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Dynamics of Circumstellar Disks III: The case of GG Tau A

(abridged) We present 2-dimensional hydrodynamic simulations using the Smoothed Particle Hydrodynamic (SPH) code, VINE, to model a self-gravitating binary system similar to the GG Tau A system. We simulate systems configured with semi-major axes of either $a=62$~AU (`wide') or $a=32$~AU (`close'), and with eccentricity of either $e=0$ or $e=0.3$. Strong spiral structures are generated with large material streams extending inwards. A small fraction accretes onto the circumstellar disks, with most returning to the torus. Structures also propagate outwards, generating net outwards mass flow and eventually losing coherence at large distances. The torus becomes significantly eccentric in shape. Accretion onto the stars occurs at a rate of a few $\times10^{-8}$\msun/yr implying disk lifetimes shorter than $\sim10^4$~yr, without replenishment. Only wide configurations retain disks by virtue of robust accretion. In eccentric configurations, accretion is episodic, occurs preferentially onto the secondary at wrates peaked near binary periapse. We conclude that the \ggtaua\ torus is strongly self gravitating and that a major contribution to its thermal energy is shock dissipation. We interpret its observed features as manifestations of spiral structures and the low density material surrounding it as an excretion disk created by outward mass flux. We interpret GG Tau A as a coplanar system with an eccentric torus, and account for its supposed mutual inclination as due to degeneracy between the interpretation of inclination and eccentricity. Although the disks persist for long enough to permit planet formation, the environment remains unfavorable due to high temperatures. We conclude that the GG Tau A system is in an eccentric, $a\sim62$~AU orbit.