The VMC survey -IX. Pilot study of the proper motion of stellar
  populations in the LMC from 2MASS and VISTA data
  We use multi-epoch near-infrared observations from the VISTA survey of the
Magellanic Cloud system (VMC) to measure the proper motion of stars of the LMC,
in one tile of 1.5 deg^2 centred at (alpha, delta) = (05:59:23.136,
-66:20:28.68) and including the South Ecliptic Pole, with respect to their
2MASS position over a time baseline of ~10 years and from VMC observations
only, spanning a time range of ~1 year. Stars of different ages are selected
from the (J-Ks) vs. Ks diagram and their average coordinate displacement is
computed from the difference between Ks band observations for stars as faint as
Ks=19 mag. Proper motions are derived by averaging up to seven 2MASS-VMC
combinations in the first case and from the slope of the best fit line among
the seven VMC epochs in the second case. Separate proper motion values are
obtained for variable stars in the field. The proper motion of ~40,000 LMC
stars in the tile, with respect to ~8000 background galaxies, obtained from VMC
data alone, is mu_alpha cos(delta) = +2.20+/-0.06 (stat) +/-0.29 (sys) and
mu_delta = +1.70+/-0.06 (stat) +/-0.30 (sys) mas/yr. This value agrees with
recent ground-based determinations in a nearby field but is larger than studies
with the HST; the cause of this discrepancy may be due to additional systematic
errors in the data. The LMC proper motion is also clearly distinct from the
proper motion derived for stars of the Milky Way. The relative proper motion
between the foreground stars and the LMC stars is ~5 mas/yr. Furthermore, we
measure a decrease of the proper motion with increasing logarithm of stellar
age for LMC stars. This study, based on just one VMC tile, shows the potential
of the 2MASS-VMC and VMC-VMC combinations for a comprehensive investigation of
the proper motion across the Magellanic system. (Abridged)
