Shedding New Light on Weak Emission-Line Quasars in the C$_{\rm IV}$-H$\beta$ Parameter Space

Weak emission-line quasars (WLQs) are a subset of Type 1 quasars that exhibit extremely weak Ly$\alpha +$N V $\lambda$1240 and/or C IV $\lambda$1549 emission lines. We investigate the relationship between emission-line properties and accretion rate for a sample of 230 `ordinary' Type 1 quasars and 18 WLQs at $z < 0.5$ and $1.5 < z < 3.5$ that have rest-frame ultraviolet and optical spectral measurements. We apply a correction to the H$\beta$-based black-hole mass ($M_{\rm BH}$) estimates of these quasars using the strength of the optical Fe II emission. We confirm previous findings that WLQs' $M_{\rm BH}$ values are overestimated by up to an order of magnitude using the traditional broad emission-line region size-luminosity relation. With this $M_{\rm BH}$ correction, we find a significant correlation between H$\beta$-based Eddington luminosity ratios and a combination of the rest-frame C IV equivalent width and C IV blueshift with respect to the systemic redshift. This correlation holds for both ordinary quasars and WLQs, which suggests that the two-dimensional C IV parameter space can serve as an indicator of accretion rate in all Type 1 quasars across a wide range of spectral properties.