ARlogo Annu. Rev. Astron. Astrophys. 1997. 35: 357-88
Copyright © 1997 by Annual Reviews. All rights reserved

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By "compact group", we mean a small, relatively isolated, system of typically four or five galaxies in close proximity to one another. Such groups do not necessarily form a distinct class, but may instead be extreme examples of systems having a range of galaxy density and population. Because of this, the properties of the groups in any particular sample may be strongly influenced by the criteria used to define the sample. The early surveys used qualitative criteria that, while successful in finding many interesting individual objects, do not easily allow one to draw broad conclusions about the groups as a whole. Thus, the focus in recent years has been on samples selected using specific, quantitative, criteria. These criteria define the minimum number and magnitude range of the galaxies, and also consider the galaxy spatial distribution.

The use of quantitative selection criteria was pioneered by Rose (1977) who searched for groups that have three or more galaxies that are brighter than a limiting magnitude of 17.5, and that have a projected surface density enhancement of a factor of 1000 compared to the surrounding background galaxy density. Searching an area of 7.5% of the sky, he found 170 triplets, 33 quartets, and 2 quintets. Unfortunately, the sample received little follow-up study. Sulentic (1983) re-examined the 35 Rose groups which contain four or more galaxies and found that only a third actually satisfied the selection criteria. This is testimony to the difficulty of visual searches. A more fundamental problem is that the fixed magnitude limit in the selection criteria makes the sample susceptible to strong distance-dependent biases.

In an attempt to reduce such effects, Hickson (1982, 1993, 1994) adopted a relative magnitude criterion, selecting systems of four or more galaxies whose magnitudes differ by less than 3.0. A distance independent (to first order) compactness criterion was employed: mubarG < 26, where mubarG is the mean surface brightness of the group calculated by distributing the flux of the member galaxies over the smallest circular area containing their geometric centers. To avoid including the cores of rich clusters, an isolation criterion was necessary so as to reject the group if a non-member galaxy, not more than 3 mag fainter than the brightest member, occurred within three radii of the center of the circle. (A non-member galaxy is a galaxy which if included in the group would cause the group to fail one or more of the selection criteria.) From a search of 67% of the sky (all the POSS prints), and using magnitudes estimated from the POSS red prints, exactly 100 groups were found satisfying these criteria (hereafter HCG's). As the HCG sample is now the most widely studied, it is important to examine the biases introduced by the criteria, and by the visual search procedure.

Any sample selected on the basis of surface density will suffer from geometric and kinematic biases. The former occurs because non-spherical systems will be preferentially selected if they are oriented to present a smaller cross-sectional area (eg. prolate systems pointed towards us); the latter because we will preferentially select systems that, owing to galaxy orbital motion, are momentarily in a more compact state (transient compact configurations). Thus, a compact group might result from a chance alignment or transient configuration within a loose group (Mamon 1986). This question will be considered in more detail in Section 6.2.

Other biases arise from the subjective nature of the search procedure. The original catalog contains a few mis-identifications, such as compact galaxies mistaken for stars, and marginal violations of the isolation criteria. In addition, when photometry was obtained for the galaxies in the catalog (Hickson et al. 1989), it was found that some groups would not satisfy the selection criteria if photometric magnitudes are used. Attempts to rectify these problems have been made by Hickson et al. (1989) and Sulentic (1997). However, it should be emphasized that changes, such as using photometric magnitudes in the selection criteria, are not corrections to the catalog, but are actually the imposition of additional a postiori selection criteria. The resulting subsample is by no means complete because the new criteria are applied only to the visually-selected HCG catalog and not to the entire sky.

Because of the difficulty of identifying faint groups, the HCG catalog starts to become significantly incomplete at an integrated magnitude of about 13 (Hickson et al. 1989, Sulentic & Rabaça 1994). A more subtle effect results from the difficulty of recognizing low-surface-brightness groups. Because of this, the catalog also becomes incomplete at surface brightnesses fainter than 24 (Hickson 1982). Yet another effect is that groups may be more noticeable if the magnitude spread of their members is small. Thus, the catalog may also be incomplete for magnitude intervals greater than about 1.5 (Prandoni et al. 1994). These effects are of critical importance in statistical analyses of the sample. One immediate conclusion is that the actual number of groups which satisfy the selection criteria may be considerably larger than the number found by a subjective search.

It has recently become feasible to find compact groups by automated techniques. Mamon (1989) used a computer to search Tully's (1987) catalog of nearby galaxies and identified one new compact group, satisfying Hickson's criteria, in the Virgo Cluster. Prandoni et al. (1994) applied similar criteria to digital scans of ~ 1300 deg2 around the southern galactic pole and detected 59 new southern compact groups (SCGs). Observations are presently underway to obtain accurate photometry and redshifts for this sample (Iovino private communication). The digitized Palomar Sky Survey II also offers new opportunities for the identification of compact groups (De Carvalho & Djorgovski 1995).

An alternative approach is to identify groups of galaxies from redshift information, as was first done by Humason et al. (1956). With the advent of large-scale redshift surveys, it has become possible to identify a reasonably-large sample compact groups in this way. Barton et al. (1996) have compiled a catalog of 89 redshift-selected compact groups (RSCGs) found by means of a friends-of-friends algorithm applied to a complete magnitude-limited redshift survey. Galaxies having projected separations of 50h-1 kpc or less and line-of-sight velocity differences of 1000 km s-1 or less are connected and the sets of connected galaxies constitute the groups. The numerical values were chosen to best match the characteristics of the HCG sample, and indeed, many of those RSCGs that have at least four members are also HCGs. There are some significant differences, however: Because foreground and background galaxies are automatically eliminated by the velocity selection criteria, this technique is more effective at finding groups in regions of higher galaxy density, which would fail the HCG isolation criterion. This criterion requires that the distance to the nearest neighbor be at least as large as the diameter of the group. The RSCG criterion, on the other hand, requires only that the nearest-neighbor distance be larger than the threshold distance (50h-1 kpc for the RSCGs), which may be considerably smaller. It will therefore allow the inclusion of groups that are physically less isolated (and therefore less physically distinct) than would the HCG criterion. One would also expect that the numbers of groups found in a given volume by the less-restrictive RSCG criteria to be larger than by the HCG criteria, as seems to be the case. While the redshift-selection method compliments the HCG angular-selection technique, one should keep in mind that it also selects groups according to apparent (projected) density - the velocity information serves only to reject interlopers. Thus it will be subject to some of the biases discussed above. Also, because the galaxy sample used is magnitude-limited, rather than volume-limited, there will be redshift-dependent biases in the RSCGs. However, the well-defined selection criteria and the completeness of the sample, should allow a quantitative determination of the effects of this bias.

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