A debris disc under the influence of a wide planetary-mass companion: the system of HD 106906

The 13-Myr old star HD 106906 is orbited by a debris disc of at least 0.067M(Moon) with inner and outer radii of 20 and 120 au, respectively, and by a planet at a distance of 650 au. We use this curious combination of a close low-mass disc and a wide planet to motivate our simulations of this system. We study the parameter space of the initial conditions to quantify the mass loss from the debris disc and its lifetime under the influence of the planet. We find that when the planet orbits closer to the star than about 50 au and with low inclination relative to the disc (less than about 10 degrees), more disc material is perturbed outside than inside the region constrained by observations on time-scales shorter than 1 Myr. Considering the age of the system, such a short lifetime of the disc is incompatible with the time-scale for planet-planet scattering, which is one of the scenarios suggested to explain the wide separation of the planet. For some configurations, when the planet orbit is inclined with respect to the disc, the latter will start to wobble. We argue that this wobbling is caused by a mechanism similar to Kozai-Lidov oscillations. We also observe various resonant structures (such as rings and spiral arms) induced in the disc by the planet.