The case for cases B and C: intrinsic hydrogen-line ratios of the broad-line region of active galactic nuclei, reddenings and accretion disc sizes

Low-redshift active galactic nuclei (AGNs) with extremely blue optical spectral indices are shown to have a mean, velocity-averaged, broad-line II alpha/II beta ratio of approximate to 2.72 +/- 0.04, consistent with a Baker-Menzel Case B value. Comparison of a wide range of properties of the very bluest AGNs with those of a luminosity-matched subset of the Dong et al. blue AGN sample indicates that the only difference is the internal reddening. Ultraviolet fluxes are brighter for the bluest AGNs by an amount consistent with the flat AGN reddening curve of Gaskell et al. The lack of a significant difference in the GALEX (far-ultraviolet-near-ultraviolet) colour index strongly rules out a steep Small Magellanic Cloud-like reddening curve and also argues against an intrinsically harder spectrum for the bluest AGNs. For very blue AGNs, the Ly alpha/II beta ratio is also consistent with being the Case B value. The Case B ratios provide strong support for the self-shielded broad-line model of Gaskell, Klimek & Nazarova. It is proposed that the greatly enhanced Ly alpha/II beta ratio at very high velocities is a consequence of continuum fluorescence in the Lyman lines (Case C). Reddenings of AGNs mean that the far-UV luminosity is often underestimated by up to an order of magnitude. This is a major factor causing the discrepancies between measured accretion disc sizes and the predictions of simple accretion disc theory. Dust covering fractions for most AGNs are lower than has been estimated. The total mass in lower mass supermassive black holes must be greater than hitherto estimated.