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 \langle z \rangle = 2.2 , drawn from the spectra of 276 QSOs .
We confirm the existence of significant clustering on comoving scales up to 100 h ^ { -1 } Mpc ( q _ { 0 } = 0.5 ) , and find that the additional cross –line–of–sight information strengthens the evidence for clustering on scales from 100 h ^ { -1 } Mpc to 150 h ^ { -1 } Mpc .
There is no evidence of absorber clustering along or across lines of sight for scales from 150 h ^ { -1 } Mpc to 300 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 cross–line–of–sight information will substantially increase clustering sensitivity .
We find that standard errors are reduced by a factor 2 to 20 on scales of 30 to 200 h ^ { -1 } Mpc , in addition to the factor of \sqrt { 300 } reduction from the larger sample size , effectively increasing the sample size by an extra factor of 4 to 400 at large distances .