HST astrometry in the 30 Doradus region: measuring proper motions of individual stars in the Large Magellanic Cloud

We present measurements of positions and relative proper motions in the 30 Doradus region of the Large Magellanic Cloud (LMC). We detail the construction of a single-epoch astrometric reference frame, based on specially-designed observations obtained with the two main imaging instruments ACS/WFC and WFC3/UVIS onboard the Hubble Space Telescope (HST). Internal comparisons indicate a sub milli-arc-second (mas) precision in the positions and the presence of semi-periodic systematics with a mean amplitude of ~0.8 mas. We combined these observations with numerous archival images taken with WFPC2 and spanning 17 years. The precision of the resulting proper motions for well-measured stars around the massive cluster R 136 can be as good as ~20 microarcsec/yr, although the true accuracy of proper motions is generally lower due to the residual systematic errors. The observed proper-motion dispersion for our highest-quality measurements is ~0.1 mas/yr. Our catalog of positions and proper motions contains 86,590 stars down to V~25 and over a total area of ~70 square arcmin. We examined the proper motions of 105 relatively bright stars and identified a total of 6 candidate runaway stars. We are able to tentatively confirm the runaway status of star VFTS 285, consistent with the findings from line-of-sight velocities, and to show that this star has likely been ejected from R 136. This study demonstrates that with HST it is now possible to reliably measure proper motions of individual stars in the nearest dwarf galaxies such as the LMC.