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# 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 tH = 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 relations7,8. 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, $rh≈GM•/σ★2$. We show that low-mass black hole seeds that accrete stars from locally dense environments in galaxies following a universal M/σ relation9,10 grow over the age of the Universe to be above $M0≈3×105M⊙$ (5% lower limit), independent of the unknown seed masses and formation processes. The mass $M0$ 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 < $S0$ ≈ 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.

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## Acknowledgements

We are grateful for discussions with Y. Alexander, J. Gair, A. Gal-Yam, J. Green, J. Guillochon, M. MacLeod, N. Neumayer, T. Piran, E. Rossi, A. Sesana, J. Silk, N. Stone and B. Trakhtenbrot. T.A. acknowledges support from the I-CORE Program of the Planning and Budgeting Committee and The Israel Science Foundation (Grant No. 1829/12). B.B.-O. acknowledges support from NASA (grant NNX14AM24G) and the NSF (Grant AST-1406166).

## Affiliations

1. ### Department of Particle Physics & Astrophysics, Weizmann Institute of Science, Rehovot 76100, Israel.

• Tal Alexander

• Ben Bar-Or

## Authors

### Contributions

T.A. and B.B.-O. developed the ideas presented in this paper together and collaborated in its writing.

### Competing interests

The authors declare no competing financial interests.

## Corresponding authors

Correspondence to Tal Alexander or Ben Bar-Or.

### DOI

https://doi.org/10.1038/s41550-017-0147