The angular correlation function of K ′ ∼19.5 galaxies and the detection of a cluster at z =0.775

We investigate (i) the clustering environment of a sample of five radio galaxies at 0.7 ≤ z ≤ 0.8 and (ii) the galaxy angular correlation function, ω (θ), on five K ′ ‐band (2.1 μm) images covering a total of 162.2 arcmin 2 to a completeness limit K ′ ≃ 19.5. Applying two methods – counting galaxies within 1.5 arcmin of each radio galaxy, and using a detection routine with a modelled cluster profile – we detect a cluster of estimated Abell richness N A =85 ± 25 (class 1 or 2), approximately centred on the radio galaxy 5C6.75 at z =0.775. Of the other radio galaxies, two appear to be in less rich groups or structures, and two in field environments. The mean clustering environment of all five radio galaxies is estimated to be of N A =29 ± 14 richness, similar to that of radio galaxies at more moderate redshifts of 0.35 < z < 0.55. The angular correlation function, ω (θ), of the detected galaxies showed a positive signal out to at least θ≃ 20 arcsec, with a ∼ 4σ detection of clustering for magnitude limits K ′ =18.5–20.0. The relatively high amplitude of ω(θ) and its shallow scaling with magnitude limit are most consistent with a luminosity evolution model in which E/S0 galaxies are much more clustered than spirals ( r 0 =8.4 compared with 4.2 h −1 Mpc) and clustering is approximately stable (ε∼ 0) to z ∼ 1.5, possibly with an increase above the stable model in the clustering of red galaxies at the highest ( z > 1.5) redshifts. Our images also show a significant excess of close (1.5–5.0 arcsec separation) pairs of galaxies compared with the expectation from ω (θ) at larger separations. We estimate that 11.0 ± 3.4 per cent of K ′ ≤ 19.5 galaxies are in close pairs in excess of the observed ω (θ), if this is of the form ω (θ) ∝θ −0.8 . This can be explained if the local rate of galaxy mergers and interactions increases with redshift as ∼ (1+ z ) m with m =1.33 −0.51 +0.36 .