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.