Innermost stable circular orbit of inspiraling neutron-star binaries: Tidal effects, post-Newtonian effects, and the neutron-star equation of state

We study how the neutron-star equation of state affects the onset of the dynamical instability in the equations of motion for inspiraling neutron-star binaries near coalescence. A combination of relativistic effects and Newtonian tidal effects causes the stars to begin their final, rapid, and dynamically unstable plunge to merge when the stars are still well separated and the orbital frequency is ≈500 cycles/sec (i.e., the gravitational wave frequency is approximately 1000 Hz). The orbital frequency at which the dynamical instability occurs (i.e., the orbital frequency at the innermost stable circular orbit) shows modest sensitivity to the neutron-star equation of state (particularly the mass-radius ratio $\frac{M}{R_0}$ of the stars). This suggests that information about the equation of state of nuclear matter is encoded in the gravitational waves emitted just prior to the merger.