Correlation between the line width and the line flux of the double-peaked broad Hα of 3C390.3

In this paper, we carefully check the correlation between the line width (second moment) and the line flux of the double-peaked broad H alpha of the well-known mapped active galactic nucleus (AGN) 3C390.3 in order to show some further distinctions between double-peaked emitters and normal broad-line AGN. Based on the virialization assumption M-BH proportional to R-BLR x V-2(BLR) and the empirical relation R-BLR proportional to L-similar to 0.5, one strong negative correlation between the line width and the line flux of the double-peaked broad lines should be expected for 3C390.3, such as the negative correlation confirmed for the mapped broad-line object NGC5548, R-BLR x V-2(BLR) proportional to L-similar to 0.5 x sigma(2) = constant. Moreover, based on the public spectra around 1995 from the AGN WATCH project for 3C390.3, one reliable positive correlation is found between the line width and the line flux of the double-peaked broad H alpha. In the context of the proposed theoretical accretion disc model for double-peaked emitters, the unexpected positive correlation can be naturally explained, due to different time delays for the inner and outer parts of the disc-like broad-line region (BLR) of 3C390.3. Moreover, the virialization assumption is checked and found to be still available for 3C390.3. However, the time-varying size of the BLR of 3C390.3 cannot be expected by the empirical relation R-BLR proportional to L-similar to 0.5. In other words, the mean size of the BLR of 3C390.3 can be estimated by the continuum luminosity (line luminosity), while the continuum emission strengthening leads to the size of BLR decreasing (not increasing) in different moments for 3C390.3. Then, we compared our results of 3C390.3 with the previous results reported in the literature for the other double-peaked emitters, and found that before to clearly correct the effects from disc physical parameters varying (such as the effects of disc precession) for long-term observed line spectra, it is not so meaningful to discuss the correlation of the line parameters of double-peaked broad lines. Furthermore, due to the probable 'external' ionizing source with so far unclear structures, it is hard to give one conclusion that the positive correlation between the line width and the line flux can be found for all double-peaked emitters, even after the considerations of disc physical parameters varying. However, once one positive correlation of broad-line parameters is found, the accretion disc origination of the broad line should be considered first.