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 BH) estimates in quasars are obtained by using the velocity widths of low-ionization emission lines, typically the Hβ λ4861 line. Unfortunately, this line is redshifted out of the optical band at z ≈ 1, leaving M BH estimates to rely on proxy rest-frame ultraviolet (UV) emission lines, such as C iv λ1549 or Mg ii λ2800, which contain intrinsic challenges when measuring, resulting in uncertain M BH estimates. In this work, we aim at correcting M BH estimates derived from the C iv and Mg ii emission lines based on estimates derived from the Hβ emission line. We find that employing the equivalent width of C iv in deriving M BH estimates based on Mg ii and C iv provides values that are closest to those obtained from Hβ. We also provide prescriptions to estimate M 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 BH estimates by 15% when compared to previous studies. Lastly, we discuss the potential of our prescriptions to provide more accurate and precise estimates of M BH given a much larger sample of quasars at 3.20 ≲ z ≲ 3.50, where both Mg ii and Hβ can be measured in the same near-infrared spectrum.