A 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 literature. We measure clustering by a volume-weighted integral of the correlation function called the reduced second-moment measure, and include information 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 three-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 (q₀ = 0.5), and find that the additional across-line-of-sight information strengthens 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 scales from 150 to 1000 h^-1 Mpc. We show that with a 300 times larger catalog, such as that to be compiled by the Sloan Digital Sky Survey (100,000 QSOs), use of the full three-dimensional estimator and across-line-of-sight information 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 sample size, effectively increasing the sample size by an extra factor of 4-400 at large distances.