Estimating Black Hole Masses in Obscured AGN from X-ray and Optical Emission Line Luminosities

S. LaMassa, I. Farrow, C. M. Urry, B. Trakhtenbrot, C. Auge, M. J. Koss, A. Peca, D. Sanders, T. J. Turner

First listed 2025-01-23 | Last updated 2025-01-23

Abstract

We test a novel method for estimating black hole masses ($M_{\rm BH}$) in obscured active galactic nuclei (AGN) that uses proxies to measure the full-width half maximum of broad H$α$ (FWHM$_{\rm bHα}$) and the accretion disk luminosity at 5100 Angstrom ($λL_{\rm 5100 Angstrom}$). Using a published correlation, we estimate FWHM$_{\rm bHα}$ from the narrow optical emission line ratio $L_{\rm [O\,III]}/L_{\rm nHβ}$. Using a sample of 99 local obscured AGN from the Swift-BAT AGN Spectroscopic Survey, we assess the agreement between estimating $λL_{\rm 5100 Angstrom}$ from the intrinsic 2-10 keV X-ray luminosity and from narrow optical emission lines. We find a mean offset of $0.32 \pm 0.68$ dex between these methods, which propagates to a factor of $\sim$2 uncertainty when estimating $M_{\rm BH}$ using a virial mass formula where $L_{\rm [O\,III]}/L_{\rm nHβ}$ serves as a proxy of FWHM$_{\rm bHα}$ ($M_{\rm BH,[O\,III]/nHβ}$). We compare $M_{\rm BH,[O\,III]/nHβ}$ with virial $M_{\rm BH}$ measurements from broad Paschen emission lines. For the 14 (12) BASS AGN with broad Pa$α$ (Pa$β$) detections, we find $M_{\rm BH,[O\,III]/nHβ}$ to be systematically higher than $M_{\rm BH,Paα}$ ($M_{\rm BH,Paβ}$) by a factor of 0.39 $\pm$ 0.44 dex (0.48 $\pm$ 0.51 dex). Since these offsets are within the scatter, more data are needed to assess whether $M_{\rm BH,[O\,III]/nHβ}$ is biased high. For 151 BASS AGN with measured stellar velocity dispersions ($σ_{\rm *}$), we find that the $σ_{\rm *}$-derived $M_{\rm BH}$ agrees with $M_{\rm BH,[O\,III]/nHβ}$ to within 0.08 dex, albeit with wide scatter (0.74 dex). The method tested here can provide estimates of $M_{\rm BH}$ in thousands of obscured AGN in spectroscopic surveys when other diagnostics are not available, though with an uncertainty of $\sim$3-5.

Short digest

Tests a proxy-based black hole mass estimator for obscured AGN that infers FWHM_bHα from the narrow-line ratio L[O III]/L_nHβ and λL5100 from either intrinsic 2–10 keV X-rays or narrow lines, using 99 local Swift-BAT/BASS AGN. The two λL5100 proxies differ by a mean −0.32 ± 0.68 dex (narrow-line estimate lower than X-ray), implying ≈2× MBH uncertainty from the luminosity choice. Compared to virial masses from broad Paschen lines (14 Paα, 12 Paβ), the proxy MBH is higher by 0.39 ± 0.44 dex and 0.48 ± 0.51 dex, respectively, though still within the scatter. σ*-based MBH for 151 BASS AGN agrees on average within 0.08 dex but with large ≈0.74 dex scatter, so the method scales to large samples with overall ≈3–5× uncertainty and a possible mild high bias needing more data.

Key figures to inspect

• Figure 1: Check how far the red best-fit line deviates from the one-to-one line and where outliers drive the −0.32 ± 0.68 dex offset; this sets how much the choice of X-ray vs narrow-line λL5100 propagates into the virial MBH error budget.
• Figure 2: Inspect the trend between log(L[O III]/L_nHβ) and FWHM(Paα/Paβ) relative to the dashed BM19+Kim10 expectation; the significant Paα (p≈0.03) but weaker Paβ correlation tests whether the BLR–NLR coupling holds for individual obscured AGN and hints at BLR extinction effects.
• Figure 3: Compare MBH,[O III]/nHβ to Paα/Paβ-based MBH and note the systematic high offset; re-evaluate the trend when excluding green squares (den Brok 2022 entries without quality flags) to see how line-fit reliability impacts the bias.
• Figure 4: Contrast σ*-derived MBH with Paα/Paβ results and with MBH,[O III]/nHβ; verify that MBH,[O III]/nHβ tracks M–σ on average (≈−0.08 dex) while Paβ shows a ≈0.38 dex high offset, and assess whether points fall within the 95% prediction band.