Innermost Stable Circular Orbit of Inspiraling Neutron-Star Binaries: Tidal Effects, Post-Newtonian Effects and the Neutron-Star Equation of State

TL;DR

This paper investigates how the neutron-star equation of state influences the innermost stable circular orbit and the gravitational wave signals during inspiral, highlighting potential for gravitational wave data to reveal nuclear matter properties.

Contribution

It combines relativistic and Newtonian tidal effects to analyze the onset of dynamical instability and its dependence on the neutron-star equation of state.

Findings

The dynamical instability occurs at orbital frequencies around 500 cycles/sec.

The instability point shows modest sensitivity to the neutron-star equation of state.

Gravitational waves prior to merger encode information about the neutron-star equation of state.

Abstract

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 cause the stars to begin their final, rapid, and dynamically-unstable plunge to merger when the stars are still well separated and the orbital frequency is $\approx$ 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, $M/R_o$, 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.