Imaging of SDSS z > 6 Quasar Fields: Gravitational Lensing, Companion Galaxies, and the Host Dark Matter Halos

Abstract

We have undertaken deep optical imaging observations of three 6.2< z < 6.5 quasar fields in the i' and z' filters. These data areused to search for foreground galaxies that are gravitationally lensingthe quasars and distant galaxies physically associated with the quasars.Foreground galaxies are found closer than 500 to the lines of sightof two of the three quasars. However, the faintness of these galaxiessuggests that they have fairly low masses and provide only weak magnifications(mu less than or similar to 1.1). No convincing galaxies physicallyassociated with the quasars are found, and the number of i'-banddropouts is consistent with that found in random fields. We considerthe expected dark matter halo masses that host these quasars underthe assumption that a correlation between black hole mass and darkmatter halo mass exists. We show that the steepness of the high-masstail of the halo mass function at this redshift, combined with realisticamounts of scatter in this correlation, leads to expected halo massessubstantially lower than previously believed. This analysis can explainthe lack of companion galaxies found here and the low dynamical massrecently published for one of the quasars.