Conditions for Optimal Growth of Black Hole Seeds

TL;DR

This paper investigates the physical conditions enabling optimal, stable super-Eddington accretion for black hole seeds, explaining how certain parameters influence rapid growth of supermassive black holes in the early universe.

Contribution

It identifies key parameters affecting black hole growth efficiency and proposes conditions under which super-Eddington accretion can occur, advancing understanding of early black hole formation.

Findings

Optimal growth depends on black hole mass and host galaxy gas density.

Seeds with initial masses >10^4 M_sun have higher growth efficiency.

Many low-mass black holes may remain undetectable as quasars, detectable only via gravitational waves.

Abstract

Super-massive black holes weighing up to $\sim 10^9 \, \mathrm{M_{\odot}}$ are in place by $z \sim 7$, when the age of the Universe is $\lesssim 1 \, \mathrm{Gyr}$. This implies a time crunch for their growth, since such high masses cannot be easily reached in standard accretion scenarios. Here, we explore the physical conditions that would lead to optimal growth wherein stable super-Eddington accretion would be permitted. Our analysis suggests that the preponderance of optimal conditions depends on two key parameters: the black hole mass and the host galaxy central gas density. In the high-efficiency region of this parameter space, a continuous stream of gas can accrete onto the black hole from large to small spatial scales, assuming a global isothermal profile for the host galaxy. Using analytical initial mass functions for black hole seeds, we find an enhanced probability of high-efficiency growth for seeds with initial masses $\gtrsim 10^4 \, \mathrm{M_{\odot}}$. Our picture suggests that a large population of high-$z$ lower-mass black holes that formed in the low-efficiency region, with low duty cycles and accretion rates, might remain undetectable as quasars, since we predict their bolometric luminosities to be $\lesssim 10^{41} \, \mathrm{erg \, s^{-1}}$. The presence of these sources might be revealed only via gravitational wave detections of their mergers.