Statistical distribution of gravitational-lensing excursion angles: Winding ways to us from the deep universe

We investigate statistical distributions of differences in gravitational-lensing deflections between two light rays, the so-called lensing excursion angles. A probability distribution function of the lensing excursion angles, which plays a key role in estimates of lensing effects on angular clustering of objects (such as galaxies, QSOs and also the CMB temperature map), is known to consist of two components; a Gaussian core and an exponential tail. We use numerical gravitational-lensing experiments in a Lambda-CDM cosmology for quantifying these two components. We especially focus on the physical processes responsible for generating those two components. We develop a simple empirical model for the exponential tail which allows us to explore its origin. We find that the tail is generated by the coherent lensing scatter by massive halos with M>10^14h^-1Msun at z<1 and that its exponential shape arises due to the exponential cut-off of the halo mass function at that mass range. On scales larger than 1 arc minute, the tail does not have a practical influence on the lensing effects on the angular clustering. Our model predicts that the coherent scatter may have non-negligible effects on angular clustering at sub-arcminute scales.