  A number of scenarios have been proposed to explain the low velocity
dispersion (and hence possible absence of dark matter) of the low surface
brightness galaxies NGC1052-DF2 and NGC1052-DF4. Most of the proposed
mechanisms are based on the removal of dark matter via the interaction of these
galaxies with other objects. A common feature of these processes is the
prediction of very faint tidal tails, which should be revealed by deep imaging
(mu_g > 30 mag/arcsec2). Using ultra-deep images obtained with the Gemini
telescopes, about 1 mag deeper than previously published data, we analyzed the
possible presence of tidal tails in both galaxies. We confirm the presence of
tidal tails in NGC1052-DF4, but see no evidence for tidal effects in
NGC1052-DF2, down to surface brightnesses of mu_g=30.9 mag/arcsec2. We
therefore conclude that while the absence of dark matter in NGC1052-DF4 could
be attributed to the removal of dark matter by gravitational interactions, in
the case of NGC1052-DF2 this explanation seems less plausible, and therefore
other possibilities such as an incorrect distance measurement or that the
system may be rotating could alleviate the dark matter problem.
