Little Red Dots as the Very First Activity of Black Hole Growth

The James Webb Space Telescope has detected massive black holes (BHs) with masses of $\sim 10^{6-8}~M_\odot$ within the first billion years of the universe. One of the remarkable findings is the identification of "Little Red Dots" (LRDs), a unique class of active galactic nuclei (AGNs) with distinct characteristics representing a key phase in the formation and growth of early BHs. Here, we analyze the occurrence rate of LRDs, which emerge around redshifts $z \sim 6-8$ and sharply decline at $z < 4$. We find that this trend follows a log-normal distribution, commonly observed in phenomena driven by stochastic and random factors. We propose a hypothesis that the first one or two AGN events associated with newly-formed seed BHs are observed as LRDs and their unique features fade in the subsequent episodes. This naturally explains the cosmic evolution of AGN abundance over $0 < z < 5$, which follows $\propto (1+z)^{-5/2}$ due to the cumulative effect of recurring AGN activity. The unique characteristics of LRDs are likely linked to the dense gas environments around the seed BHs, which create strong absorption features in the broad-line emission and enable super-Eddington accretion bursts, ultimately yielding the observed overmassive nature of BHs compared to the local relationship. An analytical expression for the redshift evolution of LRD abundance is provided for direct comparison with future observational constraints.