Gravitational Collapse of Rotating Gaseous Ellipsoids
Abstract
The work of Rossner on the finiteamplitude oscillation of a Maclaurin ellipsoid is extended to the adiabatic and nonadiabatic gravitational collapse of a rotating uniform gaseous ellipsoid. The problem is made tractable by introducing an appropriate temperature distribution in the initial ellipsoid and by assuming a special formula for the cooling rate of the gas. Solutions can be represented by trajectories in the (al,a2,a3)space, where ai, a2, and a~ are the lengths of the three principal axes of the ellipsoid. The adiabatic collapse is characterized by the same trajectories that represent nonlinear adiabatic pulsations. They never reach any plane a, = 0 (j = 1, 2, 3) but are confined within a closed zerovelocity surface. The trajectories in the (ai,a2,a3)space which represent the nonadiabatic collapse make one or more loops, depending on the cooling rate of the gas and the total angular momentum. They finally reach the plane a3 = 0; thus the ellipsoid ultimately becomes a flat disk. A small, finite, nonaxisymmetric perturbation applied to an axisymmetric ellipsoid grows in the course of the collapse. For large angular momentum the resultant figure is a very thin, needlelike ellipsoid. An ellipsoid which initially has three unequal principal axes displays a peculiar gravitational collapse under the constraint of the circulation integral. The configuration may be elongated even if the angular mo mentum is very small
 Publication:

The Astrophysical Journal
 Pub Date:
 May 1968
 DOI:
 10.1086/149569
 Bibcode:
 1968ApJ...152..523F