Estimating the Large-Scale Structure of the Universe Using Quasi-Stellar Object Carbon IV Absorbers

Galaxies have long been known to form large clusters, and cosmologists are interested in characterizing this clustering as a way of studying the large-scale structure of the universe. This work is motivated by a data catalog consisting of information on lines of sight from Earth to distant quasi-stellar objects (QSO's) and the carbon IV absorbers that lie on them. The absorbers are believed to be gas clouds near galaxies too far away to be easily observed. Thus, the absorber catalog provides a unique and interesting way to examine the large-scale structure of the universe. On large scales previous studies have mainly used pairs of absorbers on the same lines of sight to obtain estimates describing the clustering of absorbers. It is clear that absorbers on different lines of sight contain information about the degree of clustering. We develop an adaptation of the rigid motion corrected estimator of the reduced second-moment function for the absorber catalog taking into account the across-line-of-sight information. We show how to compute this estimator efficiently using the weights for an Isotropic estimator proposed in a recent study. We also show how the modified versions of the rigid motion estimators can be obtained. Simulations suggest that using the modified rigid motion correction estimator may reduce standard errors by 5-20% on scales from 50 to 250 h^-1 Mpc for a set of 100 lines of sight.