Comparing and calibrating black hole mass estimators for distant active galactic nuclei

Black hole mass (M-BH) is a fundamental property of active galactic nuclei (AGNs). In the distant universe, M-BH is commonly estimated using the Mg II, H beta, or H alpha emission line widths and the optical/UV continuum or line luminosities as proxies for the characteristic velocity and size of the broad-line region. Although they all have a common calibration in the local universe, a number of different recipes are currently used in the literature. It is important to verify the relative accuracy and consistency of the recipes, as systematic changes could mimic evolutionary trends when comparing various samples. At z = 0.36, all three lines can be observed at optical wavelengths, providing a unique opportunity to compare different empirical recipes. We use spectra from the Keck Telescope and the Sloan Digital Sky Survey to compare M-BH estimators for a sample of 19 AGNs at this redshift. We compare popular recipes available from the literature, finding that M-BH estimates can differ up to 0.38 +/- 0.05 dex in the mean (or 0.13 +/- 0.05 dex, if the same virial coefficient is adopted). Finally, we provide a set of 30 internally self-consistent recipes for determining M-BH from a variety of observables. The intrinsic scatter between cross-calibrated recipes is in the range 0.1-0.3 dex. This should be considered as a lower limit to the uncertainty of the M-BH estimators.