  We study for the first time the environment of massive black hole (BH) seeds
(~10^4-5 Msun) formed via the direct collapse of pristine gas clouds in massive
haloes (>10^7 Msun) at z>6. Our model is based on the evolution of dark matter
haloes within a cosmological N-body simulation, combined with prescriptions for
the formation of BH along with both Pop III and Pop II stars. We calculate the
spatially-varying intensity of Lyman Werner (LW) radiation from stars and
identify the massive pristine haloes in which it is high enough to shut down
molecular hydrogen cooling. In contrast to previous BH seeding models with a
spatially constant LW background, we find that the intensity of LW radiation
due to local sources, J_local, can be up to 10^6 times the spatially averaged
background in the simulated volume and exceeds the critical value, J_crit, for
the complete suppression of molecular cooling, in some cases by 4 orders of
magnitude. Even after accounting for possible metal pollution in a halo from
previous episodes of star formation, we find a steady rise in the formation
rate of direct collapse (DC) BHs with decreasing redshift from 10^{-3}/Mpc^3/z
at z=12 to 10^{-2}/Mpc^3/z at z=6. The onset of Pop II star formation at z~16
simultaneously marks the onset of the epoch of DCBH formation, as the increased
level of LW radiation from Pop II stars is able to elevate the local levels of
the LW intensity to J_local > J_crit while Pop III stars fail to do so at any
time. The number density of DCBHs is sensitive to the number of LW photons and
can vary by an order of magnitude at z=6 after accounting for reionisation
feedback. Haloes hosting DCBHs are more clustered than similar massive
counterparts that do not host DCBHs, especially at redshifts z>10. We also show
that planned surveys with JWST should be able to detect the supermassive
stellar precursors of DCBHs.

Cosmology and Nongalactic Astrophysics