ΛCDM predictions for galaxy protoclusters - I. The relation between galaxies, protoclusters and quasars at

Motivated by recent observational studies of the environment of z~6 QSOs, we have used the Millennium Run (MR) simulations to construct a very large (~20 deg²) mock redshift survey of star-forming galaxies at z~6. We use this simulated survey to study the relation between density enhancements in the distribution of i-dropouts and Lya-emitters, and their relation to the most massive halos and protocluster regions at z~6. Our simulation predicts significant variations in surface density across the sky with some voids and filaments extending over scales of 1 degree, much larger than probed by current surveys. Approximately one third of all z~6 halos hosting i-dropouts brighter than z=26. 5 mag (~M* at z=6) become part of z=0 galaxy clusters. i-dropouts associated with protocluster regions are found in regions where the surface density is enhanced on scales ranging from a few to several tens of arcminutes on the sky. We analyze two structures of i-dropouts and Lya-emitters observed with the Subaru Telescope and show that these structures must be the seeds of massive clusters-in-formation. In striking contrast, six z~6 QSO fields observed with HST show no significant enhancements in their i-dropout number counts. With the present data, we cannot rule out the QSOs being hosted by the most massive halos. However, neither can we confirm this widely used assumption. We conclude by giving detailed recommendations for the interpretation and planning of observations by current and future ground- and space based instruments that will shed new light on questions related to the large-scale structure at z~6.