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Advances in Astronomy
Volume 2012, Article ID 970858, 21 pages
Review Article

Mass Functions of Supermassive Black Holes across Cosmic Time

1High Energy Astrophysics Division, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
2Department of Physics, Broida Hall, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
3Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstraße 1, 85748 Garching, Germany

Received 10 September 2011; Accepted 1 December 2011

Academic Editor: Francesca Civano

Copyright © 2012 Brandon C. Kelly and Andrea Merloni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The black hole mass function of supermassive black holes describes the evolution of the distribution of black hole mass. It is one of the primary empirical tools available for mapping the growth of supermassive black holes and for constraining theoretical models of their evolution. In this paper, we discuss methods for estimating the black hole mass function, including their advantages and disadvantages. We also review the results of using these methods for estimating the mass function of both active and inactive black holes. In addition, we review current theoretical models for the growth of supermassive black holes that predict the black hole mass function. We conclude with a discussion of directions for future research which will lead to improvement in both empirical and theoretical determinations of the mass function of supermassive black holes.