J.C.B.: Edge modes in self-gravitating disc-planet interactions

We study the stability of gaps opened by a giant planet in a self-gravitating protoplanetary disc. We find a linear instability associated with both the self-gravity of the disc and local vortensity maxima which coincide with gap edges. For our models, these edge modes develop and extend to twice the orbital radius of a Saturn mass planet in discs with total masses Md 0.06M∗, where M ∗ is the central stellar mass, corresponding to a Toomre Q 1.5 at twice the planet’s orbital radius. The disc models, although massive, are such that they are stable in the absence of the planet. Unlike the previously studied local vortex forming instabilities associated with gap edges in weakly or non-self-gravitating discs with low viscosity, the edge modes we consider are global and exist only in sufficiently massive discs, but for the typical viscosity values adopted for protoplanetary discs. It is shown through analytic modelling and linear calculations that edge modes may be interpreted as a localized disturbance associated with a gap edge inducing activity in the extended disc, through the launching of density waves excited through gravitational potential perturbation at Lindblad resonances. We also perform hydrodynamic simulations in order t