The tidally induced warping, precession and truncation of accretion discs in binary systems: three-dimensional simulations

We present the results of non-linear, hydrodynamic simulations, in three dimensions, of the tidal perturbation of accretion discs in binary systems where the orbit is circular and not necessarily coplanar with the disc mid-plane. The accretion discs are assumed to be geometrically thin, and of low mass relative to the stellar mass so that they are governed by thermal pressure and viscosity, but not self-gravity. The parameters that we consider in our models are the ratio of the orbital distance to the disc radius, D/R, the binary mass ratio, Ms/Mp, the initial inclination angle between the orbit and disc planes, δ, and the Mach number in the outer parts of the unperturbed disc, ℳ. Since we consider non-self-gravitating discs, these calculations are relevant to protostellar binaries with separations below a few hundred au. For binary mass ratios of around unity and D/R in the range 3 to 4, we find that the global evolution of the discs is governed primarily by the value of ℳ. For relatively low Mach numbers (i.e. ℳ = 10 to 20) we find that the discs develop a mildly warped structure, are tidally truncated, and undergo a near rigid body precession at a rate which is in close agreement with analytical arguments. For higher Mach numbers (ℳ ≈ 30), the evolution is towards a considerably more warped structure, but the disc none the less maintains itself as a long-lived, coherent entity. A further increase in Mach number to ℳ = 50 leads to a dramatic disruption of the disc as a result of differential precession, since the sound speed is too low to allow efficient communication between constituent parts of the disc. Additionally, it is found that the inclination angle between the disc and the orbital angular momentum vectors evolves on a longer time-scale, which is probably the viscous evolution time-scale of the disc. The calculations are relevant to a number of observed astrophysical phenomena, including the precession of jets associated with young stars, the high spectral index of some T Tauri stars, and the light curves of X-ray binaries such as Hercules X-1 which suggest the presence of precessing accretion discs.