Models of the Cosmic Horseshoe gravitational lens J1004+4112

We model the extremely massive and luminous lens galaxy in the Cosmic Horseshoe Einstein ring system J1004+4112, recently discovered in the Sloan Digital Sky Survey. We use the semilinear method of Warren & Dye, which pixelizes the source surface brightness distribution, to invert the Einstein ring for sets of parametrized lens models. Here, the method is refined by exploiting Bayesian inference to optimise adaptive pixelization of the source plane and to choose between three differently parametrized models: a singular isothermal ellipsoid, a power-law model and a Navarro, Frenk & White (NFW) profile. The most probable lens model is the power law with a volume mass density rho proportional to r(-1.96 +/- 0.02) and an axis ratio of similar to 0.8. The mass within the Einstein ring (i.e. within a cylinder with projected distance of similar to 30 kpc from the centre of the lens galaxy) is (5.02 +/- 0.09) x 10(12) M(circle dot), and the mass-to-light ratio is similar to 30. Even though the lens lies in a group of galaxies, the preferred value of the external shear is almost zero. This makes the Cosmic Horseshoe unique amongst large separation lenses, as almost all the deflection comes from a single, very massive galaxy with little boost from the environment.