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

Abstract

Rossby modes ($r$-modes) of rotating neutron stars can be excited by the gravitomagnetic forces in coalescing binary systems. A previous study by Flanagan and Racine [Phys. Rev. D 75, 044001 (2007)] showed that this kind of dynamical tide (DT) can induce phase shifts of $\ensuremath{\sim}0.1\text{ }\text{ }\mathrm{rad}$ on gravitational waveforms, which is detectable by third-generation (3G) detectors. We study the impact of this DT on measuring neutron-star parameters in the era of 3G detectors. We incorporate two universal relations among neutron-star properties predicted by different equations of state: (i) the well-known I-Love relation between momentum of inertia and ($f$-mode) tidal Love number, and (ii) a relation between the $r$-mode overlap and tidal Love number, which we newly explore. We find that $r$-mode DT will provide rich information about slowly rotating neutron stars with frequency 10--100 Hz and spin inclination angle 18\ifmmode^\circ\else\textdegree\fi{}--110\ifmmode^\circ\else\textdegree\fi{}. For a binary neutron-star system (with a signal-to-noise ratio $\ensuremath{\sim}1500$ in the Cosmic Explorer), the spin frequency of each individual neutron star can be constrained to 6% (fractional error) in the best-case scenario. The degeneracy between the Love numbers of individual neutron stars is dramatically reduced: each individual Love number can be constrained to around 20% in the best case, while the fractional error for both symmetric and antisymmetric Love numbers are reduced by factors of around 300. Furthermore, DT also allows us to measure the spin inclination angles of the neutron stars, to 0.09 rad in the best case, and thus place constraints on neutron-star natal kicks and supernova explosion models. In addition to parameter estimation, we also develop a semianalytic method that accurately describes detailed features of the binary evolution that arise due to the DT.