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

Fourier series solutions to the deflection and magnification by a family ofthree-dimensional cusped two power-law ellipsoidal mass distributions arepresented. The cusped two power-law ellipsoidal mass distributions arecharacterized by inner and outer power-law radial indices and a break (or,transition) radius. The model family includes mass models mimicking Jaffe,Hernquist, and $\eta$ models and dark matter halo profiles from numericalsimulations. The Fourier series solutions for the cusped two power-law massdistributions are relatively simple, and allow a very fast calculation even fora chosen small fractional calculational error (e.g. $10^{-5}$). These resultswill be particularly useful for studying lensed systems which provide a numberof accurate lensing constraints and for systematic analyses of large numbers oflenses. Subroutines employing these results for the two power-law model and theresults by Chae, Khersonsky, & Turnshek for the generalized single power-lawmass model are made publicly available.