2012ApJ...755...58N

Using redshifts as a proxy for galaxy distances, estimates of the two-dimensional (2D) transverse peculiar velocities of distant galaxies could be obtained from future measurements of proper motions. We provide the mathematical framework for analyzing 2D transverse motions and show that they offer several advantages over traditional probes of large-scale motions. They are completely independent of any intrinsic relations between galaxy properties; hence, they are essentially free of selection biases. They are free from homogeneous and inhomogeneous Malmquist biases that typically plague distance indicator catalogs. They provide additional information to traditional probes that yield line-of-sight peculiar velocities only. Further, because of their 2D nature, fundamental questions regarding vorticity of large-scale flows can be addressed. Gaia, for example, is expected to provide proper motions of at least bright galaxies with high central surface brightness, making proper motions a likely contender for traditional probes based on current and future distance indicator measurements.