How Big Can a Black Hole Grow?

TL;DR

This paper establishes a theoretical maximum mass for black holes based on luminous accretion limits, suggesting that observed supermassive black holes are close to this limit, which has implications for understanding black hole growth and galaxy evolution.

Contribution

It introduces a physical limit to black hole mass based on accretion physics, linking it to observable luminosity and galaxy scaling relations.

Findings

Maximum black hole mass for luminous growth is about 5x10^{10} solar masses.

Black holes can grow beyond this limit through non-luminous processes like mergers.

Observed supermassive black holes are near the theoretical mass limit.

Abstract

I show that there is a physical limit to the mass of a black hole, above which it cannot grow through luminous accretion of gas, and so cannot appear as a quasar or active galactic nucleus. The limit is Mmax \simeq 5x10^{10}M_sun for typical parameters, but can reach Mmax \simeq 2.7x10^{11}M_sun in extreme cases (e.g. maximal prograde spin). The largest black hole masses so far found are close to but below the limit. The Eddington luminosity \simeq 6.5x10^{48} erg/s corresponding to Mmax is remarkably close to the largest AGN bolometric luminosity so far observed. The mass and luminosity limits both rely on a reasonable but currently untestable hypothesis about AGN disc formation, so future observations of extreme SMBH masses can therefore probe fundamental disc physics. Black holes can in principle grow their masses above Mmax by non-luminous means such as mergers with other holes, but cannot become luminous accretors again. They might nevertheless be detectable in other ways, for example through gravitational lensing. I show further that black holes with masses ~ Mmax can probably grow above the values specified by the black-hole -- host-galaxy scaling relations, in agreement with observation.