Other
Scientific paper
Oct 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981mnras.197..167p&link_type=abstract
Monthly Notices of the Royal Astronomical Society, vol. 197, Oct. 1981, p. 167-178. Research supported by the Science Research
Other
9
Cosmology, Disk Galaxies, Galactic Evolution, Gravitational Collapse, Rotating Fluids, Asymptotic Methods, Flow Stability, Gas Flow, Isothermal Processes, Perturbation Theory, Spiral Galaxies
Scientific paper
The homologous collapse of an isothermal disc initially at rest, with no rotation, is examined. A local stability analysis for the growth of radial perturbations shows that all wavelength modes eventually become stable because the Jean's length shrinks with the contraction. The longest wavelengths become unstable first and start to grow. The competition between these two effects leads to a critical wavelength which is eight times the ratio of the free-fall time to sound crossing time of the disc. It is also shown that the fragmentation on the scale of individual galaxies is almost inevitable. This result is only weakly dependent on the initial conditions, which explains the narrow range of the masses of all galaxies.
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