The Quasar Main Sequence explained by the combination of Eddington ratio, metallicity and orientation

We address the effect of orientation of the accretion disk plane and the geometry of the broad-line region (BLR) as part of an effort to understand the distribution of quasars in the optical plane of the quasar main sequence. We utilize the photoionization code CLOUDY to model the BLR incorporating the grossly underestimated form factor ($f$). Treating the aspect of viewing angle appropriately, we confirm the dependence of the $R_{\mathrm{FeII}}$ sequence on Eddington ratio and on the related observational trends - as a function of the SED shape, cloud density and composition, verified from prior observations. Sources with $R_{\mathrm{FeII}}$ in the range 1 -- 2 (about 10\% of all quasars, the so-called extreme Population A [xA] quasars) are explained as sources of high, and possibly extreme Eddington ratio along the $R_{\mathrm{FeII}}$ sequence. This result has important implication for the exploitation of xA sources as distance indicators for Cosmology. $\mathrm{FeII}$ emitters with $R_{\mathrm{FeII}} > 2$ are very rare (<1\% of all type 1 quasars). Our approach also explains the rarity of these highest $\mathrm{FeII}$ emitters as extreme xA sources and constrains the viewing angle ranges with increasing H$\beta$ FWHM.