Stochastic Pathways to Early Supermassive Black Hole Growth

Abstract

Abstract The rapid appearance of ∼10 9 M ⊙ black holes by z > 7 remains a major challenge for models of early black hole assembly. Standard Eddington-limited growth produces slow exponential mass increase, requiring either massive initial seeds or extended super-Eddington phases. Here I explore a minimal stochastic alternative: geometric Brownian motion with multiplicative Poisson jumps representing intermittent accretion bursts. I adopt the Itô stochastic differential equation formulation, ensuring consistency between analytic expectations and the Euler–Maruyama numerical integration. Even modest burst amplitudes ( F = 1.5–3.0) significantly accelerate median growth relative to the deterministic Eddington track, and naturally produce log-normal mass distributions reminiscent of hydrodynamic simulations variability. This short communication provides an illustrative link between deterministic accretion theory and feedback-regulated, bursty accretion models.