Measurement of the three-dimensional clustering of C IV absorption-line systems on scales of 5-1000 h(-1) MPC

We examine the three-dimensional clustering of C IV absorption-line systems using an extensive catalog of QSO heavy-element absorbers drawn from the l iterature. We measure clustering by a volume-weighted integral of the corre lation function called the reduced second-moment measure, and include infor mation from both along and across QSO lines of sight, thus enabling a full determination of the three-dimensional clustering of absorbers, as well as a comparison of along- and across-line-of-sight clustering properties. Here we present the three-dimensional reduced second-moment estimator for a thr ee-dimensional point process probed by one-dimensional lines of sight, and apply our algorithm to a sample of 345 C IV absorbers with median redshift <z > = 2.2, drawn from the spectra of 276 QSOs. We confirm the existence of significant clustering on comoving scales of up to 100 h(-1) Mpc and (q(0) = 0.5), find that the additional across-line-of-sight information strength ens the evidence for clustering on scales from 100 to 150 h(-1) Mpc. There is no evidence of absorber clustering along or across lines of sight for sc ales from 150 to 1000 h(-1) Mpc. We show that with a 300 times larger catal og, such as that to be compiled by the Sloan Digital Sky Survey (100,000 QS Os), use of the full three-dimensional estimator and across-line-of-sight i nformation will substantially increase clustering sensitivity. We find that standard errors are reduced by a factor of 2-20 on scales of 30-200 h(-1) Mpc, in addition to the factor of (300)(1/2) reduction from the larger samp le size, effectively increasing the sample size by an extra factor of 4-400 at large distances.