One possibility for the origin of GRGs is that they are otherwise normal FR II sources that reside in extremely low density gaseous environments. The environments in which radio galaxies reside have been studied in depth (e.g. [Longair & Seldner 1979]; [Heckman et al. 1986]; [Prestage & Peacock 1988]; [Hill & Lilly 1991]; [Allington-Smith et al. 1993]; [Zirbel 1997]) because the gas density and pressure in the host galaxy's ISM, any intracluster medium, and the IGM are at least partly responsible for determining the resulting radio morphology.
An intriguing result of recent studies ([Hill & Lilly 1991]; [Allington-Smith et al. 1993], [Zirbel 1997]) is that FR II galaxies are found in a range of cluster richnesses at moderate redshifts, but they are only found in poor to very poor groups at low redshift. The "richness'' of the cluster associated with a radio galaxy can be estimated in a statistical sense in the absence of redshift data on nearby galaxies. Allington-Smith et al. (1993) define the richness parameter as the number of galaxies within a projected radius of 500 kpc and with assuming the same redshift as the AGN. The number counts are corrected for contamination by foreground and background galaxies by subtracting number counts from a field offset from the radio galaxy. Zirbel (1997) gives a conversion of to Abell class as . With this conversion, the thresholds for Abell Classes 0 and 1 are and 26 respectively. Using this richness estimation technique, Zirbel (1997) found that of a sample of 29 low redshift (z < 0.2) FR IIs: (1) 41% of the sample of low z FR IIs reside in very poor groups (), and (2) more importantly, no low redshift FR II was found in a rich group with . Based on the results given in §3.5, NVSS 2146+82 appears to reside in a group with an anomalously high galaxy richness compared to other low redshift FR IIs. Although the galaxy counts from the field surrounding NVSS 2146+82 were not calculated identically to those of Zirbel (1997), the value of is likely > 25 - 30 for NVSS 2146+82.
The upper limit on the cluster X-ray emission is consistent with the NVSS 2146+82 group being at the low end of the X-ray luminosity distribution for poor clusters. [Wan & Daly (1996)] found that in a comparison of low redshift clusters with and without FR II sources, clusters that contained FR IIs were underluminous in X-rays compared to clusters without FR IIs. Although the cluster surrounding NVSS 2146+82 may be Abell Class 0, its lack of associated X-ray gas suggests that the pressure in the surrounding medium is low enough for a giant radio source to form with little disruption of the FR II jet.
Curiously, several other GRGs listed in Table 6 also appear to lie in regions with overdensities of nearby galaxies. The GRG 0503-286 appears to lie in a group of 30 or so galaxies ([Saripalli et al. 1986]). These companions are concentrated to the northeast of the host galaxy of 0503-286, and may have caused the asymmetric appearance of the northern lobe of the radio structure. Overdensities of nearby galaxies are also reported for 1358+305 ([Parma et al. 1996]) and 8C 0821+695 ([Lacy et al. 1993]); however, in both cases there is no spectroscopic confirmation of the redshifts of the candidate cluster galaxies. In a recent study of the optical and X-ray environments of radio galaxies, [Miller et al. (1999)] find that for a sample of FR I sources, all have extended X-ray emission and overdensities of optical galaxies. However of their sample of seven FR II sources, none have overdensities of optical galaxies or extended X-ray emission except for the GRG DA240, which has no extended X-ray emission but does have a marginally significant excess of optical companions. Perhaps for at least some of the GRG population, the presence of the host galaxy in an optically rich group with little associated X-ray gas is related to the formation or evolution of the radio source?