Instabilities of spiral shocks - I. Onset of wiggle instability and its mechanism

• Published in: Monthly notices of the Royal Astronomical Society Vol. 349; no. 1; pp. 270 - 280
• Main Authors: Wada, Keiichi, Koda, Jin
• Format: Journal Article
• Language: English
• Published: 23 Ainslie Place , Edinburgh EH3 6AJ , UK . Telephone [phone] Fax [phone] Blackwell Science Ltd 21-03-2004; Blackwell Science
• Subjects: Astronomy; Earth, ocean, space; Exact sciences and technology; Fundamental aspects of astrophysics; Fundamental astronomy and astrophysics. Instrumentation, techniques, and astronomical observations; galaxies: spiral; Hydrodynamics; instabilities; Normal galaxies. Extragalactic objects and systems (by type); Spiral galaxies; Stellar systems. Galactic and extragalactic objects and systems. The universe; instabilities; galaxies: spiral; hydrodynamics; Shock layer; Digital simulation; Spiral arm; Pitch angle; Numerical method; Shock waves; Spiral structure; Morphology; Hydrodynamic instability; Hydrodynamic model; Helmholtz instability; Spiral galaxies; Shear layer; Mach number
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2004.07484.x

Abstract
We found that loosely wound spiral shocks in an isothermal gas disc caused by a non-axisymmetric potential are hydrodynamically unstable, if the shocks are strong enough. High-resolution, global hydrodynamical simulations using three different numerical schemes, i.e. Advection Upstream Splitting Method (AUSM), Cubic Interpolated Propagation (CIP) and Smoothed Particle Hydrodynamics (SPH), show similarly that trailing spiral shocks with the pitch angle of larger than ∼10° wiggle, and clumps are developed in the shock-compressed layer. The numerical simulations also show clear wave crests that are associated with ripples of the spiral shocks. The spiral shocks tend to be more unstable in a rigidly rotating disc than in a flat rotation. This instability could be an origin of the secondary structures of spiral arms, i.e. the spurs/fins, observed in spiral galaxies. In spite of this local instability, the global spiral morphology of the gas is maintained over many rotational periods. The Kelvin-Helmholtz (K-H) instability in a shear layer behind the shock is a possible mechanism for the wiggle instability. The Richardson criterion for the K-H stability is expressed as a function of the Mach number, the pitch angle and the strength of the background spiral potential. The criterion suggests that spiral shocks with smaller pitch angles and smaller Mach numbers would be more stable, and this is consistent with the numerical results.