Faint K Selected Galaxy Correlations and Clustering Evolution

Angular and spatial correlations are measured for K band selected galaxies, 222 having redshifts, 40 with $z>1$, in two patches of combined area $\simeq27$~arcmin$^2$. The angular correlation at an average $K\simeq19.5$~mag is $\omega(\theta)\simeq (\theta/1.4\pm0.19^{\prime\prime}e^{\pm0.1})^{-0.8}$. From the redshift sample we find that the real space correlation of $M_K\le-24$ mag (k-corrected) galaxies is $\xi(r)\simeq(r/2.3e^{\pm0.14}\hmpc)^{-1.8}$ at a mean $z\simeq 0.6$ and $\xi(r)\simeq(r/1.4e^{\pm0.22}\hmpc)^{-1.8}$ at $z\simeq1.1$. In the $0.3\le z\le0.9$ interval the red galaxies, specified by $(U-K)_0>2$ AB mag, have a correlation amplitude about 5 times greater than the blue galaxies. In contrast to the usual power law behaviour of correlations, the cross-correlation of low and high luminosity galaxies at $z\simeq0.6$ shows a strong rise in the correlation amplitude within 100 \hkpc, possibly being a local bound population. The clustering of quasar absorption lines is put on a common basis with these measurements. The $W_{eq}({\rm C~IV})\ge0.15$\AA\ systems have $\xi(1\hmpc)\simeq 0.8$ suggesting that galaxy correlations evolve less rapidly beyond redshift one than they do at low redshifts. The weak C~IV absorption lines with $N({\rm C~IV}) > 10^{12}$ cm$^{-2}$ and $2.66 < z < 3.62$ are less clustered than the trend of galaxy correlations. The quasars themselves are much more strongly clustered than the K selected galaxies. Comparing to n-body simulations tentatively indicates that the observed clustering evolution evolves too slowly to be consistent with the density distribution in an $\Omega=1$ universe, but is broadly consistent with either the density field or dark matter halos in a low density universe.