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

TL;DR

This paper analyzes how linear tidal forces excite spiral density waves in accretion disks, revealing the dependence on Mach number and disk conditions, with implications for CVs and circumplanetary disks.

Contribution

It provides a detailed theoretical framework for understanding the scaling of tidally excited waves with Mach number, including the effects of disk edge conditions and resonances.

Findings

Ingoing waves are robustly excited when an ILR is within the disk.

Wave flux scaling with Mach number is sensitive to disk edge conditions.

Resonances can occur with acoustic-cutoff and stratification frequencies, affecting wave excitation.

Abstract

We revisit linear tidal excitation of spiral density waves in the disks 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 disk, 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 disk. The wave flux and its scaling with Mach number are then very sensitive to conditions near the disk 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-cutoff 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 disks, where Mach numbers are likely lower than in CVs.