The VMC survey - XVII. The proper motion of the Small Magellanic Cloud
  and of the Milky Way globular cluster 47 Tucanae
  In this study we use multi-epoch near-infrared observations from the VISTA
survey of the Magellanic Cloud system (VMC) to measure the proper motion of
different stellar populations in a tile of 1.5 deg sq. in size in the direction
of the Galactic globular cluster 47 Tuc. We obtain the proper motion of the
cluster itself, of the Small Magellanic Cloud (SMC), and of the field Milky Way
stars. Stars of the three main stellar components are selected from their
spatial distribution and their distribution in colour-magnitude diagrams. Their
average coordinate displacement is computed from the difference between
multiple Ks-band observations for stars as faint as Ks=19 mag. Proper motions
are derived from the slope of the best-fitting line among 10 VMC epochs over a
time baseline of ~1 yr. Background galaxies are used to calibrate the absolute
astrometric reference frame. The resulting absolute proper motion of 47 Tuc is
(mu_alpha cos(delta), mu_delta)=(+7.26+/-0.03, -1.25+/-0.03) mas/yr. This
measurement refers to about 35000 sources distributed between 10 and 60 arcmin
from the cluster centre. For the SMC we obtain (mu_alpha cos(delta),
mu_delta)=(+1.16+/-0.07, -0.81+/-0.07) mas/yr from about 5250 red clump and red
giant branch stars. The absolute proper motion of the Milky Way population in
the line-of-sight (l =305.9, b =-44.9) of this VISTA tile is (mu_alpha
cos(delta), mu_delta)=(+10.22+/-0.14, -1.27+/-0.12) mas/yr and results from
about 4000 sources. Systematic uncertainties associated to the astrometric
reference system are 0.18 mas/yr. Thanks to the proper motion we detect 47 Tuc
stars beyond its tidal radius.
