Dynamical Determination of the Innermost Stable Circular Orbit of Binary Neutron Stars

We determine the innermost stable circular orbit (ISCO) of binary neutron stars (BNSs) by performing dynamical simulations in full general relativity. Evolving quasiequilibrium (QE) binaries that begin at different separations, we bracket the location of the ISCO by distinguishing stable circular orbits from unstable plunges. We study $\Gamma =2$ polytropes of varying compactions in both corotational and irrotational equal-mass binaries. For corotational binaries, we find an ISCO orbital angular frequency somewhat smaller than that determined by applying turning-point methods to QE initial data. For the irrotational binaries, the initial data sequences terminate before reaching a turning point, but we find that the ISCO frequency is reached prior to the termination point. Our findings suggest that the ISCO frequency varies with compaction but does not depend strongly on the stellar spin.

Figure 1

Coordinate separation vs time for sequences $A$. The separation $d$ is the coordinate distance between points of maximum rest mass density and is given in units of the total rest mass of the binary $M_0$. The curves show runs with different grid sizes and resolutions which are detailed in Table . The filled circles mark the time of surface contact for the merger orbits. The empty square on the $y$ axis marks the QE estimation of the ISCO separation.

Figure 2

Coordinate separation vs time for sequences $B$.

Figure 3

Coordinate separation vs time for sequences $C$.

Figure 4

Quality control for the $(m/R{)}_{\infty }=0.142$ irrotational runs. We show from top to bottom the total gravitational mass, angular momentum, the Hamiltonian constraint, and the average of the components of the momentum constraint vs time [22]. The curves correspond to the runs from Fig. 2 labeled as Stable (solid lines) and Merger (dashed lines). The filled circle marks the time of surface contact for the merger orbit.