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In this paper, we present a derivation of the rest-frame 1400A luminosity function (LF) at redshift six from a new application of the maximum likelihood method by exploring the five deepest HST/ACS fields, i.e., the HUDF, two UDF05 fields, and two GO ODS fields. We work on the latest improved data products, which makes our results more robust than those of previous studies. We use un-binned data and thereby make optimal use of the information contained in the dataset. We focus on the analysis to a magnitude limit where the completeness is larger than 50% to avoid possibly large errors in the faint end slope that are difficult to quantify. We also take into account scattering in and out of the dropout sample due to photometric errors by defining for each object a probability that it belongs to the dropout sample. We find the best fit Schechter parameters to the z~6 LF are: alpha = 1.87 +/- 0.14, M* = -20.25 +/- 0.23, and phi*=1.77^{+0.62}_{-0.49} * 10^{-3} Mpc^{-3}. Such a steep slope suggests that galaxies, especially the faint ones, are possibly the main sources of ionizing photons in the universe at redshift six. We also combine results from all studies at z~6 to reach an agreement in 95% confidence level that -20.45<M*<-20.05 and -1.90<alpha<-1.55. The luminosity density has been found not to evolve significantly between z~6 and z~5, but considerable evolution is detected from z~6 to z~3.
While the average metallicity of the intergalactic medium rises above Z~10^{-3} Zsun by the end of the reionization, pockets of metal-free gas can still exist at later times. We quantify the presence of a long tail in the formation rate of metal-free halos during late stages of reionization (redshift z~6), which might offer the best window to detect Population III stars. Using cosmological simulations for the growth of dark matter halos, coupled with analytical recipes for the metal enrichment of their interstellar medium, we show that pockets of metal-free gas exist at z~6 even under the assumption of high efficiency in metal pollution via winds. A comoving metal-free halo formation rate d^2n/dtdV > 10^{-9} Mpc^{-3}yr^{-1} is expected at z=6 for halos with virial temperature T_{vir}~10^4 K (mass ~10^8 Msun), sufficient to initiate cooling even with strong negative radiative feedback. Under the assumption of a single Population III supernova formed per metal-free halo, we expect an observed supernova rate of 2.6x10^{-3} deg^{-2}yr^{-1} in the same redshift range. These metal-free stars and their supernovae will be isolated and outside galaxies (at distances >150 h^{-1} kpc) and thus significantly less biased than the general population of ~10^8 Msun halos at z~6. Supernova searches for metal-free explosions must thus rely on large area surveys. If metal-free stars produce very luminous supernovae, like SN2006gy, then a multi-epoch survey reaching m_AB =27 at 1 micron is sufficient for detecting them at z=6. While the Large Synoptic Survey Telescope will not reach this depth in the z band, it will be able to detect several tens of Population III supernovae in the i and r bands at z <5.5, when their observed rate is down to 3-8x10^{-4} deg^{-2} yr^{-1}.
We present a sample of $i_{775}$-dropout candidates identified in five Hubble Advanced Camera for Surveys fields centered on Sloan Digital Sky Survey QSOs at redshift $zsim 6$. Our fields are as deep as the Great Observatory Origins Deep Survey (GOOD S) ACS images which are used as a reference field sample. We find them to be overdense in two fields, underdense in two fields, and as dense as the average density of GOODS in one field. The two excess fields show significantly different color distributions from that of GOODS at the 99% confidence level, strengthening the idea that the excess objects are indeed associated with the QSO. The distribution of $i_{775}$-dropout counts in the five fields is broader than that derived from GOODS at the 80% to 96% confidence level, depending on which selection criteria were adopted to identify $i_{775}$-dropouts; its width cannot be explained by cosmic variance alone. Thus, QSOs seem to affect their environments in complex ways. We suggest the picture where the highest redshift QSOs are located in very massive overdensities and are therefore surrounded by an overdensity of lower mass halos. Radiative feedback by the QSO can in some cases prevent halos from becoming galaxies, thereby generating in extreme cases an underdensity of galaxies. The presence of both enhancement and suppression is compatible with the expected differences between lines of sight at the end of reionization as the presence of residual diffuse neutral hydrogen would provide young galaxies with shielding from the radiative effects of the QSO.
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