A bag of tricks: Using proper motions of Galactic stars to identify the Hercules ultra-faint dwarf galaxy members

Context. Discovered in the last decade as overdensities of resolved stars, the ultra-faint dwarfs (UFDs) are among the least luminous, most dark-matter dominated, and most metal-poor galaxies known today. They appear as sparse, loose objects with high mass-to-light ratios. Hercules is the prototype of the UFD galaxies. To date, there are still no firm constraints on its total luminosity due to the difficulty of disentangling Hercules bona-fide stars from the severe Galactic field contamination. Aims. To better constrain Hercules properties, we aim at removing foreground and background contaminants in the galaxy field using the proper motions of the Milky Way stars and the colour-colour diagram. Methods. We have obtained images of Hercules in the r(Sloan), B-Bessel and U-spec bands with the Large Binocular Telescope (LBT) and LBC-BIN mode capabilities. The r(Sloan) new dataset combined with data from the LBT archive span a time baseline of about 5 yr, allowing us to measure proper motions of stars in the Hercules direction for the first time. The U-spec data along with existing LBT photometry allowed us to use colour-colour diagram to further remove the field contamination. Results. Thanks to a highly-accurate procedure to derive the r(Sloan)-filter geometric distortion solution for the LBC-red, we were able to measure stellar relative proper motions to a precision of better than 5 mas yr(-1) down to r(Sloan) similar or equal to 22 mag and disentangle a significant fraction (> 90%) of MilkyWay contaminants. We ended up with a sample of 528 sources distributed over a large portion of the galaxy body (similar to 0.12 deg(2)). Of these sources, 171 turned out to be background galaxies and additional foreground stars from the analysis of the U-spec - B-Bessel vs. B-Bessel - r(Sloan) colour-colour diagram. This leaves us with a sample of 357 likely members of the Hercules UFD. We compared the cleaned colour-magnitude diagram (CMD) with evolutionary models and synthetic CMDs, confirming the presence in Hercules of an old population (t = 12 +/- 2 Gyr) with wide spread metallicity (-3.3 < [Fe/H] < 1.8). Conclusions. Our procedure to estimate star proper motions proved to be a very effective way to identify likely members for stellar systems as far as 130 kpc. The present selection, based on both proper motions and colour-colour diagram, provides a robust identification of Hercules members and a new target list for more spectroscopic investigations.