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

Abstract

In coalescing neutron star (NS) binaries, tidal force can resonantly excite low-frequency ( < ∼ 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 = 1.4M and radius R = 10 km) and modest rotation rates ( < ∼ 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 > ∼ 15 km). Significant phase shift can also be produced when the combination of stratification and rotation gives rise to a very low frequency ( < ∼ 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.

Nonparametric inference of neutron star composition, equation of state, and maximum mass with GW170817

“…The EOS determines the eigenmode spectra within a NS, and therefore our posterior processes could be used to determine the exact placement and impact of linear resonant dynamical tidal effects due to f -modes and low-order gmodes during GW-driven inspirals (e.g., Refs. [71][72][73][74]). Similarly, knowledge of the r-mode spectra could inform the CFS instabilities relevant for millisecond pulsars [64,75,76], and knowledge of the p-and g-mode spectra could improve models of non-linear, non-resonant secular fluid instabilities relevant during the GW inspiral [77][78][79][80][81].…”

Chaotic Tides in Migrating Gas Giants: Forming Hot and Transient Warm Jupiters via Lidov-Kozai Migration

“…The f-modes are calculated using the slow-rotation approximation, which gives ωα = ωα(0) − mCαΩs, and we find Cα 0.5 for both the γ = 2 and γ = 5/3 models. The i-mode result is from Xu & Lai (2017) (see their Table IV), based on calculations using a non-perturbative spectral code. Note that for m = 2, the mode frequencies in the rotating frame (ωα) and in the inertial frame (σα) are related by σα = ωα + 2Ωs.…”

Saturn's Rings as a Seismograph to Probe Saturn's Internal Structure

“…In particular, the seismology delivers Saturn's rotation period to a precision of about 1.5 minutes, an uncertainty comparable with the more model-dependent constraints based on Saturn's shape and gravity field, but significantly larger than that derived from the stability of atmospheric flows. Whether the seismology, gravity-shape, and atmospheric dynamics constraints will converge on a consistent rate for Saturn's bulk rotation thus awaits improved theoretical methods for the seismological forwarding modeling; these will take the form of either higher-order asymptotic treatments of rotation (Soufi et al, 1998;Karami, 2008), or non-perturbative methods that can treat rotation free of approximations (Reese et al, 2006;Ouazzani et al, 2012;Xu & Lai, 2017). Because the rotation contributions to the fundamental mode frequencies scale linearly with Saturn's rotation rate to leading order, if the theory can match -11-manuscript submitted to AGU Advances the data at a relative precision of 10 −5 , the existing seismology data could in principle yield Saturn's rotation period to within a second.…”