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The establishment of an ordering of galaxies into taxonomic categories is clearly only one step towards understanding the physical nature of galaxy structure. It is important first to re-state what Hubble himself emphasized: that the classification system is entirely empirical and has no basis in theory. Nevertheless, we wish to understand the physical parameters which may underlie each dimension of the RHS, and here I wish to summarize a few of the current ideas.

Table 2 lists some of the parameters which may provide the physical basis of each dimension of the RHS. The stage and family have been thoroughly discussed in reviews by Sandage (1986) and Kormendy (1981, 1982), and I refer the reader to those papers for more details. Variety was the least-known dimension of the system until recently, and here I would like to focus mainly on this dimension as it provides an opportunity for a beautiful confrontation between theory and observation.

Table 2. Possible Physical Bases of Stage, Family, and Variety

DimensionBasis Selected References

Stage (a) Initial M(h) distribution? Sandage et al. 1970
(b) Initial density? Gott and Thuan 1976
(c) Halo mass fraction? Tinsley 1981
(d) Total mass? Tully et al. 1982
(e) Initial sigmav of dark matter? Lake and Carlberg 1988
Family (a) Tmean/|W|? Ostriker and Peebles 1973
(b) Rotation curve, mass dist.? Lynden-Bell 1979
(c) Angular momentum transfer? Lynden-Bell and Kalnajs 1972
Variety (a) Bar pattern speed? de Vaucouleurs and Freeman 1972; Schwarz 1979, 1984b
(b) Rotation curve, mass dist.? Schwarz 1979
(c) Gas fraction, total mass? Huntley 1980; de Vaucouleurs and Buta 1980
(d) Bar strength? Schwarz 1984c
(e) Evolutionary state of pattern? Schwarz 1979

It is probably fairly safe to say that the main characteristic galaxies were "born" with is their bulge-to-disk ratio. Whether these two components formed together, or if one preceded the other, is still a point of controversy. Nevertheless, once the bulge and disk formed non-axisymmetric disturbances could have developed in the stellar distribution, and bars or bar-like distortions could have grown rapidly. Once these structures formed, they could stir up any remaining gas in the disk; e.g. bars could drive trailing spiral structures in the outer disk. Any patterns would evolve slowly in form, owing to gravity torques and shocks.

The ring-like patterns defining the (r)-variety as well as nuclear and outer rings are believed to be related to orbit resonances with a bar, oval distortion, or density wave (de Vaucouleurs and Freeman 1972; Duus and Freeman 1975; Schwarz 1979; Schempp 1982; Kormendy 1982 and further references therein; Athanassoula 1983). The link with resonances was most firmly established by Schwarz (1979), who used a particle dynamical scheme to simulate the flow of gas in response to a static bar potential. Using a fairly simple method to simulate dissipation via cloud-cloud collisions, he found that gas in a barred galaxy can naturally collect near the main orbit resonances: inner Lindblad resonance (ILR), outer Lindblad resonance (OLR), and the inner 4:1 ultraharmonic resonance (UHR).

The rings form because large secular effects can occur at these resonances (Lynden-Bell and Kalnajs 1972), where periodic orbits achieve their maximum local eccentricity (Contopoulos 1979). If the bar forcing is strong enough, orbits slightly within a resonance can become sufficiently elongated that they will cross orbits slightly outside a resonance which are either shaped differently (as at UHR; Schwarz 1984c) or elongated in the orthogonal sense (as at ILR and OLR; Sanders and Huntley 1976). If gas clouds are present, they will not be able to settle into such orbits without experiencing dissipation. Spiral shock fronts develop in the gas, but these slowly change their form owing to gravity torques exerted by the bar. The net effect is that gas in the spirals tends to slowly drift and settle into ring-like concentrations near one or several of the major resonances.

Schwarz identified ILR, UHR, and OLR with the nuclear, inner, and outer rings, respectively, of barred galaxies. A considerable body of observational evidence has provided support for these interpretations. This has come from studies of the distributions of apparent shapes, relative sizes, and apparent orientations of rings with respect to bars (Kormendy 1979; Athanassoula et al. 1982; Schwarz 1984a; Buta 1984, 1986a) and from surface photometry and spectroscopy of individual examples (Buta 1984 and references therein; 1986b, 1987a, b, c, 1988a, b). One of the great successes of Schwarz's work is the prediction of the distinct outer ring morphologies discussed in section 2. The morphologies arise because at OLR, spiral structure and evolution are influenced by two major families of periodic orbits, a perpendicular-aligned family slightly inside the resonance and a parallel-aligned family slightly outside the resonance. Owing to dissipation, a pseudo-ring can develop near OLR whose shape and orientation are similar to one of these families; which one dominates depends on the gas distribution, the strength of the bar, and the ability of the dissipation to deplete the other family. A natural interpretation of the mixed morphology in Figure 2b is that both of these orbits are populated, although such a circumstance ought to be disallowed as the orbits would cross. Indeed, Schwarz did not predict the existence of a mixed outer ring morphology. However, there is clearly more work to be done, and further insight into the nature of these structures may be found in models with growing bars (Elmegreen and Elmegreen 1985 and references therein).

These findings allow us to make some evaluations of the differences that might underlie the family and variety dimensions in the RHS more clearly than could be done before. First, an SB(s) spiral could be a case where the pattern speed Omegap is high enough to preclude the existence of the main ring-forming resonances within corotation (that is, ILR and UHR). OLR could still exist, so that the spiral pattern could extend to this resonance and still evolve into an outer ring or pseudo-ring. On the other hand, if Omegap is low such that the ILR and the UHR exist, then the galaxy could become an SB(r,nr). If all three resonances exist, then the galaxy could become an (R)SB(r,nr). A good example where all three probably do exist is NGC 3081.

In SA galaxies, the interpretation of inner rings seems to be different. De Vaucouleurs and Buta (1980) showed that inner ring sizes depend strongly on both family and variety, in the sense that linear and relative ring diameters decrease from SB to SA and from S0/a to Sd. The first correlation was discovered by de Vaucouleurs, and is depicted in his famous cross-sectional drawing of the RHS (de Vaucouleurs and de Vaucouleurs 1964). It can be interpreted in terms of a correlation between ring size and apparent bar strength, or in terms of different resonance associations (that is, "(r)" in SA galaxies is associated with a different resonance from "(r)" in SB galaxies). I believe the observations favor the latter interpretation. Most of the inner rings of SA galaxies are probably linked to ILR, not the UHR, although features analogous to SB inner rings and lenses are identifiable quite frequently in SA systems (Kormendy 1979; Buta 1984, 1986a). Some SA inner rings lie almost exactly at the "turnover radius" of the rotation curve (Buta 1987a), again implying a possible link with ILR rather than UHR.

This brings me to the final question I wish to discuss in this conference, the possibility that galaxies could change "cell" positions over time scales equal to or less than a Hubble time. Sandage (1986) has asked how long, at present day star formation rates, it would take for a galaxy of a given stage to use up enough of its remaining gas to change by one step in the classification. He finds, using integrated birth rate functions, that this time is a function of increasing gas fraction and decreasing luminosity, and that, depending on the mode of star formation, it could be equal to or longer than a Hubble time. In fact, Sandage believes that the evidence supports the possibility that galaxies may have acquired their final position on the Hubble Sequence not long after the initial collapse, and most have not changed by one step since that time. Of course, this would apply only in the case of isolated evolution. Mergers and collisions can modify galaxy morphology on very short time scales, as much recent research continues to establish (e.g. Hernquist and Quinn 1987; Schweizer and Seitzer 1988; Whitmore and Bell 1988; Higdon 1988 and references therein).

In the case of family and variety, and independent of any external influence, the time scales for significant change could be much less than a Hubble time. For example, in n-body numerical models of galaxy collapse, bars can develop in a few disk rotations (Hohl 1975; Miller and Smith 1979a, b), and in the n-body simulations of gas flow in bar potentials (Schwarz 1979; Combes and Gerin 1985), rings can develop after only 7-10 bar rotations. Thus, it would seem that if secular evolution is occurring in galaxy structure, the most significant changes may be among family and especially variety, since rings evolve from more open spiral patterns. If bars can grow or weaken via angular momentum transfer processes (Lynden-Bell and Kalnajs 1972), or via interactions with the spheroid (Kormendy 1979), then family could change from SB to SAB, or from SA to SAB to SB. That such evolution may be taking place is provided by non-barred, ringed S0 galaxies like NGC 7702 (Figure 3). That a galaxy with little or no obvious bar could have such a bright inner ring made purely of stars is a clear contradiction to theoretical models which rely on bar and gas dynamics for ring formation. Either NGC 7702 once had a strong bar that caused a ring to form before it vanished, or ring formation does not require the presence of a strong bar or a significant amount of gas. Clearly, such galaxies need to be studied in greater detail before we can consider our understanding of family and variety complete.

Figure 3

Figre 3. CCD image of NGC 7702 (I-band, AAT), a "non-barred" ringed S0 (note possible small nuclear bar; field stars are removed).

Note that resonances may not be able to explain all rings observed in disk galaxies. Some possibly form by accretion of gas-rich satellites. A particularly striking case may be Hoag's Object (Schweizer et al. 1987) and many "polar-ringed" galaxies (Schweizer, Whitmore, and Rubin 1983).

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