Gemini Near Infrared Spectrograph - Distant Quasar Survey: Prescriptions for Calibrating UV-Based Estimates of Supermassive Black Hole Masses in High-Redshift Quasars

The most reliable single-epoch supermassive black hole mass ($M_{\rm BH}$) estimates in quasars are obtained by using the velocity widths of low-ionization emission lines, typically the H$\beta$ $\lambda4861$ line. Unfortunately, this line is redshifted out of the optical band at $z\approx1$, leaving $M_{\rm BH}$ estimates to rely on proxy rest-frame ultraviolet (UV) emission lines, such as C IV $\lambda1549$ or Mg II $\lambda2800$, which contain intrinsic challenges when measuring, resulting in uncertain $M_{\rm BH}$ estimates. In this work, we aim at correcting $M_{\rm BH}$ estimates derived from the C IV and Mg II emission lines based on estimates derived from the H$\beta$ emission line. We find that employing the equivalent width of C IV in deriving $M_{\rm BH}$ estimates based on Mg II and C IV provides values that are closest to those obtained from H$\beta$. We also provide prescriptions to estimate $M_{\rm BH}$ values when only C IV, only Mg II, and both C IV and Mg II are measurable. We find that utilizing both emission lines, where available, reduces the scatter of UV-based $M_{\rm BH}$ estimates by $\sim15\%$ when compared to previous studies. Lastly, we discuss the potential of our prescriptions to provide more accurate and precise estimates of $M_{\rm BH}$ given a much larger sample of quasars at $3.20 \lesssim z \lesssim 3.50$, where both Mg II and H$\beta$ can be measured in the same near-infrared spectrum.