. In both cases the kinematical major axis changes its position angle with radius. In the case of an oval distortion this occurs in the inner parts, and there is a misalignment with the major axis of some of the optical structures; in the case of a warp this occurs in the outer parts, and there is alignment in the inner parts with the major axis of the bright optical disk. A number of spiral galaxies are so asymmetric in the outer parts that it is not possible to infer the geometry of the outer parts from simple arguments. Also small scale irregularities are found in all spiral galaxies, e.g. one half of a galaxy has not the same properties as the other half.

The presence of all these deviations from axial symmetry makes the determination of the axisymmetric properties difficult and sometimes impossible. For the symmetric deviations from axial symmetry it is possible to construct simple kinematical models to describe them, although at present this has not been done for many galaxies. The effects on the rotation curve of the presence of spiral arms has been studied for the galaxy M81 by Visser (1978), who found that corrections are necessary. The correction procedure is, however, dependent on some of the assumption made on the nature of spiral arms (i.e. their density wave character)

Oval distortions and warps are still so poorly understood that we can only make simple kinematical models without knowing how they are related to actual dynamical processes. In the case of oval distortions we think that there are structures in the main plane of the galaxy which cause the gas to move in broadly elliptical orbits rather than in circular ones. In the case of warps we have assumed that the gas moves in circular orbits in different planes. In some cases the warp can be seen directly in the HI distribution (edge-on galaxies); in other cases the warp has to be inferred from the kinematics (kinematical warps). The distinction between oval distortions and kinematical warps is ambiguous because the projection onto sky of a circle in one plane and an ellipse in another plane can result in the same ellipse. Nevertheless, apart from the question of alignment of axes with the optical pictures, we find that in the case of oval distortions the HI distribution, especially in earlier type galaxies, has distinct features in the outer parts, coinciding with optical emission, while in the case of kinematical warps the HI distribution continues smoothly outwards, usually beyond the optical emission visible on sky-limited IIIaJ-plates, and changing its orientation in the same way as inferred from the velocity field.

In the derivation of rotation curves we have made simple assumptions which are in most cases (ovals and warps) not backed up by an adequate theory. Therefore we must consider the results from the rotation curve analysis with a certain scepsis. We have constructed models of the mass distribution which are based on the thin disk approximation. Such models, which are relatively simple and do not have many free parameters, can only give an estimate of the amount of mass at different radii in a galaxy; the distribution of this mass in the perpendicular direction remains open. In the inner parts of galaxies the 21-cm data are affected by beamsmoothing, and in about half of the galaxies in our sample it was not possible to correct for this effect.

Nevertheless, we arrive at a few interesting conclusions from these mass models. The curves of mass within a cylinder of radius R, M(R), do not converge to a definite value in the outer parts; in other words: there must be a substantial amount of mass outside the radius of the last measured point on the rotation curve, Ro. For most of the 25 galaxies for which we calculated mass models R is larger than the Holmberg radius. In the log M - log R plane the curves of M(R) separate. The separation is correlated with the mean rotation velocity, Vm, indicating that galaxies with a high Vm are more densely packed than galaxies with a low Vm. We find that the mean mass-to-luminosity ratio is independent of type, colour or luminosity, and that the local M / L ratio increases with radius in most galaxies. The local ratio of total mass to HI gas mass density decreases with radius, but in the outer parts it tends to be more or less constant. For galaxies with large Vm this ratio is larger than for galaxies with small Vm. If we estimate corrections for the contributions of molecules to the total gas density, and if we accept that abundance gradients exist we arrive, on evolutionary grounds, at the conclusion that the mass function of stars must be different at different radii in a galaxy, in agreement with the increase in the mass-to-luminosity ratio.

We do not find simple correlations between the derived physical parameters and the morphological classes. Oval distortions are obviously associated with SB, SAB, RSA (outer ring), and PSA (pseudo outer ring) - spirals and the prominence of the distortion decreases towards later types. Warps are apparently not correlated with type, although a warped early type barred spiral has yet to be found. From the rotation curve analysis we do not arrive at conclusions which transcend those inferred from the studies of the integral properties. The correlations with Vm mentioned above are, of course, also correlations with luminosity class. The local gas mass to total mass ratio in the inner parts is much lower for early types than for late type spirals. Likewise the rise in the rotation curve is relatively steep for early type galaxies and slow for later type galaxies. But all these correlations are not one-to-one correspondences, and the uncertainties and difficulties we meet along the way to derive physical properties prevent definite conclusions.

At various places in this thesis we have already indicated what kind of future work can be done to get a better understanding of certain problems. The following list of suggestions is partly a recapitulation of those suggestions and contains some other ones, but it is of course not exhaustive. We limit ourselves to observational work which in our opinion can be used as a guidance towards a better theoretical understanding.

1. Oval distortions: These are closely connected to the whole barred spiral problem. Detailed studies (surface photometry, 21-cm line studies and kinematics from optical spectroscopy) of a carefully selected sample of SB and SAB galaxies will almost certainly be helpful in the understanding of these objects.

2. Warps: For edge-on galaxies it is easy to find out whether there is a warp or not. Thus a statistical study in the 21-cm line of several tens of galaxies can provide information on the frequency of occurrence of warps. For more face-on galaxies it would be of interest to know whether there is any warping in the disk made up by the old stars: perhaps surface photometry in the (near infra-)red can be of help.

3. Large scale asymmetries: For a number of late type spirals having these asymmetries it would be interesting to see whether the population II disk is distorted in the outer parts: in M101, for example, the main distortions are seen in the gas and the young stars.

4. Rotation curves: Observations of a few regular galaxies far out, in between two to four times the Holmberg radius, would be extremely useful to find out whether rotation curves remain indeed flat over large distances (not to be done with single dishes, because of the sidelobe problems, see chapter 6.1).

5. M / L and sigmaM / sigmaHI: It would be useful to obtain for a few regular galaxies information on the different stellar populations, from multi-colour surface photometry, to compare this with the radial distributions of M / L and sigmaM / sigmaHI.

Finally, the physical significance of the morphological classification schemes can be best studied by solving first the problems mentioned above: We have found in chapters 5, 6 and 7 that there 4 are many difficulties on the road to the determination of reliable mass distributions in different spiral galaxies; these have to be understood better, before a new attempt to relate the morphological schemes to physical parameters will be successful.


Visser, H.C.D.: , University of Groningen

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