Quantifying the accretion rate bias in optical single-epoch mass estimates

Observing campaigns targeting highly accreting quasars have revealed systematically smaller BLR radii—a factor of 3-8 times smaller than predicted by traditional size-luminosity relationships. This discovery challenges current mass estimation methods, indicating that high-accretion-rate systems need unique calibrations, paving the way for refined black hole mass and accretion rate estimates.

In Maithil et al. 2022, I introduced a new method for estimating black hole masses using single-epoch optical spectra. This approach employs a radius-luminosity relation that corrects for accretion rate bias through the optical iron-to-Hβ line strength ratio. For the first time, I demonstrate that without accretion-rate corrections (Fe-corrected), single-epoch mass estimates are overestimated—on average by a factor of two, and up to ten times for highly accreting systems. Importantly, this overestimation increases with redshift (see Fig. 1). 

By applying the corrected masses and accretion rates, we revealed the true distribution of high-accretion-rate systems. The strongest Fe-emitting quasars belong to two classes as seen in Figure 2 & 3: high-redshift quasars with rest-frame optical spectra, which given their extremely high luminosities require high accretion rates, and their low-redshift analogs, which given their low black holes masses must have high accretion rates to meet survey flux limits.

My mass prescription was pivotal in advancing our understanding of quasars. Additionally, it corrected masses for weak-line quasars, showing they are not a distinct population but align within the same correlation space as other type-1 quasars, a 2023 study I co-authored.