Astronomy and Astrophysics – Astronomy
Scientific paper
Dec 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992aas...181.6611l&link_type=abstract
American Astronomical Society, 181st AAS Meeting, #66.11; Bulletin of the American Astronomical Society, Vol. 24, p.1226
Astronomy and Astrophysics
Astronomy
Scientific paper
We discuss some results of our recent study of hydrostatic equilibrium solutions for polytropes in close binary systems. Using an energy variational method, we have constructed compressible generalizations of the classical incompressible Roche, Roche-Riemann, Darwin, and Darwin-Riemann solutions. Along all Roche and Roche-Riemann sequences, we demonstrate the existence of a point where the total energy and angular momentum of the system simultaneously attain a minimum. A similar minimum exists for Darwin-type binaries when the polytropic index n of both components is below a critical value ncrit~2. We show that such a turning point along an equilibrium sequence marks the onset of instability. This instability occurs before the Roche limit is reached in Roche-type binaries, and before the surfaces of the two components come into contact in Darwin-type binaries. We point out the critical importance of this instability in determining the final evolution of coalescing binary systems. Work supported in part by NSF Grant AST 90--15451 and NASA Grant NAGW--2364 to Cornell University. F. A. R. thanks NASA and STScI for financial support through a Hubble fellowship award.
Lai Dong
Rasio Frederic A.
Shapiro Stuart L.
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