The Angular Correlation Function of K=19.5 Galaxies and the Detection of a Cluster at z=0.775

On five K-band Omega camera images, covering a total of 162.2 sq. arcmin to K=19.5, we investigate (i) the clustering environment of 5 radio galaxies at 0.7<z<0.8 and (ii) the galaxy angular correlation function. We detect a cluster of estimated Abell richness class 1 or 2, 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 5 is similar to that of radio galaxies at more moderate redshifts of 0.35<z<0.55. The angular correlation function of the galaxies, at limits K=18.5--20.0, is most consistent with a luminosity evolution model in which E/S0 galaxies are much more clustered than spirals (r_0=8.4 compared to 4.2 1/h Mpc) and clustering is approximately stable (epsilon=0), although the clustering may exceed the stable model at the highest (z>1.5) redshifts. We also find a significant excess of 1.5--5.0 arcsec separation pairs of galaxies compared to the expectation from the inward extrapolation of omega(theta). To K=19.5, we estimate that 11.0\pm 3.4 per cent of galaxies are in close pairs in excess of omega(theta). This can be explained if the local rate of galaxy mergers and interactions increases with redshift as $\sim (1+z)^m$ with $m=1.33_{-0.51}^{+0.36}$.