Is there an advection-dominated accretion flow in radio galaxies with double-peaked Balmer lines?

In order to examine the prediction that the broad-line radio galaxies (BLRGs) with double-peaked Balmer lines harbor an accretion disk characterized by an advection-dominated accretion flow (ADAF) in their nuclei, we investigate narrow emission line flux ratios of the narrow-line regions (NLRs) which are photoionized by nuclear continuum radiation. We compile data from the literature and confirm the pioneering work of Eracleous & Halpern that the BLRGs with the double-peaked Balmer emission exhibit larger flux ratios of both [O I] λ6300/[O III] λ5007 and [O II] λ3727/[O III] λ5007 than the BLRGs without the double-peaked Balmer emission. To examine whether or not these properties are attributed to the difference in the spectral energy distribution (SED) of the ionizing radiation between the BLRGs with and without the double-peaked Balmer emission, we perform photoionization model calculations using two types of input continuum radiation; one has the strong big blue bump which is expected for standard optically thick accretion disks and the other does not exhibit a strong big blue bump as expected for optically thin ADAFs. We find that the data of the BLRGs with the double-peaked Balmer lines are consistent with the models adopting the SED without a strong big blue bump, while the data of the BLRGs without the double-peaked emission lines are well described by the models adopting the SED with a strong big blue bump. On the other hand, the observed differences in the NLR emission are hard to explain by the difference in the contribution of shocks. These results support the idea that the double-peaked Balmer lines arise at an outer region of an accretion disk which is illuminated by an inner, geometrically thick ADAF.