Detection of satellite remnants in the Galactic Halo with Gaia III.
  Detection limits for Ultra Faint Dwarf Galaxies
  We present a method to identify Ultra Faint Dwarf Galaxy (UFDG) candidates in
the halo of the Milky Way using the future Gaia catalogue and we explore its
detection limits and completeness. The method is based on the Wavelet Transform
and searches for over-densities in the combined space of sky coordinates and
proper motions, using kinematics in the search for the first time. We test the
method with a Gaia mock catalogue that has the Gaia Universe Model Snapshot
(GUMS) as a background, and use a library of around 30 000 UFDGs simulated as
Plummer spheres with a single stellar population. For the UFDGs we use a wide
range of structural and orbital parameters that go beyond the range spanned by
real systems, where some UFDGs may remain undetected. We characterize the
detection limits as function of the number of observable stars by Gaia in the
UFDGs with respect to that of the background and their apparent sizes in the
sky and proper motion planes. We find that the addition of proper motions in
the search improves considerably the detections compared to a photometric
survey at the same magnitude limit. Our experiments suggest that Gaia will be
able to detect UFDGs that are similar to some of the known UFDGs even if the
limit of Gaia is around 2 magnitudes brighter than that of SDSS, with the
advantage of having a full-sky catalogue. We also see that Gaia could even find
some UFDGs that have lower surface brightness than the SDSS limit.
