Using an empirical relation between the broad-line region size and optical continuum luminosity, we estimated the black hole mass and accretion rate for 135 active galactic nuclei (AGNs) with double-peaked broad emission lines in two samples, one from the Sloan Digital Sky Survey (SDSS) and the other from a survey of radio-loud broad emission line AGNs. With black hole masses ranging from 3 × 107 M☉ to 5 × 109 M☉, these AGNs have dimensionless accretion rates (Eddington ratios) between 0.001 and 0.1 and bolometric luminosity between 1043 and 1046 ergs s-1, both values being significantly larger than those of several previously known low-luminosity (Lbol < 1043 ergs s-1) double-peaked AGNs. The optical-X-ray spectra indices, αOX, of these high-luminosity double-peaked AGNs are between 1 and 1.9, systematically larger than those of low-luminosity objects, which are around 1. Modest correlations (with a Spearman rank correlation coefficient of 0.60) of the αOX value with the Eddington ratio and bolometric luminosity have been found, indicating that double-peaked AGNs with higher Eddington ratios or higher luminosity tend to have larger αOX values. Based on these results, we suggested that the accretion process in the central region of some high-luminosity double-peaked emission line AGNs (especially those with Eddington ratios larger than 0.01) is probably different from that of low-luminosity objects, in which a well-known ADAF-like accretion flow was thought to exist. It is likely that the accretion physics in some high-luminosity double-peaked AGNs is similar to that in normal type 1 AGNs, which is also supported by the presence of possible big blue bumps in the spectra of some double-peaked AGNs with higher Eddington ratios. We note that the prototype double-peaked emission line AGN, Arp 102B, which has a black hole mass of 108 M☉ and a dimensionless accretion rate of 0.001, may be an intermediate object between the high- and low-luminosity double-peaked AGNs. In addition, we found an apparent strong anticorrelation (with a Spearman rank correlation coefficient of -0.79) between the peak separation of double-peaked profiles and Eddington ratios. However, such an anticorrelation is probably induced by a strong correlation between the peak separation and emission-line widths and needs to be confirmed by future work. If it is real, it may provide us another clue to understanding why double-peaked broad emission lines were hardly found in luminous AGNs with Eddington ratios larger than 0.1.
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