Gravitational-wave Asteroseismology with f-modes from Neutron Star Binaries at the Merger Phase

Abstract

Gravitational-wave signals from coalescing binary neutron stars (BNSs) can yield important information about the properties of nuclear-matter equation of state. We investigate a direct link between the frequency of the quadrupolar 2 f -mode oscillation ( f 2 f ) of nonrotating and rotating neutron stars calculated by a nonlinear hydrodynamics code in the conformally flat approximation and the gravitational-wave frequency associated with the peak amplitude ( f max ) of binary neutron stars from a set of publicly available simulations. We find that f max and f 2 f differ by about 1%, on average, across 45 equal-mass systems with different total mass and equations of state. Interestingly, assuming that the gravitational-wave frequency is still approximately equal to twice the orbital frequency f orb near the merger, the result indicates that the condition for tidal resonance ( ∣ m ∣ f orb ) m = 2 = f 2 f is satisfied to high accuracy near the merger. Moreover, the well-established universal relation between f max and the tidal deformability of equal-mass binary systems can now be explained by a similar relation between f 2 f and the tidal deformability of isolated neutron stars. For unequal-mass binaries, f max increasingly deviates from f 2 f of the two stars as the mass ratio decreases from unity. Therefore, it is possible to relate the gravitational-wave signal at the merger of a BNS system directly to the fundamental oscillation modes and the mass ratio. This work potentially brings gravitational-wave asteroseismology to the late-inspiral and merger phases of BNSs.