Secular Extragalactic Parallax: Measurement Methods and Predictions for Gaia

Secular extragalactic parallax caused by the solar system's velocity relative to the cosmic microwave background rest frame may be observable as a dipole proper motion field with amplitude $78~\mu$as yr$^{-1}$ Mpc. Nearby galaxies also exhibit proper motions caused by their transverse peculiar velocities that prevent detection of secular parallax for any single galaxy, although a statistical detection may be made instead. Such a detection could constrain the local Hubble parameter. We present methods to measure secular parallax using correlated extragalactic proper motions and find a first limit on the secular parallax amplitude using proper motions of 232 nearby galaxies from Gaia Data Release 2. The recovered dipole has insignificant upper limit of 3500 $\mu$as yr$^{-1}$ Mpc. This measurement will be improved by larger sample size and reduced proper motion uncertainties in future data releases. Using the local peculiar velocity field derived from Cosmicflows-3, we simulate galaxy proper motions and predict that a significant detection ($5-10\sigma$) of the secular parallax amplitude will be possible by Gaia's end of mission. The detection is contingent on proper motions of nearby ($<5$ Mpc), bright ($G<15$ mag) galaxies, and corresponds to an insignificant upper limit on the Hubble parameter. We further investigate the implications of our simulations for the study of transverse peculiar velocities, which we find to be consistent with large scale structure theory. The peculiar velocity field additionally results in low-multipole correlated proper motions on the order of $0.3~\mu$as yr$^{-1}$ that may be confounded with other cosmological proper motion measurements, such as limits on the gravitational wave background and the anisotropy of the Hubble expansion.