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The Black Hole Mass Function across Cosmic Time. II. Heavy Seeds and (Super)Massive Black Holes

Sicilia, Alex; Lapi, Andrea; Boco, Lumen; Shankar, Francesco; Alexander, David M.; Allevato, Viola; Villforth, Carolin; Massardi, Marcella; Spera, Mario; Bressan, Alessandro; Danese, Luigi

The Black Hole Mass Function across Cosmic Time. II. Heavy Seeds and (Super)Massive Black Holes Thumbnail


Alex Sicilia

Andrea Lapi

Lumen Boco

Francesco Shankar

Viola Allevato

Carolin Villforth

Marcella Massardi

Mario Spera

Alessandro Bressan

Luigi Danese


This is the second paper in a series aimed at modeling the black hole (BH) mass function from the stellar to the (super)massive regime. In the present work, we focus on (super)massive BHs and provide an ab initio computation of their mass function across cosmic time. We consider two main mechanisms to grow the central BH that are expected to cooperate in the high-redshift star-forming progenitors of local massive galaxies. The first is the gaseous dynamical friction process, which can cause the migration toward the nuclear regions of stellar mass BHs originated during the intense bursts of star formation in the gas-rich host progenitor galaxy and the buildup of a central heavy BH seed, M• ∼ 103−5 M⊙, within short timescales of ≲some 107 yr. The second mechanism is the standard Eddington-type gas disk accretion onto the heavy BH seed through which the central BH can become (super)massive, M• ∼ 106−10 M⊙, within the typical star formation duration, ≲1 Gyr, of the host. We validate our semiempirical approach by reproducing the observed redshift-dependent bolometric AGN luminosity functions and Eddington ratio distributions and the relationship between the star formation and the bolometric luminosity of the accreting central BH. We then derive the relic (super)massive BH mass function at different redshifts via a generalized continuity equation approach and compare it with present observational estimates. Finally, we reconstruct the overall BH mass function from the stellar to the (super)massive regime over more than 10 orders of magnitudes in BH mass.


Sicilia, A., Lapi, A., Boco, L., Shankar, F., Alexander, D. M., Allevato, V., …Danese, L. (2022). The Black Hole Mass Function across Cosmic Time. II. Heavy Seeds and (Super)Massive Black Holes. Astrophysical Journal, 934(1),

Journal Article Type Article
Acceptance Date Jun 12, 2022
Online Publication Date Jul 26, 2022
Publication Date 2022
Deposit Date Sep 5, 2022
Publicly Available Date Sep 5, 2022
Journal Astrophysical Journal
Print ISSN 0004-637X
Electronic ISSN 1538-4357
Publisher American Astronomical Society
Peer Reviewed Peer Reviewed
Volume 934
Issue 1
Public URL


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Copyright Statement
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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