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

Details A numerical study of the Roche and DARWIN problems for polytropic stars A numerical study of the Roche and DARWIN problems for polytropic stars

Jul 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979mnras.188...45g&link_type=abstract

Monthly Notices of the Royal Astronomical Society, vol. 188, July 1979, p. 45-58. Australian Research Grants Committee

Computer Science

Numerical Analysis

17

Binary Stars, Dynamic Stability, Equations Of State, Polytropic Processes, Roche Limit, Stellar Motions, Circular Orbits, Numerical Analysis, Orbital Mechanics, Perturbation Theory, Ring Structures

Scientific paper

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, the gas is allowed to move arbitrarily in three dimensions. The configurations examined are similar to the classical Roche (1850) and Darwin (1910) 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 formulas 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 as well as complex ring structures. They are similar to some of those found by A. and J. Toomre (1972) 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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