Iron-corrected Single-epoch Black Hole Masses of DESI Quasars at low redshift

We present a study on the possible overestimation of single-epoch supermassive black hole (SMBH) masses in previous works, based on more than 55,000 type 1 quasars at $0.25 < z < 0.8$ from the Dark Energy Spectroscopic Instrument (DESI). We confirm that iron emission strength serves as a good tracer of the Eddington ratio, and estimate SMBH masses using an iron-corrected $R$-$L$ relation for H$β$, where $R$ is the broad line region size and $L$ is the continuum luminosity. Compared to our measurements, previous canonical measurements without the iron correction are overestimated by a factor of 1.5 on average. The overestimation can be up to a factor of 5 for super-Eddington quasars. The fraction of super-Eddington quasars in our sample is about 5%, significantly higher than 0.4% derived from the canonical measurements. Using a sample featuring both H$β$ and MgII emission lines, we calibrate MgII-based SMBH masses using iron-corrected, H$β$-based SMBH masses and establish an iron-corrected $R$-$L$ relation for MgII. The new relation adds an extra term of $-0.34R_{\mathrm{Fe}}$ to the $R$-$L$ relation, where $R_{\mathrm{Fe}}$ denotes the relative iron strength. We use this formula to build a catalog of about 0.5 million DESI quasars at $0.6<z<1.6$. If these iron-corrected $R$-$L$ relations for H$β$ and MgII are valid at high redshift, current mass measurements of luminous quasars at $z\ge6$ would have been overestimated by a factor of 2.3 on average, alleviating the tension between SMBH mass and growth history in the early universe.