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Abstract Gamma-ray bursts (GRBs) are among the most energetic events in the Universe, driven by relativistic jets launched from black holes (BHs) formed during the collapse of massive stars or after the merger of two neutron stars. The jet power depends on the BH spin and the magnetic flux accreted onto it. In the standard thin disk model, jet power is limited by insufficient magnetic flux, even when the spin approaches maximum possible value. In contrast, the magnetically arrested disk (MAD) state limits jet energy by extracting significant angular momentum, braking BH rotation. We propose a unified model incorporating both standard thin disk and MAD states, identifying a universal curve for jet power per accretion rate as a function of the magnetic flux ratio, ${\Delta }_{\mathrm{eq}}={({\Phi }_{\mathrm{BH}}/{\Phi }_{\mathrm{MAD}})}_{\mathrm{eq}}$, at spin equilibrium. For long GRBs (lGRBs), the model predicts a maximum jet energy of ∼1.5% of the accretion energy, occurring at Δ_eq ∼ 0.4, where the BH equilibrium spin isa ∼ 0.5. Both long and short GRBs are unlikely to be produced by a MAD: for short GRBs, this requires an accreted mass orders of magnitude smaller than that available, while for lGRBs, the narrow progenitor mass distribution challenges the ability to produce the observed broad distribution of jet energies. This framework provides a consistent explanation for both standard and luminous GRBs, emphasizing the critical role of magnetic flux. Both long and short GRBs require magnetic flux distributions that peak around 10²⁷G cm². 

Abstract In 2023, the Pulsar Timing Array Collaborations announced the discovery of a gravitational wave background (GWB), predominantly attributed to supermassive black hole binary (SMBHB) mergers. However, the detected GWB is several times stronger than the default value expected from galactic observations at low and moderate redshifts. Recent findings by the James Webb Space Telescope have unveiled a substantial number of massive, high-redshift galaxies, suggesting more massive SMBHB mergers at these early epochs. Motivated by these findings, we propose an “early merger” model that complements the standard merger statistics by incorporating these early, massive galaxies. We compare the early and standard “late merger” models, which assume peak merger rates in the local Universe, and match both merger models to the currently detected GWB. Our analysis shows that the early merger model has a significantly lower detection probability for single binaries and predicts a ∼30% likelihood that the first detectable single source will be highly redshifted and remarkably massive with rapid frequency evolution. In contrast, the late merger model predicts a nearly monochromatic first source at low redshift. The future confirmation of an enhanced population of massive high-redshift galaxies and the detection of fast-evolving binaries would strongly support the early merger model, offering significant insights into the evolution of galaxies and SMBHs.