Applicability of single-epoch Hα-based black hole mass scaling relations to The Cliff

Determine the validity of applying local single-epoch virial black hole mass scaling relations between Hα luminosity and Hα line width (e.g., Greene & Ho 2005; Shen 2020) to The Cliff by evaluating whether the Lorentzian broad Hα profile traces bona fide broad-line region kinematics under BH* conditions.

Background

The authors use single-epoch Hα-based scaling relations to estimate the black hole mass of The Cliff, but note that the source is unlike typical local broad-line AGN and may be affected by processes such as resonant or electron scattering that alter the line profile.

This raises concerns about whether standard virial estimators calibrated at low redshift are applicable to BH*-dominated spectra, necessitating a reassessment of mass inferences for such objects.

References

However, as no source like The Cliff has been discovered before, it is unclear that commonly-used scaling relations can be applied.

— A remarkable Ruby: Absorption in dense gas, rather than evolved stars, drives the extreme Balmer break of a Little Red Dot at $z=3.5$  (2503.16600 - Graaff et al., 20 Mar 2025) in Section 6.4 (A ‘Black hole star’?)

It is worth noting that, even for sources that are well fit with an empirical Gaussian, it remains an open question whether the calibration from single--epoch spectra to BH masses is applicable at these earlier epochs \citep{Greene_2026, Lambrides_2026_b}.

— The THRILS Factor: Investigating the properties of Little Red Dots (LRDs) at 3<z<6 with JWST/NIRSpec  (2609.10803 - Ganapathy et al., 9 Sep 2026) in Section 4.2, subsection “Implications of Exponential Fitting”

It therefore remains unclear whether these BLR emission lines trace the same BLR kinematics as in the local universe and whether locally calibrated single-epoch $$ estimators can be reliably applied at high redshift.

— SHELLQs. Black Hole Mass and Eddington Ratio Distributions of Intermediate-Luminosity Quasars at 6<z<7  (2609.09266 - Onoue et al., 8 Sep 2026) in Section 3, BH mass and Eddington Ratio