Annu. Rev. Astron. Astrophys. 1978. 16: 103-39
Copyright © 1978 by . All rights reserved

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3.1. Rotation Curve Shape and Galaxy Morphological Type

Rotation curves determined by the methods outlined above are usually characterized by a rise in the inner regions to some value Vmax at a radius Rmax, followed by a slow decline or a more-or-less constant level further out. For a detailed comparison between rotation curves and galaxy morphology one would like to have observational results spanning the range of types and, within each type, the range of luminosities. Needless to say such an extensive sample does not yet exist, although some fragments of it are becoming available. From rotation curves measured over a large part of the optical disks of M81 (Sab), M31 (Sb), and M101 (Scd), as shown in Figure 2, Roberts & Rots (1973) suggested that the mass distributions of Sa galaxies were indeed more centrally condensed than those of the Sc galaxies, as had long been inferred from the distribution of optical light. This characteristic should appear as a faster rise to Vmax, i.e. a smaller ratio of Rmax to some other, presumably constant, scale size such as the Holmberg photometric radius RH0. The ratio Rmax/RH0 has indeed been found to decrease towards the earlier morphological types in the larger samples of observations made at lower angular resolution (Brosche 1973, Huchtmeier 1975). Shostak (1977, 1978) has determined a relation between the form of the total integrated HI profile and morphological type for galaxies from Sbc to Irr and has suggested that this relation can be understood to be the result of an increase in Rmax relative to the HI size for the later types. The result is noteworthy also in that it is available from the integrated profiles, i.e. the extreme of no angular resolution at all, where the sample is largest and where observations can be most rapidly obtained.

The correlations described above have been interpreted in terms of the galaxy dynamics by Wakamatsu (1976) in a manner consistent with earlier notions based on the optical appearance of a galaxy; the bulge component becomes progressively more prominent relative to the disk as one moves from the Sc to the Sa galaxies. Although the relation between bulge-to-disk ratio and morphological type is not ideal (van den Bergh 1976), it does seem to hold on the average (Freeman 1970a, Yoshizawa & Wakamatsu 1975, de Vaucouleurs 1977).

We turn now to another dimension of the observations, namely the differing luminosities within each type (see footnote 2). Rogstad & Shostak (1972) analyzed the rotation curves of five correlation of the maximum rotation velocity Vmax with the Holmberg radius RH0. As, indicated above, Rmax scales with RH0 within a particular type. Therefore, if the forms of the rotation curves are reasonably similar, then the total mass of a galaxy (proportional to Rmax/Vmax) within the Scd type can apparently be characterized by a single parameter. Enlarging the sample any further is again possible only at the expense of giving up angular resolution. Shostak (1975) found for Scd galaxies that the inclination-corrected width of the integrated HI profile DeltaV(0) (which should be close to 2 Vmax) increases with the linear Holmberg radius.

Tully & Fisher (1977) have discovered an important correlation of DeltaV(0) with total optical luminosity for a sample of galaxies of many types. In an extensive numerical analysis, Brosche (1971) found that Vmax decreased towards late types and was nearly independent of Rmax (Brosche 1973). His correlation between Vmax and type can be understood also as a correlation between Vmax and luminosity (which in fact follows from his 1973 paper), since the later-type galaxies have statistically lower luminosities; it is therefore consistent with the relation determined by Tully and Fisher.

The results described above are so far consistent with the following highly simplified summary; with respect to a photometric radius Rph , Rmax decreases from late to early types, reflecting the increasing importance of the bulge; within a given type Rmax/Rph is roughly constant and Vmax increases with luminosity, reflecting an increase in the total mass. The former is consistent with the traditional interpretation of the morphological sequence, and the latter with the observation that the M/L ratio is roughly the same for all types of galaxies. It is immediately clear that this summary is almost certainly inadequate; however, the available observations are equally inadequate to provide a much more detailed picture. We may see an improvement in the situation in the coming years as the number of optical and high-resolution radio-HI observations of galaxy velocity fields steadily increases.

In this respect the observations have been outrun by the extensive theoretical work of Roberts et al. (1975), who offer an explanation of the two-dimensional classification of spiral galaxies by morphological type and luminosity class in the framework of density wave theory. They conclude that there are two important parameters that are related to the rotation curve and that define the classification: the total mass MT divided by a characteristic dimension Rc (the corotation radius), and the central mass concentration. The latter parameter (which is perhaps related to the bulge-to-disk ratio) determines the pitch angle of the spiral arms and hence the Hubble type (Sandage 1961). The two parameters together determine in first approximation the strength of the shocks and hence the degree of development of the spiral arms, i. e. the luminosity class (van den Bergh 1960a, b). The model is an ambitious one, and the challenge is out to observers to improve the observational material on which it is presently based; the rotation curves are often derived from only a few long-slit spectra and do not extend very far into the disks, and there is little or no data on the velocity patterns characteristic of density-wave streaming motions which would assist in estimating the corotation radii and provide valuable support for the whole model. Several questions that still need answers are: How does the observed dependence on the total luminosity (or mass) come into the picture? And what determines the corotation radius? These two things are apparently related since the MT/Rc parameter helps to define the luminosity class. Some support for the model can be found in the correlation of the compression strength with luminosity class that was discovered earlier by van der Kruit (1973c) from radio continuum observations of spiral galaxies. Finally, what is left of the idea that the Hubble type sequence is a sequence of angular momentum per unit mass (e.g. Sandage et al. 1970, but see Nordsieck 1973a, b)? It has been suggested that this latter quantity is related to the compression strength and, in particular, to the origin of the less luminous late-type galaxies (2) (van der Kruit 1973a, b, Wakamatsu 1976).



2 A source of confusion is the use of de Vaucouleurs' revised types in some studies and of van den Bergh's two-dimensional classification in others. It is evident that there is a great deal of similarity between the two systems, at least for the later types as reflected in de Vaucouleurs' (1977) luminosity index. On the average, the late revised types are faint luminosity classes: Sc approx Sc I, Scd approx Sc III, Sm approx Sc IV, etc. Many correlations with the later revised types are therefore also correlations with luminosity class. Back.

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