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We use one-dimensional radiative transfer simulations to study the evolution of H₂ gas-phase (H^- catalyzed) formation and photo-dissociation regions in the primordial universe. We find a new positive feedback mechanism capable of producing shells of H₂ in the intergalactic medium, which are optically thick in some Lyman-Werner bands. While these shells exist, this feedback effect is important in reducing the H₂ dissociating background flux and the size of photo-dissociation spheres around each luminous object. The maximum background opacity of the IGM in the H₂ Lyman-Werner bands is ₇䃒 ~ 1-2 for a relic molecular fraction x₇䃒=2 x 10^-6, about 6 times greater than found by Haiman, Abel & Rees. Therefore, the relic molecular hydrogen can decrease the photo-dissociation rate by about an order of magnitude. The problem is relevant to the formation of small primordial galaxies with masses M₃₌ 10⁴ K formed.
Ricotti et al. (Sat,) studied this question.