Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993apj...419..155a&link_type=abstract
Astrophysical Journal v.419, p.155
Astronomy and Astrophysics
Astronomy
79
Galaxies: Kinematics And Dynamics, Hydrodynamics, Solar System: Formation
Scientific paper
The existing theory of density wave excitation in two-dimensional gaseous disks by imposed gravitational potentials makes approximations which prevent a direct analytical description of the shifts in effective positions of Lindblad resonances with respect to radii satisfying orbital commensurability requirement, and of the so-called torque cutoff arising at large azimuthal numbers m of the perturbing potential's pattern. Both phenomena are related to the azimuthal forces acting on gas, neglected in the WKB approximation commonly used in the past. We extend previous theories of Lindblad resonance wherever necessary for a consistent analytical treatment of the problem, particularly for large m. Our analytical approach applies to wave excitation at Lindblad resonances in non-self-gravitating, two-dimensional gas layers (vertically averaged disks or fundamental vertical mode of three-dimensional disks). It explicitly includes the resonance shifts and torque cutoffs. The theory is valid for small perturbing potentials of arbitrary form (including highly localized potentials, e.g., point-mass potential, spiral potential with arbitrary pitch angle, etc.). We present a torque formula generalizing the standard Goldreich-Tremaine formula. Especially useful in the problem of disk-satellite interaction, the torque formula provides insight into the origin of the torque cutoff at m larger than the radius to thickness ratio of the disk. Qualitatively, the cutoff is an effect of: (i) a mild (power-law) intrinsic torque cutoff, independent of the radial profile of the imposed potential, and (ii) a sharp (exponential) cutoff due to shifts in effective resonance location away from the perturber. For m → ∞ the latter effect causes the increasingly localized potential to decouple spatially from the wave generation region. A disk annulus surrounding the corotation radius of every m-armed potential, of width comparable with twice the vertical disk scale height, remains evanescent for waves excited by that harmonic and does not contribute significantly to the total torque between the perturber and the disk. We discuss the role of gas viscosity, self-gravity, and the applicability of a two-dimensional analysis to Lindblad resonances in three-dimensional disks.
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