Gravitational Lensing in More Realistic Dark Matter Halo Models

In this study, we explore gravitational lensing using more realistic dark matter halo models, moving beyond the limitations of spherical-collapse approximations. Through analytical calculations employing various mass functions, we address critical factors often neglected in the standard Press-Schechter formalism, such as ellipsoidal collapse conditions, angular momentum dynamics, dynamical friction, and the cosmological constant. Our analysis incorporates two widely recognized halo density profiles, the Navarro-Frenk-White and Einasto profiles considering both spherical and ellipsoidal-collapse scenarios. We provide detailed calculations of key gravitational lensing observables, including Einstein radii, lensing optical depths, and time delays, across a broad range of redshifts and masses using two different lensing models: the point mass and singular isothermal sphere (SIS) models. Our results show that using more realistic dark matter halo models enhances lensing effects compared to their spherical-collapse counterparts. Additionally, our analyses of lensing optical depths and time delays reveal distinct differences between the point mass and SIS lens models. These findings underscore the importance of using realistic halo descriptions instead of simplified approximations when modeling gravitational lensing, as this approach can more accurately capture the complex structures of dark matter.