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

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries and for extracting NS information from GW data. In this paper, we use semianalytic methods to carry out a systematic study on the tidal excitation of fundamental modes (f-modes) of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is antialigned with the orbital angular momentum-where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigenmodes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. (Our treatment is at Newtonian order, including a gravitational radiation reaction at quadrupole order.) We then find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and postresonance. Using the method of osculating orbits, we obtain semianalytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in our understanding of the system's dynamics. In particular, we recover both the averaged postresonance evolution, which differs from the preresonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We fmd that, for a system with component masses of (1.4,1.4) M-circle dot at 100 Mpc, the constraints on the effective Love number of the (2,2) mode at Newtonian order can be improved by a factor of 3 similar to 4 if spin frequency is as high as 500 Hz. The relative errors are 0.7 similar to 0.8 in the Cosmic Explorer, and they might be further improved by post-Newtonian effects. The constraints on the f-mode frequency and the spin frequency are improved by factors of 5 similar to 6 and 19 similar to 27, respectively. In the Cosmic Explorer case, the relative errors are 0.2 similar to 0.4 and 0.7 similar to 1.0, respectively. Hence, the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to f-mode; it can also be applied to other types of tides.