On correlation between the line width and the line flux of the double-peaked broad H$\alpha$
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Figure \[fj\_3c390\] shows the correlation between the line width and the line flux of the double-peaked broad H$\alpha$ of 3C390.3. Linear correlation coefficient for the correlation of $f_0$ versus $\sigma$ is about 0.28 with two-sided significance of deviation from zero about $P_{null}\sim0.04$ for all the 67 spectra listed in Table 1. The coefficient for the correlation of $f_1$ (accurate line flux of H$\alpha$ from the AGNWATCH project) versus $\sigma$ is about 0.45 with $P_{null}\sim0.0002$. It is clear that there is one positive correction between the line width and the line flux of the double-peaked broad H$\alpha$ for 3C390.3. Furthermore, under considerations of the uncertainties of the parameters in both coordinates, the best fitted results for $f_1$ versus $\sigma$ can be written as $$\frac{\sigma}{{\rm \AA}}\propto (0.065\pm0.006)\times\frac{f_1}
{10^{-16}{\rm erg/s/cm^2}}$$ Certainly, we should note the accurate flux $f_1$ collected from the AGNWATCH project includes the contributions from the narrow emission lines of $H\alpha$ and \[N [ii]{}\] doublet. However, the contributions do not affect the positive correlation, because the flux of the narrow emission lines of each spectrum is constant. The best fitted results are shown as solid 