Title:A Measurement of the Three-Dimensional Clustering of C IV Absorption-Line Systems on Scales of 5 to 300 Mpc

Abstract: 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 line- and cross-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 of 2.2, drawn from the spectra of 276 QSOs. We confirm the existence of significant clustering on comoving scales up to 100 Mpc, and find that the additional cross-line-of-sight information strengthens the evidence for clustering on scales from 100 Mpc to 150 Mpc. There is no evidence of absorber clustering along or across lines of sight for scales from 150 Mpc to 300 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 cross-line-of-sight information will substantially increase clustering sensitivity. We find that standard errors are reduced by an additional factor of 2 to 20 on scales of 30 to 200 Mpc, effectively increasing the sample size by an extra factor of 4 to 400 at large distances.