  When considering gaps in debris discs, a typical approach is to invoke
clearing by an unseen planet within the gap, and derive the planet mass using
Wisdom overlap or Hill radius arguments. However, this approach can be invalid
if the disc is massive, because this clearing would also cause planet
migration. This could result in a calculated planet mass that is incompatible
with the inferred disc mass, because the predicted planet would in reality be
too small to carve the gap without significant migration. We investigate the
gap that a single embedded planet would carve in a massive debris disc. We show
that a degeneracy is introduced, whereby an observed gap could be carved by two
different planets: either a high-mass, barely-migrating planet, or a smaller
planet that clears debris as it migrates. We find that, depending on disc mass,
there is a minimum possible gap width that an embedded planet could carve
(because smaller planets, rather than carving a smaller gap, would actually
migrate through the disc and clear a wider region). We provide simple formulae
for the planet-to-debris disc mass ratio at which planet migration becomes
important, the gap width that an embedded planet would carve in a massive
debris disc, and the interaction timescale. We also apply our results to
various systems, and in particular show that the disc of HD 107146 can be
reasonably well-reproduced with a migrating, embedded planet. Finally, we
discuss the importance of planet-debris disc interactions as a tool for
constraining debris disc masses.
