  It is known that an embedded massive planet will open a gap in a
protoplanetary disc via angular momentum exchange with the disc material. The
resulting surface density profile of the disc is investigated for one
dimensional and two dimensional disc models and, in agreement with previous
work, it is found that one dimensional gaps are significantly deeper than their
two dimensional counterparts for the same initial conditions. We find, by
applying one dimensional torque density distributions to two dimensional discs
containing no planet, that the excitement of the Rossby wave instability and
the formation of Rossby vortices play a critical role in setting the
equilibrium depth of the gap. Being a two dimensional instability, this is
absent from one dimensional simulations and does not limit the equilibrium gap
depth there. We find similar gap depths between two dimensional gaps formed by
torque density distributions, in which the Rossby wave instability is present,
and two dimensional planet gaps, in which no Rossby wave instability is
present. This can be understood if the planet gap is maintained at marginal
stability, even when there is no obvious Rossby wave instability present.
Further investigation shows the final equilibrium gap depth is very sensitive
to the form of the applied torque density distribution, and using improved one
dimensional approximations from three dimensional simulations can go even
further to reducing the discrepancy between one and two dimensional models,
especially for lower mass planets. This behaviour is found to be consistent
across discs with varying parameters.
