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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 thedifficulty of disentangling Hercules bona-fide stars from the severe Galacticfield contamination. In order to better constrain Hercules properties we aim atremoving foreground and background contaminants in the galaxy field using theproper motions of the Milky Way stars and the colour-colour diagram. We haveobtained images of Hercules in the rSloan, BBessel and Uspec bands with theLarge Binocular Telescope (LBT) and LBC-BIN mode capabilities. The rSloan newdata-set combined with data from the LBT archive span a time baseline of about5 yr, allowing us to measure for the first time proper motions of stars in theHercules direction. The Uspec data along with existing LBT photometry allowedus to use colour-colour diagram to further remove the field contamination.Thanks to a highly-accurate procedure to derive the rSloan-filter geometricdistortion solution for the LBC-red, we were able to measure stellar relativeproper motions to a precision of better than 5 mas yr^-1 down to rSloan=22 magand disentangle a significant fraction (\>90\%) of Milky Way contaminants. Weended up with a sample of 528 sources distributed over a large portion of thegalaxy body (0.12 deg^2). Of these sources, 171 turned out to be backgroundgalaxies and additional foreground stars, from the analysis of the Uspec -BBessel vs. BBessel - rSloan colour-colour diagram. This leaves us with asample of 357 likely members of the Hercules UFD. We compared the cleanedcolour-magnitude diagram (CMD) with evolutionary models and synthetic CMDs,confirming the presence in Hercules of an old population (t=12\pm 2 Gyr), witha wide spread in metallicity (-3.3\<[Fe/H]\<-1.8).

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