  We investigate the evolution of the surface density of a circumbinary
accretion disc after the mass loss induced by the merger of two supermassive
black holes. We first introduce an analytical model, under the assumption of a
disc composed of test particles, to derive the surface density evolution of the
disc following the mass loss. The model predicts the formation of sharp density
peaks in the disc; the model also allows us to compute the typical timescale
for the formation of these peaks. To test and validate the model, we run
numerical simulations of the process using the Smoothed Particle Hydrodynamics
(SPH) code PHANTOM, taking fluid effects into account. We find good agreement
in the shape and position of the peaks between the model and the simulations.
In a fluid disc, however, the epicyclic oscillations induced by the mass loss
can dissipate, and only some of the predicted peaks form in the simulation. To
quantify how fast this dissipation proceeds, we introduce an appropriate
parameter, and we show that it is effective in explaining the differences
between the analytical, collisionless model and a real fluid disc.
