We present the first evidence of clear signatures of tidal distortions in the density distribution of the fascinating open cluster NGC 6791. We used deep and wide-field data obtained with the Canada-France-Hawaii-Telescope covering a 2x2 square degrees area around the cluster. The two-dimensional density map obtained with the optimal matched filter technique shows a clear elongation and an irregular distribution starting from ~300 from the cluster center. At larger distances, two tails extending in opposite directions beyond the tidal radius are also visible. These features are aligned to both the absolute proper motion and to the Galactic center directions. Moreover, other overdensities appear to be stretched in a direction perpendicular to the Galactic plane. Accordingly to the behaviour observed in the density map, we find that both the surface brightness and the star count density profiles reveal a departure from a King model starting from ~600 from the center. These observational evidence suggest that NGC 6791 is currently experiencing mass loss likely due to gravitational shocking and interactions with the tidal field. We use this evidence to argue that NGC 6791 should have lost a significant fraction of its original mass. A larger initial mass would in fact explain why the cluster survived so long. Using available recipes based on analytic studies and N-body simulations, we derived the expected mass loss due to stellar evolution and tidal interactions and estimated the initial cluster mass to be M_ini=(1.5-4) x 10^5 M_sun.
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