Orbital eccentricity can make neutron star g-mode resonances observable with current gravitational-wave detectors

Abstract

Dynamical tides can provide us vital information about the properties of neutron star (NS) matter. This is particularly true for g-modes, whose frequency and tidal coupling are highly sensitive to the composition of NSs, especially in their centers, where microphysical models are the least reliable. However, due to their weak coupling to external tidal fields, their effect on the gravitational-wave (GW) signal of binary inspirals can be difficult to observe. Here we show that the detectability of these tides can be significantly enhanced by binary NSs with moderate eccentricities. This is primarily due to higher eccentric harmonics in the early phase of the binary evolution experiencing larger phase shifts, which they transport to the sensitive band of GW detectors. In addition, g-mode tides in eccentric binaries undergo several epicyclic resonances, which also amplify the total phase shift. We demonstrate that these effects increase the detectability of g-mode dynamical tides by more than an order of magnitude for eccentricities of $e_\mathrm{10Hz}\sim0.2-0.4$, making it possible to put robust constraints on g-mode properties using current GW detectors, while all relevant models could potentially be constrained with eccentric binary NSs with Einstein Telescope.

Figures (6)

• Figure 1: Illustration of the effect of g-mode resonances in circular and eccentric binaries, considering a single g-mode. Here, the orbital phase shift due to resonances is shown as a function of the $\ell=2$ mode GW frequency. While in a circular binary the quadrupolar tides only resonate with the $\ell=2$ harmonic of the binary, in the eccentric case the total phase shift of the binary will be accumulated through several epicyclic resonances (shown by the orange NSs). These resonances occur at well-defined orbital frequencies (denoted by dashed lines), whenever the frequency of the tidal mode becomes an integer multiple of the orbital frequency.
• Figure 2: Time-domain phase shift, $\Delta\Phi$, normalized with $\Delta\Phi(e=0)$, as a function of orbital eccentricity at a reference GW frequency of $10$ Hz ($e_\mathrm{10Hz}$). Lines with different colors show results for different values of the g-mode frequency, $f_g$. The results in our parameterization are independent of the tidal coupling $\Lambda_g$.
• Figure 3: Time-domain phase shift, $\Delta\Phi$, of eccentric binary NSs due to g-mode resonances as a function of $2F = f_\mathrm{GW}^{\ell=2}$. Different lines show results for binaries with different orbital eccentricities at a reference GW frequency of $10$ Hz ($e_\mathrm{10Hz}$). The tidal parameters are chosen as $\Lambda_1^g=0.1$ and $\Lambda_2^g=0$ and the g-mode frequency is set to $f_g=100$ Hz.
• Figure 4: Characteristic strains, $h_c(f) = \tilde{h}(f)f^{1/2}$, of binary NSs at a distance of $40$ Mpc with different eccentricities at $f_\mathrm{GW}^{\ell=2}=10$ Hz (solid lines). Dashed lines correspond to the envelopes of the difference between the vacuum strains and strains from evolutions where g-mode resonances are taken into account, as defined by the second line in Eq. \ref{['eq:dSNR']}. The expectation values were used for calculating the phase shift. The parameters of the g-modes here are $f_\mathrm{g}=100$ Hz, and $\Lambda_1^g=0.1$ and $\Lambda_2^g=0$. The sensitivity curves of A+ and ET are also represented by gray dashed lines.
• Figure 5: Dependence of the $\delta$SNR of the difference signal on the eccentricity at $10$ Hz for binary NSs with different g-mode frequencies and a tidal coupling $\Lambda_g=0.1$. Dark tones represent results for A+, while semi-transparent lines correspond to ET. Dashed lines were calculated using waveforms truncated at $e_\mathrm{max}=0.9$. The pink dotted line corresponds to observations of NS-BH binaries similar to GW200105 with ET, where the vertical region represents the measured eccentricity, as given by Ref. Morras:2025xfu. Horizontal lines represent $\delta$SNR thresholds of $3$ and $8$. Results for binary NSs assume optimally oriented detectors and binaries at $40$ Mpc distance, where the phase shifts from only one of the NSs were taken into account.