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Several galaxies in Arp's Atlas (2), such as Arp 143-147, show a pronounced ring structure surrounding a seemingly empty region in which often an offcentered nucleus may be seen. The frequency of this phenomenon is difficult to estimate. Freeman & de Vaucouleurs (44) list about two dozen objects, including messy systems such as NGC 2444-2445, and derive a ratio of ring galaxies to spiral galaxies of 0.00015 from a crude estimate of their respective space densities. Arp & Madore (3, 4) estimate that 6% of the galaxies they looked at on-the ESO/SRC (IIIaJ) Southern Sky Survey are peculiar, and that among these the frequency of what they call ring galaxies is 3.13%, thus making the ratio of ring galaxies to spiral galaxies about 0.002. Their ring galaxy category includes any galaxy with an apparent luminous ring around it. They distinguish several subcategories, the first comprising the ring galaxies that we discuss here, the second a subcategory having rings with centrally located nuclei, and the third a subcategory consisting of barred spirals that have both a high-surface-brightness inner ring and a faint outer ring. The latter two subcategories are discussed in the next section.

Vorontsov-Velyaminov and Dostal & Metlov (36, 148, 149) estimate that the frequency of what the Morphological Catalog of Galaxies (MCG) calls ring galaxies is even higher. Inspection of several of these galaxies clearly shows that they are galaxies with outer rings (cf. Section 3) and not ring galaxies in the sense defined above. Moreover, estimating space densities` using a magnitude-limited catalog [or worse, magnitude-selected catalogs such as the Second Reference Catalog (RC2) and the MCG] can lead to erroneous values if the luminosity functions of the respective objects are not well known. Most likely, the frequency of ring galaxies lies somewhere between the estimates given above, i.e. 0.02-0.2% of the spirals. Thompson (134) presents a list of 40 ring galaxies around clusters and shows that their frequency inside clusters is greatly diminished. Thus we can conclude that ring galaxies are rare and occur mainly in regions of low galactic density.

Most speculations and theories put forward to explain the formation of ring galaxies are based on some variety of a collision scenario (see, however, 36, 148). Freeman & de Vaucouleurs (44) propose that the head-on collision of a normal spiral with a large intergalactic gas cloud (IGC) might remove the gas of the former. The gaseous component of the galaxy, initially in an annular shape reminiscent of M31's H I gas ring (91), is thus stopped and evolves into a ring galaxy, while the stellar part continues on its trajectory and becomes an S0. Ring galaxies would therefore always have an S0 companion, which is not the case. A more serious problem is that the IGCs would need to have a mass of 3 × 109 Modot, a radius of 15 kpc, and a space density of 25 Mpc-3. No such IGCs have been found either in the general field (e.g. 67, 92, 121) or in small groups (53).

In a systematic analysis 'of this class of objects, Theys & Spiegel (132) concentrated on the more regular-looking ring galaxies in order to ensure their true membership in this category. They distinguished RE galaxies with crisp empty rings, RN galaxies having a ring with an off-centered nucleus, and RK galaxies with a single dominant knot or condensation in their ring. The handful of objects in each class were studied in some detail. An important result, which fueled subsequent theoretical efforts, was the realization that the companion galaxy lies preferentially near the minor axis of the ring. The colors of the rings were found to be similar to those of Magellanic irregulars, and several lines of argument indicated that the masses of the ring galaxies should be of the order of 1011 Modot.

Theys & Spiegel (133) modeled the formation of rings by numerical simulations of head-on collisions of two galaxies. They first used an N-body code (81) with a very, hot stellar component and even a hot gaseous component to ensure 'stability. These high-velocity dispersions prohibit the appearance of structures, and only in the coolest 5% of the stars is a ring seen after the collision. To advance further, they introduced a simplified model in which each disk is composed of axially symmetric rings of cold particles, free to move in the vertical direction, with a softened mass point at their center. The collision knocks out the center, thus lowering the gravitational attraction on the disk, and as a result the rings expand and crowd together. A major part of the discussion focuses on the disappearance of the nucleus so as to make an RE.

A very clear picture of what actually happens during the collision is given by Lynds & Toomre (70) and Toomre (139). The stars experience a brief inward pull due to the additional gravitational attraction of the companion as it falls through. This pull causes the disk to contract, and when the intruder exits, the system rebounds strongly. The orbits crowd together, forming a transient but very high amplitude density wave propagating outward. Numerical experiments using test particles show that this. wave is not due to self-gravity but is essentially kinematic. Secondary inner rings, such as the one observed in the Cartwheel, can form naturally from a second (or third) rebound. The intruder itself is likewise affected, and if it is also a spiral, two ring galaxies ought to be observed, as is the case for II Hz 4. The tangential velocities in the ring are roughly two or three times the radial velocities, as was verified by the observations of II Hz 4 (70), the Cartwheel (43), and AM0644-741 (41). Head-on collisions result in axially symmetric ring galaxies, while as the impact parameter is increased, the "nucleus" is knocked off center. This lateral mobility of what was the central part of the galaxy may well explain the RK rings and even the seemingly empty ring galaxies. Larger values of the impact parameter result in more messy shapes, while if the companion grazes the outer parts of the disk, some very spectacular spirals may be triggered. Finally, the assumption of perpendicular impact may be relaxed, as in the example calculated by Toomre and given in (26), where the impact is offset and inclined retrograde by 45°. The result is a much poorer ring that has one side much brighter than the other, giving the impression of a one-armed spiral.

Recent spectroscopic work on several ring galaxies, in particular those in the Southern Hemisphere, has added little more than footnotes to the explanations provided by the head-on galaxy collision theory. However, the identification of the candidate intruder is not always simple. Davies & Morton (28) measured the velocity dispersion of the companion of the Cartwheel, and from that they inferred its luminosity and mass. The latter quantity seems an order of magnitude smaller than that found for the Cartwheel itself (43) and thus is perhaps too small for the companion to have caused so much damage to the Cartwheel. Yet the mass estimates are uncertain by a factor of two. Moreover, the companion is likely to be damaged itself and may lose a fair amount of its mass.

The kinematics of the ring galaxy is also sometimes more complicated than the simple model of head-on perpendicular collisions, particularly in cases where the optical image is distorted, bent, or nonaxisymmetric. Usually the ring rotates about two to three times as fast as it expands, as predicted by the theoretical models (70). A VLA synthesis map of NGC 2793 (47) shows this object to behave as expected from the collision model. Nevertheless, some lesser worries remain. In AM0644-741 the gaseous velocities in the ring are a factor of three higher than the stellar velocities (41). The difficulties can be compounded by the relatively face-on orientations of some of the observed galaxies. In the Vela object (131), for example, the quoted velocity amplitudes are much smaller than expected for a galaxy of its size. Perhaps both rings are not round and/or planar, and are seen very face-on.

The collision and its aftermath are likely to lead to enhanced star formation in the ring galaxy (cf. 65). UBVR photometry of VII Zw 466 (135) shows that the bright knots on the ring are very blue, which implies that star formation, either continuous or in the form of a burst, has occurred within the last 108 yr. One knot within the ring is much redder and could be the remnant of what was the central part of the galaxy. The "empty" region of the ring gives a faint but detectable signal at a surface brightness of 24 mag arcsec-2 in V, with peculiar, though very uncertain, colors. In NGC 985, the bright knot in the ring exhibits Seyfert characteristics (33), which lends support to the idea of it being a displaced nucleus.

Spectroscopy of the H II regions in ring galaxies shows that they are very luminous, which indicates the presence of many O stars. The line ratios suggest low abundances for the Cartwheel (43) (and thus possible mixing with a large preexisting H I envelope) but more normal abundances in other systems (31, 41). The situation is not entirely clear though, since in some regions [N II] / Halpha is very low (M. Dennefeld, private communication), while in other galaxies the abundances seem higher than expected, e.g. Abell 76 (130). The radio continuum emission (46) and the amount of neutral hydrogen emission (79, 123) are similar to those of normal spirals and irregulars.

What is the long-term evolution of a ring galaxy? A self-gravitating ring can be unstable to the "bead instability" (39, 90, 156). N-body simulations show that such rings will break into a small number of knots in a time scale of 108 yr unless stabilized by a sufficiently large central mass (as is the case for Saturn's rings) or by a massive halo (133). This is obviously only a lower limit for the case of ring galaxies, where the assumption of self-gravitation is questionable. We might be witnessing such later stages of the evolution of ring galaxies in UGC 3730 and UGC 1449 (18), NGC 2444-2445 (100), or Klemola 25 (27).

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