On the dynamics of tilted discs around young stars

Tidal perturbation of a circumstellar disc by a companion on an inclined circular orbit in a binary system of T Tauri stars is studied. The two stars have comparable masses and we suppose that the separation of the system is large enough compared to the radius of the disc to allow a linear analysis. In this paper we concentrate on the tidally induced angular momentum transport in the disc arising from (m=1) bending waves that are excited by potential perturbations with odd symmetry with respect to reflection in the disc mid-plane. These are of interest because they have a long wavelength which may in some cases by a significant fraction of the radius. Then propagation to the inner regions of the disc is facilitated. We calculate the response of the disc to tidal perturbations with both zero and non-zero perturbing frequencies. We expect the response to the zero-frequency term to be an approximate rigid body precession if the sound crossing time turns out to be short compared to the precession period. The response to the non-zero frequencies comprises long-wavelength waves excited at the outer edge of the disc and which propagate inwards transporting negative angular momentum with, in the inviscid case, an associated conserved wave action. Such conservation implies that the wave amplitude increases as it propagates inwards until non-linear effects become important and cause the wave to damp. Because the perturber rotates external to, and more slowly than, the disc, on dissipation of the wave, angular momentum is transferred from the disc to the companion, increasing the accretion rate on to the central star. If non-linear dissipation can produce a slowly decreasing wave action as the disc centre is approached, it is possible that tidal effects could induce an accretion rate which is of the order of typical accretion rates in classical T Tauri stars (namely between 10^-9 and 10^-7 M_solar yr^-1). As long as the response of the disc is wave-like, the wave angular momentum flux induced in our model discs tends to increase with increasing separation of the binary system. This is at least in part due to the fact that the response of the disc has an increasing wavelength with increasing separation. The torque exerted by the perturber on the disc leads to the evolution of the relative inclination of the disc and the orbital planes, but not necessarily towards coplanarity. In some cases, the only stable equilibrium position of the system does not correspond to coplanarity. The time-scale for this evolution is of the order of magnitude of the time needed by tidal effects to remove the angular momentum content of the disc. We conclude that, when the orbit is highly inclined with respect to the disc, tidal effects may play a significant role in the accretion process in the circumprimary disc.