Estimating Black Hole Masses in Obscured Active Galactic Nuclei from X-Ray and Optical Emission Line Luminosities

We test a novel method for estimating black hole masses (M_BH) in obscured active galactic nuclei (AGN) that uses proxies to measure the FWHM of broad Hα (FWHM_bHα) and the accretion disk luminosity at 5100 Å (λL_{5100 Å}). Using a published correlation, we estimate FWHM_bHα from the narrow optical emission line ratio L_{[O iii]}/L_nHβ. Using a sample of 99 local obscured AGN from the Swift Burst Alert Telescope AGN Spectroscopic Survey (BASS), we assess the agreement between estimating λL_{5100 Å} from the intrinsic 2 to 10 keV X-ray luminosity and from narrow optical emission lines. We find a mean offset of 0.32 ± 0.68 dex between these methods, which propagates to a factor of ∼2 uncertainty when estimating M_BH using a virial mass formula where L_{[O iii]}/L_nHβ serves as a proxy of FWHM_bHα (M_{BH,[O iii]/nHβ}). We compare M_{BH,[O iii]/nHβ} with virial M_BH measurements from broad Paschen emission lines. For the 14 (12) BASS AGN with broad Paα (Paβ) detections, we find M_{BH,[O iii]/nHβ} to be systematically higher than M_BH,Paα (M_BH,Paβ) by a factor of 0.39 ± 0.44 dex (0.48 ± 0.51 dex). Since these offsets are within the scatter, more data are needed to assess whether M_{BH,[O iii]/nHβ} is biased high. For 151 BASS AGN with measured stellar velocity dispersions (σ_*), we find that the σ_*-derived M_BH agrees with M_{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_BH in thousands of obscured AGN in spectroscopic surveys when other diagnostics are not available, though with an uncertainty of ∼3-5.