An extended size–luminosity relation for the reverberation-mapped AGNs: the role of the accretion rate

Abstract

ABSTRACT For a compiled sample of 120 reverberation-mapped AGNs, the bivariate correlations of the broad-line region (BLR) size (RBLR) with the continuum luminosity at 5100 Å (L5100) and the dimensionless accretion rates ($\dot{\mathscr {M}}$) are investigated. Using our recently calibrated virial factor f, and the velocity tracer from the H β full width at half-maximum (FWHM(H β)) or the line dispersion (σH β) measured in the mean spectra, three kinds of supermassive black hole (SMBH) masses and $\dot{\mathscr {M}}$ are calculated. An extended RBLR(H β)–L5100 relation including $\dot{\mathscr {M}}$ is found to be stronger than the canonical RBLR(H β)–L5100 relation, showing smaller scatters. The observational parameters, RFe (the ratio of optical Fe ii to H β line flux) and the line profile parameter DH β ($D_{\rm H\,\beta } =\rm FWHM(H\,\beta)/\sigma _{\rm H\,\beta }$), have relations with three kinds of $\dot{\mathscr {M}}$. Using RFe and DH β to substitute $\dot{\mathscr {M}}$, extended empirical RBLR(Hβ)–L5100 relations are presented. RFe is a better ‘fix’ for the RBLR(H β)–L5100 offset than the H β shape DH β. The extended empirical RBLR(H β)–L5100 relation including RFe can be used to calculate RBLR, and thus the single-epoch SMBH mass MBH. Our measured accretion rate dependence is not consistent with the simple model of the accretion disc instability leading the BLR formation. The BLR may instead form from the inner edge of the torus, or from some other means in which BLR size is positively correlated with accretion rate and the SMBH mass.