VLBI Observations of the Gravitational Lens System 0957+561: Structure and Relative Magnification of the A and B Images

We observed the putative gravitationally lensed images of the quasar, 0957+561, at 13 cm wavelength with a six-antenna VLBI array having nearly milliarcsecond resolution. Using four elliptically shaped Gaussian components to model the observed surface brightness distribution of each of the A and B images, we found that the resultant models offer strong evidence in support of the gravitational lens hypothesis. A simple, 2 x 2 magnification matrix relates quantitatively the brightness distributions of the two "long" jet components in one image to those in the other. The flux density, size, shape, and orientation of these two jet components, one each of length ~10 and 50 milliarcsecond, are likely to change only on a time scale long compared to the difference in light propagation times from source to observer ("time delay") for the two images. Thus the magnification matrix provides a value for the magnitude of the relative image magnification, B/A, of 0.64 +/- 0.03; in addition, the elements of the matrix can be used to constrain models of the mass distribution of the lens. The ratio, B/A, of the flux density of the ~ 1 milliarcsecond diameter core components in one image to that in the other is 0.82 +/- 0.02, apparently inconsistent with the relative magnification determined for the long jet components. This apparent inconsistency is evidence for changes in the brightness distribution of the quasar core, on a time scale comparable to, or shorter than, the time delay. Thus continued monitoring with VLBI of the flux density in each component of each image might provide a reliable determination of this time delay. Our analysis of the differences of the interferometer phases associated with these images yielded the difference in position between their brightest components, with a standard error of about 20 microarcsecs.