A Realistic Grid of Models for the Gravitationally Lensed Einstein Cross (Q2237+0305) and Its Relation to Observational Constraints

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Abstract
A detailed study of a power-law lens model is presented for the gravitational lens system Q2237+0305, also known as the Einstein Cross. The adopted three-dimensional distribution for the mass of the lens is more realistic than in previous models and is described by ρ(X, Y, Z) = ρ0[1 + (X/a)2 + (Y/b)2 + (Z/c)2]-ν/2. Hubble Space Telescope (HST) optical positions of the image components and the center of the galactic bulge (Crane et al.) along with radio flux density ratios of the image components (Falco et al.) are used to constrain the model [8 (four relative optical positions) + 3 (relative magnifications) = 11 constraints]. The goodness of fit χ2 is defined using these constraints. The best model has χ2 ≈ 14, which is a better fit than all previous models. We investigate the characteristics of models within the 99% confidence region of parameter space around the best model. We find that the lensing properties (i.e., total image magnification, relative image magnifications, and time delays between image pairs) of models are well described by the ellipticity of the projected mass of the lens, and we calculate a grid of models that illustrates how the lensing properties depend on the ellipticity. We discuss how future observations, such as placing tighter constraints on the brightness of any fifth image, can be used to further constrain the grid of models presented here. The possibility of using the grid of models to place constraints on the Hubble constant is also discussed.