A numerical study of the Roche and Darwin problems for polytropic stars

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Abstract
This paper presents a numerical study of the disruption of compressible stars in unstable binary systems. The gas is assumed to be inviscid, and the equation of state polytropic, but otherwise no restrictive assumptions are made. In particular, we allow the gas to move arbitrarily in three dimensions. The configurations we examine are similar to the classical Roche and Darwin problems. They are binaries initially in synchronous, circular orbits which become dynamically unstable when the orbital radius is sufficiently small. The results show that the classical formulae for the onset of disruption, where they can be tested, are also reasonably accurate for compressible stars. The final states of the unstable systems reveal a variety of one- and two-armed spirals, and complex ring structures. They are similar to some of those found by A. and J. Toomre, and corroborate their view that rotating systems, under the influence of strong non-axisymmetric perturbations, produce thin tails and spiral structure very easily.

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