9.3. Intrinsic Shapes and Orientations
Inner and Outer Rings, Pseudorings, and Lenses
Determining the intrinsic shapes and orientations of galactic rings with respect to bars is one of the most important means of connecting rings to specific orbital resonances. Test-particle models described in section 12.2 show that a resonance can impress its ``stamp'' on the morphology of a gaseous ring which forms near it, owing to the distinctive nature of periodic orbits in a bar potential. Contopoulos (1979) illustrated the properties of these orbits and showed that alignments changed by 90° across a major resonance and that orbits achieved their maximum local eccentricity near a major resonance. Schwarz (1984a) showed that model gaseous rings formed from slow secular evolution of bar-driven spiral structure, and that the gas collects into the largest periodic orbit near a resonance which does not cusp and which does not cross another orbit. Model gaseous rings took on the oval shapes and bar alignments of these orbits.
The intrinsic shapes and orientations of galactic rings have been deduced from distributions of apparent axis ratios and relative bar/ring position angles under the assumption of random orientations of the spin axes. De Vaucouleurs (1956; see de Vaucouleurs & Buta 1980a) produced the first catalogue of apparent major and minor axis dimensions of inner and outer rings and lenses that later could be used for this purpose (Athanassoula et al. 1982; Buta 1984). The sample included 532 galaxies of all Hubble types. Kormendy (1979a) measured diameters and angles for his small sample of SB galaxies, and was the first to really attempt to deduce intrinsic shapes from such measurements. Other sources of diameters include Pedreros & Madore (1981), who measured rings in a similar-sized sample for the distance scale, and Corwin et al. (1985), who provided measurements of ring diameters in a sample of 2000 southern galaxies. The early studies of intrinsic shapes and orientations by Kormendy (1979a), Athanassoula et al. (1982), Buta (1984, 1986a), and Schwarz (1984c) provided some evidence for oval intrinsic shapes and preferred alignments, but were not very definitive because the samples used were either too small or ill-suited to statistics, or the observational errors were not explicitly taken into account.
The Catalog of Southern Ringed Galaxies (Buta 1995 = CSRG) has provided the largest samples and the best statistics of intrinsic ring shapes and orientations. It is based on uniform searches of the Science Research Council (SRC) IIIa-J Southern Sky Survey, which is the highest quality of all of the available sky surveys. The J filter-plate match has an effective wavelength between Johnson B and V filters but is closer to B than V, thus making the plates ideal for detecting the typically blue rings (see section 9.4). Other advantages of the SRC-J survey for ringed galaxy studies are the fine grain of the emulsion, which counters the small image scale and allows rings as small as 0'.2 to be resolved well enough to measure at least axis ratios; and the depth of exposure of the plates, which is sufficient to reveal rings which are as faint as 1% of the night sky brightness. The principal disadvantage of the J plates is the frequent overexposure of galaxy core regions, but ESO-B and ESO-R films usually provided the necessary information in such cases.
Together, the three southern sky surveys have provided a very large database of apparent ring diameters, axis ratios, relative bar/ring position angles, and morphologies. The CSRG includes 3,692 galaxies and information on 4661 ring, pseudoring, and lens features. We illustrate in Figures 28, 29, 30 three sets of distributions from Buta (1995), where the filled circles refer to the CSRG data, and summarize in Table 7 the best current estimates of the intrinsic shapes and orientations derived under the assumption of random orientations of the spin axes (solid histograms). The principal result from these kinds of studies is that rings in galaxies are, in general, noncircular on average. The distributions in Figure 28 are for inner and outer rings, pseudorings, and lenses irrespective of family. In the analysis of Buta (1995), rings and lenses were not treated as distinct features. Selection effects in the observed distributions are discussed by Buta (1995), the main effect being inclination. For the best model fits, which allow for observational error, both inner and outer features have an average intrinsic axis ratio of 0.85 with a dispersion of 0.1. When the samples are subdivided by family or feature subtype as in Table 7, some possibly significant differences are found. For example, both inner and outer rings, pseudorings, and lenses in SA galaxies may be rounder on average than those in SB galaxies. Inner rings and ring/lenses seem to be more oval on average than inner pseudorings, while outer rings and ring/lenses may be slightly less oval than outer pseudorings. SAB inner and outer features have characteristics that are not necessarily intermediate between those for SA and SB features.
The shape results for outer rings in Table 7 can be compared with statistics of isophotal disk shapes, since outer rings are preferentially located in the outer regions of a disk. Fasano et al. (1993) have used a volume-limited sample of 1064 RC3 galaxies to deduce that early-type spiral galaxies have a more triaxial disk than late-types. The distribution of intrinsic shapes, inferred by inversion (Lucy 1974), gave a peak at planar axis ratio b/a = 0.8, comparable to SB outer rings and pseudorings. However, the ring and disk samples are very different in nature, and the significance of the agreement in intrinsic shapes is unclear.
The distribution of relative bar/ring position angles is very interesting from these kinds of studies. The distributions are inconsistent with random alignments between bars and rings (see Figure 10 of Buta 1986a). As shown in Figure 29, SB inner and outer features have about the same distribution of apparent axis ratios, and hence about the same average intrinsic shape, but the angle distributions are very different. The distribution of angles for outer features can be modeled with two populations of features having perpendicular and parallel alignments relative to the bar. The two maxima in this distribution favor that 64% of SB outer rings are aligned perpendicular to the bar and 36% are aligned parallel to the bar. The distribution of angles for inner rings favors parallel alignment exclusively. Figure 30 shows that the two maxima in the angle distribution for SB outer features are connected to the ``OLR'' subclasses, R'1 and R'2. The latter are found to be rounder on average than the former, and their perpendicular relative alignments are strikingly illustrated. For SAB galaxies, the same two alignments are probably present, but in a greatly different proportion: 85% parallel-aligned, and 15% perpendicular-aligned.
The statistics described above give a very good indication of the properties of the average ring, but do not tell us the extremes possible for any given features. Buta (1986a), in a preliminary study of the CSRG data available at the time, deduced that inner rings in SB galaxies have a wide range of intrinsic axis ratios: from 0.6 to 0.95. Among low-inclination barred galaxies, extremely oval inner rings are found in NGC 1433 (Figure 3), NGC 6782 (Figure 76), IC 1438 (Figure 9), ESO 296-2, and ESO 325-28 (Figure 17), while nearly circular inner rings are found in NGC 53, 6761, and 7329 (Figure 43). The differences are not obviously connected to apparent bar strength (i.e., SB versus SAB).
|Feature||< q0 > ± ( q0 )||< 0 > ± ( 0 )||N|
|inner features, all families||0.84 ± 0.10||-||787|
|SB inner features||0.81 ± 0.06||0° ± 1°||396|
|SB(r,rl) only||0.78 ± 0.04||0° ± 3°||251|
|SB(rs) only||0.88 ± 0.04||0° ± 1°||122|
|SAB inner features||0.78 ± 0.14||0° ± 8°||215|
|SA inner features||0.92 ± 0.09||-||172|
|outer features, all families||0.87 ± 0.14||-||775|
|R1, R'1||0.74 ± 0.08||90° ± 9°||187|
|R2, R'2||0.87 ± 0.06||0° ± 6°||135|
|SB outer features||0.82 ± 0.07||0° ± 6° (36%) |
90° ± 9° (64%)
|(R,RL)SB only||0.84 ± 0.04||0° ± 6° (26%) |
90° ± 9° (74%)
|(R')SB only||0.80 ± 0.11||0° ± 6° (42%) |
90° ± 9° (58%)
|SAB outer features||0.94 ± 0.16||0° ± 6° (85%) |
90° ± 9° (15%)
|SA outer features||0.97 ± 0.21||-||138|
Nuclear Rings and Pseudorings
The intrinsic shapes and orientations of nuclear rings and their pseudoring counterparts cannot be obtained at the same level of precision as for inner and outer features. The reason is that most nuclear features are too small or overexposed to detect on sky survey material, and as a consequence it is currently not possible to build up the large samples required to make a definitive analysis. Less than 100 examples are currently known in galaxies ranging in type from S0 to Sc. Buta & Crocker (1993) have used low-inclination galaxies to deduce that nuclear rings range in intrinsic axis ratio from 0.7 to 1.0. If oval, they are generally misaligned with the main bar at an intermediate angle between 0° to 90°, although cases of exactly parallel (NGC 4314) or perpendicular (NGC 1317) alignments are known.