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We extend the existing analytical model of reionization by Furlanetto et al.(2004) to include the biasing of reionization sources and additional absorptionby Lyman Limit systems. Our model is, by construction, consistent with theobserved evolution of the galaxy luminosity function at z<8 and with theobserved evolution of Ly-{\alpha} forest at z<6. We also find that, for a widerange of values for the relative escape fraction that we consider reasonable,and which are consistent with the observational constraints on the relativeescape fraction from lower redshifts, our reionization model is consistent withthe WMAP constraint on the Thompson optical depth and with the SPT and EDGESconstraints on the duration of reionization. We, therefore, conclude that it ispossible to develop physically realistic models of reionization that areconsistent with all existing observational constraints.

Effect of halo bias and Lyman Limit Systems on the history of cosmic reionization