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We propose a new numerical method to calculate irrotational binary systemscomposed of compressible gaseous stars in Newtonian gravity. Assumingirrotationality, i.e. vanishing of the vorticity vector everywhere in the starin the inertial frame, we can introduce the velocity potential for the flowfield. Using this velocity potential we can derive a set of basic equations forstationary states which consist of (i) the generalized Bernoulli equation, (ii)the Poisson equation for the Newtonian gravitational potential and (iii) theequation for the velocity potential with the Neumann type boundary condition.We succeeded in developing a new code to compute numerically exact solutions tothese equations for the first time. Such irrotational configurations of binarysystems are appropriate models for realistic neutron star binaries composed ofinviscid gases, just prior to coalescence of two stars caused by emission ofgravitational waves. Accuracies of our numerical solutions are so high that wecan compute reliable models for fully deformed final stationary configurationsand hence determine the inner most stable circular orbit of binary neutron starsystems under the approximations of weak gravity and inviscid limit.Comment: 32 pages, 25 bitmapped ps files, to appear in ApJ supplemen

Stationary Structures of Irrotational Binary Systems: Models for Close Binary Systems of Compact Stars