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Correlation between Line Width and Line Flux of Double-Peaked Broad Halpha of 3C390.3

In this manuscript, we carefully check the correlation between the line width and the line flux of the double-peaked broad H$α$ of the well-known mapped AGN 3C390.3, in order to show some further distinctions between double-peaked emitters and normal broad line AGN. Based on the Virialization assumption and the empirical relation about $R_{BLR}$, one strong negative correlation of line parameters 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. But, based on the public spectra around 1995 from the AGNWATCH project for 3C390.3, one reliable positive correlation is found. In the context of the proposed theoretical accretion disk model for double-peaked emitters, the unexpected positive correlation can be naturally explained, due to different time delays for inner parts and outer parts of disk-like BLR of 3C390.3. Moreover, the Virialization assumption is checked and found to be still available for 3C390.3. However, time-varying size of the BLR of 3C390.3 can not be expected by the empirical relation $R_{BLR}\propto L^{\sim0.5}$, 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 effects from disk physical parameters varying for long-term observed line spectra and effects from the probable 'external' ionizing source with so far unclear structures, it is hard to give one conclusion that the positive correlation can be found for all double-peaked emitters. However, once one positive correlation of broad line parameters was found, the accretion disk origination of the broad line should be firstly considered.