Domain of validity for pseudo-elliptical NFW lens models
  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.
