Abstract
We present a new approach for fast calculation of gravitational lensing properties, including the lens potential, deflection angles, convergence, and shear, of elliptical Navarro–Frenk–White (NFW) and Hernquist density profiles, by approximating them by superpositions of elliptical density profiles for which simple analytic expressions of gravitational lensing properties are available. This model achieves high fractional accuracy better than 10−4 in the range of the radius normalized by the scale radius of 10−4–103. These new approximations are ∼300 times faster in solving the lens equation for a point source compared with the traditional approach resorting to expensive numerical integrations, and are implemented in glafic software.
Highlights
Gravitational lensing provides an important means of studying the Universe
We have presented a new approach for fast calculation of gravitational lensing properties of the elliptical NFW and Hernquist density profiles
The elliptical NFW and Hernquist density profiles are approximated by superpositions of the cored steep ellipsoid for which simple analytic expressions of gravitational lensing properties are available
Summary
Gravitational lensing provides an important means of studying the Universe. With its purely gravitational nature and well-known underlying physics, gravitational lensing can be used to measure the dark matter distribution in galaxies and clusters of galaxies as well as to probe cosmological parameters (see e.g., Bartelmann & Schneider 2001; Treu 2010; Kneib & Natarajan 2011; Limousin et al 2013; Treu & Marshall 2016; Oguri 2019; Umetsu 2020, for reviews). Golse & Kneib (2002) consider the elliptical NFW potential, in which the ellipticity is introduced in isopotential contours rather than in isodensity contours (see Meneghetti et al 2003) While this model enables fully analytic calculations of gravitational lensing properties, is used for measuring projected ellipticities of cluster-scale dark matter halos (e.g., Richard et al 2010), and is widely implemented in strong lens modeling softwares including gravlens (Keeton 2001b, 2010), lenstool (Jullo et al 2007), glafic (Oguri 2010), and lenstronomy (Birrer & Amara 2018), it predicts unphysical density distributions (e.g., dumbbell-like isodensity contours and negative densities) when the ellipticity is large. We propose models that approximate elliptical NFW and Hernquist density profiles and have analytic expressions for their gravitational lensing potentials, deflection angles, convergence and shear. Gravitational lensing properties of this elliptical model can be computed by one-dimensional numerical integrations (Schramm 1990; Keeton 2001a)
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