On the Prevalence of Super-Massive Black Holes over Cosmic Time

We investigate the abundance of Super-Massive Black Hole (SMBH) seeds in primordial galaxy halos. We explore the assumption that dark matter halos outgrowing a critical halo mass M_c have some probability p of having spawned a SMBH seed. Current observations of local, intermediate-mass galaxies constrain these parameters: For $M_c=10^{11}M_\odot$, all halos must be seeded, but when adopting smaller M_c masses the seeding can be much less efficient. The constraints also put lower limits on the number density of black holes in the local and high-redshift Universe. Reproducing z~6 quasar space densities depends on their typical halo mass, which can be constrained by counting nearby Lyman Break Galaxies and Lyman Alpha Emitters. For both observables, our simulations demonstrate that single-field predictions are too diverse to make definitive statements, in agreement with mixed claims in the literature. If quasars are not limited to the most massive host halos, they may represent a tiny fraction (~10^-5) of the SMBH population. Finally, we produce a wide range of predictions for gravitational events from SMBH mergers. We define a new diagnostic diagram for LISA to measure both SMBH space density and the typical delay between halo merger and black hole merger. While previous works have explored specific scenarios, our results hold independent of the seed mechanism, seed mass, obscuration, fueling methods and duty cycle.