Large-scale QSO-galaxy correlations and weak lensing

Several recent studies show that bright, intermediate- and high-redshift op tically and radio-selected QSOs are positively correlated with nearby galax ies on a range of angular scales up to a degree. Obscuration by unevenly di stributed Galactic dust can be ruled out as the cause, leaving weak statist ical lensing as the physical process responsible. However, the amplitude of correlations on less than or similar to 1 degrees angular scales is at lea st a factor of a few larger than lensing model predictions. A possible way to reconcile the observations and theory is to revise the weak lensing form alism. We extend the standard lensing formulation to include the next highe r order term (second order) in the geodesic equation of motion for photons. We derive relevant equations applicable in the weak tensing regime, and di scuss qualitative properties of the updated formulation. We then perform nu merical integrations of the revised equation and study the effect of the ex tra term using two different types of cosmic mass density fluctuations. We find that nearby large-scale coherent structures increase the amplitude of the predicted lensing-induced correlations between QSOs and foreground gala xies by similar to 10% (not a factor of several required by observations), while the redshift of the optimal, i.e., "most correlated," structures is m oved closer to the observer compared to what is predicted using the standar d lensing equation.