Several recent studies show that bright, intermediate-and high-redshift optically and radio-selected QSOs are positively correlated. with nearby galaxies on a range of angular scales up to a degree. Obscuration by unevenly distributed Galactic dust can be ruled out as the cause, leaving weak statistical lensing as the physical process responsible. However, the amplitude of correlations on ≲1° angular scales is at least 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 formalism. We extend the standard lensing formulation to include the next higher order term (second order) in the geodesic equation of motion for photons. We derive relevant equations applicable in the weak lensing regime, and discuss qualitative properties of the updated formulation. We then perform numerical integrations of the revised equation and study the effect of the extra 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 galaxies by ∼10% (not a factor of several required by observations), while the redshift of the optimal, i.e., " most correlated," structures is moved closer to the observer compared to what is predicted using the standard lensing equation.
- Gravitational lensing
- Large-scale structure of universe