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Gas in nonaxisymmetric galaxies is driven inward inside corotation, and outwards at larger radii. This behavior contrasts with that of the stars (Section 3.5); dissipation allows the gas to stay dynamically cool while experiencing large changes in Lz. Secular evolution of this type is believed to be responsible for the formation of most rings observed in galaxies. The faint outer light profiles of galaxies also manifest features, but their origin is less clearly attributable to secular evolution.

Encounters between galaxies are invoked to explain other types of galaxy rings (Lynds & Toomre 1976; Struck 2010; Eliche-Moral et al. 2011) or polar rings (e.g. Sparke et al. 2008), which are not, therefore, the result of secular evolution.

7.1. Rings

Long-lived perturbations, such as bars, can drive gas radially until the flow stalls at resonances where rings of star-forming gas build up. Buta (1995) identifies three types of ring: outer rings, inner rings, and nuclear rings, all of which are commonly found in barred galaxies, but some are known in unbarred galaxies also. Outer rings, which are divided into two subtypes depending on their elongation relative to the bar, are generally believed to occur at the OLR of the bar. Inner rings have mean radii that are about as large as the bar semi-major axis, while nuclear rings are deep inside the bar. The rings are thought to depart from circles because of the quadrupole field of the bar, and the distortion is enhanced by being located at a resonance.

Outer rings have been identified in the light profiles of 66 early-type barred galaxies by Erwin et al. (2008a), who found an occurrence rate (or a feature at the expected radius) in 35% of the cases. Buta et al. (2010b) are conducting an on-going search using their deep 3.6 µm survey with Spitzer (dubbed S4G) for additional outer rings, but are finding few new cases, perhaps because these features tend to be quite blue.

The outer, inner, and nuclear rings are widely believed to form though secular evolution in, mostly barred, galaxies. Buta & Combes (1996) give a thorough review of rings and the theory of secular formation of rings, and though written some years ago, remains reasonably up-to-date as the subject has not advanced much since. A more recent review of the properties of such rings and their formation mechanisms was included in Kormendy & Kennicutt (2004).

The gas in a nonaxisymmetric potential must shock when periodic orbits cross (see Section 5.5), causing an irreversible change to the orbital motion. The shock is generally offset from the potential minimum, resulting in an angular momentum exchange between the gas and the bar or spiral. The position of the shock relative to the potential minimum determines the sign of the exchange: gas loses angular momentum inside corotation, whereas it gains outside this resonance, since the gas flow relative to the wave is in the opposite sense. Thus gas is driven away from corotation until the flow stalls, at an OLR, or where the dominant orbit family switches orientation in the nuclear region of a strong bar. Two orbit families can support rings at the OLR; just inside the resonance, orbits are elongated perpendicular to the bar, whereas the elongation is parallel to the bar just outside that resonance. The early simulations by Schwarz (1981), which employed sticky particles, were able to produce rings of both orientations, and there is evidence for both types in real galaxies (see Buta & Combes 1996 for examples). More recent models for the formation of outer rings were presented by Bagley et al. (2009) as the response of collisionless test particles to bar forcing, and they also compare their models with rear-infrared images of galaxies.

Inner rings are believed to be located at the ultraharmonic resonance (UHR, see Section 2.3) of the bar, where the potential supports 4:1 orbits (dotted in Fig. 11). Buta & Combes (1996) suggest that inflow from corotation stalls at the UHR to make this ring, which is perhaps consistent with the behavior also found in Schwarz's work (Simkin et al. 1980). There the ring is simply a pointy oval, a shape that is often found in real galaxies. However, if the 4:1 resonant family is responsible, it is somewhat surprising that such rings are not more boxy; perhaps the theoretical interpretation of inner ring formation deserves further study.

Subsequent to the review by Buta & Combes (1996), most attention has focused on nuclear rings. Bars appear to be efficient at driving gas inwards until the flow stalls in a nuclear ring, as described in Section 5.5. The gas concentrations in these nuclear rings appear to be forming stars at a prodigious rate (Hawarden et al. 1986; Maoz et al. 2001; Benedict et al. 2002; Mazzuca et al. 2008, Mazzuca et al. 2011).

7.2. Outer light profiles

While galaxy disks are frequently described as exponentials, few galaxies have light profiles that can be fitted with a single exponential over several length scales. The light profiles reported by Freeman (1970) did not extend to very faint light levels, by the standards of today. Yet he identified both type I profiles, which were good exponentials over the limited dynamic range of his data, and type II, in which the surface brightness of the inner disk rises less rapidly than the inward extrapolation of the outer exponential. Both these types have been found in modern, much deeper photometry (Pohlen et al. 2002; Bland-Hawthorn et al. 2005; Erwin et al. 2005, 2008aErwin et al. ; Hunter & Elmegreen 2006; Pohlen & Trujillo 2006), which also revealed type III, in which the light profile at large radii declines less steeply than the inner exponential. Erwin et al. (2008b) found that type II profiles are more common in barred galaxies. The fraction having type III profiles rises to late Hubble types, but galaxy interactions also appear to play a role (Erwin et al. 2005).

The origin and significance of this variety of behavior is still not fully understood, and may be related to galaxy formation, environment, or star-formation efficiency (Sánchez-Blázquez et al. 2009; Martánez-Serrano et al. 2009). However, some aspects may be due to internal disk evolution (Debattista et al. 2006; Folye et al. 2008; Minchev et al. 2012a). Martán-Navarro et al. (2012) proposed that breaks might be phenomena related to a threshold in the star formation, while truncations are more likely a real drop in the stellar mass density of the disk associated with the maximum angular momentum of the stars. On the other hand Roskar et al. (2008a) and Muñoz-Mateos et al. (2013) suggested internal secular evolution may be the cause.

While Trujillo et al. (2009) assert that the extended type III disk in M94 is not a ring, they nevertheless suggest it could be formed by an outflow in the disk that was driven by a rotating oval distortion in the inner part of the disk. Also noteworthy is the suggestion by Roskar et al. (2008a) that the radial decline in the mean ages of disk stars, caused by inside-out disk formation, could be reversed in the far outer disk by the outward migration of older stars. An attempt to verify this prediction (Yoachim et al. (2012)) met with mixed results, however.

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