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, quasi‐stellar objects and also the cosmic microwave background temperature map), is known to consist of two components: a Gaussian core and an exponential tail. We use numerical gravitational‐lensing experiments in a ΛCDM cosmology for quantifying these two components. We especially focus on the physical processes responsible for generating these 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 haloes with M > 10 14   h −1  M ⊙ 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 arcmin, 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 subarcminute scales.