The Mass Function of Active Black Holes in the Local Universe

We present the first measurement of the black hole (BH) mass function for broad-line active galaxies in the local Universe. Using the ∼ 9000 broad-line active galaxies from the Fourth Data Release of the Sloan Digital Sky Survey, we construct a broad-line luminosity function that agrees very well with the local soft X-ray luminosity function. Using standard virial relations, we then convert observed broad-line luminosities and widths into BH masses. A mass function constructed in this way has the unique capability to probe the mass region < 106 M⊙, which, while insignificant in terms of total BH mass density, nevertheless may place important constraints on the mass distribution of seed BHs in the early Universe. The characteristic local active BH has a mass of ∼ 107 M⊙ radiating at 10% of the Eddington rate. The active fraction is a strong function of BH mass; at both higher and lower masses the active mass function falls more steeply than one would infer from the distribution of bulge luminosity. The deficit of local massive radiating BHs is a well-known phenomenon, while we present the first robust measurement of a decline in the space density of active BHs at low mass. Subject headings: galaxies: active — galaxies: nuclei — galaxies: Seyfert 1. THE LOCAL BLACK HOLE MASS FUNCTION There is strong evolution in both the number density and typical luminosity of active galactic nuclei (AGNs) over cosmic time (e.g., Ueda et al. 2003; Richards et al. 2006), but from luminosity functions alone it is difficult to determine whether mass or luminosity evolution is the predominant agent of these changes. One thing we do know is that the growth of black holes (BHs) and galaxies are coordinated such that, in local spheroids, BH mass is strongly correlated with spheroid luminosity (Marconi & Hunt 2003) and stellar velocity dispersion (the MBH −σ∗ relation; Gebhardt et al. 2000a; Ferrarese & Merritt 2000; Tremaine et al. 2002; Barth et al. 2005). Charting the mass accretion history of the Universe thus may provide important insight into the growth of galaxies. It has become possible, using the MBH −σ∗ relation, to calibrate virial scaling relations between AGN luminosity and the size of the broad-line region (Gebhardt et al. 2000b; Ferrarese et al. 2001; Onken et al. 2004; Nelson et al. 2004; Greene & Ho 2006b); these techniques have been used to investigate BH mass functions at intermediate to high redshift (e.g., Vestergaard 2004; McLure & Dunlop 2004; Kollmeier et al. 2006), but not in a systematic way for nearby systems. A good measurement of the local active BH mass function provides an essential boundary condition for models of the evolution in active BH mass. Furthermore, we can probe significantly further down the mass function at the present day than at any other epoch. In fact, BH mass functions built from local broad-line AGN samples have the unique capability to probe BH masses MBH. 106.5 M⊙. Mass functions derived from stellar velocity dispersions (whether they be inactive [Yu & Tremaine 2002] or narrow-line active galaxies [Heckman et al. 2004]) are necessarily limited to the current spectral resolution limits of largearea spectroscopic surveys such as the Sloan Digital Sky Survey (SDSS; e.g., Bernardi et al. 2003). At the same time, the conversion from galaxy luminosity to BH mass is completely unconstrained at these low masses. Direct dynamical mass measurements in this mass range are beyond the spatial resolving power of current instrumentation for all but the nearest systems. Thus broad-line AGNs currently provide the only means to systematically explore the BH mass function below 106 M⊙ (“intermediate-mass” BHs; e.g., Greene & Ho 2004). Although such objects constitute a negligible fraction of the present-day BH mass density, it is actually quite important to characterize the low-mass end of the local BH mass function. For one thing, it provides one of the only available observational constraints on models of the initial mass spectrum and halo occupation fraction of BH seeds in the early Universe (e.g., Volonteri et al. 2003). Furthermore, anisotropic gravitational radiation from unequal mass BH-BH mergers imparts a net linear angular momentum or “kick” to the merger remnant with a velocity that may exceed the escape velocity of dwarf galaxies (e.g., Favata et al. 2004; Merritt et al. 2004). We may test this picture with observational constraints on the number of local dwarf galaxies that host BHs. Once we have characterized the zero-redshift broad-line BH mass function, we may investigate whether broad-line AGNs trace the same local population as samples selected by alternate means. For instance, we expect the soft X-ray luminosity to come from unobscured sources with broad lines, and thus we expect very similar luminosity functions for the two populations. Also, it would be instructive to compare our results to those of the complementary study of Heckman et al. (2004), which uses the MBH − σ∗ relation to infer the BH mass function for local narrow-line AGNs. Our methodology, based on AGN physics rather than indirectly on the MBH − σ∗ relation, provides an important alternate measure of the local active BH mass density. Furthermore, we may compare the space density of narrowand broad-line objects as a function of mass; a well1Hubble and Princeton-Carnegie Fellow 1