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.
