Diagnostic properties of moving gravitational lenses

Abstract

Gravitational lensing has provided important information about the mass and density of the intervening galaxies which image more distant quasars, and has placed limits on the properties of massive objects which might perturb the microwave background. In most studies it has been assumed that the lensing object is stationary; some work has been done on moving lenses, but these have mostly been concerned with the effects of motion on the light curve, particularly as caustics sweep past the observer on the redshift pattern and surface brightness of a moving background, or as a cause of microlensing. Here we point out several properties of moving lenses that do not appear to have been noted before: moving lenses always produce two-dimensional velocities; they impose specific relations between observed velocities and positions; they magnify relative source velocities; they convert linear into rotary motion; and they convert radial into transverse velocity. The mass and distance of a moving lens can be separately determined. We point out some useful astronomical diagnostic properties of moving lenses, for which the Very-Long-Baseline Array under construction will be particularly useful.