Resonantly Excited Waves in Gaseous Disks: Asymptotic Theory versus Numerical Hydrodynamics

Abstract

The nonlinear asymptotic theory of bar-driven spiral density waves, developed by Yuan & Kuo, is tested by numerical hydrodynamical calculations using a relaxation scheme proposed by Jin & Xin. The scheme is of second-order accuracy and uses a local relaxation approximation. We have shown that the asymptotic theory, which is based on the assumption of tightly wound spirals, is valid even for relatively open spirals. We present two numerical results, one for waves excited at the outer Lindblad resonance (tightly wound spirals) and one for waves excited at the inner Lindblad resonance (relatively open spirals). Both are in good agreement with the asymptotic theory.