Gravitationally coupled scale-free discs

Abstract

In a composite fluid system of two gravitationally coupled barotropic scale-free discs bearing a rotation curve $v\propto r^{-\beta }$ and a power-law surface mass density ${\Sigma }_0\propto r^{-\alpha }$ with $\alpha =1+2\beta$, we construct coplanar stationary aligned and spiral perturbation configurations in the two discs. Due to the mutual gravitational interaction, there are two independent classes of perturbation modes with surface mass density disturbances in the two coupled discs being either in-phase or out-of-phase. We derive analytical criteria for such perturbation modes to exist and show numerical examples. We compute the aligned and spiral perturbation modes systematically to explore the entire parameter regime. For the axisymmetric $m=0$ case with radial oscillations, there are two unstable regimes of ring-fragmentation and collapse corresponding to short and long radial wavelengths, respectively. Only within a certain range of the rotation parameter $D_s^2$ (square of the effective Mach number for the stellar disc), can a composite disc system be stable against all axisymmetric perturbations. Compared with a single-disc system, the coupled two-disc system becomes less stable against such axisymmetric instabilities.

23 pages, MNRAS in press

References in corpus (8)

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• Non-axisymmetric, scale-free, razor-thin discs
• Stability of Power-Law Disks I -- The Fredholm Integral Equation
• Magnetohydrodynamic Density Waves in a Composite Disk System of Interstellar Medium and Cosmic-Ray Gas
• Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs
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• Stationary Nonaxisymmetric Configurations of Magnetized Singular Isothermal Disks

Cited by in corpus (10)

• Dispersal of Gaseous Circumstellar Discs around High-Mass Stars
• Structures in a class of magnetized scale-free discs
• Correlations among Multi-Wavelength Luminosities of Star-Forming Galaxies
• Global Perturbation Configurations in a Composite Disc System with an Isopedic Magnetic Field
• On stability and spiral patterns in polar disks
• Axisymmetric stability criteria for a composite system of stellar and magnetized gaseous singular isothermal discs
• Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs
• Global structures in a composite system of two scale-free discs with a coplanar magnetic field
• Scale-Free Thin Discs with an Isopedic Magnetic Field
• Global non-axisymmetric perturbation configurations in a composite disc system with an isopedic magnetic field: relation between dark matter halo and magnetic field