Black Hole Growth to z = 2 - I: Improved Virial Methods for Measuring
  M_BH and L/L_Edd
  We analyze several large samples of AGN 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 SDSS, 2QZ and 2SLAQ
surveys at z<2, and a compilation of smaller samples with 0<z<5. We critically
evaluate the usage of the MgII(2798A) and CIV(1549A) 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 Hbeta. We present a new,
luminosity-dependent bolometric correction for the monochromatic luminosity at
3000A, L_3000, which is lower by a factor of 1.75 than those used in previous
studies. We also re-calibrate the use of L_3000 as an indicator for the size of
the broad emission line region (R_BLR) and find that R_BLR is proportional to
L_3000^0.62. We find that FWHM(MgII)\simeqFWHM(Hb) for all sources with
FWHM(MgII)<6000 km/s. Beyond this FWHM, the MgII line width seems to saturate.
The spectral region of the MgII line can thus be used to reproduce Hb-based
estimates of M_BH and L/L_Edd, with negligible systematic differences and a
scatter of 0.3 dex. The width of the CIV line, on the other hand, shows no
correlation with either that of the Hb or the MgII lines and we could not
identify the reason for this discrepancy. The scatter of M_BH(CIV), relative to
M_BH(Hb) is of almost 0.5 dex. Moreover, 46% of the sources have
FWHM(CIV)<FWHM(Hb), in contrast with the basic premise of the virial method,
which predicts FWHM(CIV)/FWHM(Hbeta)~1.9. Thus, the CIV line cannot be used to
obtain precise estimates of M_BH. We conclude by presenting the observed
evolution of M_BH and L/L_Edd with cosmic epoch. The steep rise of L/L_Edd with
redshift up to z~1 flattens towards the expected maximal value of L/L_Edd~1,
with lower-M_BH sources showing higher values of L/L_Edd at all redshifts.
[Abridged]
