The Sloan Digital Sky Survey Reverberation Mapping Project: Estimating Masses of Black Holes in Quasars with Single-epoch Spectroscopy

Abstract

It is well known that reverberation mapping of active galactic nuclei (AGNs) reveals a relationship between AGN luminosity and the size of the broad-line region, and that use of this relationship, combined with the Doppler width of the broad emission line, enables an estimate of the mass of the black hole at the center of the active nucleus based on a single spectrum. An unresolved key issue is the choice of parameter used to characterize the line width, either FWHM or line dispersion s line (the square root of the second moment of the line profile). We argue here that use of FWHM introduces a bias, stretching the mass scale such that high masses are overestimated and low masses are underestimated. Here we investigate estimation of black hole masses in AGNs based on individual or "singleepoch" observations, with a particular emphasis in comparing mass estimates based on line dispersion and FWHM. We confirm the recent findings that, in addition to luminosity and line width, a third parameter is required to obtain accurate masses, and that parameter seems to be Eddington ratio. We present simplified empirical formulae for estimating black hole masses from the Hβ λ4861 and C IV λ1549 emission lines. While the AGN continuum luminosity at 5100 Å is usually used to predict the Hβ reverberation lag, we show that the luminosity of the Hβ broad component can be used instead without any loss of precision, thus eliminating the difficulty of accurately accounting for the host-galaxy contribution to the observed luminosity.

Reverberation mapping of active galactic nuclei: From X-ray corona to dusty torus

“…Several studies show that many AGNs, including some of the highest accretion rate objects, fall below the usual R BLR À L AGN relation (see Figure 9; Du et al, 2015Du et al, , 2016Du et al, , 2018Grier et al, 2017b;Fonseca Alvarez et al, 2020). While the reason is not currently understood, some ascribe it to physical changes arising from high accretion rates (e.g., Dalla Bontà et al, 2020) while others have suggested that is related to differences in the shape of the ionizing continuum (e.g., Fonseca . Nevertheless, what is clear is that local Seyferts may not, in fact, be appropriate models for high-z quasars, and estimating M BH for large numbers of AGNs that span the full range of observed properties is more complicated than previously assumed.…”

Jetted Narrow-Line Seyfert 1 Galaxies & Co.: Where Do We Stand?

“…An acceptable compromise is the use of single-epoch spectra with proper calibration relationships. Among the different options, the use of the line dispersion σ line yields better results than the FWHM one, because the σ line is less affected by the inclination and the accretion rate [43,48,49]. One would expect that for a given mathematical profile the two quantities are related, but observations indicate something different and I refer to the excellent works by [43,48,49] for more detailed analyses.…”

Broad line region and black hole mass of PKS 1510-089 from spectroscopic reverberation mapping

“…Both the resolutioncorrected FWHM and σ line measured from the mean and rms spectra of Hβ are used as ∆V. A value of f = 4.47 (1.12) is adopted when σ line (FWHM) is considered as ∆V (Woo et al 2015), however, note that FWHM is a non-linear function of σ line (e.g., Peterson 2014;Bonta et al 2020). Finally, four different black hole masses are determined based on the four different choices of line widths (see Table 4).…”