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Most numerical models of binary stars - in particular neutron stars incompact binaries - assume the companions to be either corotational orirrotational. Either one of these assumptions leads to a significantsimplification in the hydrodynamic equations of stationary equilibrium. In thispaper we develop a new formalism for the construction of binary stars withcirculation intermediate between corotational and irrotational. Generalizingthe equations for irrotational flow we cast the Euler equation, which is analgebraic equation in the case of corotational or irrotational fluid flow, asan elliptic equation for a new auxiliary quantity. We also suggest aparameterized decomposition of the fluid flow that allows for a variation ofthe stellar circulation.

A formalism for the construction of binary neutron stars with arbitrary circulation