VLT/ISAAC Spectra of the Hbeta Region in Intermediate-Redshift Quasars III. Hbeta Broad Line Profile Analysis and Inferences about BLR Structure

[Abridged] We present new VLT ISAAC spectra for 30 quasars, which we combine with previous data to yield a sample of 53 intermediate redshift (z ~ 0.9 - 3.0) sources. The sample is used to explore properties of prominent lines in the Hbeta spectral region of these very luminous quasars. We find two major trends: (1) a systematic increase of minimum FWHM Hbeta with luminosity (discussed in a previous paper). This lower FWHM envelope is best fit assuming that the narrowest sources radiate near the Eddington limit, show line emission from a virialized cloud distribution, and obey a well defined broad line region size vs. luminosity relation. (2) A systematic decrease of equivalent width of [OIII] (from W ~ 15 to ~ 1 A) with increasing source bolometric luminosity (from log L ~ 43 to log L ~ 49). Further identified trends required discrimination between so-called Population A and B sources. We generate median composite spectra in six luminosity bins Pop. A sources show reasonably symmetric Lorentzian Hbeta profiles at all luminosities while Pop. B sources require two component fits involving an unshifted broad and a redshifted very broad component. Very broad Hbeta increases in strength with increasing L while the broad component remains constant resulting in an apparent "Baldwin effect" with equivalent width decreasing from W ~ 80 to ~ 20 A over our sample luminosity range. The roughly constant equivalent width shown by the Hbeta very broad component implies production in optically-thick, photoionized gas. The onset of the redshifted very broad component appears to be a critical change that occurs near the Pop. A-B boundary at FWHM Hbeta ~ 4000 km/s which we relate to a critical Eddington ratio (~ 0.2 +/- 0.1).