Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits: Polytropic equations of state

We investigate close binary neutron stars in quasiequilibrium states in a general relativistic framework. The configurations are numerically computed assuming (1) the existence of a helicoidal Killing vector, (2) conformal flatness for spatial components of the metric, (3) irrotational velocity field for the neutron stars, and (4) masses of neutron stars to be identical. We adopt the polytropic equation of state and the computation is performed for a wide range of the polytropic index $n(=0.5,0.66667,0.8,1,1.25\mathrm{}),$ and compactness of neutron stars ${\mathrm{}(M/R)\mathrm{}}_{\infty }(=0.03\mathrm{}-0.3),$ where M and R denote the mass and radius of neutron stars in isolation. Because of the assumption of the irrotational velocity field, a sequence of fixed rest mass can be identified as an evolutionary track as a result of the radiation reaction of gravitational waves. Such solution sequences are computed from distant detached to innermost orbits where a cusp (inner Lagrange point) appears at the inner edges of the stellar surface. The stability of the orbital motions and the gravitational wave frequency at the innermost orbits are investigated. It is found that the innermost stable circular orbits (ISCO) appear for the case of a stiff equation of state with $n\lesssim 2/3.$ We carefully analyze the ISCO for $n=0.5\mathrm{}$ and show that the ISCO are mainly determined by a hydrodynamic instability for ${\mathrm{}(M/R)\mathrm{}}_{\infty }\lesssim \mathrm{0.2.}$ We also investigate the total angular momentum and the specific angular momentum distribution of the binary configuration at the innermost orbits, where the final merger process starts. From these quantities, we expect the final outcomes of the binary neutron star coalescence.