The orbital separation of compact binary stars will shrink with time due to the emission of gravitational radiation .
This inspiralling phase of a binary system ’ s evolution generally will be very long compared to the system ’ s orbital period , but the final coalescence may be dynamical and driven to a large degree by hydrodynamic effects , particularly if there is a critical separation at which the system becomes dynamically unstable toward merger .
Indeed , if weakly relativistic systems ( such as white dwarf–white dwarf binaries ) encounter a point of dynamical instability at some critically close separation , coalescence may be entirely a classical , hydrodynamic process .
Therefore , a proper investigation of this stage of binary evolution must include three–dimensional hydrodynamic simulations .

We have constructed equilibrium sequences of synchronously rotating , equal–mass binaries in circular orbit with a single parameter – the binary separation – varying along each sequence .
Sequences have been constructed with various polytropic as well as realistic white dwarf and neutron star equations of state .
Using a Newtonian , finite–difference hydrodynamics code , we have examined the dynamical stability of individual models along these equilibrium sequences .
Our simulations indicate that no points of instability exist on the sequences we analyzed that had relatively soft equations of state ( polytropic sequences with polytropic index n = 1.0 and 1.5 and two white dwarf sequences ) .
However , we did identify dynamically unstable binary models on sequences with stiffer equations of state ( n = 0.5 polytropic sequence and two neutron star sequences ) .
We thus infer that binary systems with soft equations of state are not driven to merger by a dynamical instability .
For the n = 0.5 polytropic sequence , the separation at which a dynamical instability sets in appears to be associated with the minimum energy and angular momentum configuration along the sequence .
Our simulations suggest but do not conclusively demonstrate that , in the absence of relativistic effects , this same association may also hold for binary neutron star systems .