Imaging of SDSS z > 6 quasar fields:: Gravitational lensing, companion galaxies, and the host dark matter halos

We have undertaken deep optical imaging observations of three 6.2 < z < 6.5 quasar fields in the i' and z' filters. These data are used to search for foreground galaxies that are gravitationally lensing the quasars and distant galaxies physically associated with the quasars. Foreground galaxies are found closer than 500 to the lines of sight of two of the three quasars. However, the faintness of these galaxies suggests that they have fairly low masses and provide only weak magnifications (mu less than or similar to 1.1). No convincing galaxies physically associated with the quasars are found, and the number of i'-band dropouts is consistent with that found in random fields. We consider the expected dark matter halo masses that host these quasars under the assumption that a correlation between black hole mass and dark matter halo mass exists. We show that the steepness of the high-mass tail of the halo mass function at this redshift, combined with realistic amounts of scatter in this correlation, leads to expected halo masses substantially lower than previously believed. This analysis can explain the lack of companion galaxies found here and the low dynamical mass recently published for one of the quasars.