A Slowly Contracting or Expanding Fluid Sphere and its Stability
Abstract
It has been pointed out by Thomas that, if a solution of the equations of equilibrium for a slowly contracting or expanding fluid sphere has been obtained, the exact conditions of dynamical stability can be applied without difficulty. A particular solution of the equations of radiative equilibrium for a fluid sphere contracting homologously without internal generation of energy has been obtained. The opacity was assumed to obey Kramers formula. By assuming a central temperature and total pressure of the order of magnitude expected for stellar interiors, the logarithmic rate of contraction was adjusted so that the boundary conditions, viz., P=0, T=0, for a finite r and m, were satisfied. This solution has been found to be dynamically stable (at least for radial displacements) for values of the ratios of specific heats of material between 53 and 1 corresponding to all possible values of the specific heat at constant volume of a perfect gas.
 Publication:

Physical Review
 Pub Date:
 February 1932
 DOI:
 10.1103/PhysRev.39.525
 Bibcode:
 1932PhRv...39..525R