Gaia reference frame amid quasar variability and proper motion patterns
  in the data
  Gaia's very accurate astrometric measurements will allow the International
Celestial Reference Frame (ICRF) to be improved by a few orders of magnitude in
the optical. Several sets of quasars are used to define a kinematically stable
non-rotating reference frame with the barycentre of the Solar System as its
origin. Gaia will also observe a large number of galaxies which could obtain
accurate positions and proper motions although they are not point-like. The
optical stability of the quasars is critical and we investigate how accurately
the reference frame can be recovered. Various proper motion patterns are also
present in the data, the best known is caused by the acceleration of the Solar
System Barycentre, presumably, towards the Galactic centre. We review some
other less-well-known effects that are not part of standard astrometric models.
We model quasars and galaxies using realistic sky distributions, magnitudes and
redshifts. Position variability is introduced using a Markov chain model. The
reference frame is determined using the algorithm developed for the Gaia
mission which also determines the acceleration of the Solar System. We also
test a method to measure the velocity of the Solar System barycentre in a
cosmological frame. We simulate the recovery of the reference frame and the
acceleration of the Solar System and conclude that they are not significantly
disturbed in the presence of quasar variability which is statistically
averaged. However, the effect of a non-uniform sky distribution of the quasars
can result in a correlation between the reference frame and acceleration which
degrades the solution. Our results suggest that an attempt should be made to
astrometrically determine the redshift dependent apparent drift of galaxies due
to our velocity relative to the CMB, which in principle could allow the
determination of the Hubble parameter.
