Stellar motion induced by gravitational instabilities in protoplanetary discs

We test the effect of assumptions about stellar motion on the behaviour of gravitational instabilities (GIs) in protoplanetary discs around solar-type stars by performing two simulations that are identical in all respects except the treatment of the star. In one simulation, the star is assumed to remain fixed at the centre of the inertial reference frame. In the other, stellar motion is handled properly by including an indirect potential in the hydrodynamic equations to model the star's reference frame as one which is accelerated by star/disc interactions. The discs in both simulations orbit a solar mass star, initially extend from 2.3 to 40 au with a pi-1/2 surface density profile, and have a total mass of 0.14 M-circle dot. The gamma = 5/3 ideal gas is assumed to cool everywhere with a constant cooling time of two outer rotation periods. The overall behaviour of the disc evolution is similar, except for weakening in various measures of GI activity by about at most tens of per cent for the indirect potential case. Overall conclusions about disc evolution in earlier papers by our group, where the star was always assumed to be fixed in an inertial frame, remain valid. There is no evidence for independent one-armed instabilities, like the Stimulation by the Long-range Interaction of Newtonian Gravity (SLING), in either simulation. On the other hand, the stellar motion about the system centre of mass (COM) in the simulation with the indirect potential is substantial, up to 0.25 au during the burst phase, as GIs initiate, and averaging about 0.9 au during the asymptotic phase, when the GIs reach an overall balance of heating and cooling. These motions appear to be a stellar response to non-linear interactions between discrete global spiral modes in both the burst and asymptotic phases of the evolution, and the star's orbital motion about the COM reflects the orbit periods of disc material near the corotation radii of the dominant spiral waves. This motion is, in principle, large enough to be observable and could be confused with stellar wobble due to the presence of one or more super-Jupiter mass protoplanets orbiting at 10's au. We discuss why the excursions in our simulation are so much larger than those seen in simulations by Rice et al.