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line of sight view through vertical resonant bar orbits (e.g. Abbott et al. 2017). The classifications SBx and SABx are used for boxy/peanut bulges. In some cases, both a boxy/peanut bulge and ansae occur in the same system (as in NGC 5445; Figure 1.12). In such cases, the classification is SBax or SBxa.

      Although the CVRHS bar family classification can be consistently applied, it is still a visual judgment and is not the most effective way of quantifying bar strength. It is also technically based on blue light images (the historical waveband of galaxy classification) where the appearance of the bar may be affected by dust and star formation. More quantitative approaches to bar strength include the maximum ellipticity in the bar region, the maximum relative m = 2 Fourier intensity amplitude A2 = (I2/I0)max and the ratio of the maximum tangential force to the mean radial force in the bar region, all based on near-infrared images (e.g. Combes and Sanders 1981; Buta and Block 2001; Buta 2012). Garcia-Gómez et al. (2017) describe the application of a two-dimensional Fourier transform technique to more reliably characterize the strengths of bars in disk galaxies.

      Inner rings are most common in barred galaxies, but also appear in non-barred galaxies. Some non-barred galaxies with rings could be evolved remnants of an earlier barred phase, owing to the possibility that bars may dissolve in much less than a Hubble time due to a buildup of the central mass concentration (Norman et al. 1996).

Photos depict a sequence of increasing apparent bar strength. Photos depict enhanced handles, or ansae. Photos depict three edge-on galaxies showing boxy/peanut-type bulges.

      The relation between inner rings and inner lenses is unclear. One possibility is that an inner lens is a highly evolved inner ring. This might account for the existence of inner ring-lenses (rl), which appear to be low contrast inner rings. However, Kormendy (1979; see also Bournaud and Combes 2002; Gao et al. 2018) proposed another interpretation: that inner lenses represent dissolved bars. Bar dissolution is possible because the presence of a bar not only heats the disk component, but also causes resonance effects that force stars onto orbits that do not support the bar. An example of the latter is the formation of a nuclear bar, which is a small secondary bar that forms inside a primary bar. Such features are recognized with the symbol (nb) in the CVRHS classification system, and are often significantly misaligned with a primary bar if present.

      Another interesting aspect of inner rings is that these features have a wide range of intrinsic shapes (deprojected minor-to-major axis ratio 0.5 to 1.0; Buta 2019) and are often regions of intense star formation. The distribution of star formation in inner rings is sensitive to this range: the more elongated the ring, the greater the concentration of HII regions around the major axis points (Crocker et al. 1996; Grouchy et al. 2010). The effect is especially evident in cuspy-shaped inner rings, of which NGC 6782 is the best example (Lin et al. 2008). It is also seen in NGC 3081 (Buta and Purcell 1998).

Photos depict examples of different inner varieties. Photos depict examples of spiral galaxies having a nuclear ring.

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