Broad Paschen lines as black hole mass tracers: A reverberation mapping calibration

Abstract

Single-epoch (SE) black hole mass estimators based on rest-frame ultraviolet or optical broad lines can be limited by dust attenuation or wavelength coverage. We calibrate estimators based on broad Paschen P$\alpha$ and P$\beta$ directly against reverberation mapping (RM) masses. We obtained LBT/LUCI near-infrared spectra of 27 SDSS-RM quasars and combined them with archival Paschen measurements for AGNs with RM masses. After continuum subtraction, we measured line luminosities and full widths at half maximum (FWHMs) using multi-component and single-Gaussian profile models. We fitted $\log(M_{\rm BH}/M_\odot)=a+b\log(L/10^{41}\,{\rm erg\,s^{-1}})+c\log({\rm FWHM}/10^3\,{\rm km\,s^{-1}})$, including intrinsic scatter. The fiducial relations use photometrically corrected line luminosities and FWHMs of the combined broad profiles. For P$\alpha$, we obtain $(a,b,c)=(6.86^{+0.24}_{-0.25},0.47^{+0.11}_{-0.10},1.24^{+0.49}_{-0.48})$ with an intrinsic scatter of $0.28^{+0.08}_{-0.06}$ dex. For P$\beta$, we obtain $(7.00\pm0.24,0.48^{+0.10}_{-0.09},0.91^{+0.46}_{-0.47})$ with a scatter of $0.32^{+0.08}_{-0.06}$ dex. Relations using single-Gaussian widths, 5100 {\AA} continuum luminosities, or fixed virial slopes have scatters consistent within the uncertainties. These relations provide complementary mass estimators when ultraviolet or optical broad lines are attenuated or unavailable. They should be applied within the parameter ranges of the calibration sample and remain subject to the systematic uncertainty associated with the RM virial factor.