Domain of validity for pseudo-elliptical NFW lens models
Mass distribution, mapping to elliptical models, and arc cross section
H. S. Dúmet-Montoya1,2, G. B. Caminha1,2 and M. Makler1,2
1 Instituto de Cosmologia, Relatividade e Astrofísica – ICRA, Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, CEP 22290-180, Rio de Janeiro, RJ, Brazil
2 Laboratório Interinstitucional de e-Astronomia – LIneA, Rua Gal. José Cristino 77, CEP 20921-400, Rio de Janeiro, RJ, Brazil
Received: 18 November 2011
Accepted: 4 June 2012
Context. Owing to their computational simplicity, models with elliptical potentials (pseudo-elliptical) are often used in gravitational lensing applications, in particular for mass modeling using arcs and for arc statistics. However, these models generally lead to negative mass distributions in some regions and to dumbbell-shaped surface density contours for high ellipticities.
Aims. We revisit the physical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model, 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). We compare the arc cross section for both models, aiming to determine a domain of validity for the PNFW model in terms of its mass distribution and for the cross section.
Methods. We defined a figure of merit to i) measure the deviation of the iso-convergence contours of the PNFW model to an elliptical shape, ii) assigned an ellipticity εΣ to these contours, iii) defined a corresponding iso-convergence contour for the ENFW model. We computed the arc cross section using the “infinitesimal circular source approximation”.
Results. We extend previous work by investigating the shape of the mass distribution of the PNFW model for a broad range of the potential ellipticity parameter ε and characteristic convergence Ks. We show that the maximum value of ε to avoid dumbbell-shaped mass distributions is explicitly dependent on Ks, with higher ellipticities (ε ≃ 0.5, i.e., εΣ ≃ 0.65) allowed for small Ks. We determine a relation between the ellipticity of the mass distribution εΣ and ε valid for any ellipticity. We also derive the relation of characteristic convergences, obtaining a complete mapping from PNFW to ENFW models, and provide fitting formulae for connecting the parameters of both models. Using this mapping, the cross sections for both models are compared, setting additional constraints on the parameter space of the PNFW model such that it reproduces the ENFW results. 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.
Conclusions. We conclude that the PNFW model is well-suited to model an elliptical mass distribution on a larger ε–Ks parameter space than previously expected. However, if we require the PNFW model to reproduce the arc cross section of the ENFW well, the ellipticity is more restricted, particularly for low Ks. 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, for example.
Key words: gravitational lensing: strong / galaxies: clusters: general / galaxies: halos / dark matter
© ESO, 2012