In an isotropic and homogeneous Hubble expansion, all transverse motion is peculiar. Like the radial peculiar velocities of galaxies, transverse peculiar velocities are a means to trace the density of matter that does not rely on light tracing mass. Unlike radial peculiar velocity measurements that require precise redshift-independent distances in order to distinguish between the Hubble expansion and the observed redshift, transverse peculiar velocities can be measured using redshifts alone as a proxy for distance. Extragalactic proper motions can therefore directly measure peculiar velocities and probe the matter power spectrum. Here we develop two-point transverse velocity correlation statistics and demonstrate their dependence on the matter power spectrum. We predict the power in these correlation statistics as a function of the physical separation, angular separation, and distance of pairs of galaxies and demonstrate that the effect of large-scale structure on transverse motions is best measured for pairs of objects with comoving separations less than about 50 Mpc. Transverse peculiar velocities induced by large-scale structure should be observable as proper motions using long baseline radio interferometry or space-based optical astrometry.
展开▼
