The hydrodynamical response of a tilted circumbinary disc: linear theory and non-linear numerical simulations

Open Access
Publisher Website
Google Scholar
Abstract
In this paper we present an analytical and numerical study of the response of a circumbinary disc subject to the tidal-forcing of a binary with a fixed circular orbit. We consider isentropic fluid discs with a range of thicknesses, and binaries with a range of mass ratios, orbital separations and inclination angles. Our numerical simulations are implemented using a smoothed particle hydrodynamics (SPH) code such that we can consider the hydrodynamics fully in three dimensions. For our unperturbed disc models, we find the numerical shear viscosity to be equivalent to a constant kinematic viscosity, and we calibrate its magnitude. Writing a scaling relation for the shear viscosity manifest in our models, we deduce that the disc thickness cannot be varied without affecting the viscosity in these kinds of SPH disc models, as is supported by our numerical results. It is found that maintenance of an inner cavity owing to the tidal truncation of the disc is effective for non-zero orbital inclinations. Also, we show that our model discs may precess approximately like rigid bodies, provided that the disc is able to communicate on a length-scale comparable to the inner boundary radius by either sonic or viscous effects, in a sufficiently small fraction of the local precession period. It is found also that the surface density in the disc should not decrease too rapidly with increasing radius, otherwise the disc may separate into disconnected annuli. Furthermore, the disc precession period may tend to infinity if the disc outer edge is allowed to become arbitrarily large, the disc suffering only a modest quasi-steady warp near the inner boundary. When the disc response is linear, or weakly non-linear, the precession periods and the forms of warping that we measure in our numerical results yield reasonable quantitative agreement with the analytical expressions that we derive from a linear response calculation. For a stronger disc response the results can agree poorly with our linear analysis, although some qualitative features of the response remain intact. We demonstrate that the response of a disc of non-interacting particles is qualitatively different, showing a much larger kinematic disturbance and an ultimate global thickening of the disc. This work is of relevance to a number of astrophysical phenomena of current interest in star and planet formation; these include tidal truncation and gap formation in accretion discs, and the observational characteristics of some young stellar objects.
All Related Versions

This publication has 0 references indexed in Scilit: