Probing Intrinsic Ellipticity in Neutron Star Binaries

TL;DR

The paper introduces a spin-orbit resonance mechanism in neutron-star binaries, enabled by a finite ellipticity $ε$ that can arise from internal magnetar fields, and shows how resonance locking transfers angular momentum between the orbit and the neutron star, imprinting a measurable 2PN phase correction in the gravitational waveform. It develops a pendulum-like dynamical framework, derives the locking probability $\mathcal P_{\rm lock} \approx \frac{4\sqrt{3}}{\pi}\left(\frac{q}{1+q}\right)^{1/2}ε^{1/2}$, and identifies a breaking frequency $f_{\rm br}$ that signals the end of locking, with the phase correction $\delta\psi_{\rm lock}(f)$ entering the waveform. Through injection studies and analysis of GW events up to O4a, no definitive resonance signal is found, but next-generation detectors (CE+ET) could precisely measure $ε$ and the neutron-star moment of inertia, enabling tests of the EOS via the I-Love relation and constraining the magnetar fraction in NS binaries. The work also provides a generalizable framework for eccentric orbits and extensions to crustal or exotic compact object scenarios, highlighting the potential of resonance locking as a new probe of dense matter and strong-field gravity.

Abstract

We present a novel resonance mechanism that can naturally occur in neutron star binaries: a spin-orbit resonance. This resonance locks the binary into a unique state where the neutron star spin evolves alongside the orbit. The resonance requires a finite neutron star ellipticity $ε$ possibly sourced by strong internal magnetic fields in magnetars, which are motivated by population study of eccentric neutron star-black hole binary GW200105. We find that the locking probability is proportional to $\sqrtε$. We derive the phase correction in the gravitational waveform due to this resonance locking effect, and have conducted a search in all neutron star binaries up to the O4a gravitational-wave catalog, with no positive event found so far. Observations by next-generation detectors such as Einstein Telescope and Cosmic Explorer, or even the upcoming upgrade of Advanced LIGO, have the potential to detect such locking signals, enabling precise measurements of both neutron star's ellipticity and moment of inertia. Future searches should be performed to discover this resonance, or, if undetected, to place constraints on the magnetar fraction in neutron star binaries.

Figures (11)

• Figure 1: Schematic diagram of the binary $M-M^\prime$, where the neutron star has a finite ellipticity. The long axis of the neutron star lies in the orbital plane and makes an angle $\theta$ with a reference axis fixed in inertial space. $f$ is the true anomaly.
• Figure 2: The evolution of the orbital frequency and neutron star spin frequency with time for a specific locking example, where $M = 1.4\,M_\odot$, $q=3$, and $\epsilon = 5 \times 10^{-5}$. The initial phase is set as $f-\theta=0.3986$.
• Figure 3: Posterior distributions of breaking frequency $f_{\rm br}$ and moment of inertia $I$ for different recovered injections. The injection values are marked with blue lines.
• Figure 4: Posterior distributions of breaking frequency $f_{\rm br}$ for the search in several GW events. Here, $f_{\rm low}$ indicates the minimum frequency of our search range. Note that the results for GW190814 shown in the figure are based on the Hanford data only.
• Figure 5: Posterior distributions of breaking frequency $f_{\rm br}$ and moment of inertia $I$ with Hanford-Livingston-Virgo data (black, grey shading), Livingston data only (red) and Hanford data only (blue), for GW190814.