Do both black holes spin in merging binaries? Evidence from GWTC-4 and astrophysical implications

TL;DR

Using the GWTC-4 BBH catalog, the paper tests whether natal BH spins follow the traditional near-zero expectation or require spin-up channels. It introduces a four-component spin-magnitude mixture and performs hierarchical Bayesian inference to infer population fractions and spin distributions for two baseline spin regimes and their spin-up extensions. The main finding is evidence for two subpopulations where both BHs have non-negligible spins (one around $χ \approx 0.1$ and another around $χ \approx 0.8$), with little support for non-spinning binaries or binaries with only one spinning component, challenging standard angular-momentum transport theories. The results hint at formation channels that spin up both BHs, such as chemically homogeneous evolution or accretion in AGN disks, while emphasizing potential model limitations and the need for further data and broader spin-magnitude parametrizations.

Abstract

Angular momentum transport in high-mass stars is commonly modeled by extrapolating the behavior of better-observed low-mass stars. According to the conventional picture, the cores of most black hole progenitors lose almost all of their angular momentum when their outer layers are ejected before core collapse. Accordingly, most black holes are expected to be born with dimensionless spin magnitudes of $χ\lesssim 0.01$, even if some black holes are born with non-negligible spin due to tidal interactions in a progenitor binary. One might therefore expect to find a large fraction of $χ\lesssim 0.01$ black holes in merging binary black hole (BBH) systems. We find that the conventional picture of angular momentum transport is in tension with data from LIGO--Virgo--KAGRA's fourth gravitational-wave transient catalog. We find no support for a sub-population of BBH systems with $χ\lesssim 0.01$. Neither do we find support for a sub-population with only one spinning black hole as expected for tidal spin-up scenarios. Instead, we find evidence for two subpopulations in which both black holes have non-negligible spin. Approximately 84% of BBH systems contain two black holes with modest spins $χ\approx 0.1$ and approximately 16% contain two black holes with large spins $χ\approx 0.8$. These estimates come from our best-fit model, which is favored with natural log Bayes factors $\ln B \gtrsim 3$ over models that require a sub-population of $χ\lesssim 0.01$ black holes, and models that do not contain multiple spin sub-populations. These results are difficult to reconcile with our current understanding of angular momentum transport.

Figures (10)

• Figure 1: Posterior distributions for population branching fractions assuming non-spun-up black holes have spin magnitudes of $\chi_0=0$. The fractions $\lambda_0$, $\lambda_1$, $\lambda_2$ and $\lambda_b$ represent subpopulations of binaries in which neither black hole is spun up, the primary black hole is spun up, the secondary black hole is spun up, and both black holes are spun up, respectively. From darkest to lightest, contours in two-dimensional panels give the 50%, 90% and 99% credible regions of the posterior. We see strong support for $\lambda_b \approx 1$, implying that almost all black holes in merging binaries have some measurable spin magnitude. This may indicate that nearly all black holes are spun up, or that it is incorrect to assume that black holes are typically born with negligibly small spins in the absence of a spin-up mechanism.
• Figure 2: Population predictive distribution for the best-fit model when assuming black holes are typically born with $\chi_0=0$ (blue). The left panel gives the marginal distribution for one component ($\chi_1$ and $\chi_2$ are identically distributed in this model), while the right panel gives the joint spin magnitude distribution. Both panels give probability in logarithmic scale. In this best-fit model, $\lambda_b=1$ implying all black holes in the population are spun-up. This results in a Gaussian distribution of spin magnitudes. Over-plotted in orange is the $\text{\ooalign{\hidewidth--\hidewidth\cr$\pi$\cr}}$ fit to GWTC-4 from pistroke. In the one-dimensional plot, the solid and dashed tails give the $\text{\ooalign{\hidewidth--\hidewidth\cr$\pi$\cr}}$ fit for $\chi_1$ and $\chi_2$ respectively. The heights of the points are scaled such that the tallest point coincides with the median fit to the population model. The color-bar gives the normalized weight.
• Figure 3: Comparison of spin scenarios for the 153 BBH events in GWTC-4. The horizontal axis gives the natural log Bayes factor comparing the hypothesis that at least one component in the binary has a non-zero spin magnitude, to the hypothesis that both components have spin magnitudes of zero. The colour of each marker is also determined by the same natural log Bayes factor; this helps guide the eye to the events that are most clearly spinning. The vertical axis gives the natural log Bayes factor comparing the hypothesis that both components in the binary spin to the hypothesis that only one component spins. Events tend to cluster around zero -- presenting no evidence in any direction. As events show more evidence for component spins of any sort, they consistently show more evidence for both components in the binary having a non-zero spin magnitude, as opposed to only one.
• Figure 4: Posterior distributions for population branching fractions assuming non-spun-up black holes have non-zero, Gaussian distributed spin magnitudes. The fractions $\lambda_0$, $\lambda_1$, $\lambda_2$ and $\lambda_b$ represent subpopulations of binaries in which neither black hole is spun up, the primary black hole is spun up, the secondary black hole is spun up, and both black holes are spun up beyond their initial Gaussian distributed spin, respectively. From darkest to lightest, contours in two-dimensional panels give the 50%, 90% and 99% credible regions of the posterior. We find a peak at $\lambda_0 \approx 0.8$, indicating that most, but likely not all black holes follow some Gaussian like distribution of small spin magnitudes. Meanwhile, $\lambda_1$ and $\lambda_2$ peak at zero, indicating that systems in which only one black hole is spun up are rare. On the other hand, $\lambda_b$ peaks at $\approx 0.1$, meaning the data favors a considerable fraction of binaries in which both components are spun up beyond spins typical of the rest of the population.
• Figure 5: Population predictive distribution for the best-fit model when assuming black holes are typically born with non-zero, Gaussian-distributed spins. This is the best-fit model of all considered in this paper. In blue, the left panel gives the marginal distribution for one component ($\chi_1$ and $\chi_2$ are identically distributed), while the right panel gives the joint spin magnitude distribution. Both panels are in logarithmic scale. In this best-fit model, only $\lambda_0$ and $\lambda_b$ are allowed to be non-zero, implying that for any given system, neither black hole is spun up, or both black holes are spun up. The 90% credible contributions from these two subpopulations are over-plotted in solid and dashed gray lines respectively. Over-plotted in orange, is the $\text{\ooalign{\hidewidth--\hidewidth\cr$\pi$\cr}}$ fit to GWTC-4 from pistroke. In the one-dimensional plot, the solid and dashed tails give the $\text{\ooalign{\hidewidth--\hidewidth\cr$\pi$\cr}}$ fit for $\chi_1$ and $\chi_2$ respectively. The heights of the points are scaled such that the tallest point coincides with the median fit to the population model. The color-bar gives the normalized weight.