Torque wiggles -- a robust feature of the global disc-planet interaction

Abstract

Gravitational coupling between planets and protoplanetary discs is responsible for many important phenomena such as planet migration and gap formation. The key quantitative characteristics of this coupling is the excitation torque density -- the torque (per unit radius) imparted on the disc by planetary gravity. Recent global simulations and linear calculations found an intricate pattern of low-amplitude, quasi-periodic oscillations in the global radial distribution of torque density in the outer disc, which we call torque wiggles. Here we show that torque wiggles are a robust outcome of global disc-planet interaction and exist despite the variation of disc parameters and thermodynamic assumptions (including $\beta$-cooling). They result from coupling of the planetary potential to the planet-driven density wave freely propagating in the disc. We developed analytical theory of this phenomenon based on approximate self-similarity of the planet-driven density waves in the outer disc. We used it, together with linear calculations and simulations, to show that (a) the radial periodicity of the wiggles is determined by the global shape of the planet-driven density wave (its wrapping in the disc) and (b) the sharp features in the torque density distribution result from constructive interference of different azimuthal (Fourier) torque contributions at radii where the planetary wake crosses the star-planet line. In the linear regime the torque wiggles represent a weak effect, affecting the total (integrated) torque by only a few per cent. However, their significance should increase in the non-linear regime, when a gap (or a cavity) forms around the perturber's orbit.