Very Large H II Regions Around Proto-Clusters of Galaxies During   Reionization
  The physical basis for the belief that the abundant old dwarf galaxies seen in present-day galaxy clusters formed before reionization of the universe is very compelling, because (1) the observed faint end slope of the galaxy luminosity function ascends from a shallower slope at brighter magnitudes and tracks that of dark matter halo mass function, and (2) that steep power-law slope is observed to extend all the way to galaxies of inferred velocity dispersion of ~10km/s. We then show that the number of ionizing photons emitted by these dwarf galaxies should be able to produce an H II region at least as large as each proto-cluster region, occupying at least 20% of the entire IGM volume at z >= 6. A more likely scenario is that our estimate of the ionizing photon production rate based on these dwarfs under-estimates the true rate from proto-clusters by a factor of ~5 for a variety of physically plausible reasons, in which case a fully self- consistent picture emerges. Specific implications include (1) Strong clustering of sources would collectively produce very large individual H II regions of sizes up to ~100Mpc before overlapping with others, having important implications for upcoming radio and CMB observations. There should be large spatial fluctuations of neutral fraction in the intergalactic medium up to cluster scales of ~100Mpc. We give an H II region size function. (2) The ionizing sources at z~6 are expected to be highly biased with a bias factor >=15. (3) Large H II regions would enable largely unattenuated transmission of flux of a significant number of sources prior to reionization. When more sensitive observations become available, one should expect to see clusters of fainter sources in the vicinity of known galaxies at z>6. 
Renyue Cen