Reanalysis of the association of high-redshift 1-Jansky quasars with   IRAS galaxies
  We develop a new statistical method to reanalyse angular correlations between background QSOs and foreground galaxies that are supposed to be a consequence of dark matter inhomogeneities acting as weak gravitational lenses. The method is based on a weighted average over the galaxy positions and is optimized to distinguish between a random distribution of galaxies around QSOs and a distribution which follows an assumed QSO-galaxy two-point correlation function, by choosing an appropriate weight function. With simulations we demonstrate that this weighted average is slightly more significant than Spearman's rank-order test which was used in previous investigations. In particular, the advantages of the weighted average show up if the two-point correlation function is weak. We then reanalyze the correlation between high-redshift 1-Jansky QSOs and IRAS galaxies, taken from the IRAS Faint Source Catalog; these samples were analyzed previously using Spearman's rank-order test. In agreement with the previous work, we find moderate to strong correlations between these two samples; considering the angular two-point correlation function of these samples, we find a typical scale of order $5'$ from which most of the correlation signal derives. However, the statistical significance of the correlation changes with the redshift slices of the QSO sample one considers. Comparing with simple theoretical estimates of the expected correlation, we find that the signal we derive is considerably stronger than expected. On the other hand, recent direct verifications of the overdensity of matter in the line-of-sight to high-redshift radio QSOs obtained from the shear field around these sources, indicates that the observed association can be attributed to a gravitational lens effect. 
Armin Bartsch, Peter Schneider and Matthias Bartelmann   (Max-Planck-Institut f. Astrophysik)