Radiation pressure effects in the oscillations of compressible rotating homogeneous spheroids

Abstract

Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10 M⊙ and 30 M⊙ in which the effects of radiation pressure are expected to be important. Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models. From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diameters a1 and a3, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a1, a3) phase space, and of both a1 and the total central pressure Pc against time. It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of both a1 and Pc are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of the a1 oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peak Pc. When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both the a1 and Pc oscillations also increase with mass. When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of the a1 oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period. Some astrophysical implications of this work are briefly discussed. © 1993 Kluwer Academic Publishers.