The gravitational-wave fingerprint of dynamically assembled primordial black hole cluster seeds in JWST's Little Red Dots

Abstract

The James Webb Space Telescope (JWST) has revealed compact, red, overmassive accreting black holes - the so-called ``Little Red Dots'' (LRDs) - in chemically near-pristine hosts at $z\simeq5 - 9$, straining standard heavy-seed models. We show that a population of strongly clustered primordial black holes (PBH) with a broad mass function predicted by a QCD-epoch thermal history naturally realizes the configuration that assembles LRD-scale seeds: an intermediate-mass PBH \emph{nucleus} $M_{\rm BH}\sim10^3$-$10^5\,M_\odot$ surrounded, within a few parsecs, by a swarm of light ($m\sim30\,M_\odot$) PBHs embedded in dense baryonic gas. Gas dynamical friction keeps the loss cone full and lets the core contract, so the swarm sinks and is swallowed on $t_{\rm seed}\sim10$-50 Myr, well inside the cosmic time at $z\sim10$-$15$. Because a heavy nucleus is present \emph{ab initio}, the captures occur at extreme mass ratio $q\sim10^{-4}$-$10^{-2}$: the remnant is retained against gravitational recoil, and each capture reaches the innermost stable orbit under gravitational-wave (GW) emission, radiating $\simeq0.06\,m c^2$ so that the assembly efficiency is $ζ\simeq0.06$ independent of $M_{\rm BH}$. The superposed swarm inspirals form a stochastic background $Ω_{\rm GW} h^2\sim10^{-13}$-$10^{-11}$ with a $Ω_{\rm GW}\propto f^{2/3}$ shape truncated below the gas-decoupling frequency and topped by a ringdown ``comb'' at $f_{\rm ring}(M_{\rm BH})\simeq13$ mHz for $10^5\,M_\odot$ and $\simeq1.3$ Hz for $10^3\,M_\odot$ nuclei at $z_f\simeq12$. The few comparable-mass nucleus-nucleus coalescences are instead individually resolvable LISA/deci-Hz sources. Detection, and discrimination of these signatures from a directly formed PBH seed of the same mass, would identify the LRDs as PBH-nucleus seeded black holes.