Astrophysical Implications of Eccentricity in Gravitational Waves from Neutron Star-Black Hole Binaries

TL;DR

This work quantifies the measurability and detectability of orbital eccentricity in NSBH mergers using eccentric inspiral waveforms and HM-enabled models, finding typical minimum detectable eccentricities near $e_{ m min,10} \\sim \\mathcal{O}(0.01)$ (lower for HM-rich cases) and showing that spin precession and mass ratio can further lower this threshold. It demonstrates that a population of NSBHs formed via field triples would be substantially under-detected by quasi-circular searches, with around 27% recovery, and that incorporating eccentric and precessing templates increases recovery substantially. Using a Poisson-based detection framework, the study shows that if ~1/3 of current NSBH detections are measurably eccentric, the observed sample could be fully consistent with an isolated field-triple origin; more detections would tighten the constraints on the triple-branch fraction $\beta_t$. Overall, the results highlight a significant population of eccentric NSBHs that may be missing from current LVK analyses and motivate development of dedicated eccentric waveform templates and search strategies.

Abstract

The gravitational-wave signal from the neutron star-black hole (NSBH) merger GW200105 is consistent with this binary having significant orbital eccentricity close to merger. This raises the question of how an eccentric NSBH might form. Compact object binaries that form via isolated binary star evolution should radiate away any orbital eccentricity long before their gravitational-wave signal enters the sensitive frequency range of the LIGO-Virgo-KAGRA detector network. Meanwhile, dynamical environments -- which can be conducive to mergers on eccentric orbits -- produce very few NSBHs. We estimate the minimum measurable eccentricity of NSBHs at 10 Hz orbit-averaged gravitational-wave frequency, $e_{\mathrm{min},10}$, finding that for GW200105, GW200115, and GW230529-like systems, $e_{\mathrm{min},10}$ is O(0.01). For a GW190814-like unequal-mass binary with significant higher-order mode content, $e_{\mathrm{min},10}=0.003$; this is an order of magnitude lower than when higher-order modes are not present. For dominant-mode signals from eccentric binaries with $m_2=1.5$ M$_\odot$ and a range of total masses from $3\,{\rm M_\odot} \leq M \leq50\,\rm M_\odot$, we find $0.008\leq e_{\mathrm{min},10}\leq0.022$. The relationship between $M$ and $e_{\mathrm{min},10}$ is linear when the binaries are non-spinning. When the binaries are maximally spin-precessing, $e_{\mathrm{min},10}$ decreases as mass ratio becomes more unequal. We estimate the sensitivity of a quasi-circular templated search to a population of NSBHs from field triples, finding that we recover only 27% of our simulated population. Finally, we show that if ~1/3 of present NSBH detections are measurably eccentric, then all of them are consistent with an isolated field triple origin.

Figures (6)

• Figure 1: Left: The translucent blue filled histogram shows the eccentricity defined at a peak GW frequency of $10$ Hz, output by the triple simulations of StegmannKlencki2025. The translucent orange filled histogram shows these same eccentricities but evolved to the $10$ Hz $22$-mode frequency using the standard eccentricity definition scripts of Vijaykumar2024 (see also 2023:Shaikh:ecc) or the analytic solutions of 2021PhRvD.104j4023T, assuming no redshifting. The green unfilled histogram shows the source-frame eccentricity of systems that are recovered by the optimal quasi-circular aligned-spin search described in the text, averaging every injected system over $500$ possible $d_L$---$\ell$ pairs and $10^7$ sets of extrinsic parameters, taking into account the effects of redshifting in the injection. Our mock quasi-circular search recovers only $27\%$ of the injected signals. The vertical purple line shows the median $e_{22,10}$ recovered in 2025arXiv250315393M for GW200105 using the same waveform model as is used here, and the translucent purple band spans the $90\%$ credible interval around this median. Right: The found percentage of events with $\log_{10}(e'_{10})$ equal to or greater than the value shown on the horizontal axis.
• Figure 2: Scatter plot of total mass vs estimated minimum measurable eccentricity calculated via the method described in the text, for injections of pyEFPE waveforms with either minimum or maximum values of $\chi_\mathrm{p}$. The H1 SNR of the quasi-circular versions of these injections is within $\pm 0.4$ of $\rho_{0, H1}=22$. For a fixed SNR, the minimum detectable eccentricity correlates with total mass when $\chi_\mathrm{p}=0$. When $\chi_\mathrm{p}$ is maximal ($\chi_1^\perp = 0.99$; we assume the secondary is non-spinning), the relationship is not linear, and measurability improves for more extreme mass ratios. The colour range indicates the mass ratio $q$.
• Figure 3: Constraints on the detectable branching fraction of NSBH-producing field triples, $\beta_t$, as a function of the number of NSBH observations, $N_\mathrm{obs}$, given a number of eccentric NSBH observations $N_\mathrm{ecc}$. Diagonal shaded coloured bands encompass the 95% symmetric credible region of the likelihood on $\beta_t$. The limit $\beta_t=1$ is marked with a thick horizontal black line. Observations above this limit would indicate either problems with the astrophysical simulations, or more eccentric observations than can be explained by this formation channel alone. The vertical red shaded band encompasses the range of possible $N_\mathrm{obs}$ so far, including marginal candidates and candidates with ambiguous secondary masses to reach the maximum.
• Figure 4: The probability distribution over the triple branching fraction $\beta_t$ given number of NSBH observations $N_\mathrm{obs}=3$ (blue) and $N_\mathrm{obs}=11$ (gold) assuming $N_\mathrm{ecc} = 1$.
• Figure 5: Oscillations seen in the overlap calculated using SEOBNRv5EHM for (left) a GW190814-like injection with different sampling frequencies, and (right) a GW200105-like injection with different source inclinations. All other parameters are as shown in Table \ref{['tab:settings']}. We see that the highest value of $e_{22,10}$ at which the metric $(1 - \mathcal{O}) * \rho^2_0$ becomes $> 1$ is similar in all variations.