Parameter degeneracy in models of the quadruple lens system Q2237+0305

Abstract

The geometry of the quadruple lens system Q2237+0305 is modeled with a simple astigmatic lens: a power-law mass distribution: m \propto r^βwith an external shear γ. The image positions can be reproduced with an accuracy better than 0.01 arcsec for any 0.0 < β< 1.85 and the corresponding value of γ= 0.1385 - 0.0689 β. This is a factor of about 4 more precise than what can be achieved by the best constant M/L lens models. The image intensity ratios and the time delay ratios are almost constant along our one parameter family of models, but the total magnification varies from 8 to > 1000, and the maximum time delay (between leading image B and trailing image C) for H_0 of 75 km/sec/Mpc varies from more than 20 hours to about 1.5 hours, while βincreases from 0.0 to 1.85.