  We study how the first galaxies were assembled under feedback from the
accretion onto a central black hole (BH) that is left behind by the first
generation of metal-free stars through self-consistent, cosmological
simulations. X-ray radiation from the accretion of gas onto BH remnants of
Population III (Pop III) stars, or from high-mass X-ray binaries (HMXBs), again
involving Pop III stars, influences the mode of second generation star
formation. We track the evolution of the black hole accretion rate and the
associated X-ray feedback starting with the death of the Pop III progenitor
star inside a minihalo and following the subsequent evolution of the black hole
as the minihalo grows to become an atomically cooling galaxy. We find that
X-ray photoionization heating from a stellar-mass BH is able to quench further
star formation in the host halo at all times before the halo enters the atomic
cooling phase. X-ray radiation from a HMXB, assuming a luminosity close to the
Eddington value, exerts an even stronger, and more diverse, feedback on star
formation. It photoheats the gas inside the host halo, but also promotes the
formation of molecular hydrogen and cooling of gas in the intergalactic medium
and in nearby minihalos, leading to a net increase in the number of stars
formed at early times. Our simulations further show that the radiative feedback
from the first BHs may strongly suppress early BH growth, thus constraining
models for the formation of supermassive BHs.
