Gravitational lensing properties of isothermal universal halo profile
  N-body simulations predict that dark matter halos with different mass scales
are described by a universal model, the Navarro-Frenk-White (NFW) density
profiles. As a consequence of baryonic cooling effects, the halos will become
more concentrated, and similar to an isothermal sphere over large range in
radii ($\sim 300$ $h^{-1}$kpc). The singular isothermal sphere model however
has to be truncated artificially at large radii since it extends to infinity.
We model a massive galaxy halo as a combination of an isothermal sphere and an
NFW density profile. We give an approximation for the mass concentration at
different baryon fractions and present exact expressions for the weak lensing
shear and flexion for such a halo. We compare the lensing properties with a
Singular Isothermal Sphere and NFW profiles. We find that the combined profile
can generate higher order lensing signals at small radii and is more efficient
in generating strong lensing events. In order to distinguish such a halo
profile from the SIS or NFW profiles, one needs to combine strong and weak
lensing constraints on small and large radii.
