Physics
Scientific paper
Aug 1998
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998ijpam..29..855r&link_type=abstract
Indian J. Pure Appl. Math., Vol. 29, No. 8, p. 855 - 870
Physics
1
Jets: Instabilities, Galaxies: Spiral Arms
Scientific paper
The self-gravitating instability of a perturbed gas jet (density ρ1 and radius R) coaxial with double perturbed fluid cylinder (density ρ2 and radius qR with 1 < q < ∞) ambient with a self-gravitating tenuous medium is developed. A general dispersion relation is derived, discussed analytically and the results are confirmed numerically and interpreted physically. Concerning Chandrasekhar's classical case as ρ2 = 0, it is found that the model is gravitational unstable for small axisymmetric wavelengths and stable in all the rest. For Radwan's stationary recent case with ρ1 ≠ 0, ρ2 ≠ 0 and q→∞ it is, predicted gravitationally that the model is marginally stable as ρ1 = ρ2 purely unstable even for short wavelengths as ρ1 < ρ2 while as ρ1 > ρ2 it is stable or unstable according to restrictions. In the present case it is found that the streaming (velocity U in longitudinal direction) has a strong destabilizing influence and increasing the unstable domains for all perturbation modes. The marginal stability states do not occur at ρ1 = ρ2 but they depend on U and the wavenumber k values. As ρ1 < ρ2, the stable domains are increasing while those of instability are shrinking with increasing q values but never be suppressed. As ρ1 < ρ2, the principle of exchange of instability is valid for the most cases specially for large values of q. One has very little stable domains for very long wavelengths and all the rest are unstable, this matter is (physically interpreted) related to the behaviour of the spiral arms of galaxies.
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