Compact groups of galaxies are defined to be groups of at least 4 galaxies within a range of 3 magnitudes (a factor 16 in luminosity) to lie so close to one another that the galaxies often overlap on the plane of the sky. Compact groups thus constitute a uniquely dense environment of galaxies, but are these groups as dense in real 3d space as they appear compact on the plane of the sky?

Comparing the observations of the well-studied Hickson Compact Groups (HCGs) with his dynamical simulations (Mamon 1987) of evolving groups, Mamon (1986) concluded that most HCGs were not physically dense, but caused by chance alignments of galaxies along the line-of-sight within larger groups. He verified the chance alignment conjecture with analytical calculations (Walke & Mamon 1989), which showed that HCGs by chance alignments should occur more often in clusters, and when he searched for HCG-like groups in the nearby Virgo cluster, he indeed found one (Mamon 1989).

However, through the analysis of mock HCG catalogs built from cosmological simulations, it turns out that only 1/3 of mock compact groups are caused by chance alignments (Díaz-Giménez & Mamon 2010; Díaz-Giménez et al. 2012). It is now clear that in his work during the 80s, Mamon had been misled by the incompleteness of the HCG (and other compact group catalogs): in particular, the new sample of compact groups selected from the 2MASS survey is the first one to show strong signs of luminosity segregation and of a magnitude gap at the bright end of the luminosity function, as he had found in his dynamical simulations (Mamon 1987) and also in the mock compact groups (Díaz-Giménez et al. 2012).

Gary Mamon's important papers on the topic are:

• Mamon (1986), Are compact groups of galaxies physically dense?, Astrophysical Journal 307, 426

• Mamon (1987), The dynamics of small groups of galaxies. I - Virialized groups, Astrophysical Journal 321, 622

• Mamon (1989), A compact group in Virgo, Astronomy & Astrophysics 219, 98

• Walke & Mamon (1989), The frequency of chance alignments of galaxies in loose groups,

• Dos Santos & Mamon (1999), Clumpy diffuse X-ray emission from the spiral-rich compact galaxy group HCG 16, Astronomy & Astrophysics 352, 1

• Mamon (2008), The nature of the nearest compact group of galaxies from precise distance measurements, Astronomy & Astrophysics 486, 113

• Díaz-Giménez & Mamon (2010), Compact groups from the Millennium Simulations - I. Their nature and the completeness of the Hickson sample, Monthly Notices of the Royal Astronomical Society 409, 1227

• Díaz-Giménez, Mamon, Pacheco, Mendes de Oliveira & Alonso (2012), Compact groups of galaxies selected by stellar mass: The 2MASS Compact Group catalogue, Monthly Notices of the Royal Astronomical Society, 426, 296