All Transverse Motion is Peculiar: Connecting the Proper Motions of Galaxies to the Matter Power Spectrum

TL;DR

This paper introduces a method to connect galaxy proper motions with the matter power spectrum, enabling direct measurement of peculiar velocities through redshifts alone, and predicts observable correlations at certain scales.

Contribution

It develops new two-point transverse velocity correlation statistics and demonstrates their dependence on the matter power spectrum, providing a novel way to probe large scale structure.

Findings

Transverse peculiar velocities can be measured using redshifts alone.

Correlation effects are strongest for galaxy pairs less than 50 Mpc apart.

Proper motions induced by large scale structure are observable with current technology.

Abstract

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.