5.4. Inner and Outer Rings
Two distinct kinds of rings are observed in barred galaxies. Inner rings (r) such as that in NGC 2523 (Figure 40) are always the same size as the bar. They are narrow and quite well defined. Sometimes inner rings occur at the rim of a lens (e.g., NGC 936); in late-type galaxies there is usually no lens (e.g., NGC 2523). Outer rings (R) are distinguished from inner rings by their well-defined larger sizes, <r(R) / rB> = 2.21 ± 0.02 (dispersion / 131/2), see Kormendy (1979a). Outer rings are also broader than inner rings. An example is NGC 1291 (Figure 40), others are illustrated in the Hubble Atlas and in Kormendy (1979a). Neither inner nor outer rings generally contain as much total light as do other components discussed in previous sections. I discuss them because they contribute considerably to our understanding of secular evolution.
Inner rings are extremely common (7), especially in late-type galaxies. Kormendy (1979a) finds that they occur in ~ 19% of SB0-a galaxies, and in ~ 63% of SBab-c galaxies. Evidently the process that leads to inner ring formation is not unusual, but is an integral part of SB dynamics.
Outer rings are rarer. Kormendy (1979a) identified outer rings in ~ 6 of 121 galaxies, and even de Vaucouleurs (1975) found a maximum frequency of only ~ 30% at S0/a, with lower frequencies for earlier and later types. Much less rare are pseudorings (R); i.e. distorted spiral arms. We will see below that the distinction between outer rings and pseudorings is not fundamental.
An interesting but not well known morphological result is the observation that true inner and outer rings almost never occur together in barred galaxies. One of the rare exceptions is NGC 7428.
The shapes of inner and outer rings are quite different. Inner rings are similar in shape to lenses, as illustrated by the frequent occurrence of rings on the rims of lenses (de Vaucouleurs and Buta 1980). In particular, they are elongated parallel to the bar. Typical axial ratios range from ~ 0.7 to near 1.0 (Athanassoula et al. 1982). Outer ring axial ratios are more difficult to determine. In NGC 1291 where the inclination is known to be 84° ± 2°, the true axial ratio is the observed one, 0.90 ± 0.02. As Figure 40 shows, the long axis of the ring is perpendicular to the bar. A similar conclusion is reached for several other galaxies studied in Kormendy (1979a), and for some galaxies with well-measured velocity fields (e.g., NGC 4151, see Fig. 4). Athanassoula et al. (1982) find that outer rings in SA galaxies have axial ratios between 0.8 and 1.0, while outer rings in barred galaxies are round. The latter result is at variance at least with the results on NGC 1291. The sample studied (de Vaucouleurs and Buta 1980) suffers from problems discussed in the above footnote. There are also other systematic effects; e.g., if the ring major axis is not correctly identified, the measured axial ratio will be too close to 1.0. A more accurate study of outer ring shapes is needed. The present evidence tentatively suggests that they have axial ratios between ~ 0.8 and 1.0, with the long axis generally perpendicular to the bar. They are not as elliptical as axial ratio 0.76 (Kormendy 1979a) because this value was deduced by assuming that inner rings are round. The observations are certainly consistent with the assumption that some outer rings are round, and a few may be elongated parallel to the bar.
The formation of rings provides an excellent example of secular evolution driven by the bar. The details of the process are not worked out, but a general understanding of ring formation is provided by a large number of discussions and calculations of the response of disk gas to a rotating bar. These include: Prendergast (1962, 1964); Freeman (1965); Pikel'ner (1971); Roberts (1971); Duus and Freeman (1975); Sørensen, Matsuda and Fujimoto (1976); Sanders and Huntley (1976); Sakurai (1976); Liebovitch and Lin (1977); Sanders (1977); Chevalier and Furenlid (1978); Huntley (1978); Huntley, Sanders and Roberts (1978); Karamitsos (1978); Kato and Inagaki (1978); Liebovitch (1978); Berman, Pollard and Hockney (1979); Roberts, Huntley and van Albada (1979); Schempp and Wolstencroft (1979); Schwarz (1979); Athanassoula (1980); Huntley (1980); Petersen and Huntley (1980); Sanders and Tubbs (1980); van Albada and Roberts (1981); Schwarz (1981); see Roberts (1979a, b) for reviews. Both analytical and numerical techniques have been used. Some numerical calculations have solved for the steady-state flow, others have followed the development of the system with time. All of the calculations except those of Athanassoula (1980) and Huntley (1980) neglect self-gravity in the gas. Viscosity is handled in a variety of ways; it varies greatly in strength in different calculations, and a significant and highly variable fraction of it is numerical. Thus there are certainly still problems with most calculations. This observational review is restricted to a brief summary of the most secure results concerning ring formation.
The bar rearranges the disk gas as follows.
(1) Interior to a radius somewhat inside of corotation, the gas spirals in toward the center. The calculations listed above have been almost unanimous in predicting that angular momentum is lost at a straight shock which slightly leads the bar's potential minimum in the rotation direction (e.g., van Albada and Roberts 1981). Possible effects of this inward transport of gas were discussed in sections 2.5.2 and 5.2.
(2) Within an annulus surrounding corotation, gas is concentrated or even focussed (Roberts, Huntley and van Albada 1979) into a ring at the end of the bar. This is identified with inner rings.
(3) Gas at larger radii is driven into trailing spiral arms, which generally have smaller pitch angles at larger radii (like a pseudoring). A spiral shock in these arms forms the continuation of the straight shock in the bar. The presence of the spiral is a signature of the transport of angular momentum from the bar to the disk. The eventual result is to drive the gas outward to the vicinity of outer Lindblad resonance where it forms an outer ring.
The timescale for all of these processes is poorly known but much less than a Hubble time.
Observations of barred galaxies support the above scenario.
(1) The existence of two kinds of rings, i.e., narrow inner rings and broad outer rings, is consistent with the calculations.
(2) The fact that rings are common is also to be expected. Complete outer rings are not common in late-type galaxies, but pseudorings or spiral arms distorted in the same way as the calculated arms are almost universal in barred galaxies (Kormendy 1979a). The suggestion is that the evolution is not complete in these galaxies.
(3) The observed ratio of outer and inner ring diameters is ~ 2.2, with a relatively small dispersion (Kormendy 1979a; Athanassoula et al. 1982). This is the value which one would expect, given V ~ constant rotation curves, if the rings occurred at outer Lindblad resonance and at corotation, respectively (Athanassoula et al. 1982).
(4) The fact that inner rings are elongated parallel to the bar is correctly reproduced by the models, at least qualitatively. For outer rings the situation is less clear. Many calculations produce outer rings or pseudorings which are elongated perpendicular to the bar, as observed (e.g., Sanders and Huntley 1976; Sanders 1977). However the clearest rings are produced in Schwarz's (1979, 1981) calculations, and these are most frequently elongated parallel to the bar. Since it is clear that the ring shapes depend on poorly known viscosities and initial conditions in the models, and on poorly known inclinations and systematic effects in the observations, a definitive confrontation of the two is not yet possible.
(5) The stellar and gaseous content of rings is clearly consistent with the above formation mechanism. That is, both inner and outer rings have disk-like populations. This is especially clear in barred galaxies of intermediate Hubble stages, such as NGC 2523 (SBb, see Figure 40). In these objects the bulge and bar have similar smooth, generally red populations, while the disks are actively forming stars. Like the disks, the inner rings in these objects are rich in H II regions and clumps of blue stars, as shown by H photographs (Hodge 1974) and color photographs (Wray 1979). Outer rings are fainter and therefore less well studied. However, Kormendy (1979a) and Gallagher and Wirth (1980) note that they sometimes contain blue patches indicative of star formation. Also, outer-ring galaxies are observed to be unusually rich in H I (Bieging and Biermann 1977; Bieging 1978; Krumm and Salpeter 1979). In cases when sufficient resolution is available, the gas appears to be associated with the ring (Bosma, Ekers and Lequeux 1977a; Bosma, van der Hulst and Sullivan 1977b; Mebold et al. 1979).
(6) Sandage (1961) notes that prominent dust lanes on the rotationally leading side of the bar are seen only in SB(s) and not in SB(r) galaxies (contrast NGC 1300 and NGC 2523 in Figure 40 and in the Hubble Atlas). Is this so because the above evolution is more nearly complete in SB(r) galaxies, with one result being that gas has been completely swept out of the region between the inner ring and the center? H II emission lines are in fact difficult to detect inside inner rings (e.g., NGC 3351, Peterson et al. 1976).
(7) The non-circular gas velocity fields predicted by the above calculations are in good agreement with the observed H I and H II velocity fields (Huntley 1978; Chevalier and Furenlid 1978; Sancisi, Allen and Sullivan 1979; Sanders and Tubbs 1980; Rubin 1980; Peterson and Huntley 1980; Pence 1981).
In summary, calculations which suggest that a bar rearranges disk gas into the nucleus and into inner and outer rings have been qualitatively successful in reproducing many observations. However, the details are still very uncertain. Much work is needed to further test these processes, and to determine their detailed properties.
7 Considerable caution is required in estimating ring frequencies. The first problem is that Revised Morphological Types (RC2) do not distinguish between inner rings and lenses, but denote both as (r). (Therefore, we cannot determine from the RC2 whether a galaxy has a lens.) The second problem is that spiral structure in barred and oval galaxies is distorted into pseudorings which resemble real rings. The dividing line between rings and pseudorings is not well defined, but probably also not physically meaningful. Third, an (unpublished) examination of catalogues such as that of de Vaucouleurs and Buta (1980, see also RC2) suggests that a heterogeneous collection of features is identified as inner rings in SA galaxies. Finally, de Vaucouleurs and Buta identify some very weak features as rings. The present discussion is restricted to a relatively conservative identification of rings. Back.