On statistical lensing and the anticorrelation between 2dF QSOs and foreground galaxies

We study the cross-correlation of Automated Plate Measurement and Sloan Digital Sky Survey galaxies with background quasi-stellar objects (QSOs) taken from the 2dF QSO Redshift Survey, and detect a significant (2.8σ) anticorrelation. The lack of a similar signal between stars in the 2dF survey and our galaxy samples gives us confidence that the anticorrelation is not due to a systematic error. The possibility that dust in the foreground galaxies could produce such an anticorrelation is marginally rejected, at the 2σ level, through consideration of the colours of QSOs behind these galaxies. It is possible that a dust model that obscures QSOs without reddening them, or preferentially discards reddened QSOs from the 2dF survey sample, could produce such an anticorrelation; however, such models are at odds with the positive QSO–galaxy correlations found at bright magnitudes by other authors. Our detection of a galaxy–QSO anticorrelation is consistent with the predictions of statistical lensing theory. When combined with earlier results that have reported a positive galaxy–QSO correlation, a consistent and compelling picture emerges that spans faint and bright QSO samples showing positive or negative correlations according to the QSO N(m) slope. We find that galaxies are highly anti-biased on small scales. We consider two models that use quite different descriptions of the lensing matter and find that they yield consistent predictions for the strength of galaxy bias on 0.1 h−1 Mpc scales of b∼ 0.1 (for a ΛCDM cosmology). Whilst the slope of our power-law fit to the QSO–galaxy cross-correlation does not allow us to rule out a linear bias parameter, when we compare our measurement of b on 100 h−1 kpc scales to independent methods that determine b∼ 1 on h−1 Mpc scales, we conclude that bias, on these small scales, is scale-dependent. These results indicate that there appears to be more mass present, at least on the 100 h−1 kpc scales probed, than predicted by simple ΛCDM biasing prescriptions, and thus constrain halo occupation models of the galaxy distribution.