Evolution and Instability of Galactic Gas Disks inresponse to A Spiral Density-wave Potential

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We revisit the classic problem of the response of the gas in a galactic disk to an imposed spiral density-wave potential of stellar origin. The results show the distinct difference between waves generated by resonance excitation and forced oscillation. To avoid the confusion of mixing these two types of waves, we systematically reduce the strength of the spiral potential or the force near the primary Lindblad resonances. So we can study the original problem of shock formation and star formation problem formulated by Roberts (1969). For the cases without self-gravitation of the gas disk, in addition to the primary doubly periodic shocks, the presence of the branch-like structures which correspond to the ultra-harmonic resonances is pronounced. On the other hand, once the self-gravitation is included, unlike the work of Chakrabarti et al. (2003), the sub-structures associated with the ultra-harmonics are not necessarily enhanced by the self-gravity. Their growth may be deteriorated by the growth of the primary shocks. Sub-structures other than those identified with the ultra-harmonics may result from shear instability of Rayleigh's kind or gravitational instability of Toomre's kind. They are responsible for the branches, feathers or chaotic sub-structures observed in nearby galaxies in far infra-red. The work is in parts supported by a grant from National Science Council, Taiwan NSC95-2752-M-001-009-PAE.

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