In-plane Black-hole Spin Measurements Suggest Most Gravitational-wave Mergers Form in Triples

TL;DR

The paper addresses the problem of identifying the dominant formation channels for merging binary black holes by analyzing spin-orbit tilt distributions. It employs hierarchical Bayesian inference with astrophysically motivated parametric spin-population models applied to GWTC-4.0 data, finding that a Gaussian tilt component peaking at near-perpendicular orientations ($\cos\theta\approx0$) dominates the low-mass population ($\tilde{m} \approx 44\,M_\odot$ transition to isotropy above this mass). The inferred parameters are $\mu_t = 0.20^{+0.21}_{-0.11}$, $\sigma_t = 0.55^{+0.25}_{-0.16}$, and mixing $\xi = 0.86^{+0.10}_{-0.55}$, with a Bayes-factor disfavouring aligned-spin models ($|\Delta\ln\mathcal{B}| \approx 1.6$ to $6.3$). This supports a scenario in which hierarchical triples, via Lidov–Kozai dynamics, dominate BBH mergers, challenging traditional isolated-binary formation and implying a need to revise binary-evolution models as more detections become available.

Abstract

The spin-orbit tilt angles $θ_{1(2)}$ of merging stellar-mass black holes provide key insights into their astrophysical origin. The LIGO, Virgo, and KAGRA Collaborations (2025a, arXiv:2508.18083) report that the spin-orbit tilt distribution of mergers in the latest Gravitational-Wave Transient Catalog 4.0 exhibits a global peak at near-perpendicular directions $\cosθ_{1(2)}\approx0$. Here, we recover this feature using hierarchical Bayesian inference with parametric models that are tailored to enhance the diagnostic power about astrophysical formation channels. We find that the spin distribution of the low-mass bulk of the binary black hole merger population $(m_1\lesssim 44.3^{+8.7}_{-4.6}\,\rm M_\odot)$ can be well-modelled by a dominant Gaussian component that peaks at $\cosθ_{1(2)}\approx0$, possibly mixed with a subdominant isotropic component. Models that include a component with spins preferentially aligned with the orbit are disfavoured by current data (with Bayes factors $|Δ\ln\mathcal{B}|\approx1$ to $3$) and constrain its contribution to be small ($ξ\sim\mathcal{O}(1)\,\%$). If these findings are reinforced by more detections, they would challenge any major contribution from the traditional isolated-binary formation scenario yielding closely aligned spins. Instead, the dominant component with near-perpendicular spins qualitatively matches expectations from the evolution of isolated massive stellar triples in the galactic field, where the Lidov-Kozai effect naturally produces a unique overabundance of mergers with $\cosθ_{1(2)}\approx0$.

Figures (8)

• Figure 1: Schematic overview of the parametric spin population model described in Equation \ref{['eq:pi']}. Below a mass cut-off $m_1\lesssim\tilde{m}$ the population is described by a mixture between a component whose spin directions $\cos\theta_{1(2)}=\boldsymbol{\hat{\chi}}_{1(2)}\cdot\boldsymbol{\hat{L}}$ follow a truncated Gaussian distribution (mixing fraction $\xi$) and a component with isotropic spin directions (mixing fraction $1-\xi$). Above $m_1\gtrsim\tilde{m}$ the spins also follow an isotropic distribution. Each of the three components are allowed to follow different spin magnitude distributions.
• Figure 2: Posterior predictive distribution (PPD) of the black hole spin tilts of the low-mass population ($m_1\lesssim\tilde{m}= 44.3^{+8.7}_{-4.6}\,\rm M_\odot$) in our parametric Gaussian + Isotropic + Cut model (blue). The PPD is constructed by taking the quantiles (median indicated by dashed lines, 90% interval by shaded envelope) across MCMC samples (thin lines). The left panel shows the PPD of only the low-mass Gaussian component, the right panel includes the low-mass isotropic component. The green colour shows the non-parametric B-Spline model of GWTC4popGWTC4pop-zenodo. The red line shows simulation outcomes of binary black hole mergers which are caused by the Lidov--Kozai effect in hierarchical triples Antonini2018. The orange lines show simulation outcomes of binary black hole mergers from isolated binary star evolution Olejak2024 assuming high natal kicks at black hole formation that are drawn from a Maxwellian velocity distribution with $\sigma=133\,\rm km\,s^{-1}$ (dash-dotted) or natal kicks lowered by fallback Fryer2012 with $\sigma=265\,\rm km\,s^{-1}$ (solid). Since we cut the y-axis, the small inset (linear axes) shows that the orange models are strongly concentrated at $\cos\approx1$. In the right panel, the binary black hole sketch depicts a merger with $\cos\theta_{1(2)}\approx0$, where, for visualisation purposes, we pick near-opposite in-plane directions (which is generally poorly constrained from the data).
• Figure 3: PPD of the black hole spin magnitude distribution in the Gaussian Isotropic Cut model. Blue shows the magnitude distribution of the low-mass Gaussian component (parametrised by $\mu_\chi$ and $\sigma_{\chi}$), orange of the low-mass isotropic component ($\mu^{\rm Iso}_\chi$ and $\sigma^{\rm Iso}_{\chi}$), and purple of the high-mass isotropic component ($\mu^{\rm HighIso}_\chi$ and $\sigma^{\rm HighIso}_{\chi}$). The transition between low- and high-mass components is inferred at a primary mass cut-off of $\tilde{m}\approx 44.3^{+8.7}_{-4.6}\,\rm M_\odot$. The green colour shows the non-parametric B-Spline model of GWTC4popGWTC4pop-zenodo. Solid lines and shaded envelopes indicate medians and $90\,\%$ credible intervals, respectively.
• Figure 4: Joint and marginal posteriors for the mean $\mu_t$ and standard deviation $\sigma_t$ of the Gaussian component, its mixing fraction $\xi$, and the mass cut-off $\tilde{m}$ in the Gaussian + Isotropic + Cut model.
• Figure 5: Marginal posterior distributions of the Gaussian mixing fraction $\xi$. The left panel shows the probability density function (PDF); the right panels its cumulative density function (CDF). The fraction $\xi$ refers to the mixing fraction of the Gaussian component, which is enforced at alignment in the Aligned + Isotropic model ($\mu_t=1$) or moves freely in all others ($-1\le\mu_t\le1$), whereas $1-\xi$ refers to the isotropic fraction. For the Gaussian + Isotropic + Cut and Aligned + Isotropic + Cut models the fractions $\xi$ and $1-\xi$ describe the mixing in the low-mass population ($m_1\lesssim\tilde{m}$).