A universal minimal mass scale for present-day central black holes

Abstract

The early stages of massive black hole growth are poorly understood¹. High-luminosity active galactic nuclei at very high redshift² z further imply rapid growth soon after the Big Bang. Suggested formation mechanisms typically rely on the extreme conditions found in the early Universe (very low metallicity, very high gas or star density). It is therefore plausible that these black hole seeds were formed in dense environments, at least a Hubble time ago (z > 1.8 for a look-back time of t_{H = 10 Gyr)}³. Intermediate-mass black holes (IMBHs) of mass M_• ≈ 10²−10⁵ solar masses, M_⊙, are the long-sought missing link⁴ between stellar black holes, born of supernovae⁵, and massive black holes⁶, tied to galaxy evolution by empirical scaling relations^7,8. The relation between black hole mass, M_•, and stellar velocity dispersion, σ_★, that is observed in the local Universe over more than about three decades in massive black hole mass, correlates M_• and σ_★ on scales that are well outside the massive black hole’s radius of dynamical influence⁶, $r_{\mathrm{h}}\approx G{M}_{•}/{\sigma }_{★}^2$. We show that low-mass black hole seeds that accrete stars from locally dense environments in galaxies following a universal M_•/σ_★ relation^9,10 grow over the age of the Universe to be above ${\mathcal{M}}_0\approx 3\times {10}^5{M}_{\odot }$ (5% lower limit), independent of the unknown seed masses and formation processes. The mass ${\mathcal{M}}_0$ depends weakly on the uncertain formation redshift, and sets a universal minimal mass scale for present-day black holes. This can explain why no IMBHs have yet been found⁶, and it implies that present-day galaxies with σ_★ < ${\mathcal{S}}_0$ ≈ 40 km s^–1 lack a central black hole, or formed it only recently. A dearth of IMBHs at low redshifts has observable implications for tidal disruptions¹¹ and gravitational wave mergers¹².