tokens: how the SMBH population evolves over cosmic time, we populate the halo tree according to our recipe. When a halo for the first time reaches a mass M c , with chance p it is marked as occupied by a black hole. The occupation is inherited by the merger tree descendant. As a consequence, in our seeding framework black holes are not only “born” in the high-redshift universe. To show this, the left panel of Figure 5 presents birth rates over cosmic time. Seeding is most frequent at early times ( z > 4). Depending on the model parameters, the median seeding time lies in the second, third, or forth billion years. At z 6, the model curve shapes are almost independent of the input parameters. Regarding the normalization, we note that a 100% seeding above mass M c creates a black hole population at a similar rate as 10% seeding at mass 10% × M c (left panel of Figure 5 ). Figure 5. Left panel: the birth rate of black holes over cosmic time. Curves show different seeding fractions p and mass thresholds M 0 . Center panel: merger rate of halos occupied by black holes. The kink at z ∼ 1 is due to the simulation’s cosmic variance, i.e., a large overdensity merging at that redshift. Right panel: the total number of halos with black holes. We compare with space densities of AGN with luminosities (AGN) and (QSOs) measured by X-ray surveys sensitive to unobscured and obscured accretion (Buchner et al. 2015 ). Comparing the model curves and observations, we see that only a very small fraction (1:10 to 1:10,000) of black holes accrete at these luminosities. As halos containing black holes merge, interactions of multiple SMBHs are possible. The middle panel of Figure 5 shows mergers of halos hosting black holes. The normalization again scales as just described for the birth rate. Changes in the critical mass shift the peak slightly. We explore the possible merging of the black holes themselves in the next section. The right panel of Figure 5 presents the total number of massive black holes over cosmic time. For p = 1, this is just the number of halos above the mass threshold. Overall, we find a present-day SMBH space density of >0.01 Mpc −3 (with models not ruled out in Figure 4 ). In the local universe, the fraction of occupied halos is mass-dependent in the way presented in Figure 3 . The comparison between the number of SMBHs to the observed number of AGN provides the fraction of actively accreting black holes in excess of that luminosity threshold. Modern surveys detect hard X-ray emission even in heavily obscured AGN, and recover the intrinsic accretion luminosity using X-ray spectra (e.g., Buchner et al. 2015 ). In Figure 5 we include the space density of AGN at L (2–10 keV) > 3 × 10 42 erg s −1 and >10 44 erg s −1 , which correspond approximately to accretion rates of 5 × 10 6 and 5 × 10 8 M ⊙ Gyr −1 (Marconi et al. 2004 ), respectively, assuming 10% radiative efficiency. The AGN density inferred from observations is 1–3 orders of magnitude below the
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