Physics
Scientific paper
Feb 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976apl....17....7k&link_type=abstract
Astrophysical Letters, vol. 17, no. 1, 1976, p. 7-9.
Physics
13
Hydrodynamic Equations, Oblate Spheroids, Planetary Nebulae, Spherical Shells, Acceleration (Physics), Angular Distribution, Pressure Effects, Prolate Spheroids
Scientific paper
Hydrodynamic shaping of an initially slightly oblate spheroidal shell by a prolonged acceleration of that shell is proposed as a mechanism which leads to a wide variety of planetary-nebula shapes. Equations governing the evolution of a spheroidal shell are selected on the basis of four assumptions: (1) the shell is an initially homogeneous spheroid for which the equipotential surfaces are separated by a constant fraction of the radius, (2) the shell maintains its spheroidal shape as it expands, (3) the angular distribution of mass remains constant, and (4) the mass and temperature of the material providing the pressure inside the shell remain constant. Results of numerical solutions to these equations show that an initially slightly oblate spheroidal shell of constant mass is transformed into a substantially prolate spheroidal shell due to prolonged acceleration by a uniform, decreasing internal pressure. Several shortcomings of the analysis are discussed, and some progenitor rotational velocities are estimated.
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