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The orbital separation of compact binary stars will shrink with time due tothe emission of gravitational radiation. This inspiralling phase of a binarysystem's evolution generally will be very long compared to the system's orbitalperiod, but the final coalescence may be dynamical and driven to a large degreeby hydrodynamic effects, particularly if there is a critical separation atwhich the system becomes dynamically unstable toward merger. Indeed, if weaklyrelativistic systems (such as white dwarf-white dwarf binaries) encounter apoint of dynamical instability at some critically close separation, coalescencemay be entirely a classical, hydrodynamic process. Therefore, a properinvestigation of this stage of binary evolution must include three-dimensionalhydrodynamic simulations. We have constructed equilibrium sequences ofsynchronously rotating, equal-mass binaries in circular orbit with a singleparameter - the binary separation - varying along each sequence. Sequences havebeen constructed with various polytropic as well as realistic white dwarf andneutron star equations of state. Using a Newtonian, finite-differencehydrodynamics code, we have examined the dynamical stability of individualmodels along these equilibrium sequences. Our simulations indicate that nopoints of instability exist on the sequences we analyzed that had relativelysoft equations of state (polytropic sequences with polytropic index $n=1.0$ and1.5 and two white dwarf sequences). However, we did identify dynamicallyunstable binary models on sequences with stiffer equations of state ($n=0.5$polytropic sequence and two neutron star sequences). We thus infer that binarysystems with soft equations of state are not driven to merger by a dynamicalinstability.Comment: 29 pages (AASTeX4.0) & 16 figures [in 24 eps files]; more direct  comparison with results of previous authors, discussion of secular-type  evolution of stable models added; accepted for publication in The  Astrophysical Journa

The Relative Stability against Merger of Close, Compact Binaries