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

For a compiled sample of 120 reverberation-mapped AGNs, the bivariate correlations of the broad-line region (BLR) size (R-BLR) with the continuum luminosity at 5100 angstrom (L-5100) and the dimensionless accretion rates (<(M)over dot>) are investigated. Using our recently calibrated virial factor f, and the velocity tracer from the H beta full width at half-maximum (FWHM(H beta)) or the line dispersion (sigma(H beta)) measured in the mean spectra, three kinds of supermassive black hole (SMBH) masses and <(M)over dot> are calculated. An extended R-BLR(H beta)-L-5100 relation including <(M)over dot> is found to be stronger than the canonical R-BLR(H beta)-L-5100 relation, showing smaller scatters. The observational parameters, R-Fe (the ratio of optical Fe II to H beta line flux) and the line profile parameter D-H beta (D-H beta = FWHM(H beta)/sigma(H beta)), have relations with three kinds of <(M)over dot>. Using R-Fe and D-H beta to substitute <(M)over dot>, extended empirical RBLR(H beta)-L-5100 relations are presented. R-Fe is a better 'fix' for the R-BLR(H beta)-L-5100 offset than the H beta shape D-H beta. The extended empirical R-BLR(H beta)-L-5100 relation including R-Fe can be used to calculate RBLR, and thus the singleepoch SMBH mass M-BH. 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.