2.2. Morphology of Ring Galaxies and Ring Galaxy Samples
The first paper that attempted to classify collisional ring galaxies was Theys and Spiegel's first, mainly observational, paper on ring galaxies (Theys and Spiegel 1976). They compiled a list of likely collisional rings based on miscellaneous early accounts of rings and developed a simple morphological classification scheme. Theys and Spiegel defined three basic ring types. The first, in some sense the "pure" ring, was the RE galaxy, defined as a galaxy which appears photographically as a well defined, approximately elliptical ring without a central nucleus. Although sometimes referred to as "Empty Rings", we now know, through modern CCD observations, that the rings are filled with redder light throughout the interior of the galaxy. Perhaps a better description of the empty rings would be to call them "centrally smooth" rings. Examples of this kind of ring are Arp 146, Arp 147, VIIZw466 and AM 0051-271. However, in order to extend the study to objects that they considered to be close relatives of the RE galaxy, they also defined RN galaxies as galaxies containing an off-centered nucleus and the RK galaxies as ring-like galaxies with a prominent knot embedded within a markedly asymmetric light distribution. Perhaps the most famous of the RN galaxies is the Cartwheel (A0035-33) shown in visible light in Figure 1. Although the Cartwheel is almost certainly a collisional ring system, Theys and Spiegel were aware of the sometimes difficult task of distinguishing between rings which may have been formed by collisions and the "resonance" ringed or pseudo-ringed galaxies first discussed by De Vaucouleurs and recently catalogued by Buta (1994, see also Athanassoula and Bosma, 1985). The RN class could potentially contain rings formed by processes other than that of galaxy collisions, although most of the resonance rings appear to contain symmetrical nested rings, whereas the RN rings are notable because the inner ring or nucleus is offset from the geometrical center of the ring. Theys and Spiegel (1976) also noted that the rings became increasingly elliptically shaped along the classification sequence RE, RN and RK. In addition, they also pointed out that very few rings were more flattened than b/a = 0.4 (b/a is the ratio of the minor to major axis dimensions). This latter point is an indication of strong selection effects in many samples of ring galaxies, since ring galaxies seen nearly edge-on would be hard to recognize.
Very few ring galaxies have more than one ring. The Cartwheel has two rings, and the Vela ring galaxy has at least two rings, the inner of which emits strongly in H emission (Dennefeld, Laustsen and Materne 1979; Taylor and Atherton 1984). Recently it was discovered that Arp 10 has two H emitting rings and segments of a third outer ring (Charmandaris Appleton and Marston 1993). In these cases, the multiple ring systems are physically large. The development of multiple ring structure is not unexpected from the collisional models of Lynds and Toomre (1976) and their existence is a sign that the collision was not recent. Multiple rings and their relative spacing can be used to constrain the mass distribution of the target galaxy (see Section 4).
In the presentation of their small ring sample, Theys and Spiegel (1976) discussed a number of possible interpretations for ring galaxies. They noticed that, with the exception of II Zw28 (a small RK ring), all of the other ring galaxies had small companions within a few ring radii and that many of them lay within a few degrees of the projected minor axis of the ring. It was suggested that one very likely explanation for their structure was that the companion had passed through the center of the disk and was caught leaving the scene of the crime! In the simplest situation, that of a companion passing down the spin-axis of the target disk, one would expect the companion to be seen close to the projected minor axis of the ring as observed. However, there was an apparent complication. It was not clear that the rings were intrinsically circular. For example, if the rings were truly elliptical but seen at some random viewing angle projected onto the sky, then the minor axis of the observed ring galaxy would not in general coincide with the rotation axis of the target disk projected onto the sky. Theys and Spiegel (1976) were concerned that the degree of flattening of the rings did not appear to be consistent with the position of the companion galaxy on the sky. Most of these problems have now been removed since it has been demonstrated that quite good rings can be created even with highly inclined collision trajectories and with moderately off-center collisions (Huang and Stewart 1988; Appleton and James 1990). In slightly off-center collisions, the companion does not travel exactly down the spin-axis of the target and so, in general would not be expected to appear projected onto the center of the ring when viewed almost perpendicularly to the disk.
A less detailed classification scheme, but statistically more significant piece of work was performed by Few and Madore (1986) based on the extensive southern galaxy surveys of Arp and Madore (1977) and the Catalogue of Southern Peculiar Galaxies and Associations (CPGA) by Arp and Madore (1987). By a careful analysis of southern ESO and SERC J Schmidt plates, Few and Madore separated 69 ring galaxies into two main classes, the O-type and P-type galaxies. The O-type galaxies contained a central nucleus and smooth regular ring, whereas the P-type systems often contained an offset nucleus with a knotted ring. Both classes contained a fraction of barred galaxies. If the ring galaxies were caused by a collision, the authors argued, then companion galaxies should be found close to the ring at a higher frequency than that expected by chance. They therefore searched for companion galaxies in an area of up to 5 times the angular-diameter of the ring. In order to estimate the possibility of chance coincidences, control fields were also studied from each plate containing a ring galaxy, in order to estimate the local average surface density of galaxies in a similar direction to the ring on the sky. The results of the statistical tests were that P-type rings showed an excess of companions with small separations (separations of less than 2 ring galaxy diameters). For larger separations, the number of possible companions was found to be indistinguishable from that expected by chance. The O-type galaxies did not show any enhancement of possible companions over that expected by chance. They concluded that the P-type galaxies were good candidates for collisional galaxies and that the majority of the O-type galaxies were not. The O-type galaxies were found to be similar to the (R)S galaxies of de Vaucouleurs, de Vaucouleurs and Corwin (1976).
An important contribution made by Few and Madore was an estimate of the space density of ring galaxies. 214 ring galaxies are listed in the CPGA and the catalog is complete up to a declination of -21°. They estimated that the volume space density of ring galaxies is 5.4 × 10-6 h3 Mpc-3 (here h = H0/100). This corresponds to an average of one ring galaxy in every spherical volume of radius 35 h-1 Mpc. This value is probably the most reliable measurement obtained so far for ring galaxies, and is in approximate agreement with two earlier, but less rigorous estimates made by Freeman and de Vaucouleurs (1974) and Thompson (1977).
The volume space density of rings derived above is about a factor of 104 less than the space density of average moderately luminous disk galaxies. Few and Madore were able to show that the scarcity of rings in nearby galaxy samples is consistent with the collisional formation picture. For example, the authors estimated that, because of the need to restrict the collisions to nearly bulls-eye impacts, only one in 5000 collisions would be expected to produce a ring (these restrictions may be a little conservative, see Section 5). Furthermore, the short lifetime of the ring phenomenon (typically a few × 108 yrs) further reduces the probability that a ring galaxy would be observed at any given instant. No comparable study has yet been made in the northern sky.
A question that is relevant to the statistics of nearby companions of rings is whether the companion always survives the encounter. In Appleton et al. (1987) we speculated that the long HI plume associated with Arp 143 might be the remnant of a galaxy disrupted by the impulse it received after passing through the center of NGC 2445. In cases such as Arp 284 or AM 1724-622, small companions are probably seen in the process of at least partial disruption. This process will become more significant if the intruder is both small and loosely bound. It is possible that, if the impulse the intruder receives becomes larger than its own binding energy, that is if (V)impulse2 2GM' / R', the companion is unlikely to survive the encounter and would be severely disrupted. In such a case, the companion would likely be spread over a large area of sky, making its detection difficult, at least at optical wavelengths. Extremely deep optical and HI radio imaging around empty rings is long overdue to search for "relics" of such ill-fated companions.