On tidally induced shocks in accretion discs in close binary systems

We present linear and non-linear calculations of the tidal interaction of an accretion disc in close binary systems with mass ratios of unity and one tenth. We consider characteristic Mach numbers of the Keplerian flow between 10 and 50 and both inviscid discs and discs with an internal shear viscosity. We calculate the angular momentum transfer between the disc and the companion star and indicate how the excited spiral density waves can be understood in terms of a linear tidal response calculation. In agreement with earlier work it is found that hot, extended discs with Mach numbers $$\mathcal{M} \leq 10$$, such as those in close binary T Tauri stars, are subject to strong tidal coupling with the companion star, whereby the disc loses a sufficient amount of angular momentum through shock dissipation to enable disc matter to accrete on to the central star. For cool discs with Mach numbers $$\mathcal{M} \geq 25$$, thought typical for discs in cataclysmic variable and X-ray binaries, however, the wavelength of the tidal response is much shorter than the length-scale of the tidal force so that the tidal interaction becomes inefficient and, although adequate to truncate the disc, it produces little wave-driven accretion on to the central star.