Measuring transverse velocities in gravitationally lensed extragalactic systems using an annual parallax effect

A parallax method to determine transverse velocity in a gravitationally lensed system is described. Using the annual motion of the Earth around the Sun allows us to probe the local structure of the magnification map that, under certain assumptions, can be used to infer the effective transverse velocity. The method is applied to OGLE data for QSO2237+0305 and the velocity value is estimated to be about 15 ± 10 kms if attributed to the lensing galaxy or about 420±300 kms if attributed to the quasar. We find this estimate unreasonably small and conclude that we have not measured a parallax effect. We give a short list of properties that a system should possess to allow a successful implementation of this method.