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

Hercules is the prototype of the ultra-faint dwarf (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. In order 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. We have obtained images of Hercules in the rSloan, BBessel and Uspec bands with the Large Binocular Telescope (LBT) and LBC-BIN mode capabilities. The rSloan new data-set combined with data from the LBT archive span a time baseline of about 5 yr, allowing us to measure for the first time proper motions of stars in the Hercules direction. The Uspec data along with existing LBT photometry allowed us to use colour-colour diagram to further remove the field contamination. Thanks to a highly-accurate procedure to derive the rSloan-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 rSloan=22 mag and disentangle a significant fraction (\>90\%) of Milky Way contaminants. We ended up with a sample of 528 sources distributed over a large portion of the galaxy body (0.12 deg^2). Of these sources, 171 turned out to be background galaxies and additional foreground stars, from the analysis of the Uspec - BBessel vs. BBessel - rSloan 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\pm 2 Gyr), with a wide spread in metallicity (-3.3\<[Fe/H]\<-1.8).