The Form and Evolution of the Clustering of QSO Heavy-Element Absorption-Line Systems

We have analyzed the clustering of C IV and Mg II absorption-line systems on comoving scales from 1 to 16 \hMpc, using an extensive catalog of heavy-element QSO absorbers with mean redshift 2.2 (C IV) and 0.9 (Mg II). We find that, for the C IV sample as a whole, the absorber line-of-sight correlation function is well-fit by a power law with index $\gamma = 1.75 ^{+0.50}_{-0.70}$ and comoving correlation length $r_0 = 3.4 ^{+0.7}_{-1.0}$ \hMpc ($q_0=0.5$). The clustering of absorbers at high redshift is thus of a form like that of galaxies and clusters at low redshift, and of amplitude such that absorbers are correlated on scales of galaxy clusters. We also trace the evolution of the mean amplitude $\xi_0(z)$ of the correlation function from $z=3$ to $z=0.9$. We find that, when parametrized as $\xi_0(z)\propto (1+z)^{-(3+\epsilon)+\gamma}$, the amplitude grows rapidly with decreasing redshift, with maximum-likelihood value for the evolutionary parameter of $\epsilon = 2.05 \pm 1.0$ ($q_0=0.5$). When extrapolated to zero redshift, the correlation length is $r_0 = 30 ^{+22}_{-13}$ \hMpc . This suggests that the strong C IV and Mg II absorbers, on megaparsec scales, are biased tracers of the higher-density regions of space, and that agglomerations of strong absorbers along a line of sight are indicators of clusters and superclusters. This is supported by recent observations of ``Lyman break'' galaxies. The rapid growth seen in the clustering of absorbers mimics that expected in a a critical universe from linear theory of gravitational instability, and is consistent with gravitationally induced growth of perturbations.