Black hole growth to z = 2-I. Improved virial methods for measuring M_BH and L/L_Edd

We analyse several large samples of active galactic nuclei (AGNs) in order to establish the best tools required to study the evolution of black hole mass (M_BH) and normalized accretion rate (L/L_Edd). The data include spectra from the Sloan Digital Sky Survey, 2dF QSO Redshift survey and 2dF SDSS LRG And QSO survey public surveys at z < 2, and a compilation of smaller samples with 0 < z < 5. We critically evaluate the usage of the MgΠ λ2798 and C IV λ1549 lines, and adjacent continuum bands, as estimators of M_BH and L/L_Edd, by focusing on sources where one of these lines is observed together with Hβ. We present a new, luminosity-dependent bolometric correction for the monochromatic luminosity at 3000 Å, L₃₀₀₀, which is lower by a factor of ~1.75 than those used in previous studies. We also re-calibrate the use of L₃₀₀₀ as an indicator for the size of the broad emission-line region (R_BLR) and find that R_BLR α L^0.62 ₃₀₀₀, in agreement with previous results. We find that FWHM(MgΠ) {minus tilde} FWHM(Hβ) for all sources with FWHM(MgΠ) {less-than or approximate} 6000 km s^-1. Beyond this full width at half-maximum (FWHM), the MgΠ line width seems to saturate. The spectral region of the MgΠ line can thus be used to reproduce Hβ-based estimates of MBH and L/L_Edd, with negligible systematic differences and a scatter of ~0.3 dex. The width of the C IV line, on the other hand, shows no correlation with either that of the Hβ or theMg Π lines and we could not identify the reason for this discrepancy. The scatter of MBH(C IV), relative to MBH(Hβ), is of almost 0.5 dex. Moreover, 46 per cent of the sources have FWHM(CIV) {less-than or approximate} FWHM(Hβ), in contrast with the basic premise of the virial method, which predicts FWHM(CIV)/FWHM(Hβ) {minus tilde} √3.7, based on reverberation mapping experiments. This fundamental discrepancy cannot be corrected based on the continuum slope or any C IV-related observable. Thus, the C IV line cannot be used to obtain precise estimates of MBH. We conclude by presenting the observed evolution of MBH and L/L_Edd with cosmic epoch. The steep rise of L/L_Edd with redshift up to z {minus tilde} 1 flattens towards the expected maximal value of L/L_Edd {minus tilde} 1, with lower MBH sources showing higher values of L/L_Edd at all redshifts. These trends will be further analysed in a forthcoming paper.