With and without spectroscopy: Gaia DR2 proper motions of seven
  Ultra-Faint Dwarf Galaxies
  We present mean absolute proper motion measurements for seven ultra-faint
dwarf galaxies orbiting the Milky Way, namely Bo\"{o}tes III, Carina II, Grus
II, Reticulum II, Sagittarius II, Segue 2 and Tucana IV. For four of these
dwarfs our proper motion estimate is the first ever provided. The adopted
astrometric data come from the second data release of the Gaia mission. We
determine the mean proper motion for each galaxy starting from an initial guess
of likely members, based either on radial velocity measurements or using stars
on the Horizontal Branch identified in the Gaia ($G_{\rm BP}$-$G_{\rm RP}$,$G$)
colour-magnitude diagram in the field of view towards the UFD. We then refine
their membership iteratively using both astrometry and photometry. We take into
account the full covariance matrix among the astrometric parameters when
deriving the mean proper motions for these systems. Our procedure provides mean
proper motions with typical uncertainties of $\sim0.1$ mas/yr, even for
galaxies without prior spectroscopic information. In the case of Segue 2 we
find that using radial velocity members only leads to biased results,
presumably because of the small number of stars with measured radial
velocities. Our procedure allows to maximize the number of member stars per
galaxy regardless of the existence of prior spectroscopic information, and can
therefore be applied on any faint or distant stellar system within reach of
Gaia.
