Other
Scientific paper
Sep 1999
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999dda....31.1501m&link_type=abstract
American Astronomical Society, DDA meeting #31, #15.01
Other
Scientific paper
It has been known since the days of George Darwin that a binary is unstable to mass transfer if its component stars approach each other within a certain distance. Recently, I showed that a second type of tidal instability exists in close binaries when their orbits are eccentric (Mardling 1995, ApJ, 450,722). This instability involves a chaotic interaction between the orbit and the tides of at least one of the stars with the possibility of huge tides being raised, in contrast to normal tidal interactions where tidal energies are relatively small. In this talk I will show that the binary-tides problem is intimately related to the three-body problem. While the stability against exchange in a hierarchical triple may be examined in a way similar to Roche stability against mass transfer in a close binary, stability against escape of the outer body of a hierarchy, in particular one which is forbidden energetically to exchange with an inner component, has not been well understood. I will propose a correspondence between the binary-tides problem and the three-body problem, and show that stability against escape in a triple is predicted by a formula almost identical to that which predicts chaotic tidal interactions in a close binary. I will outline a framework based on the notion of ``modes of oscillation'' of a binary and show how this may be used to predict approximately the evolution and final (unbound) configuration of an unstable hierarchical triple with arbitrary masses and initial configuration.
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