Inspiralling eccentric binary neutron stars: Orbital motion and tidal resonance

We study the orbital evolution of eccentric binary neutron stars. The motion follows a quasi-Keplarian orbit with perturbations due to tidal couplings. We find that the tidal interaction between stars contributes to orbital precession in addition to the post-Newtonian procession. The coupling between the angular and radial motion of the binary also excites a series of harmonics in the stars’ oscillation. In the small eccentricity limit, this coupling mainly gives rise to an additional orbital resonance, with the orbital frequency being one third of the f-mode frequency. For a binary with initial eccentricity $\sim 0.2$ at 50 Hz orbital frequency, the presence of this tidal resonance introduces $\sim \mathcal{O}(0.5)$ phase shift in the gravitational waveform till merger, subject to uncertainties in neutron star equation of state and the distribution of binary component masses. Such phase shift in the late-inspiral stage is likely detectable with third-generation gravitational-wave detectors.

Figure 1

$\delta t-f$ plot comparing two individual evolutions. Here $f_{\mathrm{orb}}$ is the orbital frequency, and $\delta t≔t_{\mathrm{full}}-t_{\mathrm{part}}$ is the difference in time between two evolutions up to a given frequency. The “full” evolution incorporates the flux, energy, and angular momentum formulas derived in Appendix pp3 and Sec. 3. The “partial” evolution uses only previous known formulas, which do not contain correction at the $e^2\lambda$ order. The initial eccentricity at $f_{\mathrm{orb}}=50\mathrm{Hz}$ is 0.2, the NS mass is $1.3M_{\odot }$, and the compactness is assumed to be 0.16.