Host Galaxies of z=4 Quasars

We have undertaken a project to investigate the host galaxies and environments of a sample of quasars at z~4. In this paper, we describe deep near-infrared imaging of 34 targets using the Magellan I and Gemini North telescopes. We discuss in detail special challenges of distortion and nonlinearity that must be addressed when performing PSF subtraction with data from these telescopes and their IR cameras, especially in very good seeing. We derive black hole masses from emission-line spectroscopy, and we calculate accretion rates from our K_s-band photometry, which directly samples the rest-frame B for these objects. We introduce a new isophotal diameter technique for estimating host galaxy luminosities. We report the detection of four host galaxies on our deepest, sharpest images, and present upper limits for the others. We find that if host galaxies passively evolve such that they brighten by 2 magnitudes or more in the rest-frame B band between the present and z=4, then high-z hosts are less massive at a given black hole mass than are their low-z counterparts. We argue that the most massive hosts plateau at <~10L*. We estimate the importance of selection effects on this survey and the subsequent limitations of our conclusions. These results are in broad agreement with recent semi-analytical models for the formation of luminous quasars and their host spheroids by mergers of gas-rich galaxies, with significant dissipation, and self-regulation of black hole growth and star-formation by the burst of merger-induced quasar activity.