= Solution
The <ionizing background> is produced mainly by hot stars in <star-forming galaxies> and by accretion-powered <quasars>. The stellar contribution depends on <star formation> and the <ionizing photon escape fraction>; the <quasar> contribution depends on its evolving <luminosity function>. <Radiative transfer> through the <intergalactic medium>, including absorption, recombination emission, and cosmological redshifting, determines the radiation actually available for <photoionization>.
In the picture relevant to this 2009 paper, increasingly rare <quasars> cannot by themselves explain the high-redshift hydrogen ionizing field, so galaxies become especially important above $z\sim3$. Harder <quasar> radiation is important for doubly ionizing helium around $z\sim3$. Hydrogen <reionization> must be largely accomplished by $z\sim6$. At lower redshift the evolution reflects declining source emissivity together with the increasing propagation distance of ionizing photons; near <reionization>, short absorption lengths and spatially uneven ionized regions prevent a simple uniform-background description. The background rate need not follow the <quasar> population alone: a roughly flat hydrogen <photoionization rate> over $2\lesssim z\lesssim4$ is compatible with a changing mixture of galaxies and <quasars>. https://arxiv.org/abs/0901.4554[Faucher-Giguère and collaborators' 2009 background calculation] and https://arxiv.org/abs/0807.4177[their preceding opacity analysis] give this interpretation. These redshifts describe the broad historical picture, rather than precise universal transition times.
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