Investigation of the possible third image and mass models of the gravitational lens PMN J1632-0033

We present multifrequency VLBA(2) observations of PMN J1632-0033, one of the few gravitationally lensed quasars suspected of having a central odd'' image. The central component has a different spectral index than the two bright quasar images. Therefore, either the central component is not a third image, and is instead the active nucleus of the lens galaxy, or else it is a third image whose spectrum is inverted by free-free absorption in the lens galaxy. In either case, we have more constraints on mass models than are usually available for a two-image lens, especially when combined with the observed orientations of the radio jets of the two bright quasars. If there is no third quasar image, the simplest permitted model is a singular isothermal sphere in an external shear field: beta = 2.05(-0.10)(+0.23) (2 sigma), where rho(r) proportional to r(-beta). If the central component is a third image, a hypothesis that can be tested with future high-frequency observations, then the density distribution is only slightly shallower than isothermal: beta = 1.91 +/- 0.02 (2 sigma). We also derive limits on the size of a constant-density core, and the break radius and exponent of an inner density cusp.