The linear theory of tidally excited spiral density waves: application to CV and circumplanetary discs

Abstract

We revisit linear tidal excitation of spiral density waves in the discs of cataclysmic variables (CVs), focusing on scalings with orbital Mach number in order to bridge the gap between numerical simulations and real systems. If an inner Lindblad resonance (ILR) lies within the disc, ingoing waves are robustly excited, and the angular momentum flux they carry is independent of Mach number. But in most CVs, the ILR lies outside the disc. The wave flux and its scaling with Mach number are then very sensitive to conditions near the disc edge. If the temperature and sound speed vanish there, excitation tends to be exponentially suppressed. If the Mach number remains finite in the outer parts but the radial and vertical density scale lengths become comparable due to subKeplerian rotation, resonance can occur with acoustic cut-off and stratification frequencies. These previously neglected resonances excite waves, but the Mach-number scaling remains very steep if the radial scale length decreases gradually. The scaling can be less strong - algebraic rather than exponential - if there are sharp changes in surface density at finite sound speed. Shocks excited by streamline crossing or by the impact of the stream from the companion are unlikely to be important for the angular momentum budget, at least in quiescence. Our results may also apply to circumplanetary discs, where Mach numbers are likely lower than in CVs.