Spin-orbit misalignment and residual eccentricity are evidence that neutron star-black hole mergers form through triple star evolution

TL;DR

This work investigates whether NSBH mergers originate predominantly from hierarchical triple evolution in the field, driven by octupole von Zeipel–Kozai–Lidov dynamics. By modeling a population of massive triples from ZAMS through two SN events and long-term three-body dynamics, it shows that a small but non-negligible fraction of triples survive to produce tertiary-driven mergers with residual eccentricity ($e_{20}$) and spin–orbit misalignment ($\cos\theta_{\rm BH}$) that align with some LVK observations. Strong octupole effects and non-adiabatic spin evolution enable mergers across a wide range of initial configurations, often with short delays that track the cosmic star-formation rate. The predicted NSBH merger rate ($R_{\rm NSBH}\sim1$–$23\ \,\rm Gpc^{-3}\,yr^{-1}$) and the fraction with $e_{20}>0.1$ or $\cos\theta_{\rm BH}<0$ are broadly consistent with current data, supporting the interpretation that triple dynamics may be the dominant channel if eccentric and misaligned events are robustly confirmed.

Abstract

There is growing evidence that a substantial fraction of the neutron star-black holes (NSBHs) detected through gravitational waves merge with non-zero eccentricity or large BH spin-orbit misalignment. This is in tension with the leading formation scenarios to date. Residual eccentricity rules out formation through isolated binary star evolution, while NS natal kicks and the unequal masses of NSBHs inhibit efficient pairing in dense stellar environments. Here, we report that all observed properties-NSBH merger rate, eccentricity, and spin-orbit misalignment-are explained by the high prevalence of massive stellar triples in the field. Modelling their evolution from the ZAMS, we investigate NSBH mergers caused by gravitational perturbations from a tertiary companion. We show that the formation of the NS decisively impacts the triple stability, preferentially leaving behind surviving NSBHs in compact triple architectures. The rich three-body dynamics of compact, unequal-mass triples enables mergers across a wide range of orbital parameters without requiring fine-tuned highly inclined tertiary orbits and provides a natural explanation for an abundance of residual eccentricity and spin-orbit misalignment. We infer a total NSBH merger rate of $R\sim1-23\,\rm Gpc^{-3}\,yr^{-1}$, with more than a few 10% exhibiting eccentricity $e_{20}>0.1$ or large spin-orbit misalignment $\cosθ_{\rm BH}<0$, consistent with current observations. Tertiary-driven NSBH mergers closely track the cosmic star formation rate due to their short delay times, include a substantial fraction of burst-like highly eccentric systems ($e_{20} > 0.9$), and almost universally retain eccentricities $e_{20}>10^{-3}$, potentially detectable by next-generation detectors. If evidence for eccentric and misaligned events solidifies, our results suggest that triple dynamics is the dominant formation channel of NSBH mergers.

Figures (8)

• Figure 1: Cartoon of hierarchical NSBH triples whose formation and evolution is studied in this work. The two inner binary stars form an NSBH with masses $m_1=m_{\rm BH}$ and $m_2=m_{\rm NS}$ which is orbited by a distant tertiary companion star with mass $m_3$. The inner and outer orbits are ellipses (denoted by indices "1" and "2", respectively) that can be characterised by eccentricity vectors $\mathbf{e_1}$ and $\mathbf{e_2}$ that point towards the orbital periapses and have magnitudes equal to the orbital eccentricities $|\mathbf{e_1}|=e_1$ and $|\mathbf{e_2}|=e_2$, and by dimensionless orbital angular momentum vectors $\mathbf{j_1}$ and $\mathbf{j_2}$ which are perpendicular to the orbital planes Tremaine2009. The two semi-major axes of the inner and outer orbits are hierarchical in the sense that the semi-major axes satisfy $a_1\ll a_2$. We also consider the evolution of the BH spin vector $\mathbf{S}_{\rm BH}$ and its angle $\theta_{\rm BH}$ with respect to $\mathbf{j_1}$.
• Figure 2: Distributions of the inner semi-major axis (left panel) and semi-major axis ratio (right panel) of triples studied in this work. Grey patches indicate the distributions of $N_{\rm tot}=10^7$ stellar triples at ZAMS (initial conditions), black lines show all triples which survive the first SN and form a BHOB in the inner binary, blue lines show all inner binaries which survive the second SN and form an NSBH (regardless of whether the outer binary remained stable or not), and blue and turquoise patches highlight the subset of NSBHs that underwent some sort of mass transfer and a common-envelope evolution, respectively. Red lines show all stable triples which develop an NSBH in the inner binary, red patches show those that eventually lead to an NSBH merger, and gold solid and dashed lines highlight the subset of those which retain residual eccentricity upon merging ($e_{20}>0.1$) and coalesce with large BH spin-orbit misalignment ($\cos \theta_{\rm BH}<0$), respectively.
• Figure 3: Parameter space of BHOB triples before the second SN. Blue contours show the density of triples with inner binaries that survive the second SN and form stable NSBH binaries. Red contours represent systems successfully forming stable NSBH triples. Scatter points highlight systems which will lead to tertiary-driven NSBH mergers with the colour indicating their residual eccentricity $e_{20}$ at a dominant GW frequency $f_{\rm GW}=20\,\rm Hz$Wen2003. The parameter window for surviving NSBH triples (red) can be understood as a result of several constraining limits, marked with hatched and dotted regions: Diagonally hatched and dotted regions indicate regions where the natal kick tends to disrupt the inner binary, the natal kick tends to disrupt the outer binary, and the SN mass-loss disrupts the outer binary, respectively (see Eqs. \ref{['eq:a1']} -- \ref{['eq:a1a2']}). Below $a_1\approx10\,\rm R_\odot$ inner binaries would undergo a stellar merger at ZAMS (horizontally hatched), and may only be occupied by systems surviving a common-envelope phase. The square hatched region indicates region of dynamical instability of the triple. The black dashed line shows $j_{\rm GW}=j_{\rm GR}$ for a fiducial triple with $m_1=10\,\rm M_\odot$, $m_2=1.5\,\rm M_\odot$, $m_3=1\,\rm M_\odot$, and $e_2=0.67$, respectively.
• Figure 4: Distribution of inner semi-major axis $a_1$ (top panel) and semi-major axis ratio $a_2/a_1$ (bottom panel) before the second SN of systems that successfully form stable NSBH triples. Different colours refer to different natal kick models and the distributions are normalised with respect to the total number of NSBH triples formed in each model.
• Figure 5: Properties of surviving triples harbouring an NSBH in the inner binary (red line) and of the subset leading to mergers (red patches). NSBHs which retain significant residual eccentricity ($e_{20}>0.1$) upon merging and which coalesce with large BH spin-orbit misalignment ($\theta_{\rm BH}>90\,\rm deg$) are highlighted by solid and dashed golden lines, respectively. All parameters are shown at the time when the NSBHs form (i.e., after the second SN). The fractions on the y-axes are defined with respect to the total number of all massive triples ($10\,{\rm M_\odot}<m_1<100\,{\rm M_\odot}$) at ZAMS.