Fast and Accurate Fourier Series Solutions to Gravitational Lensing by a General Family of Two–Power‐Law Mass Distributions

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Abstract
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two-power-law ellipsoidal mass distributions are presented. The cusped two-power-law ellipsoidal mass distributions are characterized by inner and outer power-law radial indices and a break (or transition) radius. The model family includes mass models mimicking Jaffe, Hernquist, and η models and dark matter halo profiles from numerical simulations. The Fourier series solutions for the cusped two-power-law mass distributions are relatively simple and allow a very fast calculation, even for a chosen small fractional calculational error (e.g., 10-5). These results will be particularly useful for studying lensed systems that provide a number of accurate lensing constraints and for systematic analyses of large numbers of lenses. Subroutines employing these results for the two-power-law model and the results by Chae, Khersonsky, & Turnshek for the generalized single-power-law mass model are made publicly available.
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