In coalescing neutron star ( NS ) binaries , tidal force can resonantly excite low-frequency ( \lesssim 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 non-perturbative 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 parameterized 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 _ { \odot } and radius R = 10 km ) and modest rotation rates ( \lesssim 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 \gtrsim 15 km ) .
Significant phase shift can also be produced when the combination of stratification and rotation gives rise to a very low frequency ( \lesssim 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 can not be excited during the inspiral phase of NS binaries .