THE MOST MASSIVE GALAXIES AT 3.0 ≤ z < 4.0 IN THE NEWFIRM MEDIUM-BAND SURVEY: PROPERTIES AND IMPROVED CONSTRAINTS ON THE STELLAR MASS FUNCTION

We use the optical to mid-infrared coverage of the NEWFIRM Medium-Band Survey (NMBS) to characterize, for the first time, the properties of a mass-complete sample of 14 galaxies at 3.0 <= z < 4.0 with M-star > 2.5 x 10(11) M-circle dot, and to derive significantly more accurate measurements of the high-mass end of the stellar mass function (SMF) of galaxies at 3.0 <= z < 4.0. The accurate photometric redshifts and well-sampled spectral energy distributions (SEDs) provided by the NMBS combined with the large surveyed area result in significantly reduced contributions from photometric redshift errors and cosmic variance to the total error budget of the SMF. The typical very massive galaxy at 3.0 <= z < 4.0 is red and faint in the observer's optical, with a median r-band magnitude of < r(tot)> = 26.1, and median rest-frame U - V colors of < U - V > = 1.6. About 60% of the mass-complete sample has optical colors satisfying either the U- or the B-dropout color criteria, although similar to 50% of these galaxies has r > 25.5. We find that similar to 30% of the sample has star formation rates (SFRs) from SED modeling consistent with zero, although SFRs of up to similar to 1-18 M-circle dot yr(-1) are also allowed within 1 sigma. However, > 80% of the sample is detected at 24 mu m, resulting in total infrared luminosities in the range (0.5-4.0) x 10(13) L-circle dot. This implies the presence of either dust-enshrouded starburst activity (with SFRs of 600-4300 M-circle dot yr(-1)) and/or highly obscured active galactic nuclei (AGNs). The contribution of galaxies with M-star > 2.5 x 10(11) M-circle dot to the total stellar mass budget at 3.0 <= z < 4.0 is similar to 8(-3)(+13)%. Compared to recent estimates of the stellar mass density in galaxies with M-star approximate to 10(9)-10(11) M-circle dot at z similar to 5 and z similar to 6, we find an evolution by a factor of 2-7 and 3-22 from z similar to 5 and z similar to 6, respectively, to z = 3.5. The previously found disagreement at the high-mass end between observed and model-predicted SMFs is now significant at the 3 sigma level when only random uncertainties are considered. However, systematic uncertainties dominate the total error budget, with errors up to a factor of similar to 8 in the densities at the high-mass end, bringing the observed SMF in marginal agreement with the predicted SMF. Additional systematic uncertainties on the high-mass end could be potentially introduced by either (1) the intense star formation and/or the very common AGN activities as inferred from the MIPS 24 mu m detections, and/or (2) contamination by a significant population of massive, old, and dusty galaxies at z similar to 2.6.