We investigate close binary neutron stars in quasiequilibrium states in a general relativistic framework .
The configurations are numerically computed assuming ( 1 ) 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 ) , and compactness of neutron stars ( M / R ) _ { \infty } ~ { } ( = 0.03 - 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 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 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 stiff equation of state with n \lesssim 2 / 3 .
We carefully analyze the ISCO for n = 0.5 and show that the ISCO are mainly determined by a hydrodynamic instability for ( M / R ) _ { \infty } \mathrel { \raise 1.72 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 3.01 pt \hbox { % $ \sim$ } } 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 .