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