Domain of validity for pseudo-elliptical NFW lens models

TL;DR

This study assesses the physical limitations of pseudo-elliptical NFW lens models, establishing their valid parameter ranges and providing a mapping to elliptical mass distribution models to improve gravitational lensing simulations.

Contribution

It introduces a mapping between PNFW and ENFW models, and defines the parameter space where PNFW models are physically valid for gravitational lensing applications.

Findings

PNFW models are valid for larger ellipticities than previously thought.

Negative convergence regions are far from arc formation zones.

The mapping aids in inverse modeling and fast arc simulations.

Abstract

Models with elliptical potentials (pseudo-elliptical) are often used in gravitational lensing applications. Nevertheless, they generally lead to nonphysical mass distributions in some regions. In this paper we revisit the physical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model, for a broad range of the potential ellipticity parameter \epsilon\ and characteristic convergence \kappa_s focusing on the behavior of the mass distribution close to the tangential critical curve, where tangential arcs are expected to be formed. We investigate the shape of the mass distribution on this region and the presence of negative convergence. We obtain a mapping from the PNFW to the NFW model with elliptical mass distribution (ENFW) and provide fitting formulae for connecting the parameters of both models. We compare the arc cross section for these models using the "infinitesimal circular source approximation". We find that the PNFW model is well-suited to model an elliptical mass distribution on a larger \epsilon\ - \kappa_s parameter space than previously expected. In particular values as large as \epsilon\ ~ 0.65 are allowed for small \kappa_s. However, if we require the PNFW model to reproduce the arc cross section of the ENFW well, the ellipticity is more restricted. We also find that the negative convergence regions occur far from the arc formation region and should therefore not be a problem for studies with gravitational arcs. The determination of a domain of validity for the PNFW model and the mapping to ENFW models could have implications for the use of PNFW models for the inverse modeling of lenses and for fast arc simulations.