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UV radiation from early astrophysical sources could have a large impact on subsequent star formation in nearby protogalaxies. Here we study the radiative feedback from the first, short-lived stars using hydrodynamical simulations with transient UV backgrounds (UVBs) and persistent Lyman-Werner backgrounds (LWBs) of varying intensity. We extend our prior work in Mesinger et al. (2006), by studying a more typical region whose proto-galaxies form at lower redshifts, z~13-20, in the epoch likely preceding the bulk of reionization. We confirm our previous results that feedback in the relic HII regions resulting from such transient radiation, is itself transient. Feedback effects dwindle away after ~30% of the Hubble time, and the same critical specific intensity of J_UV~0.1 x 10^{-21} ergs/s/cm^2/Hz/sr separates positive and negative feedback regimes. Additionally, we discover a second episode of eventual positive feedback in halos which have not yet collapsed when their progenitor regions were exposed to the transient UVB. This eventual positive feedback appears in all runs, regardless of the strength of the UVB. However, this feedback regime is very sensitive to the presence of Lyman-Werner radiation, and notable effects disappear under fairly modest background intensities of J_LW>10^{-3} x 10^{-21} ergs/s/cm^2/Hz/sr. We conclude that UV radiative feedback in relic HII regions, although a complicated process, seems unlikely to have a major impact on the progress of cosmological reionization, provided that present estimates of the lifetime and luminosity of a PopIII star are accurate. More likely is that the build-up of the LWB ultimately governs the feedback strength until a persistent UV background can be established. [abridged]
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