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It is known that an embedded massive planet will open a gap in aprotoplanetary disc via angular momentum exchange with the disc material. Theresulting surface density profile of the disc is investigated for onedimensional and two dimensional disc models and, in agreement with previouswork, it is found that one dimensional gaps are significantly deeper than theirtwo dimensional counterparts for the same initial conditions. We find, byapplying one dimensional torque density distributions to two dimensional discscontaining no planet, that the excitement of the Rossby wave instability andthe formation of Rossby vortices play a critical role in setting theequilibrium depth of the gap. Being a two dimensional instability, this isabsent from one dimensional simulations and does not limit the equilibrium gapdepth there. We find similar gap depths between two dimensional gaps formed bytorque density distributions, in which the Rossby wave instability is present,and two dimensional planet gaps, in which no Rossby wave instability ispresent. This can be understood if the planet gap is maintained at marginalstability, even when there is no obvious Rossby wave instability present.Further investigation shows the final equilibrium gap depth is very sensitiveto the form of the applied torque density distribution, and using improved onedimensional approximations from three dimensional simulations can go evenfurther to reducing the discrepancy between one and two dimensional models,especially for lower mass planets. This behaviour is found to be consistentacross discs with varying parameters.

The role of gap edge instabilities in setting the depth of planet gaps in protoplanetary discs