  We have succeeded in obtaining exact configurations of irrotational binary
systems for compressible (polytropic) equations of state. Our models correspond
to binaries of equal mass neutron star systems in the viscosity free limit. By
using the obtained sequences of stationary states, the evolution of binary
systems of irrotational neutron stars due to gravitational wave emission has
been examined. For inviscid binary systems the spin angular velocity of each
component in a detached phase is smaller than the orbital angular velocity at a
contact phase. Thus the irrotational approximation during evolution of binary
neutron stars due to gravitational wave emission can be justified. Our
computational results show that the binary will never reach a dynamically
unstable state before a contact phase even for rather stiff polytropes with the
index N > 0.7, as the separation of two components decreases due to
gravitational wave emission. This conclusion is quantitatively different from
that of Lai, Rasio & Shapiro who employed approximate solutions for polytropic
binary systems.
