Dynamical tides during the inspiral of rapidly spinning neutron stars: Solutions beyond mode resonance
arxiv(2024)
摘要
We investigate the dynamical tide in coalescing binaries involving neutron
stars (NSs). The deformed NS is assumed to spin rapidly, with its spin axis
anti-aligned with the orbit. Such an NS may exist if the binary forms
dynamically, and it can lead to a strong tide because the NS f-mode can be
resonantly excited during the inspiral. We present a new analytical solution
for the f-mode resonance by decomposing the tide into a resummed equilibrium
component varying at the forcing frequency and a dynamical component varying at
the mode eigenfrequency. This solution simplifies numerical implementations by
avoiding the subtraction of two diverging terms. It also extends the solution's
validity to frequencies beyond mode resonance. When the dynamical tide back
reacts on the orbit, the effective Love number alone is insufficient because it
does not capture the tidal torque on the orbit that dominates the back reaction
during resonance. An additional dressing factor is therefore introduced to
model the torque. The dissipative interaction between the NS and the orbital
mass multipoles is computed including the dynamical tide and shown to be
subdominant compared to the conservative interaction. We show that orbital
phase shifts caused by the l=3 and l=2 f-modes can reach 0.5 and 10 radians
at their respective resonances. Because of the large impact of the dynamical
tide, a linearized description becomes insufficient, calling for future
developments to incorporate higher-order corrections. After mode excitation,
the orbit cannot remain quasi-circular, and the eccentricity excited by the
l=2 dynamical tide can approach nearly e≃ 0.1, leading to
non-monotonic frequency evolution. Lastly, we demonstrate that the GW radiation
from the resonantly excited f-mode alone can be detected with a signal-to-noise
ratio exceeding unity at a distance of 50 Mpc with the next-generation GW
detectors.
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