Dependence of the broad Fe K$\alpha$ line on the physical parameters of AGN

In this paper, the dependence of the broad Fe K$\alpha$ line on the physical parameters of AGN, such as the black hole mass $M_{BH}$, accretion rate (equivalently represented by Eddington ratio $\lambda_{Edd}$), and optical classification, is investigated by applying the X-ray spectra stacking method to a large sample of AGN which have well measured optical parameters. A broad line feature is detected ($>3\sigma$) in the stacked spectra of the high $\lambda_{Edd}$ sub-sample ($\log\lambda_{Edd}>-0.9$). The profile of the broad line can be well fitted with relativistic broad line model, with the line energy consistent with highly ionized Fe K$\alpha$ line (i.e. Fe xxvi). A model consisting of multiple narrow lines cannot be ruled out, however. We found hints that the Fe K line becomes broader as the $\lambda_{Edd}$ increases. No broad line feature is shown in the sub-sample of broad-line Seyfert 1 (BLS1) galaxies and in the full sample, while a broad line might be present, though at low significance, in the sub-sample of narrow-line Seyfert 1 (NLS1) galaxies. We find no strong dependence of the broad line on black hole masses. Our results indicate that the detection/properties of the broad Fe K$\alpha$ line may strongly depend on $\lambda_{Edd}$, which can be explained if the ionization state and/or truncation radius of the accretion disc changes with $\lambda_{Edd}$. The non-detection of the broad line in the BLS1 sub-sample can be explained if the the average EW of the relativistic Fe K$\alpha$ line is weak or/and the fraction of sources with relativistic Fe K$\alpha$ line is small in BLS1 galaxies.