The Convergence of Heavy and Light Seeds to Overmassive Black Holes at Cosmic Dawn

The James Webb Space Telescope has revealed low-luminosity active galactic nuclei at redshifts of z ≳ 4–7, many of which host accreting massive black holes (BHs) with BH-to-galaxy mass (MBH/M⋆) ratios exceeding the local values by more than an order of magnitude. The origin of these overmassive BHs remains unclear but requires potential contributions from heavy seeds and/or episodes of super-Eddington accretion. We present a growth model coupled with dark matter halo assembly to explore the evolution of the MBH/M⋆ ratio under different seeding and feedback scenarios. Given the gas inflow rates in protogalaxies, BHs grow episodically at moderate super-Eddington rates, and the mass ratio increases early on, despite significant mass loss through feedback. Regardless of seeding mechanisms, the mass ratio converges to a universal value ∼0.1–0.3, set by the balance between gas feeding and star formation efficiency in the nucleus. This behavior defines an attractor in the MBH–M⋆ diagram, where overmassive BHs grow more slowly than their hosts, while undermassive seeds experience rapid growth before aligning with the attractor. We derive an analytical expression for the universal mass ratio, linking it to feedback strength and halo growth. The convergence of evolutionary tracks erases seeding information from the mass ratio by z ∼ 4–6. Detecting BHs with ∼105−6M⊙ at higher redshifts that deviate from the convergence trend would provide key diagnostics of their birth conditions.