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 ∼0.1 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°-110°. For a binary neutron-star system (with a signal-to-noise ratio ∼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.

$f$-mode Imprints in Gravitational Waves from Coalescing Binaries involving Aligned Spinning Neutron Stars

“…This set of EOS is the same as those adopted in [69], and we note that the latter formula (25) has been introduced there. The former universal relation connects the tidal overlap of fmode to the tidal deformability, which is newly pointed out here, while that for r-mode has been developed in [70] (see the right panel of Fig. 7 therein).…”

“…In reality, the effect of tides in the tidal evolution and dephasing is 3-fold: gravito-electric, gravito-magnetic tides, and the change in the waveform shape induced from the gravito-electric tidal field [99][100][101]. We focus in the present article the gravito-electric tides, while we note that some excitations ignited by the gravito-magnetic tidal field [70,102] may become comparable to the gravito-electric excitations under certain conditions [103]. In addition, although we consider the spininfluenced tidal effects in GW phase, we do not include the spin-corrected orbital motion, and the rotationinduced deformation of NSs in the present article.…”

Uncertainty limits on neutron star radius measurements with gravitational waves

“…However, they provide a projection that GWs could result in a ∼100 m radius measurement within the decade with Voyager and beyond with 3G detectors. This radius constraint would also improve if effects such as dynamical tides [65][66][67] are detected as they are qualitatively different than the standard adiabatic tides considered here and not captured by the ρ −1 scaling. Reaching this projected precision relies on ascertaining that every aspect of the GW analysis induces potential systematic errors that are fully quantified and brought below statistical uncertainties.…”

Relativistic Correction to the r-mode Frequency in Light of Multimessenger Constraints

“…A couple of recent studies (Ma et al 2021;Gupta et al 2022) have also looked into the possible resonant r-mode detection in the inspiral phase of the binary mergers using the thirdgeneration detector Einstein telescope (Punturo et al 2010;Hild et al 2011). The r-mode introduces an additional phase to the waveform model that is estimated from the r-mode frequency κ as a function of the dimensionless tidal deformability of the NS.…”