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Abstract: Gravitational lenses on galaxy scales are plausibly modelled as havingellipsoidal symmetry and a universal dark matter density profile, with a Sersicprofile to describe the distribution of baryonic matter. Predicting all lensingeffects requires knowledge of the total lens potential: in this work we giveanalytic forms for that of the above hybrid model. Emphasising that complexlens potentials can be constructed from simpler components in linearcombination, we provide a recipe for attaining elliptical symmetry in eitherprojected mass or lens potential. We also provide analytic formulae for thelens potentials of Sersic profiles for integer and half-integer index. We thenpresent formulae describing the gravitational lensing effects due tosmoothly-truncated universal density profiles in cold dark matter model. Forour isolated haloes the density profile falls off as radius to the minus fifthor seventh power beyond the tidal radius, functional forms that allow allorders of lens potential derivatives to be calculated analytically, whileensuring a non-divergent total mass. We show how the observables predicted bythis profile differ from that of the original infinite-mass NFW profile.Expressions for the gravitational flexion are highlighted. We show howdecreasing the tidal radius allows stripped haloes to be modelled, providing aframework for a fuller investigation of dark matter substructure in galaxiesand clusters. Finally we remark on the need for finite mass halo profiles whendoing cosmological ray-tracing simulations, and the need for readily-calculablehigher order derivatives of the lens potential when studying catastrophes instrong lenses.

Author: Edward A. Baltz, Phil Marshall, Masamune Oguri



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