## LSU Historical Dissertations and Theses

1988

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

Joel Edward Tohline

#### Abstract

Evolutions of rapidly rotating, self-gravitating objects initially in axisymmetric equilibrium have been studied using a 3-D Newtonian hydrodynamic computer code with an eye toward understanding angular momentum transport in dynamically evolving protostars. First, a number of evolutions have been modeled using an existing explicit, Eulerian, finite difference code that is accurate to first-order in its spatial differences. The bar-mode dynamic instability has been explored by considering several models with different degrees of compressibility. This instability occurs in models having $\beta > \beta\sb{d} \equiv$ 0.27, where $\beta$ is the ratio of the rotational to the gravitational potential energy. A two-armed spiral, with a well-defined pattern speed and growth rate that match the pattern speed and growth rate predicted by linear theory, develops from each of the axisymmetric equilibria. The models with greater compressibility exhibit spirals which are more tightly wound. As the nonaxisymmetric distortion becomes large in an extended evolution, the object does not undergo binary fission as had been thought earlier. Instead, the spiral elongates and then wraps up on itself, forming a central pulsating triaxial object surrounded by a more diffuse "ring-like"disk. Angular momentum and mass are dynamically redistributed by gravitational torques during the evolution, and $\beta$ is reduced below $\beta\sb{d}$. Since this gravitational-rotational dynamic instability is a general feature of gaseous systems, this study may have application to theta galaxies and to rapidly rotating neutron stars, as well as to protostars. The hydrodynamic code has been modified to include second-order-accurate spatial differences and has been rewritten so that it now vectorizes well. The results obtained from running a model in the second-order code are qualitatively similar to the results obtained from the first-order code. Quantitatively, however, the answers are somewhat different and are, presumably, more reliable. In the second-order code, growth rates no longer need to be corrected for the effects of numerical viscosity to agree with the predictions of linear theory. Higher order nonaxisymmetric Fourier modes are also no longer damped.

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