THE MASS-DISTRIBUTION OF THE LENS GALAXY IN MG-1131+0456

We present the results of modeling 5, 8, and 15 GHz maps of the gravitational lens MG 1131+0456 using the LensClean algorithm. Two models for the mass distribution in the lens were fitted: a de Vaucouleurs model and a model with the two-dimensional potential phi = b(2-alpha)(r(2) + s(2))(alpha/2)/alpha, both in an external shear field. The best-fit de Vaucouleurs model has an effective radius of R(e) = 0''.83 +/- 0''.13, larger than that measured at optical wavelengths. The best-fit ''alpha-model'' has alpha = 0.6 +/- 0.2 and a core radius of s = 0''.19 +/- 0''.07. An isothermal model (alpha = 1) is inconsistent with the data. The best alpha-model fits the 8 GHz map significantly better than the best de Vaucouleurs model, and it is a good fit at all three frequencies. Although the peak residuals in the best reconstructions are less than 5% of the map peak and it is difficult to distinguish visually the original image and the reconstructions, none of the models is statistically consistent with the data. Experiments on the effects of using Clean maps suggest that systematic errors are not the source of the discrepancy. We believe the primary problem is that an external shear is an inadequate model for the angular structure of the lens galaxy. The finite core radius in the models is required by the structure of the extended ring, so we confirm that the central component in the 8 GHz map is a central, lensed image of the source rather than the lens galaxy. Two galaxies 3'' from the ring add an external shear to the lens model that is within 3 degrees of the fitted model. The alignment is remarkable, but the two galaxies cannot account for the magnitude of the shear unless the effective ratio of their luminosity to the primary lens galaxy is 25 times larger than the measured ratio. The model lens positions, the position angle of the shear, and the mass interior to the ring are determined very precisely by the lens models. The time delay between the compact components is predicted with an uncertainty we estimate to be at most +/-9%; the formal uncertainty is +/-4%.