Transverse Velocities of Galaxies From Microlens Parallaxes

The transverse velocity of a spiral galaxy can be measured to an accuracy $\sim 60\text{kms}$ by making parallax observations of quasars being microlensed by stars in the disk of the galaxy. To make the measurement, a quasar must be located behind the disk of the galaxy between about 1 and 2 scale lengths from the center. The quasar must then be monitored for microlensing events and the events followed simultaneously from the Earth and a satellite in solar orbit, preferably at $\sim 30$AU. A systematic search in a volume within $21,000\text{kms}$ could locate quasars with $B<23$ behind a total of $\sim 1900$ galaxies. The rate of lensing events (and hence galaxy velocity measurements) would be $\sim 3{\mathrm{y}\mathrm{r}}^{-1}$. The events would have typical characteristic times ${\omega }^{-1}\sim 3$yr. Under the assumption that the mass spectrum of lensing objects is the same in other spiral galaxies as in our own, the observations could be used to measure the Hubble parameter to an accuracy of 5%.