The VMC survey XXVIII. Improved measurements of the proper motion of the Galactic globular cluster 47 Tucanae

We use deep multi-epoch PSF photometry taken with the Visible and Infrared Survey Telescope for Astronomy (VISTA) to measure and analyze the proper motions of stars within the Galactic globular cluster 47 Tucanae (47 Tuc, NGC 104). The observations are part of the ongoing near-infrared VISTA survey of the Magellanic Cloud system (VMC). The data analyzed here corresponds to one VMC tile and covers a total sky area of 1.77 deg^2. Absolute proper motions with respect to ~9070 background galaxies are calculated from a linear regression model applied to the stellar positions in 11 epochs in the Ks filter. The data extend over a total time baseline of ~17 months. We found a median proper motion of the stars within 47 Tuc of (mu_a cos(d), mu_d) = (+5.89 +/- 0.02(stat) +/- 0.13(sys), -2.14 +/- 0.02(stat) +/- 0.08(sys)) mas/yr, based on the measurements of ~35000 individual sources between 5' and 42' from the cluster center. We compared our result to the proper motions from the newest US Naval Observatory CCD Astrograph Catalog (UCAC5) which includes data from the Gaia data release 1. Selecting cluster members (~2700 stars) we found a median proper motion of (mu_a cos(d), mu_d) = (+5.30 +/- 0.03(stat) +/- 0.70(sys), -2.70 +/- 0.03(stat) +/- 0.70(sys)) mas/yr. The values derived from the VMC data are consistent with the UCAC5 result, and are close to literature measurements obtained using HST. We combined our results with literature radial velocity measurements and reconstructed the orbit of 47 Tuc, finding that the cluster is on a low-ellipticity orbit and is confined within the inner ~7.5 kpc of the Galaxy. We show that the use of an increased time baseline combined with PSF-determined stellar centroids in crowded regions significantly improves the accuracy of the method. In future works, we will apply this method to more VMC tiles to study in detail the kinematics of the Magellanic Clouds.