Once considered stationary objects, galaxies are increasingly becoming an interest in proper motion studies. As the precision of astrometry increases, extragalactic proper motion can be used to trace the real-time evolution of cosmological phenomena, such as the growth of large-scale structure. Large-scale structure density fluctuations cause correlated peculiar galaxy motions on various angular scales. Characterizing the overall proper motion field as a function of angular scale and/or redshift requires precisely modeling and distinguishing between a variety of competing cosmological and observer-induced proper motion signals. The acoustic scale in the clustering of matter offers an opportunity to predict a correlated proper motion signal at a precise angular scale. Caused by the baryon acoustic oscillations in the early universe, the acoustic scale serves as a robust cosmological standard ruler. However, at low redshift, gravity among large-scale structure creates flows on the ~10 Mpc scale, causing galaxy pairs originally separated by the acoustic scale to shift to smaller scales. As these pairs of galaxies shift closer together, a redshift-dependent pattern of converging galaxies should appear at the angular acoustic scale. We present a theoretical framework for the proper motion signal caused by the non-linear shift of the acoustic scale. Our prediction is redshift dependent and reaches a minimum of -0.025 μas yr-1 (negative for converging motion) at a redshift of z = 0.018.
The authors acknowledge support from NSF grant AST-1411605 and NASA grant 14-ATP14-0086.