We model the extremely massive and luminous lens galaxy in the Cosmic Horseshoe Einstein ring system, recently discovered in the Sloan Digital Sky Survey. We use the semi-linear method of Warren & Dye (2003), which pixelises the source surface brightness distribution, to invert the Einstein ring for sets of parameterised lens models. Here, the method is refined by exploiting Bayesian inference to optimise adaptive pixelisation of the source plane and to choose between three differently parameterised models: a singular isothermal ellipsoid, a power law model and a NFW profile. The most probable lens model is the power law with a volume mass density that scales as r^(-1.96+/-0.02) and an axis ratio of ~0.8. The mass within the Einstein ring (i.e., within a cylinder with projected distance of ~30 kpc from the centre of the lens galaxy) is (5.02+/-0.09)*10^12 M_solar, and the mass-to-light ratio is ~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.
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