Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. III. Identical and different mass stars with $\gamma =2\mathrm{}$

We present the first computations of quasiequilibrium binary neutron stars with different mass components in general relativity, within the Isenberg-Wilson-Mathews approximation. We consider both cases of synchronized rotation and irrotational motion. A polytropic equation of state is used with the adiabatic index $\gamma =2.\mathrm{}$ The computations have been performed for the following combinations of stars: ${\mathrm{}(M/R)\mathrm{}}_{\infty ,\mathrm{star}1}$ vs ${\mathrm{}(M/R)\mathrm{}}_{\infty ,\mathrm{star}2}=0.12\mathrm{}\mathrm{vs}\mathrm{}(0.12,0.13,0.14),$ $0.14\mathrm{vs}\mathrm{}(0.14,0.15,0.16),$ $0.16\mathrm{vs}\mathrm{}(0.16,0.17,0.18),$ $\mathrm{and}0.18\mathrm{vs}0.18,$ where ${\mathrm{}(M/R)\mathrm{}}_{\infty }$ denotes the compactness parameter of infinitely separated stars of the same baryon number. It is found that for identical mass binary systems there is no turning point of the binding energy (ADM mass) before the end point of the sequence (mass shedding point) in the irrotational case, while there is one before the end point of the sequence (contact point) in the synchronized case. On the other hand, in the different mass case, the sequence ends by the tidal disruption of the less massive star (mass shedding point). It is then more difficult to find a turning point in the ADM mass. Furthermore, we find that the deformation of each star depends mainly on the orbital separation and the mass ratio and very weakly on its compactness. On the other side, the decrease of the central energy density depends on the compactness of the star and not on that of the companion.