On Statistical Lensing and the Anti-Correlation Between 2dF QSOs and Foreground Galaxies

Abstract

We cross-correlate APM and SDSS galaxies with background QSOs from the 2dF QSO Redshift Survey, and detect a significant (2.8sigma) anti-correlation. The lack of a signal between 2dF stars and our galaxy samples suggests the anti-correlation is not due to a systematic error. The possibility that dust in the foreground galaxies could produce the anti-correlation is marginally rejected, at the 2sigma level through consideration of QSO colours. It is possible that dust that obscures QSOs without reddening them, or preferentially discards reddened QSOs from the 2QZ sample, could produce such an anti-correlation, 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 anti-correlation is consistent with statistical lensing theory. When combined with earlier results that have reported a positive galaxy-QSO correlation, a consistent, 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 different descriptions of the lensing matter and find they yield consistent predictions for the strength of galaxy bias on 0.1Mpc/h scales of b~0.1 (for LCDM). Whilst the slope of our power-law fit to the QSO-galaxy cross-correlation does not rule out linear bias, when we compare our measurement of b on 100 kpc/h scales to independent methods that determine b~1 on Mpc/h scales, we conclude that bias, on these small scales, is scale-dependent. These results indicate more mass, at least on the 100 kpc/h scales probed, than predicted by simple LCDM biasing prescriptions, and can thus constrain halo occupation models of the galaxy distribution.