The local density in black holes grown by accretion with efficiency can be computed using the integral argument originally proposed by Soltan (1982). An excellent review of the method, along with a detailed discussion of the most recent determinations of the black hole mass density, is presented by Fabian (2004). Here I limit myself to estimating the black hole mass accreted during the Compton thick phase, (CT), under the hypothesis that the Compton thick source contribution to the XRB is that reported in Figure 3.
The unabsorbed 2 - 10 keV X-ray flux that enters into the computation of (CT) is obtained by assuming = 2 and NH = 3 × 1024 cm-2,
The calculation of (CT) then requires the knowledge of the bolometric correction term, the average redshift of the sources, and the accretion efficiency. For the latter, a standard value of = 0.1 is assumed, while for the average redshift, the latest results of optical identifications suggest <z> ~ 1 (e.g., Gilli 2004). The bolometric correction from the unabsorbed 2 - 10 keV luminosity to the total luminosity is known to be a function of the X-ray luminosity. Correction factors in the range kbol ~ 10 - 20 appear to be appropriate for low luminosity Seyfert-like objects (Fabian 2004), to be compared with values in the range 30 - 50 for high luminosity unobscured quasars (Elvis et al. 1994). As far as the two well studied prototype Compton thick sources NGC 6240 and IRAS 09104+4109 are concerned, a direct calculation from broadband literature data, including the contribution of the host galaxy, provides remarkably similar results: kbol ~ 10. A more precise estimate of the bolometric correction factor as a function of the X-ray properties is not possible with the present data. Spitzer Space Telescope observations of well defined samples of obscured AGN will provide a significant step forward in this direction.
Taking the above estimates for kbol, , and <z> at face value, the black hole mass density accreted in the Compton thick phase is about 3 × 104 M Mpc-3. This value could be slightly higher (up to 5 × 104 M Mpc-3) if the intrinsic spectral parameters are different. Based on the same argument, but following a slightly different approach, Fabian (2004) concluded that (CT) < 105 M Mpc-3. Unless the estimates of kbol, the average redshift, and the relative contribution of Compton thick sources to the XRB are revised upwards (which seems rather unlikely), they only account for some 10% of the black hole mass density grown by accretion. Thus, most of the black hole mass density is due to less obscured Compton thin sources and unobscured quasars (see Cowie & Barger, this volume).