Resonant tidal excitation of oscillation modes in merging binary neutron stars: Inertial-gravity modes

摘要

In coalescing neutron star (NS) binaries, tidal force can resonantly excite low-frequency (approx<500 Hz) oscillation modes in the NS, transferring energy between the orbit and the NS. This resonant tide can induce phase shift in the gravitational waveforms, and potentially provide a new window of studying NS interior using gravitational waves. Previous works have considered tidal excitations of pure g-modes (due to stable stratification of the star) and pure inertial modes (due to Coriolis force), with the rotational effect treated in an approximate manner. However, for realistic NSs, the buoyancy and rotational effects can be comparable, giving rise to mixed inertial-gravity modes. We develop a nonperturbative numerical spectral code to compute the frequencies and tidal coupling coefficients of these modes. We then calculate the phase shift in the gravitational waveform due to each resonance during binary inspiral. Given the uncertainties in the NS equation of state and stratification property, we adopt polytropic NS models with a parametrized stratification. We derive relevant scaling relations and survey how the phase shift depends on various properties of the NS. We find that for canonical NSs (with mass M = 1.4 M_⊙ and radius R = 10 km) and modest rotation rates (approx<300 Hz), the gravitational wave phase shift due to a resonance is generally less than 0.01 radian. But the phase shift is a strong function of R and M, and can reach a radian or more for low-mass NSs with larger radii (R approx> 15 km). Significant phase shift can also be produced when the combination of stratification and rotation gives rise to a very low frequency (approx<20 Hz in the inertial frame) modified g-mode. As a by-product of our precise calculation of oscillation modes in rotating NSs, we find that some inertial modes can be strongly affected by stratification, we also find that the m = 1 r-mode, previously identified to have a small but finite inertial- frame frequency based on the Cowling approximation, in fact has essentially zero frequency, and therefore cannot be excited during the inspiral phase of NS binaries.