Gravitational Wave Evidence of Spin Energy Extraction from Stellar-Mass Black Holes

TL;DR

The work tackles whether jet energy in compact objects arises from BH spin energy extraction versus accretion power. It develops an analytic MAD+BZ framework that predicts a universal natal BH spin χ_eq, independent of mass or accretion history, and demonstrates χ_eq depends only on horizon-flow parameters h and η. Using GWTC-4.0 data and hierarchical Bayesian inference, it detects a dominant population of second-born BH spins centered at χ_2 ≈ 0.05, aligning with χ_eq and supporting spin-energy extraction in GRB natal remnants. This has implications for GRB progenitor channels, near-horizon accretion physics, and the role of MAD/BZ processes in shaping BH spin distributions observed through gravitational waves.

Abstract

Relativistic jets have been found for decades as a key phenomenon in active galactic nuclei (AGNs), compact binary systems, and gamma-ray bursts (GRBs), yet their energy resources remain a mystery. Two competing ideas prevail: one attributes jet energy to accretion power of the black hole (BH), the other, more interestingly, to magnetic extraction of rotational energy from the BH. A decisive observational distinction between them is still elusive. We propose that BHs remnant from their natal GRB activity can serve as a critical testbed to discriminate between these two scenarios. Via analytical approaches, we demonstrate that extraction of rotational energy to power jets during the GRB phase drives the remnant BH to a universal equilibrium spin, independent of accretion history, initial spin, and mass. This model predicts a stellar-mass BH population with this universal spin, a hallmark of BH spin energy extraction. Testing against the 4th gravitational wave (GW) catalogue (GWTC-4.0), we find a statistically robust dominant population where secondary BH spins are narrowly centered at $\sim0.05$. These findings provide strong new evidence for BH spin energy extraction.

Figures (6)

• Figure 1: The function $f(\chi; h, \eta)$ for different values of $h$ and $\eta$. The dashed line indicates the zero line, where the equilibrium spin $\chi_{\rm eq}$ is located. The intersection points between the curves and the zero line indicate the equilibrium spin for different values of $h$ and $\eta$.
• Figure 2: The corner plot of the posterior distribution of the relevant hyper-parameters of the spin distribution of the 2nd-born BH. The spin distribution is modeled as a composed of a narrow Gaussian and a wide Gaussian. The parameters $\mu_{\chi,narrow}$ and $\sigma_{\chi,narrow}$ are the mean and standard deviation of the narrow Gaussian component, respectively; $\eta_\chi$ is the fraction of the narrow Gaussian component in the total distribution.
• Figure 3: The contour plot of the equilibrium spin $\chi_{\rm eq}$ as a function of $h$ and $\eta$.
• Figure 4: The evolution of the spin parameter $\chi$ (upper panel) and the mass of the BH $M_{\bullet}$ (lower panel) for a population of BHs with different initial conditions.
• Figure 5: Dependence of the variance of the log-likelihood on the variance $\sigma_{\chi}$ of an identical Gaussian spin distribution.