Excitation of f -modes during mergers of spinning binary neutron star

Detecting resonant tidal excitations of Rossby modes in coalescing neutron-star binaries with third-generation gravitational-wave detectors

“…Then, in the postresonance regime, there is a small oscillation on top of the major deviation, which is caused by the r-mode oscillation. We also saw this feature in the case of the f-mode [53]. Note that _ ϕ ðnumÞ ∼ 2π × 10 2 − 2π × 10 3 Hz for the time interval that we present.…”

“…We can see that our formulas are accurate in all regimes: adiabatic, resonance, and postresonance. The evolutions of A and B are similar to those of the f-mode [53], except the fact that A increases toward infinity as the two stars become close to each other (recall that the amplitude of A for the f-mode remains constant after the resonance). This can be easily understood from Eq.…”

“…III of Ref. [53], we define two real-valued quadratures, A and B, from the r-mode amplitude, A þ iB ¼c 1 e iϕ−imΩ s1 t and m ¼ 2; ð45Þ with A determining the radial force and B the torque backreacting onto the orbit, respectively. Here m ¼ 2 since we are focusing on the ðl ¼ 2; m ¼ 2Þ mode.…”

“…Following Ref. [53], we first sample the numerical hðtÞ in the time domain with a rate of 8192 Hz, then use the fast Fourier transform algorithm to transform the data to FD. Finally, we select data in the frequency band ½2F 0 ; 2F contact .…”

“…For nonspinning NSs in binaries with circular orbits, only g-modes can be resonantly excited, but their effect on gravitational waveforms is negligible [42][43][44][45]. However, DT can be enhanced by orbital eccentricity [46][47][48][49] and rotation [50][51][52][53].…”