Black hole mass and growth rate at high redshift

We present new H- and K-band spectroscopy of 15 high-luminosity active galactic nuclei (AGNs) at redshifts 2.3-3.4 obtained with Gemini South. We combined the data with spectra of an additional 29 high-luminosity sources to obtain a sample with 10(45.2) < lambda L-lambda(5100 angstrom) < 10(47.3) ergs s(-1) and a black hole (BH) mass range, using reverberation mapping relationships based on the H beta method, of 10(8.8)-10(10.7) M-circle dot. We do not find a correlation of L/L-Edd with M-BH, but we do find a correlation with lambda L-lambda(5100 angstrom), which might be due to selection effects. The L/L-Edd distribution is broad and covers the range of similar to 0.07-1.6, similar to what is observed in lower redshift, lower luminosity AGNs. We suggest that this consistently measured and calibrated sample gives the best representation of L/L-Edd at those redshifts, and note potential discrepancies with recent theoretical and observational studies. The lower accretion rates are not in accord with growth scenarios for BHs at such redshifts, and the growth times of many of the sources are longer than the age of the universe at the corresponding epochs. This suggests earlier episodes of faster growth at z greater than or similar to 3 for those sources. The use of the C-IV lambda 1549 method gives considerably different results and a larger scatter; this method seems to be a poor M-BH and L/L-Edd estimator at very high luminosity.