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Imaging and spectroscopic data (Yee et al. 1987; Ellingson et al. 1991; Yee et al. 1992) indicate that quasars are found in environments significantly richer than those of average galaxies. The data show a positive association of quasars with neighboring galaxies.

Optically selected quasars to z ltapprox 0.7 exhibit a quasar-galaxy cross-correlation function amplitude, Aqg, that is approximately 2.3 times stronger than the galaxy-galaxy correlation amplitude (to separations r ltapprox 0.25h-1 Mpc):

Equation 51 (51)

This excess correlation suggests that the quasars are typically located in groups of galaxies with a mean richness

Equation 52 (52)

(where ng appeq 0.015 Mpc-3 is the mean density of galaxies). The range of individual group richnesses is, however, wide.

Radio-loud quasars at z ltapprox 0.5 are found in similar environments to those of the optical quasars above. At 0.5 ltapprox z ltapprox 0.7, the radio quasars appear to be located in richer environments, with

Equation 53 (53)

This cross-correlation amplitude corresponds to a mean environment of rich clusters (R ~ 0, NR ~ 40). Radio quasars at these redshifts are thus typically found in rich clusters.

The average galaxy velocity dispersion of the parent clusters associated with the quasars (Ellingson et al. 1991; Yee et al. 1992) is

Equation 54 (54)

The observed auto-correlation function of optically selected quasars is approximately (Shaver 1988)

Equation 55 (55)

The quasar correlation strength is intermediate between the correlation of individual galaxies and the correlation of rich clusters. This correlation strength is consistent with the quasars location in groups of the above mean richness, as would be suggested by the richness-dependent cluster correlation function (Section 10). The quasars may thus trace the correlation function of their parent clusters (Bahcall and Chokshi 1991).

Similar results are observed for the association of radio galaxies with groups and clusters. This association explains the observed increase in the strength of the radio galaxy correlation function over the general galaxy correlations (Bahcall and Chokshi 1992).

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